Population Dynamics of the Spruce Budworm Choristoneura Fumiferana
Author(s): T. Royama
Source: Ecological Monographs, Vol. 54, No. 4 (Dec., 1984), pp. 429-462
Published by: Ecological Society of America
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Ecological Monographs,54(4), 1984, pp. 429-462
? 1984 by the Ecological Society of America
POPULATION DYNAMICS OF THE SPRUCE BUDWORM
CHORISTONEURA FUMIFERANA'
T. ROYAMA
MaritimesForestResearch Centre,Canadian ForestryService,
Departmentof theEnvironment,P.O. Box 4000, Fredericton,
New BrunswickE3B 5P7, Canada
Abstract.Usingthelatestobservations,
experiments,
and theoretical
studies,I have reanalyzed
sprucebudwormdata fromtheGreenRiverProject,and now proposea newinterpretation
of the
populationdynamics
ofthespecies.
Sprucebudwormpopulations
in theProvinceofNew Brunswick
have beenoscillating
moreor
lessperiodically
forthelasttwocenturies,
theaverageperiodbeing z35 yr.Local populations
over
theprovincetendto oscillatein unison,thoughtheiramplitudes
and meanlevelsarenotalwaysthe
same.
The local populationprocessin thesprucebudwormis composedof twomajorparts,a basic
and secondaryfluctuations
oscillation,
aboutthisbasic oscillation.The basic oscillationis largely
determined
bythecombinedactionof severalintrinsic
(density-dependent)
mortality
factors
during
thethirdto sixthlarvalinstars.Thesefactors
includeparasitoids
and,probably,
diseases(e.g.,microsporidian
infection),
and,mostimportant,
an intriguing
complexofunknown
causes,whichI term
"thefifth
agent"(a largenumberoflarvaewithno clearsymptoms
diedduring
thepopulation
decline
in thelate 1950s).
Othermortality
factors,
foodshortage,
including
predation,
andlossesduringthespring
weather,
and falldispersalofyounglarvae,arenotcausesofthebasic,universally
oscillation.
occurring
Becauseof immigration
and emigration
of egg-carrying
moths,theratioof all eggslaid to the
numberoflocallyemerged
moths(theE/Mratio,or theapparentoviposition
rate)fluctuates
widely
fromyearto yearbutindependently
ofthebasicoscillationofdensityin thelocal populations
that
werestudied.The fluctuation
in thisratiois themainsourceofthesecondary
in density
fluctuation
aboutthebasicoscillation,
and is highlycorrelated
withthemeteorological
conditions
thatgovern
theimmigration
andemigration
ofmoths.TheE/Mratiois themajordensity-independent
component
ofbudworm
populationdynamics.
to commonbelief,thereis no evidenceto indicatethatinvasionsofegg-carrying
Contrary
moths
fromotherareas upsetthe assumedendemicequilibrium
stateof a local populationand trigger
outbreaks.
Mothinvasionscan onlyaccelerate
an increasein a localpopulation
to an outbreak
level,
butthishappensonlywhenthepopulation
is alreadyin an upswing
phaseofan oscillation
causedby
highsurvivalofthefeeding
larvae.In otherwords,the"seed" ofan outbreak
liesin thesurvivalof
larvaein thelocality,
feeding
and mothinvasionscan actonlyas "fertilizers."
The weightofevidenceis againsttheidea thatan outbreak
occursin an "epicenter"
and spreads
tothesurrounding
areasthrough
mothdispersal.
theegg-mass
datain NewBrunswick
Rather,
survey
since1952favoran alternative
Ifthetrough
ofa population
explanation.
in a certainarea
oscillation
stayscomparatively
in the 1960s,or ifthearea is moreheavily
high,as in centralNew Brunswick
invadedby egg-carrying
mothswhenthepopulationsin thatarea are in an upswingphase,these
populations
levelslightly
mightreachan outbreak
aheadofthesurrounding
all ofwhich
populations,
areoscillating
in unison.
If a localpopulationoscillatesbecauseoftheactionofdensity-dependent
factors
intrinsic
to the
local budwormsystem,
it mayappearto be difficult
to explainwhymanylocal populations
overa
wideareaoscillateinunison.However,Moran's(1953)theory
showsthatdensity-independent
factors
thatarecorrelated
(suchas weather)
localpopamonglocalitieswillbringindependently
oscillating
ulationsintosynchrony,
evenifweather
itselfhas no oscillatory
trend.I illustrate
thiswitha simple
time-series
model.The samemodelalsoillustrates
a principle
behindthefactthatoutbreaks
occurred
in New Brunswick
and Quebecduringthepasttwocenturies
fairly
regularly
butrathersporadically
in otherregionsofeasternCanada.
Finally,I reviewthecommonly
ofoutbreaks
basedon thedichotomy
acceptedtheory
ofendemic
and epidemicequilibrium
statesand arguethatthetheorydoes notapplyto thesprucebudworm
system.
Keywords: Choristoneura
fumiferana
(Clem.);GreenRiverProject;insectlife-table
analysis;insectoutbreaks;
mothdispersal;
population
sprucebudworm.
dynamics;
INTRODUCTION
Almost 20 yr have passed since publication of the
monograph(Morris 1963a) based on theclassic spruce
I Manuscript
received23 December1982;revisedand accepted15 August1983;finalversionreceived28 November
1983.
budwormpopulationstudyoftheGreenRiver Project.
During those 20 yr, spruce budworm populations in
theProvinceofNew Brunswickdeclinedonce and subsequentlyhave risento thecurrentoutbreaklevel.Now,
again,we are in themidstofcontroversy
about whether
430
T. ROYAMA
"to spray or not to spray" insecticidesto protectthe
forests.A few years ago, a task forcewas formedto
evaluate budwormcontrolalternativesforbetterforest
resource management of the province (Baskerville
1976). This task forcerelied heavily on a forestecosystemmodel thatwas based primarilyon the Morris
(1 963a) monograph.However, thispioneeringworkis
20 yr old and, in many respects,inadequate froma
currentpointofview. Besides thelack ofadequate data,
the major problems of the early work were its inappropriatetreatmentof time-seriesdata and its inadequate understandingof the concept of densitydependence (Royama 1977, 198la, b). Unfortunately,
certain
of its interpretations
have continued to be accepted
virtuallyunchanged even in the most recent Royal
Commission reporton the sprucebudwormoutbreak
in Newfoundland(Hudak and Raske 1981).
The presentpaper reinterprets
theoriginallifetables
fromthe Green River Project,incorporatingrecentinformationfromfieldobservations,laboratoryexperiments,and theoreticalstudies. The task is somewhat
like restoringa prehistoricanimal fromfragmentsof
fossilized bones. Morris's life tables provide a basic
skeletal structurebut are insufficient
for full restoration; missingpieces have had to come frominference
or supposition.WheneverI need to deduce indirectly,
I argue only qualitatively,steeringbetweenthe riskof
makinga falseinferenceand thatofhesitatingto adopt
a potentiallycorrecthypothesis.
This paper consists of fourmajor sections. First,I
brieflydescribe the life cycle of the spruce budworm
and the cyclic patternof its population fluctuation,
restoredfromrecentquantitativeinformation
and supplementedby more qualitative records of outbreaks.
These records include the results of the analysis of
radial growthringsof some host trees that survived
budwormattacksin the past two centuries.':
In the second section,the analysis of the life-table
data, I identifytwo major components that govern
yearlychangesin sprucebudwormpopulations,namely, survival of larvae duringtheir feedingstage and
apparentovipositionrate (i.e., the ratio of all eggslaid
to thenumberoflocallyemergedmoths;E/M ratiofor
short). The larval survival rate determinesthe basic
oscillatorypatternin population fluctuations,a trend
that is subject to perturbationby the E/M ratio. Immigrationand emigrationof egg-carrying
mothscause
the E/M ratio to fluctuatewidely fromyear to year,
butwithoutanynoticeabletrend.I raiseall conceivable
factorsthatcould influencethe two componentsand,
by elimination,I narrowthe possibilitiesto the few
most plausible ones.
In the thirdsection,I attemptto synthesizespruce
budwormpopulationdynamicsbysimulationsthatuse
a simple time-seriesmodel. In the last section,I show
how myview ofthepopulationdynamicsofthe spruce
budwormdiffers
fromothertheories,whichhave been
elaborated in models such as the one incorporatedin
Ecological Monographs
Vol. 54, No. 4
the Baskerville(1976) task-forcereport.In particular,
I criticallyexamine the notion of a dichotomyof endemic and epidemic statesand the alleged role of climate and moth dispersal in the initiationand spread
of outbreaks.
Life cycle
The spruce budworm (Choristoneurafumiferana
[Clem.],Lepidoptera:Tortricidae)is univoltinein easternCanada. Moths emergefrommid-Julyto earlyAugust in the Green River area of northwesternNew
Brunswick.Females lay eggs over several days. Egg
masses are laid on the foliageof conifers,mainlybalsam fir,Abies balsamea (L.), and severalspruce(Picea)
species. Each egg mass contains an average of about
20 eggs. Females raised in normal feedingconditions
lay from 100 to 300 eggs,with an average of :200,
butheavydefoliationcaused bya highdensityoflarvae
can reduce fecundityto one-half.The eggs hatch in
10 d. Soon afterhatching,the first-instar
larvae disperse withintree or stand, or even beyond by wind.
Survivinglarvae spin hibernaculawithinwhich they
moltto thesecondinstar.No feedingoccursuntilspring.
Second-instarlarvae overwinterin hibernaculauntil
earlyMay. Soon afteremergence,theydisperseagain
and settleat feedingsites on host trees.They mine in
1-2 yr old needles, or in seed and pollen cones when
available. Duringthethirdto sixthinstars,fromabout
earlyJuneto earlyJuly,larvae feedon thecurrent-year
shoots.Ifcurrent-year
shootsbecome depleted,thelarvae will feed on older foliage,but this oftenresultsin
reduced size and fecundityof adults. Pupation normally takes place on the foliagein early July.Moths
eclose in :8-12 d, completingthe cycle.
Recent radar studies of moth dispersal (Greenbank
et al. 1980) have revealed thatboth femaleand male
sprucebudwormmothsare strongfliers.Dispersaltakes
place in the evening. Female moths usually emigrate
afterlayingpart of theiregg complementat the place
of emergence.Moths in exodus flightclimb decisively
to > 100 m in altitudeand thenflyto new sites,which
are normally50-100 km downwind,but whichcan be
as faras 450 km (the distance betweenthe east coast
of New Brunswickand the west coast of Newfoundland). Female moths usually deposit at least some of
their eggs where they firstland, but they may leave
thereand deposit eggs at othersites over several evenings.
Dispersal flightis governedby meteorologicalconditions,particularlytemperature;no exodus occurs at
< 14'C, and if the moths encountersuch a low temperaturein flight,theydescend withwingsfolded.No
flightwas observed at temperatures> 300.
Patternofpopulationfluctuation
Local budworm populations fluctuatebetween extremelevels. At highdensities,budwormlarvae cause
extensivedamage to firand spruce stands, and even
SPRUCE BUDWORM
December 1984
431
150 _-s
0.05
I
S4
E
.
04
-
0.14194
16195
Fores
Resarch
ent4).-
195
195
1950
1955
17
95
18
0.05-
1945
1960
1965
1970
1975
1980
Generationyear
offoliage,
NewBrunsYearlychangesin sprucebudworm.
density
(number/rn2
logarithmic
scale)in northwestern
wickbetween1945 and 1980. 0 third-to fourth-instar
larvaein plotG4 neartheGreenRiverfieldstation;0 egg-mass
densitiessampledin wider,unsprayed
theGreenRiverarea (data providedby E. G. Kettela,Maritimes
areas,including
ForestResearchCentre).
FIG. 1.
kill trees. In contrast,when larvae are scarce, even
intensivesamplingover a wide area may findonly a
fewlarvae (Greenbank 1963a).
Commencingin 1945, densitiesof third-to fourthinstar larvae in a few selected study plots in northwesternNew Brunswickwere determinedannuallyby
intensivesampling (Fig. 1, 0), as part of the Green
River Project (see Introduction:Source of Data). AlthoughtheGreenRiverProjectwas terminatedin 1972,
a less intensive egg-mass sampling in many sample
plots over all of New Brunswickhas been carriedout
to date formonitoringbudwormdensityin relationto
theprovince'sprogramofaerial sprayingofinsecticide.
The graphwithsolid circlesin Fig. 1 shows the annual
changes in the average densityof egg masses in some
ofthosesampleplotsthatwerefreefromaerial spraying
in the northwestern
cornerof the province,including
the Green River area. An egg mass contains, on average, :20 eggs,and : 15% of the eggswill surviveto
third-to fourth-instar
larvae. Therefore,the egg-mass
graphin Fig. 1, ifshiftedupwardby about one steponthe vertical(logarithmic)scale, can be used to approximate annual changesin larval densityfrom1968 on.
It looks as thoughbudwormpopulations oscillate.
This patternof populationchangeis not an isolated
local case, but occurs widelyover New Brunswick,as
revealed in egg-masssurveyssince 1952. I divided the
provinceinto 30 blocks and, in each block, calculated
the average egg-massdensity(Fig. 2). We see some
in thepatternofpopulationchange.
regionaldifferences
In particular,the troughtends to be much shallower
in centralregionsthan in both northernand southern
parts of the province. Also, the populations in the
southeasterncornerappear to have startedincreasing
slightlyahead oftherestoftheprovince.Nevertheless,
despite fuzzyyear-to-yearfluctuations,the troughin
each graphis clearlyconcurrentamong all populations.
In other words, the budworm populations in New
Brunswickhave been changingin unison forat least
the past 30 yr.
An earlier widespread budworm outbreak in New
Brunswickbegan about 1912 and subsidedabout 1920
(Tothill 1922, Swain and Craighead 1924). From then
untilthemid-1940s,budwormpopulationsthroughout
the province remained extremelylow (Greenbank
1963a). One otheroutbreakthatoccurredaround 1878
is well documentedin the local literature(Swain and
Craighead 1924), which noted that the budworm became scarce afterseveral yearsof extremelyhighdensity.We have now begunto see a patternof oscillation
in budwormpopulation change,which has completed
threefullcyclesin the past 100 yr.
Even older outbreaksof the budwormcan be traced
by examiningradial growthpatternsofsome foodtrees
that survived severe defoliationcaused by the budworm (Swain and Craighead 1924, Blais 1962). These
reoutbreaks,markedby the firstsign of growth-ring
tardation,began about 1770, 1806, 1878, 1912, and
1949 (Blais 1958, 1968, Greenbank 1963a); the last
threecoincide withthe directexperiencealreadymentioned. The presentoutbreakis probablyat its peak.
Similarly,Blais (1965) foundevidence of outbreaksin
theLaurentidePark regionofQuebec, northofQuebec
City,beginningabout 1710, 1755, 1812, 1838, 1914,
1953, and the currentoutbreak concurrentwith the
one in New Brunswick.
Synthesizingthe above facts,I restoredthe pattern
ofbudwormpopulationdynamicsin Fig. 3. The graph
priorto 1945 is a schematicrepresentationof the historical documents and the tree-ringanalyses already
quoted; after1945, the graphis based on actual sampling,as in Fig. 1. The intervalsbetween periods of
heavy defoliationregisteredin the tree rings are rein New Brunswick(solid
markablyregular,particularly
arrows),withtheexceptionofa wide gap between1806
and 1878; thisgap is about twiceas longas theaverage
432
T. ROYAMA
F
Quebec
Ecological Monographs
Vol. 54, No. 4
A
Year
0) 0) 0)
0)
400
M0
U
0
E
50
VI
A
MaineIl
1
-~~~~~
-
2
3
4
5
Nova Scotia
41J
~~~~~~
6
7
FIG. 2. Yearly variationsin average egg-massdensity(number/M2of foliage,logarithmicscale) across New Brunswick
(outlinedby brokenlines) since 1952, calculated fromthe Aerial Spray Programdata provided by E. G. Kettela (Maritimes
Forest Research Centre).In each block, egg-massdensityis plottedon the verticalaxis (logarithmicscale) and calendaryears
on the horizontalaxis as shown in block E6.
intervalbetweenothersuccessiveoutbreaks.A similar
gap occurredin Quebec between the 1838 and 1914
outbreaks(dottedarrows).This led Blais (1968) to remark that "data on past outbreaksindicate that epidemics of thisinsectdo not recurat regularintervals."
However,therewerecomparativelylightdefoliation
marksin treesfromQuebec around 1838, when there
was littlesignin the specimensfromNew Brunswick;
conversely,therewere clear marksin treesfromNew
Brunswickaround 1878, when therewere few in the
Quebec specimens. Is it not likelythen that the populations in both provincespeaked more or less at the
same time, as in otheroutbreaks,but that the populationsin one provincedid notreacha levelhighenough
to affectthe tree rings?The supportingfactsforsuch
a hidden peak are that (1) otheroutbreaksin the two
provincestendedto occurfairlycloselytogether
in time,
(2) the populations in New Brunswickin recentyears
have oscillatedin unison(Fig. 2), and (3) peak densities
of some local populationsin theGreen River area duringthe 1949 outbreakdid notreacha level highenough
to cause heavy defoliation.Nevertheless,these populations did oscillate in parallel withotherpopulations
thatreachedan extremelyhighdensity.The population
fromplot G4 in Green River ( Fig. 1) is one such lowdensitycase. Thus, placinga small peak at about 1840
in Fig. 2 restoresthe regularity
of oscillations.I know
ofno tree-ring
data fromNew Brunswickfortheperiod
around 1710, when the Quebec specimensshowed defoliationmarks.
Includingthepossiblehiddenpeaks,theaveragecycle
lengthwas 35 yrin New Brunswick(7 peaks over 210
yr),and 38.5 yrin Quebec (8 peaks over 270 yr).The
longeraverage forQuebec is due to two long intervals
between1710 and 1812. This degreeofdifference
would
not be unusual betweentwo series of stochasticpopulation processes that share a common endogenous
structureand, hence, the same exdensity-dependent
pected (mean) periodicity.
Even duringthe low-densityperiods betweenmajor
outbreaksin this century,a few scatteredpatches of
comparativelyhigh densityalways remained on the
budworminfestationmaps of easternCanada (Brown
1970,Kettela 1983). These are probablytheareas where
the troughsof population oscillationsstayedcomparativelyhigh,as in centralregionsof New Brunswick
in the 1960s (Fig. 2). I discuss the stochasticnatureof
these population oscillationsin Synthesis.
December 1984
SPRUCE
BUDWORM
1800
1850
433
.0
0
I
75
CL
CL
0
1700
1750
1900
1950
Year
FIG. 3. Sprucebudworm
population
cycles(logarithmic
restored
fromsampling
scale)inthepasttwocenturies,
datasince
1945(- **; afterFig. 1),fromhistorical
), andfromradialgrowth-ring
recordssince1878(
analysisofsomesurviving
trees(-- -). Arrowsindicatetheyearsoffirst
Solidand dottedarrowsare forNew Brunswick
signofringretardation.
and
Fora smallpeakaround1840,see text.
Quebec,respectively.
Source of data
Life-tablestudies of the Green River Project were
carried out in locations freefromaerial sprayingof
DDT and werebased mainlyon samplingfirand spruce
foliageat threephases in the life cycle of the spruce
budworm;namely,(1) soon afterall eggshad hatched,
(2) when the majorityof larvae were in the thirdand
fourthinstars,and (3) at the time of 60-80% moth
eclosion. The lengthof a foliatedsample branch was
multiplied by its midpoint width to calculate the
"branch (or foliage) surfacearea." Budworm density
was thenexpressedas numberper square metre(originallynumberper 10 ft2)of the foliagesurface.
The above sampling schedule determined(1) egg
density,(2) initial densityof first-instar
larvae (i.e.,
thoseeggssuccessfully
hatched),(3) densityof "feeding
larvae," the majoritybeing in thirdto fourthinstars,
(4) densityof pupae, includingemptypupal cases still
remainingattachedto the sample foliage,and (5) total
numberof moths thatemerged.
Althoughsamplingwas carriedout at some 20 scattered plots, the period duringwhich most plots were
sampled extendedover onlya fewyearsand is not long
enough foranalysis of temporalchanges in budworm
density.Only one plot,G4, a maturefirstandthatwas
>50 yr old in 1945, yielded 12 yr of uninterrupted
samplingdata between 1947 and 1958, a period coveringa major part of the outbreakin the province in
the early 1950s. Since it covered the longestperiod,
the set of data fromthis plot is the main source of
informationused in the presentanalysis.
However, in plot G4 the budworm densitynever
reacheda level highenoughto cause heavy defoliation
and tree mortality.The investigatorsconsidered the
plot to be atypicalsinceit was isolated fromotherparts
of the forestby earlierclear-cutting
operations.Nonetheless,the rise and fall of population densityin this
plot followedmuch the same patternas in the other
areas wheredensityclimbed to extremelevels. Thus,
fromthe point of view of budworm population dynamics, I do not see thatthe population in plot G4 is
atypical.
The second longest set of life-tabledata, the 9 yr
between 1949 and 1957, comes fromplot G5, 5 km
northof plot G4. This was an "immature" firstand
(<40 yrold in 1945). Again, it was an isolated, "atypical" stand,wherebudwormdensitystayedeven lower
thanthatin plot G4. Nevertheless,thepatternof populationchangeduringthestudyperiodwas again much
the same as in otherareas.
Additionallife-tabledata used in thepresentanalysis
are fromplots K1 (maturein 1945, as in G4) and K2
(immature,as in G5), both 15 km northeastof G4.
These two plots are partof an extensivefirforest,typical ofnorthwestern
New Brunswick,wherea highdensity of budworms caused successive years of heavy
defoliationand much tree mortality.Unfortunately,
the data fromthese plots covered no more than 7 yr
(1952-1958) of the decliningphase of the outbreak.
Plot G2, 5 km south of G4 and with similar stand
characteristics,
yieldedan even shorterset of life-table
data, whichwill be used in thepresentanalysisas supplementaryinformationonly.
After 1959, budworm densityin the Green River
area fell so low that it became extremelydifficultto
findlarvae late in the season. Consequently,it became
technicallyimpossibleto carryon a fulllife-tablestudy.
larvae continuedto be samOnlythird-to fourth-instar
pled at plots G4 and K1. Unfortunately,
egg sampling
was also discontinuedafter1959. Althoughthe population began to increase after 1968, leading to the
was termicurrentoutbreak,the project,regrettably,
nated afterthe 1972 season.
Long-rangemothdispersalhas been studiedby aircraftand radarin recentyears(Greenbanket al. 1980).
Some resultsfromthisstudywillbe used in thepresent
analysis.
Notationand terminology
In thispaper,densityof the insectis denoted by the
lowercaselettern, and the rateof changein n between
two points in the life cycle by h; this is the survival
rate in the intervaldefined,with the exceptionof the
adult-to-eggrate of change. The naturallogarithmsof
434
T. ROYAMA
Ecological Monographs
Vol. 54, No. 4
TABLE1. Life-table
notationand life-history
stages.
n,
=
hi!
=
N, =
=
H3t =
hg, =
h5t
H,, =
Rst =
R.! =
R3t =
a. Summaryof life-tablenotation.
Density at the beginningof stages in generationt (s = 1 to 5)
log n,,
ns+I /nst (s = 1 to 4): survival rate in stages
+/n5t:apparentovipositionrate (or E/M ratio)
n,,t
log h3t
survivalrate
intrageneration
survivalrate
HI + H2 + H3 + H4: log(intra)generation
N3t+1- Nt: log rate of change in densityfromstages in generationt to the same stage in generationt + 1
H4v+ H5t:log rate of change in egg density
(L3) density
H3t + H4t+ H5t+ HI I,' + H2t+3,:log rate of change in third-to fourth-instar
b. Parameternotationand stage designationsin life-tabledata.
Stage
sur-
Gen- Initial
era- den-
Stage
Period
tion sity
Remark
Stage Code (s)t
1
E
Eggs
All eggslaid
Late summer
t
n,
of year t - 1
Young
larvae
Old larvae
LI
L3
2
3
Fall ofyear
t- 1
t
Earlysummer t
of year t
n2t
n3t
All eggshatched*
P
4
Mid-summer t
ofyeart
n4t
All pupaeand pupalcasesat time
of60-80%mothemergence
Moths
M
5
Late summer
ofyeart
n5t
All pupalcasesat timeof
60-80%mothemergence,
and
Eggs
E
1
Late summer t + 1
ofyeart
rate
Egg(E) survival
h2,
Survivalofyoung
(L1)larvaet
h3t
Survivalofold
(L3)larvae?
h4,
Pupal(P) survivall
h5t
E/Mratio(apparent
oviposition
rate)JI
moths rearedfromremaining
pupae*
nl,+
Remark
he
Majorityin 3rdand 4thinstars*
Pupae
t
vival
t s numbersas in Table 1a.
* Timesampled;see Introduction:
SourceofData.
to as "smalllarvae"in Morris(1963a).
t Referred
to as "largelarvae"in Morris(1963a).
? Referred
SourceofData.
11Mainlylaterpartofpupalstage;see Introduction:
? Eggspermothon foliage.
in the calendar year t - 1 belong to generationyear t,
and the subscriptt in Nt, Ht, etc. indicates the generation year. In graphs,these parametersare normally
plottedagainstgenerationyear t; only in a fewgraphs
are theyplottedagainstcalendar years.
The parameterand stage symbols used throughout
this paper are summarized in Table 1; details of the
timingof the fivestages listed in the table have been
givenin Introduction:
SourceofData. As alreadynoted,
=
for
4
s
1
to
is
a
survivalrate. In many pubstage
hs
(la)
hat= ns+llnst
lished works, the survival rates h3 and h4are often
referredto as "large larval survival" and "pupal suror, takingthe logarithms,
H=Ns -N
(l b) vival" after the Green River Project terminology.
However, h3includes the effectof mortalityin partof
As mentionedin Introduction:Life Cycle, one gen- the pupal stage,and, conversely,h4excludes the early
erationin the budwormlifecycle spans fromthe late part of pupal mortality.Unlike other h's, h5tdefined
summerofone yearto thatofthefollowingyear.Thus, as n 1t+l/n5t
is not a survival rate,but is an apparent
the eggs,the firstinstar,and part of the second instar oviposition rate per moth (male and female moths
n and h are denoted by the correspondinguppercase
lettersN and H (the same notationswereused in Royama 198 la, b). Throughoutthis paper, naturallogarithmsare identifiedwiththe abbreviation"log."
Life-cyclestages and generationsare indicated by
two subscripts.For example, n,, and NS, are density
and log densityat thebeginningofstages ofgeneration
t. The survival rate fromthe beginningof stage s to
thatof stage s + 1 withingenerationt is then:
SPRUCE BUDWORM
December 1984
combined),as it includesthe effectsof gain and loss of
eggsthroughmoth migration.I shall call this rate the
"E/M ratio."
In the presentdata, H5 is always positive (or h5 >
1) despite the physicalpossibilityof a negativevalue
resultingfroman extremelyhigh rate of emigration.
As opposed to this,the H's in all otherstagesare negative; i.e., a net loss, though net gain of larvae has
actually been observed in a few plots at the time of
second-instardispersal (Miller 1958).
Some successive H values may be lumped. For instance, lumpingthe firsttwo stages,Hit + H2,, gives
the log survivalrate fromeggto thirdto fourthinstar
in generationt. Lumping fromHit to H4,, and designatingthe sum as H,,, gives the log intrageneration
survivalrate,thoughthistermassumes zero mortality
in egg-layingmoths; the effectof the moth mortality
is in factincluded in H5t,the log E/M ratio. We may
lump all log stage survivalrates to H5t,givingthe log
rateof changein eggdensityfromgenintergeneration
erationst to t + 1. This will be denoted by RI,; i.e.,
Rlt=
-NNt+-Nit
= Hit + H2t + ..*+
= Hg1+ H5t.
Hot
(2)
In general,we may defineR1t(s = 1, 2, . . .) such that
Rst =
Nst+
-Nst
= Hst + Hs+1 t +
+ Hs- It+l-
(3)
(log)
For example, R3t is the t to t + 1 intergeneration
densityand
rateofchangein thethird-to fourth-instar
is the sum H3t + H4t + . . . + H2,t + 1
rate of change in densityof
The log intergeneration
a given stage(R in Eq. 3) has oftenbeen referredto in
the literatureas the "index ofpopulationtrend,"since
Balch and Bird (1944) coined the term(Morris 1957).
because the yearThis is an unfortunateterminology,
to-yearrateofchangecannotindicatepopulationtrend
in the usual statisticalsense; i.e., a fairlyconsistent
tendencyover a comparativelylongperiod oftime.To
reveal a trend,observationsmust extend many more
than 2 yr.
A tendencyfora population to increaseor decrease
overa comparativelyshortperiodoftime(forexample,
not much morethan 10 yr)may be called a short-term
trend,thoughit could have been merelyan increasing
or decreasingphase of an oscillation of many more
yearsin length.Furtherobservationsmightreveal that
thesystemis merelyoscillatingabout a horizontallevel,
in which case the systemwould be said to have no
long-termtrend or, alternatively,to exhibit a shorttermtrendthat changesits directionperiodically,dependingon whichaspect is emphasized. In thispaper,
I use the term"trend" in the above sense ratherthan
in the Balch-Birdsense.
Note also thata "trend" in a seriesof no more than
five or six points can occur by chance, as would be
in a purelyrandom series.
observed not infrequently
435
To implythatthis "trend" is a section of a trendin a
longerseries requiresadditional knowledge.
Reliabilityof data
Sprucebudwormsamplingin the Green River Project was very intensiveto ensure a high level of reliability(Morris 1954, 1955). Nonetheless,thedata suffervarious types of errorsor loss of information.In
thefirstfewyearsoftheproject,eggand pupal densities
were not adequately determined,and the corresponding survivalrateswere indirectlyestimated.Although
a large sample was taken each time to ensure an accurateestimateof density,no sample was takenin the
(L3) and pupal
intervalbetweenthird-to fourth-instar
(P) stages (Table lb), so that littlewas known about
changesin densityduringthatimportantinterval.
The pupal density(n4) tends to underestimatethe
actual numberof larvae thatpupated, because predators, for example, could have removed some pupae
withouttracebeforethe scheduledsampling.Also, the
value n5 in Table lb tends to overestimatethe total
number of moths that actually emerged in the field,
and this, in turn,underestimatesthe E/M ratio (h5).
This is because n5 is the sum of all pupal exuviae on
thesample foliageplus thenumberofremainingpupae
rearedto adults in the laboratory,the latterbeingprotected frompredation or loss in the field.These are
probablyminorerrors,however.The variationin the
timingof L3 samplingfromyearto yearinfluencedthe
estimationsof h2and h3,the survivalofyoungand old
larvae. I discuss thisin detail in Analysis:Analysisby
Stage Survival Rates.
Graphedlifetables
Graphs oflife-tabledata fromplots G4, G5, K1, and
K2 are shown in Figs. 4 to 7. As mentionedin Introduction:reliabilityof data, densitiesat some stagesin
the firstfew years are indirectestimates,as are the
subsequentlycalculated survival rates. These indirect
estimatesare indicatedby open circlesin the figures.
ANALYSIS OF LIFE-TABLE DATA
Two major componentsofpopulation
fluctuations
Fig. 8 is equivalent to Fig. 1, but plots log year-toyear rate of change in density(i.e., Rt = N,,, - Nt,
ratherthan Ntin Fig. 1) againstgenerationyear t. The
about
lograteR exhibitsfrequentsecondaryfluctuations
its principal oscillation. (Note that the oscillation in
log density[Fig. 1] and the oscillation in the log rate
of change in density[Fig. 8] lag in phase; a peak or a
troughin Fig. 1 correspondsto a zero in Fig. 8.] I shall
now showthattheloggenerationsurvivalrateHgmainly
determinesthe basic oscillation(smooth curve in Fig.
8), and the log E/M ratio H5 is largelyresponsiblefor
the secondaryfluctuations.
Recall thatthelog rateof changein eggdensity(R1t)
436
T. ROYAMA
b
H2-21
y+@
-2
-6
I
b
-1
H2 -2
-3
-3
-4
-5-
+
'
CI
H3-2
H
72
-4
H
195
h
-6 V
4-
Ra3-4
7-e
60
50
2
I
3 -0
-2
6 -f
4 -N3
N
3
2
I
k
2
R3
L2? se
0
-1
-2
0 o R4d
rto
-2
Grpe lif tale inpltG erth
FIG
-34. /-3
-42
1945
50
55
60
1945
50
re
55
ie
lation, and that the log E/M ratio (H5) is largelyresponsible forsecondaryfluctuationabout the trend.
The log generationsurvivalrate Hg, however,does
not always show a smoothoscillation,but shows some
sporadic dips, as in the 1953 generationin plot G4
(Fig. 9b) and in 1947 and 1951 in plot G5 (Fig. Si); a
verylow Hg in 1952 in plot K1 (Fig. 6i) is probably
one such dip, thoughthe data series is too short.Inall thesedips in thegenerationsurvivalrate
terestingly,
are caused by dips in survival rates among feeding
larvae (H3); compare graph c with graph i in Figs. 4,
5, and 6. These dips in Hg thatare caused by H3 may
in turncause dips in thelog rateofchangein eggdensity
(R1); for example, the one in the 1951 generationin
plot G5 (Fig. Si and j). Therefore,Hg, like H5, can be
a cause of secondary fluctuationsin the log rate of
change in density(Fig. 8). However, a dip in H3 may
be counteredby a high log E/M ratio (H5), as in the
1953 generationin plot G4; consequently,the dip in
H3 would not show in the log rate of change R, (Fig.
4e, i, and j). On thewhole,thevariationin thelog E/M
ratioH5 is a farmoreimportantcause ofthesecondary
fluctuationin the log rate of population change than
are sporadic dips in the log generationsurvival rate
Hg, thoughthe latteris an importantsubjectfromthe
60
Generation year
4. GraphedlifetablesinplotG4 neartheGreenRiver
fieldstation.Log survivalratesin (a) eggs(H,), (b) young
larvae(H2), (c) old larvae(H3), (d) pupae(H4); (e) logE/M
ofeggs(N,),old larvae(N3),and
ratio(H.); (f) log densities
FIG.
Ecological Monographs
Vol. 54, No. 4
a
H1HI 0a0 Ia
~J
+_ -2
-3 -
-I
-2 pupae (N4); (g) log survivalrate frombeginningof egg stage
-3
to end of younglarval stage (H, + H2); (h) log survivalrate
to end of old larval stage(H, + H2 + H3); (i) log intrageneration survivalrate (Hg = H, + H2 + H3 + H4); () log inter- H3~
-6 generationrate of change in egg density(R. = Hg + H.); log
-41
rates of change in densities of (k) old larvae and (1) pupae
(R3 and R4, respectively).o- -o indirectestimates.
H4 5
Hg
z
-4 -
-5
g
0
f
d
-6
0
-3
0
Hg -5
-6 -
7-
2 j
fromgenerationt to t + 1 is partitionedinto the log H5 6 1
41
generationsurvival (H.1) and the log E/M ratio (H,,);
0-01R1
c
RI
3
=
I
In
Hgt
+
Fig.
9,
duplicate
la).
i.e., R1,
H., (Table
the relevantgraphs fromFig. 4 (life-tabledata from
-2
6 plot G4) forease of comparison. It is obvious that a
5 --3
4-f
k
2N
decliningtrendand a secondaryfluctuationabout the
trendin R1 (Fig. 9a) are determined,respectively,by
~~R3 0
22~~~~~~~~
Hg (Fig. 9b) and H. (Fig. 9c).
We do not have data on the rate of change in egg
62--R
density(R1) after1959. However, R1 is highlycorreN 3
-2
N
lated withR3 (log rateof changein L3 density,Fig. 9a,
-4 ~
~ 4
-20). No doubt, the correlationmust have held after
-5
1959; as I show later,survival fromeggs to third-or
6
-6 O'-3
larvae is largelydensityindependent,so
fourth-instar
55 60
50
1945
50
1945
the above correlationis unlikelyto be affected.Therefore,we can substituteR3 in Fig. 8 for R1 and can
Generation
year
conclude,by extrapolation,thatthelog generationsur4
FIG. 5. Same as Fig. butin plotG5.
vival rate Hg determinesthe basic population oscil-
55
60
December 1984
SPRUCE BUDWORM
biological controlpoint of view. What causes the dips
is currentlyunknown.
0- a
_
Ha-2 it+
0
H2-2 -
b
I?
12 2-
C
-2
55
5 d
H4
-3
6
- e
7-4
6
N
f
N1
-
dd.,
.-6
Hg5-
76
H
e
5 a3
7 6
5 -
j
2i
l
|
l
l
lRl
l
-gj
N-2
fN
0N3
FIG
N4
2
2
R3S
-2-
N i--2
k5
0
-I
-4~~~~~~~~~~
n 0: number2ofmoths that emerge-2
-31
50
55
60
1945
50
55
60
h
n,: numberof mothsthatemergedlocally
A: mean potentialfecundityofa local moth,including
males
p1: proportionoff laid locally beforeemigration
m: numberof immigrants
f2: mean number of eggs carried per immigrant,includingmales
P2: proportionoff2laid at the landing site beforereemigration
-56
H -61:-
Note thatPi takes into account the effectsof the rate
of emigration,the preemigrationrate of oviposition,
and thepreemigration
mortalityamong theemigrants;
P2 takes into account the same effectsapplied to the
immigrantsthatreemigrate.
The total number of eggs laid locally is the sum
~~~~~~~~4
-2
23
5 -32
k
3
~~~~R3_I
2 N-2
I
2
0
FIG 6. Sam
Fi.4btinpo
RI
-1
R4 0I
-2
/%
-3 --4
-2-5b50
55
60
1945
1945
50
55
Generation year
FIG.
h
Generation year
I
3-
\~
FIG. 7. Sameas Fig.4 but in plot K2.
2-
-
-4
-5 -
- C-3
-2-3
-3
-6
55
t
I
-I6
H
g
9
-3
'-3
-209-
-3
7-
H 5
|
b
-3
-2 -
+-4
i
H3
X
IF
-3
H2
~
I
X
+ I 92
-2
IE
-5
1945
HI
W
a
.
HI 0L a
E/M ratio
Fig. 10 compares the graphs of H5 (log E/M ratio)
taken fromFigs. 4-7. The dashed line in each graph
indicatesone-halfof themean potentialfecundity(full
eggcomplement)of a local femalemoth;I call thisthe
mean fecundityper moth (includingmales) and refer
to it by the symbolfi. I use this measure to compare
with the E/M ratio because the denominatorof the
ratio includes all locally emerged moths, whose sex
ratio is usually 1:1 (McKnight 1968, T. Royama, personal observation).If neithermoth dispersalnor mortalityhas occurredin the localityconcerned,the E/M
ratio should coincide withthe dashed line.
Note threefeaturesin the graphsof Fig. 10: (1) the
log E/M ratios(H5) oftendeviatewidelyfromthemean
potentialfecundityper moth (logsf,---); (2) theH5's
oftenfluctuatein unisonbetweenplots,butat distinctly
lower levels (as compared with---) in the K than in
the G plots; (3) no trendis apparentin the H5's in the
G plots (the seriesin the K plots are too short).
To aid in explainingthese features,I use a model
composed of the followingsix parameters.
437
6. Sameas Fig.4 butin plotKi.
ftpln5
+ f2p2m,
and dividing
E/M ratio h5;i.e.,
the sum by n, gives the
h5 =f1p1 +f2p2m/n5.
60
(4)
This equation applies, withoutnotationalchange,to a
more generalsituation,as in Appendix 1.
Deviation ofE/M ratiofromfecundity.
-The potential fecundityof a femalemoth (2f1)is linearlyrelated
to its pupal size, is usually <250 eggs,and is rarely
>300 eggs(Miller 1963a: Fig. 13.3). The dashed lines
438
T. ROYAMA
Ecological Monographs
Vol. 54, No. 4
3
C
e02
.s
0
0
-
*~-3
0
0
1945
1950
1955
1960
1965
1970
1975
1980
Generation year, t
FIG. 8. Equivalent to Fig. 1, but shows yearlyfluctuationin log rate of changein L3 density(R31, 0) fromgenerationt to
t + 1, plotted against t, and the log rate of change in egg-massdensity(Rlt, 0). The smooth trendcurve is drawn by eye.
Arrowsindicate yearsof moth invasions fromoutside; see Analysis:Frequencyof Moth Invasions.
in Fig. 10 are theaveragef's estimatedfromthepupal
size sampled in each plot (Miller 1957, 1963a). Low
fecundityin the K plots is associated with heavy deo
foliationof the current-year
shoots (Table 2).
An
E/M
ratio
well
above
the
dashed line indicates
I
I
immigrationof egg-carrying
moths. Because of mortalityamong laying moths, only 60-80% of the full
I
Qo d
It
complementof eggsmay be laid locally (Thomas et al.
1980, and Appendix 2), even iflocal femalemothsdo
0
'1,0
-2
not emigrate.Therefore,an E/M ratio fallingbetween
a
-3
thepotentialfecundity
f and 0.6f1does not necessarily
indicate
emigration.
However,
many pointsin Fig. 10
-3_
are well below log 0.6f1,indicatingnet emigration.
-4 _-H
Note that althoughthe lowest average fecundityin
-5
the heavily defoliatedK plots was as low as one-half
of thatin the G plots,such a difference
had littleeffect
-6
b
ae
in
on
the
E/M
in fevariation
ratio.
variation
Thus,
-7 cundityis a trivialfactorin budwormpopulation dynamics relativeto moth dispersal.
Climaticinfluenceon E/M ratio.-Fig. 11 compares
the
average net moth dispersal over the Green River
7
area withthreemeteorologicalfactorsduringtheadult
period forthe years 1950-1958. The threefactorsare
(1) number of cold frontspassing over the area, (2)
number of thunderstorms,
and (3) mean daily mini6
mum
relative
humidity
(data
takenfromthe firstnine
3
rows in Greenbank's [1963b] Table 14.3). Note that
Greenbank's net moth dispersal (fifthcolumn in his
N14
4
is proportionalto my E/M ratio. The inverted
table)
3i
mean dailyminimumrelativehumidity(graphc) seems
2
to be the best predictorof the log E/M ratio H5.
A good correlationbetween inverted mean daily
minimum relativehumidityand E/M ratio seems to
1945
1950
1955
1960
hold over a much longerperiod. As shown in Fig. 9,
we have a directmeasurementof the E/M ratio in a
Generation year
few plots, but only between 1946 and 1958. During
in plotG4 this period,the fluctuationin the log E/M ratio H5 in
FIG. 9. The log rateofchangein eggdensity
intolog generation
(R., 0, grapha) is partitioned
survival
(Hg,graphb) andlogE/Mratio(H5,graphc). The lograteof plot G4 was nearlyidenticalwith that in the log rate
correlated
with ofchangein L3 density(R3),exceptfora decliningtrend
changein L3density
(R3, grapha, 0) is highly
in R3 and a lack of it in H5. Thus, allowing for this
R1.All graphsherearetakenfromFig.4.
R
Hg
b
H55F_______
December 1984
SPRUCE BUDWORM
oflocalfemalemoths
2. Averagepotential
fecundity*
shootson balsam
ofcurrent-year
in relationto defoliation
fir,Abiesbalsamea,in GreenRiverarea.
TABLE
rG4
G plotst
Defoliation
Fecundity
(%)
(eggs/9)
5
normal?
Year
1947
4
I2
~~~~~~~I
~~ I
i
3
I
-
_
5
_
2
_A
17
7
24
11
9
normal
normal
186
178
178
26
normal
11
1953
1954
2
6
1948
1949
1950
1951
1952
1955
1956
K plotst
Defoliation Fecundity
(%)
(eggs/9)
_1
-
176
10
13
K
159
139
99
121
51
170
99
normal
normal
17
1957
normal
* Estimatedfrompupal size; see text.
,,
-
73
96
93
58
68
136
150
t AverageofG2, G4, and G5.
t AverageofKI and K2.
? Normal(unstarved)
pupalsize,indicating
theaveragefewas ;200 eggs.
cundity
IIDash indicatesno data.
fromthe meteorologicalrecordin each year (Fig. 13,
0). The series of these estimateddegree-daysis well
correlatedwith the series of log E/M ratios (H5; Fig.
13, 0) from 1946 to 1958 and is still quite well correlatedwith the series of R3 (log rate of change in L3
1945
1950
1955
1960
0 FW8 --
Generation year
FIG. 10. Patterns
offluctuations
inthelogeggs/moth
(E/M)
ratio (H5) in plots G4, G5, K1, and K2. Dashed line in each
6k-
.0
2 -
7o
graphis thelogmeanpotential
fecundity
perlocallyemerged
moth(logs,);detailsare in thepresent
section.
difference,
we could use R3 in Fig. 8 (plot G4) as an
indicatorof fluctuationin H5 after1959. We also have
daily readings of minimum relative humidityat the
Green River fieldstation,2.5 km south of G4, from
1946 to 1972. However, I have to estimatethe dates
of the adult period in each year indirectlyin the followingway.
First,accumulatedheat units(in degree-days)above
a thresholdtemperatureof 5.60C can adequately predict the developmentof the spruce budworm (Miller
et al. 1971). We have thedates on whichmotheclosion
peaked each year at the Green River stationbetween
1949 and 1957 (Fig. 12, 0), fromwhich I calculated
theaverageaccumulatedheat unitsto be 607.2 degreedays. The date on which this number of degree-days
was accumulated in each year was in turnread from
the meteorologicalrecordat the station;I take this as
the day of peak moth eclosion foreach year (Fig. 12,
0). Over an intervalof 20 d, withthe estimatedpeakday in the middle, as an effectiveadult period, I calculated the mean daily minimum relative humidity
C
a
,
00 e
0
Z~~ :~
I
I
I
I
I
IX
I
0-
4)
.0
-a
1905
-35
3--]0
&_.
)
52
65
75
0c
I
I
0
-2
E
~~~~~~E
I
195051 52 53 54 555657
1
58
Year
FIG. 11. Effect
ofclimateon theeggs/moth
(E/M)ratio,
after
Greenbank
(1963b:Table 14.3).a. Numberofcoldfronts
passingover the GreenRiverarea duringthe mothflight
period.b. Numberofthunderstorms.
c. Meandailyminimum
relative
humidity
(%, *, inverted
scaleon theright),
and the
logarithms
ofGreenbank's
indexofnetmothdispersal(proportionalto myE/Mratio)averagedovertheGreenRiver
area(0, scaledon theleft).
T. ROYAMA
440
o
0
Ecological Monographs
Vol. 54, No. 4
10
5
5
>
a
20
e=Lo <>20ttO~~~~~~~~l
;
0
0
10 _
1946 48 50 52 54 56 58 60 62 64 66 68 70 72
a
Year
peakeclosion
ofdatesofpeakmotheclosionin theGreenRiverareafrom1946to 1972.0 recorded
FIG. 12. Estimation
to,on average,607.2 degree-days
above 5.60C. 0 dateson whichheatunitshad
dateson whichheatunitshad accumulated
to 607.2 degree-days.
justaccumulated
density,x ), a substitutefortheH. seriesbetween1959
and 1971. Note thatboth R3 and invertedmean daily
minimumrelativehumidityexhibitedan upwardtrend
after1963, whichwas probablycoincidental(see Analysis: influenceof weather).
The minimumrelativehumidityof a day normally
occursin theearlyafternoon,and mothdispersaltakes
place in the evening. Then, why is there an inverse
correlationbetweenE/M ratio and mean daily minimum relativehumidity?Probably,meterologicalconditionsthataffectmothdispersalactivityin theevening
are correlatedwith the minimum relative humidity.
Greenbanket al. (1980) observed thatthe eveningexodus flightof a moth usually occurredbetween 1930
(AtlanticDaylightSavingTime) and midnight(thepeak
was at about 2130), and mostly at temperaturesat
canopy level of between 180 and 230C; no exodus was
observed below 14.5?, above 29.50, in heavy rain, or
in still air. Their observationsby radar and aircraft
revealed that moths on the wing, immigratingfrom
elsewhere,were forcedto land withtheirwingsfolded
whenencountering
a cold air mass (presumably< 140C);
iftemperatures
remainhighenough,however,themoths
mightcontinueto flyeven aftermidnight.Lightinten-
.
8 _
3
la 2
_ 20
1~~~~~
7
V)
a,
sityis anothercontrollingfactor.Moths do not take
offmuch before 1900 regardlessof temperature(an
exception was the unusually earlier flightsduringa
95% sun eclipse in New Brunswickat 1735 on 10 July
1972).
Greenbanket al. (1980) have shownthatpeak hours
of exodus tend to be earlier on cold nightsthan on
warm nights.However, a cold nightis likelyto reduce
the overall chance forexodus. A cold nightmay also
forceimmigrantsto land if theyhappen to be flying
over the area. Therefore,in a year when cold nights
prevail,more eggstendto be depositedlocally,resulting in a high E/M ratio in the area, and vice versa.
Since a low minimum relativehumiditytends to indicatea cool night(and vice versa),we gettheobserved
inverserelationbetweenE/M ratioand themean daily
minimumrelativehumidity.
The warmthof a nightmay be indicatedby average
temperaturesbetween 1930 and midnight.However,
as shown in Fig. 14, a nightwith a high initial temperatureand a steep decline (curve a) could be just as
"warm" as one witha lower initialtemperatureand a
less-steepdecline (curve b). Chances forexodus flight
probablyare less on a "cold" night,as in curved rather
:
-
Lo0
3
.
I
0~~~~~~0
1950
-30
/
15 ,
I~~t
96
I
195
196
95
4965
17
197
Year
FIG. 13. Comparison
betweenfluctuations
in meandailyminimum
relativehumidity
(%,0; invertedscale)duringthe
estimated
effective
adultperiod,andthelogeggs/moth
(E/M)ratio(He, 0), supplemented
bylograteofchangein L3 density
(R3,x) after1959. Data fromplotG4. Fortheestimation
ofeffective
adultperiod,see Analysis:ClimaticInfluence
on E/M
Ratio.
December1984
SPRUCE BUDWORM
25
0Q
b
E
20
0)
14
2000
2100 2200 2300 0000
Hour (A.D.T.)
FIG.
14. A schematic
representation
of"warmnight"con-
ditions (
a and b) and "cold night" conditions ( --- c
andd) inrelation
tomothdispersal
activities.
HourisAtlantic
DaylightSavingTime. For details,see Analysis:Climatic
Influence
on E/MRatio.
than curve c, even if the average temperatureis the
same. As faras I am aware, Greenbank et al. (1980)
did not discuss the effectof these differences.
Synchronous
fluctuations
between
plots,and spatial
density-dependence
inE/M ratio.-Fig. 10revealsthat
thelog E/M ratioH5 oftenfluctuatedin unisonbetween
plots. But H5 in the G plots varied about the log potential fecundity per moth (logf; - - -), whereas in the
K plots, H5 was nearlyalways below log f1; compare,
in particular,plots G5 and K1. These differences
must
be related to differencesin local population density.
To test this idea, I regressedthe log E/M ratio H5
againstthelog densityoflocallyemergedmothsN5 for
all plots wheredata were available in each of the calendar years 1954, 1955, and 1956 (Fig. 15). Since my
presentinterestis the differences
betweenplots, data
fromeach of the 3 yrare shown separately;therewere
insufficient
plots in other years for such an analysis.
The 1955 and 1956 data show similar inverse relationshipsbetweenH5 and N5,whereasthe relationship
is somewhatdifferent
in 1954.
Variationsin fecundityand mothmortalitycould be
densitydependent,but the effectsof these variations
are unlikelyto be a major cause of the inverse relationshipin Fig. 15. This is because the variation in
oviposition rate withoutdispersal would be confined
mostlywithinnarrowlimits,withthe upper one being
the average potential fecundity(Jjin Eq. 4) and the
lowerone due to mothmortality(;0.6f, forthereason
givenin Appendix 2). Many pointsin Fig. 15 are outside theselimits,suggesting
thattherelationshipin Fig.
15 must be due to densitydependence in moth dispersal.
Greenbank(1 963b) remarkedthatif moth invasion
441
occurredevenlyover an area containingseveral plots,
theE/M ratioshouldbe highin a plotwherethedensity
of local femalesis low, and vice versa. This idea, however, does not adequately explain the observed relationshipin Fig. 15, because net emigrationevidently
occurred toward the higherend of the densityspectrum.
Immigrantsare probablyunable accuratelyto assess
local population density(n5) beforetheyland, so their
number,m in Eq. 4, would be essentiallyindependent
of n5in each plot. However,as longas climatepermits,
theimmigrantscould reemigrateifthelocal population
was highenoughto have caused substantialdefoliation.
In otherwords, it must be emigration,reemigration,
and preemigrationoviposition rates that become inverselydependent on local density,at least above a
certaindensitylevel; thatis, a majorpartofthepreemigrationoviposition rates P1 and P2 in Eq. 4 must be
inverselydependent on n5 at highervalues. (I shall
discuss a low-densitysituationshortly.)
In 1954, log E/M ratios (H5) in those plots in Fig.
15 whereN5 < 2 were much lowerthan those in 1955
and 1956 forthe same rangeof log moth densityN5,
were less towardthe higherend of
thoughdifferences
the densityspectrum.This implies eitherthatno plots
received immigrantsin 1954, or that, under the favorableweatherconditionsindicatedby thehighmean
daily minimum relative humidityin 1954 (Fig. 11),
emigrationand reemigrationoutweighedimmigration
by a substantiallygreatermargin than in 1955 and
1956.
Thus, the proportionof eggs the immigrantslay at
theplace theyland is dependenton thelevel ofdefoliation and the duration of the immigrants'stay at that
place, which in turndepends on climatic conditions.
Because theimmigrantsstayat least untilthefollowing
evening,some proportionof eggswould be deposited
there,even ifdefoliationwas heavy; it is veryunlikely
"'
6
6
5 X
:E
N
LU
a)
0
X-
3 _
2
X0
'x
(O
x
\
x
X
-3 -2 -I
0
2
3 4 5
log moth density, N5
FIG. 15. Thedependence
ofthelogeggs/moth
(E/M)ratio
(H5) on log mothdensity(N5) ofthevariousplotsin years
1954(x), 1955(0), and 1956(0). Thecurveis drawnbyL
eye
the 1955 and 1956 data. Upper- -- log potential
through
fecundity(log fl); lower---
log l.6fl
442
T. ROYAMA
that the immigrantslay no eggs duringtheirstay. It
makes sense,then,thatthe log E/M ratiosshould fluctuate in unison between the plots (Fig. 10), but at a
much lower level in the K than in the G plots.
Data on mothdispersaland ovipositionraterelative
to local populationdensitythatmightsupporttheabove
deductionare mostlycircumstantial.Greenbanket al.
(1980: Table 8) summarizeda setofobservations,made
between 1971 and 1976, on the rate of emigration(directcountofmothstakingoff)relativeto pupal density
at fivelocalitiesscatteredwidelyover New Brunswick,
and anotherset made in 1976 at fourlocalitiesin Ontario.The data show thattherateofemigrationtended
to be much lower in low-densitythan in high-density
localities. However, no clear relation was detected
localities(10-50 moths/
among the seven high-density
m2 of foliage)in New Brunswick.Indeed, in two plots
the rate of emigrationwas negligibledespite moderately high moth densities of 23 and 50 moths/M2 of
foliage.Differencesin climate betweenyears and betweendistantlocalities probablymasked the relationship.
Blais (1953) observedthatfemalemothsin a severely
defoliatedstand "were able to flyin an upward direction [thismust have been an exodus flight]soon after
emergence."In 1982, in a severelydefoliatedfirstand
near Fredericton,New Brunswick,we (E. Eveleighand
thatmany
confirmed
T. Royama,personalobservations)
had laid verylittle
mothscaughtin theirexodus flights
of theircomplementof eggs.Because of the favorable
weatherin the 1982 season, the rateof emigrationwas
high.No immigrationoccurredin thesample area, and
consequentlytheE/M ratioh5was < 15 (i.e., H5 < 2.6).
I will now discuss the rate of emigrationin a lowdensitysituation.If high densityand consequent defoliationnecessarilyinduce a high rate of emigration,
one mightconverselyexpect a low rate of emigration
froma plot of low densityand littledefoliation.However, this does not seem to be the case in the Green
River data. The rate of emigrationappears to have
been unexpectedlyhighin thetwo lowestdensityplots
in 1955 and 1956 (Fig. 15); my explanationforthisis
as follows.
Suppose emigrationwas negligiblein a low-density
plot (the null hypothesis)and local mothslaid on average 60-90% of theireggs in the plot due to moth
mortality(Appendix 2). Because of littledefoliation,
the mean fecundityof local moths (Jj) is ; 100 eggs.
Then, the value of fpt in Eq. 4 is 60 to 90. If the
densityof local moths (n5) and the E/M ratio (h5) in
theplotare known,then,undertheabove assumptions,
we can calculate an expectednumberof eggs(per unit
foliagearea) laid by immigrants(f2p2m)by using Eq.
= n5(H5 - fiPl).
4; i.e., f2p2m
There is a set of six plots in 1955 and 1956 in which
the E/M ratio was well above the potentialfecundity
oflocal moths(Fig. 15), whichsuggeststhattheseplots
received immigrants.In the two lowest-densityplots,
Ecological Monographs
Vol. 54, No. 4
the observed n, and h5 were on average 0.065 (N5 =
-2.8) and 700 (H5 = 6.55), respectively.The calculatedf2p2m in thesetwoplotsis, by theabove equation,
in the orderof 40 eggs/M2 of foliage.In the otherfour
plots, where the observed n5 and h5 were on average
0.75 (N5 = -0.29) and 415 (H5 = 6.0), the calculated
is in the order of 250 eggs,which is more than
f2p2m
six times largerthan the calculated value forthe two
lowestdensityplots. Certainly,in the two lowestdensityplots,immigrationcould have been, by chance, as
low as calculated.However, I thinkthatin theseplots
was high,rather
therateof emigrationor reemigration
thanthattherateofimmigrationwas low. Presumably,
at theheightofwidespreadoutbreaks,a verylow density means a poor habitat for the budworm, which
mighthave provokedemigrationand/orreemigration.
Finally,the spatial density-dependenceof the E/M
ratiohas an importantimplicationin thesynchronized
population oscillation between plots. Notice in Figs.
4-7 thatthe log generationsurvival rate (Hg, graphi)
over thesame generationswas on averagemuchhigher
in the K than in the G plots. This tendencywas associated withlower log E/M ratios (H5) in the K than
in the G plots because H5 is spatiallydensity-dependent. Thus, Hg and H5 cancelled each other's effects
rate of change in egg density
on the intergeneration
(R1), which is the sum Hg + H5 (Eq. 2). As a result,
populations in these plots peaked (or R1 zeroed) at
more or less the same year (about 1953). If this had
not been the case (i.e., if the H5's were not densitydependentin space) thepopulationoscillationin these
two groupsof plots would have been offphase.
in E/M raLack of temporaldensity-dependence
tio.-The within-plot
relationshipbetweenH5t(log E/M
ratio) and N5t(log moth density),which is analogous
to thebetween-plotrelationshipin Fig. 15,is theregression of Ht on N5tin a givenplot (Fig. 16). Only in Fig.
16a (G plots) is H5tinverselycorrelatedwithN5t,and
even that relationshipis not as clear as the betweenplotrelationshipin Fig. 15. As a generalrule,thespatial
density-dependenceof a population parameterdoes
notimplythatitstemporalseriesis necessarilydensitydependent(Royama 1981a). Unlike Fig. 15, however,
the regressionsin Fig. 16 do not provide insightinto
the relationships,because a correlationin trendbetweenthe time series is indistinguishablefroma correlationin fluctuationaftertrendsare removed.
We have therequiredtime-seriesinformationin Fig.
9. It shows thatthe seriesof H5t(graphc) has no trend
thatis correlatedwiththeincreasingtrendfollowedby
thedecreasingtrendin theseriesofN1t(log eggdensity,
graph d), and one mightsuppose that the E/M ratio
(H5t) is temporally density-independent.Curiously,
however,H5tdoes showa clearinversecorrelationwith
N1tduringthe period between 1950 and 1957, when
N1tfluctuatedat a plateau withouttrend.This correlation betweenH5tand N1tis the cause of the inverse
correlationin Fig. 16a because N5t(log moth density
December1984
FIG.
a
*.
(E/M) ratio (H5t)and log moth density(N5,)at fourseparate
plotsoverseveralyears. a. PlotsG4 (t = 1945 to 1958;0)
and G5 (t = 1946 to 1957; *). b. Plots K1 (t = 1951 to 1958;
0) and K2 (t = 1951 to 1957; 0).
at the end of generationt) is correlatedwith N1, (log
egg densityat the beginningof the generation).
However, Fig. 16a includes data when N1, (hence,
N5,)was eitherincreasingor decreasing.Such a trend
in densityconsiderablyweakenstheinversecorrelation
withthe log E/M ratiobecause the latterhas no trend.
The correlationis even worse in Fig. 16b than in Fig.
16a because mothdensitywas steeplydecliningin the
K plots duringthe period observed (cf. Figs. 6f and
7f).
443
Then, the populations in which the immigrantsoriginate
and the populations that receive them are likely
00
6 - .
to be in phase. It followsthat,in a given year t, the
5_
number of immigrantsmt and the number of local
mothsn5tare likelyto be positivelycorrelated,and, by
4
*
0 0
Eq. 4, thiscorrelationtendsto nullifythe dependence,
in
trend,of H5ton N5,
3LO
The life-tabledata fromthe Green River Projectdid
2_
not encompass even one full cycle of population oscillation,and we do not know if E/M ratiosincreased
II
_
I
in the K plots afterthe recoveryof the forestfromthe
1950 budworm outbreak,as it mighthave if healthy
b
3
foliageinducednetimmigration.A seriesofE/M ratios
0
mightshow a trendiftherelativelevel ofdensitygrad*
ually changesbetweenthe local population and one in
whichimmigrantsoriginate.Temporal changesin the
0
2
0
.0
E/M ratio would also be dependenton the degree of
in populationoscillationsbetweenlocalities
synchrony
withinthe reach of moth dispersal. In my view, the
-5 -4 -3 -2 -I 0 1 2 3 4 5
densitydependence of the E/M ratio will not show
clearlyin time seriesforthe above reasons; hence, for
log moth density, N5t
most practical purposes, I treat the series of H5t as
16. Observedrelationships
betweenlog eggs/moth densityindependent.
7
0
-
SPRUCE BUDWORM
But, why is log E/M ratio (H5,) correlatedwith log
egg density(N,,) only when N1,has no trend?This is,
in fact,an interesting
propertyof a stochasticprocess,
in whichtheinversecorrelation,unlikethe one in Fig.
15, does not implydensitydependence. I have shown
(Royama 198 la) that,even if H5, is a series of completelyindependentrandom numbers,hence,without
trendand independentof N1t,H5, would stillshow an
inversecorrelationwithN1,onlyin an intervalin which
N,, has no trend (Appendix 3). Thus, the observed
relationship(Fig. 9c and d) makes sense if we assume
thatthe E/M ratio in a given plot is densityindependent. I now need only to explain why the time series
of E/M ratiosbehaves as thoughit is densityindependent.
The originof the majorityof immigratingmoths is
within100 km oflandingsites(Greenbanket al. 1980),
and Fig. 2 suggeststhat local budworm populations
within such distances must be oscillatingin unison.
Generationsurvivalrate
In this section,I analyze generationsurvivalin two
ways(first,
by stagesurvivalratesand, second,by mortalityfactors)to findstage survivaland mortalityfactorsthatcause population oscillation. Stage divisions
are eggs,younglarvae (L1 to L2), old larvae (L3 to L6),
and pupae. Mortalityfactorsto be examined are dispersal losses in young larvae, parasitism,predation,
food shortage,weather influence,and a complex of
disease and undeterminedmortality(which I call the
"fifthagent") in old larvae.
I findthatsurvivalof old larvae is the main driving
forceof population oscillation. Survival of younglarvae, thougha significant
contributorto generationsurvival, does not cause the basic oscillation. Both egg
and pupal survival rates have a minor influenceon
generationsurvival.I findthe evaluation of mortality
factorsmore difficult
than the evaluation of stagesurvival rates,because of insufficient
data on mortality.
However, by eliminationI deduce thata combination
of parasitismand the "fifthagent" is the most likely
cause of population oscillation.
Analysisby stage survivalrates
In Figs. 4 to 7, generationsurvival (Hg, graph i) is
partitionedinto H1 (egg survival,grapha), H2 (young
larval survival,graphb), H3 (old larval survival + early part of pupal survival;graphc), and H4 (latterpart
ofpupal survival,graphd). The patternoffluctuations
in H1 and H4 is almost identicalamong plots. In every
plot, H4 contributedslightlyto the decliningtrendin
Hg, while H1 did not. Both H1 and H4, however,were
such minorcontributorsto Hg that I will not discuss
them furtherin this paper.
T. ROYAMA
444
-3
NG4
I3
h
-4 _
-
-5
'
%O -6
G5
?
X 5
-6-
f3K
K2
-4_
_5_
-6
II,,
.
I,&[
94648 50 52 54 56 58
Ecological Monographs
Vol. 54, No. 4
situationdoes not apply to the K plots,wherethe H3's
are much higherthan in the G plots but the H2's are
more or less the same as H2 in G4. I will returnto this
point.
The curious compensations between survival of
young(H2) and old (H3) larvae resultfromthevariation
in the timingof sample collections.Usually, in a life
table,the end of one stageconstitutesthe beginningof
the next stage, so the calculated survival rate in one
stage is not independentof that in the other stage;
generally,theyare inverselycorrelatedwitheach other.
bias" in a lifetable.
I call this "stage-framing
As shown in Table lb, the survivals of young and
old larvae weredeterminedby sampling(1) thenumber
larvae successfullyhatched,(2) the numof first-instar
ber of larvae sampled when most larvae were in the
thirdto fourthinstars,and (3) all pupae and pupal
cases found at the time of 60-80% moth emergence.
The timingof sample collectiondoes not much influence the estimation of (1) and (3), because egg and
pupal cases remain attached to foliage for a while.
However,the midpointsamples (2) werecollectedjust
whena comparativelyheavymortalitybeganto deplete
40 -
Generation year
in thelogtotalsurvivalrate
FIG. 17. Yearlyfluctuations
0
oflarvae(H2 + H3) in plotsG4, G5, Kl, and K2. 0-GraphedLifeTables.
see Introduction:
indirect
estimates;
Survival of both young larvae (H2) and old larvae
(H3) contributedthe most to the yearlyvariation in
generationsurvival (Hg). However, a decliningtrend
in H3 was the cause of the same trendin Hg, whereas
H2 did not show such a trend,as is clear in plots G4
and G5 (Figs. 4 and 5). As already discussed, the decliningtrendin Hg in the 1950s is the decreasingpart
of its oscillation.Therefore,I conclude that H3 is the
drivingforceofpopulationoscillation.Only in plot K2
did H2 show an apparentlydecreasingtrend(Fig. 7b),
but I do not take this short-termtrendto be the decreasingsection of an oscillation.
Now notice a tendencyforH3 to fluctuateabout its
downwardtrendbut in the opposite directionto H2,
as typicallyexemplifiedin theG4 data; comparegraphs
b (H2) and c (H3) in Fig. 4. As a result,fluctuationsin
H3 about its trendtendedto cancel thosein H2, so that
the sum H2 + H3 revealed an almost smooth downward trend(Fig. 17), except forthe occasional dips in
H3 mentionedabove.
The survival of old larvae (H3) in the G plots not
onlycompensatesforfluctuationsin survivalof young
larvae (H2), but also tendsto counteractthemean level
of H2. Thus, H2 tended to be higherin plot G5 (Fig.
5b) than in plot G4 (Fig. 4b), while the reversewas
trueforH3 (Figs. 4c and 5c). Consequently,the sums,
(H2 + H3)'s, are similarin thetwo plots (Fig. 17). This
1951
30
20 -
?
L4 L.
~~~~~~~P
>,
C
.> 303
Eo
~-
-
20 -
1952
+
<
X03: lo
L3L3L
2-
m 2
50 40 -
L
~~~4L5
. L6
-__+
1954
30 _
20 10
0
--
o
L3 L3 L 4L5
May
June
July
Aug.
of
density(number/M2
FIG. 18. Decreasein population
fromsecond-instar
(L2)topupal(P) stageson selected
foliage)
treesin plotG4 in threeyears.The arrowsindicatethedates
intheplotin eachyear.AdaptedfromMiller
ofL3-sampling
data (MaritimesForest
(1955: Fig. 2) and his unpublished
ResearchCentre).
SPRUCE BUDWORM
December 1984
G2 q
-10
2
-10
01~~~~~~0
IE
I I
10r
.
G0
4
%_
-1 t1
KI
Im
C
t
,I
I
,
2
-0>
-br~~~~~~~'?'m
~ ~l ~~l ~l~ l
52 s4
~94
~
500
I
I
l -3
l
445
to the level at which H2 = -1 (or 37% survival). Because annual larval developmentwas recordedin only
one plot, and not even in the same plot each year,the
true mid-date betweenthe two peak dates in a given
plot could be in errorby a fewdays. Despite this,we
see a good matchin thepatternsoffluctuationbetween
H2 and the relativetimingof samplingin most plots,
revealinga clear influenceof stage framing.
Partitioninginto youngand old larval stages is desirablein budwormlife-tablestudiesbecause thetypes
of mortalitychange distinctlybetweenthe two stages.
However, withouta techniqueto estimatereliablythe
numberof larvae thatsuccessfullymolt into the third
instar,bias in framingthe consecutivestages is practicallyunavoidable.
Nevertheless,fromthe relationsin Fig. 19 we could
bias and adjust survival of
reduce the stage-framing
young larvae to the developmentallystandard time,
themid-datebetweenpeaks ofthirdand fourthinstars.
q5 -30
-
0 -
>
KI0
I
I
948 505254565
I
G2
-2 _
Generation year
FIG. 19.
Comparison between log survival rate in young
ofL3-samand thetiming
larvae(H2,@*,scaledon theright)
plingrelativeto themid-datebetweenpeaksof third-and
(0). Relativetimingis measuredas deviation
fourth-instars
in days(scaledon theleft);a negativedeviationindicatesa
and viceversa.Zerodeviationof
earliersampling,
relatively
scale,
onthevertical
matched,
datewasarbitrarily
a sampling
differ
in thelevelofmatching
withH2 = -1 and differences
fromplotto plot.Fordetails,see AnalysisbyStageSurvival
Rates.
II-
-I
L
0
? -I -
0 -2 _
so
0r
KKI
I
-I 4)
thelarval population everyday (Fig. 18). Therefore,a
comparativelyearlymidpointsamplingwould tendto
E
overestimatethe survival of young larvae (H2) and
0 underestimatethe survivalof old larvae (H3), and vice
versa.
To demonstratethis,in each yearbetween 1948 and
K2
1958 I took the mid-date between the peaks of the
thirdand fourthinstarsobservedneartheGreen River
-2 fieldstationwhere the G plots clustered(see Point 2
in Area 1 in Fig. 1.1 of Morris 1963a). The deviations
1948 50 52 54 56 58
of the actual dates sampled in each plot fromthese
mid-datesare shown in Fig. 19 (0). A negativedeviaGeneration year
tion indicatesearliersampling,and vice versa. DeviaFIG. 20. Estimatedlog younglarvalsurvival(H2). Obtionsare comparedwiththeH2's (0) takenfromgraph servedH2 wasadjustedtothemid-date
thepeaksof
between
b of Figs. 4-7. For convenience of comparison,zero- thirdand fourth
see
instars.For themethodofadjustment,
deviation of a samplingdate was arbitrarilymatched Appendix4.
T. ROYAMA
446
Fig. 20 shows a resultof one such adjustment(details
in Appendix 4), thoughlack of exact phenologicalinformationin individualplotsmakesitdifficult
to adjust
the mean level of H2.
The adjustedlog survivalratesin younglarvae (H2's)
do not show a decliningtrendin most plots,and even
wheretheydo (e.g., G4), the trendis too weak to account forthe decreasingtrendin H2 + H3 in Fig. 17.
Thus, althoughthe method of adjustmentis quantitativelycrude, it is adequate to demonstratethat the
survivalrate of younglarvae is unlikelyto be a major
source of population oscillation. It follows that the
main cause of the oscillationmust lie in the mortality
of old larvae.
Analysisby mortality
factors
Ecological Monographs
Vol. 54, No. 4
stantial differencesin the physical structureof these
stands (see Table 4.1 in Morris 1963a). The distinctly
higherH2's in plot G5 wereprobablydue to theearlier
average samplingdates, as already discussed.
Loss of young larvae duringdispersal was consistentlyhighin all years(Miller 1958); thoughnota cause
of population oscillation,this could be a major factor
determiningthe level about which the population oscillates.However,as faras I am aware,no reliabledata
existon whetherthe rateoflarval dispersalloss differs
among different
foresttypes.
Mortalityof old larvae.1. Parasitism.-Several hymenopterousand dipterous parasitoidsattack spruce budworm larvae at differentstages (Miller 1955, Miller and Renault 1976).
The two most common wasps, Apantelesfumiferanae
(Braconidae) and Glyptafumiferanae(Ichneumonidae), attackthe first-and second-instarbudwormlarvae in thelatesummer,and thesecond-generation
wasps
emergeand kill theirhosts in the followingsummer,
whenthehost larvae are at theirfourthor laterinstars,
though these parasitized larvae develop much more
slowlythanunparasitizedones. The rate of parasitism
by thesespecies can be determinedaccuratelyby rearing larvae that have been collected fromhibernacula
beforespringemergence.
Other parasitic wasps (e.g., Meteorus trachynotus
[Braconidae]and severaltachinidflies)attackthethirdto fifth-instar
larvae,and adultparasitoidsemergefrom
the sixth-instar
larvae or pupae. M. trachynotus
often
leaves hoststhatstayalive fora while,butneverpupate
(E. Eveleigh and T. Royama, personal observations).
Therefore,accurateestimationsof parasitismby these
species would requirefrequentsampling.Sampling at
intervalsof -7-10 d, supplementedby graphicalinterpolation(Miller 1955: Figs. 2, 3), probablyunderestimates parasitism. Keeping this in mind, I have
shown Miller's results on annual parasitism (by all
parasitoids) in Table 3, part of which has been published (Miller 1963b: Table 34.1). Also, letting100p
be the percentageparasitism in Table 3, I plotted
100(1 - P)% in log scale over generation'yearin Fig.
Mortalityof young larvae.-Miller (1958) showed
thatmost of the mortalityin younglarvae occurs duringdispersalin the falland the spring.Othermortality
(e.g., mortalitywithinhibernacula,or mortalitydue to
failureto spin hibernacula,to loss of hibernacula,or
to diapause-freedevelopment)was eitherminoror did
notvarymuchfromyearto yearor fromstandto stand.
Many larvae drop on silk threads, and some are
carriedaway by air currentsduringfalldispersal(when
theyare searchingforoverwintering
sites) and during
springmigrationfromthe hibernaculato feedingsites.
Dropping on silk mightbe triggeredby contact with
otherlarvae or by othertactile stimuli,but mostlyit
seems to be a reactionto light(Wellingtonand Henson
1947, Henson 1950). Then, dispersal in younglarvae
mustbe largelyindependentofpopulationdensity.This
is consistentwith the lack of trend in H2 that was
discussed in the precedingsection,but disagreeswith
Mott's (1963) earlier analysis, in which average survival rates of young larvae exhibited an apparently
hyperbolicinverserelationship
withdensity(Mott 1963:
Fig. 9.2). However, in Mott's more detailed Fig. 9.5,
in whichindividualdata pointsare plotted,theinverse
relationshipin the averages can be seen to be heavily
dependenton one single outlierat the lowest end of
the densityspectrum.In addition, Mott's data points
in his Fig. 9.5 were scatteredwidely and were influenced by the framingbias already noted. Thus, there 21.
is no firmevidence of density-dependent
The number 1 - p is the proportionof old larvae
survival of
younglarvae.
that escaped parasitism,of which, let us say, 1 - q
Mott (1963) and Morrisand Mott (1963) concluded proportionsurvived fromall other mortalityfactors.
that the survival of young larvae was dependent on The overall survival rate of old larvae (H3) is then
some physicalcharacteristics
ofthestand,suchas stand approximately
density,foliagethickness,stand continuity,and level
H3 = log(l - p) + log(l - q)
(5)
of defoliation,that influencethe larvae's chances of
landingon suitablefeedingsites.For instance,dispersal (Miller 1963b, Royama 1981b). Therefore,the graphs
loss could be less in denserstands,and vice versa (see in Fig. 21 are the contributionsof parasitism to log
Figs. 9.1 and 29.1 and Table 29.1 in Morris 1963a). survival of old larvae (H3) in the four sample plots.
data on this were not explicit,so there Comparingthegraphsin Fig. 21 withthe correspondUnfortunately,
is no way to reassesstheirconclusion.Rather,existing inggraphsoftotallarval survival(H2 + H3) in Fig. 17,
data (Fig. 20) reveal no clear heterogeneity
in thelevel we see thatthedecliningtrendin log(l - p) is notlarge
of H2 among plots G2, G4, Ki, and K2, despite sub- enough to account forthe same but steepertrendin
SPRUCE BUDWORM
December 1984
TABLE
447
3. Percentparasitism(all parasitoids)in old larvae.*
Year
Plot
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
G4
12
13
10
41
47
52
18
6
19
36
25
33
38
48
G5
21
17
52
8
16
6
37
41
19
36
39
.
K
16
8
20
18
25
19
35
K2
16
19
34
29
26
18
* Data fromMiller (1 963b: Table 34.1) and his unpublisheddata (on fileat the MaritimesForest Research Centre,Fredericton,New Brunswick,Canada).
H2 + H3. In otherwords,parasitismalone cannot be
a major source of the declining trend in generation
survival rate and, hence, cannot be by itselfa main
cause of the observed population oscillation.
2. Predation.-Major predatorsare small insectivorous birds,such as warblersof the familyParulidae,
and a complexofinvertebrates,
predominantlyspiders
(Morris 1963c). The rate of predation was not adequatelyquantifiedin the Green River Project(nor,for
thatmatter,in anypublishedworkson the sprucebudworm, as far as I am aware); nevertheless,I deduce
thatpredationis unlikelyto be a primarycause of the
budwormpopulation oscillations.
Mitchell (1952) analyzed gizzard contentsof some
songbirdsover 2 yr(1949 and 1950) ofhighbudworm
densityin a Maine spruce-fir
forest.His resultsshowed
thatseveralspeciesofbirdsconsumedbudwormlarvae
and pupae in varyingdegrees(Mitchell 1952: Table 1),
of which about a dozen species (Mitchell 1952: Table
2) contained the budworm in substantialproportions
(in volume) of theirstomach contents.On the other
hand, a series of experimentsby Miller and Renault
(1981) over 5 yr(1959-1963) oflow budwormdensity
in the Green River area, in which caged and uncaged
larvae wereused, has shownlittlesignofbirdpredation
on the insect.
In the experimentsby Miller and Renault, secondinstarlarvae were collectedand individually"replanted" in threegroups on practicallybudworm-freebalsam firbranches.The larvae of one group were completelyprotectedfrompredationand parasitismin cages
coveredwithveryfinenylonmesh,thoughsome small
predatorswere occasionallycaged withthe larvae and
some larvae were alreadyparasitized.A second group
of larvae, placed in a cage withcoarse wire mesh,was
protectedonlyfrombirdsand largeinvertebratepredators. In a thirdgroup, each larva was placed on a
markedbut completelyexposed branch.Each planted
larva in all groupswas frequently
inspectedand its fate
recordeduntil it disappeared, was found dead on the
foliage,or survivedto themothstage(or lefttheempty
pupal case on the branchin the exposed and semiexposed groups). I have summarizedthe resultsin Fig.
22.
Needless to say, bird predation should show as a
in the "disappeared" category(grapha) bedifference
tween the exposed (@) and semiexposed (0) groups.
and we cannotattribute
Thereis no obvious difference,
the loss in the exposed group to bird predation.
From the above observations,I deduce that birds
took a substantialnumberof budwormlarvae and pupae when insect densitywas high, and ignored this
source of food when the insect was scarce. This is in
accord with the theoryof predation by profitability:
birds tend to pay more attentionto a more profitable
(usually more abundant) source of food but tend to
rejectan unprofitable(usually scarce) source (Royama
1970, 1971). Predationunderthismechanismis probprocess (i.e., dedensity-dependent
ably a first-order
pendenton preydensityin thecurrentgenerationonly)
thatdoes notgeneratean oscillationin a predator-prey
interactionsystem(Royama 1981a). For bird predation to be a primarycause of a population oscillation,
it must be at least a second-orderdensity-dependent
process; that is, the rate of predationmust be dependent on the initial prey density,both of the current
generationand of the previous generation.For birds
thisis unlikely,because theydo notmultiplyeffectively
G4
600
.
X
00
x
G5
o10060 35
60
KI
I
100I60 -35
I
K2
I
l
l
l
I
194648 50 52 54 56 58
Generation year
in theproportion
oflarvaeunFIG. 21. Yearlyvariations
100(1 - P)%,plottedon a logscale,p beingtotal
parasitized,
of old larvaeparasitized;lOOp%is givenin Taproportion
ble 3.
T. ROYAMA
448
50 a
40
30
20 - x
X
@
:a.
o
0.
(0
X a
?
l
30l
O
C~~~~~~~~~~'
v
0
X
*Q
0.N
.
20 - i
10 - x
I
?
*
?
*
100
,
0
~
?
X
X
~~~~~~~~I
~~~C
20200
.0~~~
E
?
X
x
20
501b
40 - x
o
,
X
0X
l
44
*
o
~
1959 60
0
'C
I
I
61 62
'
1
63
Year
by Millerand
FIG. 22. Resultsof thecage experiments
b.
oflarvaethata. disappeared;
Renault(1981).Proportions
of
percentage
werefounddead; and c. had beenparasitized,
larvaein graphd. x finetheinitialnumbersofthird-instar
cages,and * openbranches.
meshcages,0 coarse-mesh
in numbersfromone yearto the next,as thebudworm
does.
Some bird species were reportedto be more abundant duringbudworm outbreaksthan at other times
(Kendeigh 1947, Morris et al. 1958, Gage and Miller
1978). But many otherspecies, thoughfeedingon the
budwormwhenitwas abundant(Mitchell 1952), either
did not noticeablychange in abundance, or became
even less abundant at high budwormdensity.On the
whole, therewere only twice as many birds of all insectivorousspecies duringoutbreaksin some Green
River studyplots in the 1950s as therewere duringa
period in the 1960s afteroutbreaksthere (Gage and
Miller 1978). A change in the bird population of this
on thebudworm
magnitudewould have had littleeffect
population, which changed much more drastically.
Moreover, a correlationin abundance between the
budworm and some birds could be coincidental.Inconsistentresponses to changes in budworm density
by many bird species (Morris et al. 1958, Gage and
Miller 1978) that fed on budworms at high density
(Mitchell 1952) supportthis idea. Some of the correlation could have been due to the factthat birds redistributedthemselvesin responseto local differences
in budworm density.However, such spatial density-
Ecological Monographs
Vol. 54, No. 4
dependence of a predatorpopulation need not necesprocess,
sarilyimplya second-orderdensity-dependent
as would be necessaryto induce the budworm oscillation.
It is unlikelythat breedingpopulations of birds increase throughhigh reproductivesuccess in the previous yearin responseto highbudwormdensity.Mook
(1963) foundthatbirdsdid nottakethesmallbudworm
larvae beforethe sixthinstar.Only 10% (presumably,
in numbers)of the larvae found in the gizzards were
or youngerinstars.This impliesthatthe birdsfed
fifth
foronlya fewweeks,at most,
on budwormseffectively
each season. It is hardlyconceivable thatyear-to-year
changes in breedingbird populations could be determinedprimarilyby the abundance of a particulartype
foronlya few
of food thatcould be utilizedeffectively
weekseach year.A highbudwormdensitymightassure
a highnestingsuccess in some bird species,but is unlikelyto assure highfledglingsurvival,forby the time
the young become independent,they can no longer
utilize this once-abundantsource of food.
A similarargumentapplies to omnivorousinvertebratepredatorsthatutilizea narrowrangeofpreysize.
Budwormsrapidlydevelop in size duringthe season,
and the lengthof the period duringwhich a predator
species can utilize budwormsis undoubtedlylimited.
Perhaps,fewpredatorspecies depend entirelyon budworms throughouttheirlife cycle,and so few,if any,
to budwormabundance.In fact,
respondreproductively
Renault and Miller (1972) have shown that some spiders(e.g.,ofgenusDictyna)could consumemanyyoung
budwormlarvae,butthe species
(mainlysecond-instar)
compositionand densityof spidersstayedremarkably
theearlier
constantduringtheir8-yrstudy,confirming
conclusionofLoughtonet al. (1963) thatspidersshowed
littlechange in densityduringthe 1950s.
Predation,thoughunlikelyto be a primarycause of
budwormpopulationoscillations,may nonethelessinfluencethemean level ofthoseoscillations.Littlequantitativeinformationon this subject is available, however.
3. Food shortage.-If budworms kill a large proportion of trees in a stand, the budworm population
per unitarea of the stand mustdecrease as well. However,treemortalitydid not necessarilyimplya decline
in survivalof old larvae (H3) in theGreen River study,
because survivalwas measuredby the reductionin the
numberoflarvae per unitfoliagesurfacearea on living
trees.
In his laboratorystudies,Miller (1977) found that
nearly90% of the total food consumptionby a larva
occurredafterit became sixth instar.Thus, even the
shoots at veryhigh
total consumptionof current-year
budwormdensity,and the subsequentfeedingon older
foliage,would occur only towardthe end of the larval
stage.Food shortageoftenretardslarval development
or produces small female moths with reduced fecundity,but does not necessarilyproduce weak larvae or
December 1984
SPRUCE BUDWORM
449
cause mortalityamonglarvae,unlessreinforced
byother factors,such as diseases (discussed later).
When highdensitiesofsecond-or third-instar
larvae
I10
are miningintobuds, current-year
shootscan be totally 4 15-V
destroyedwell beforethe larvae reach theirfinalstage
*20of feeding(Blais 1979). However, each larva in these
ao 25 earlystageseats so littlethatveryheavy defoliationof
30
the current-year
shoots and subsequent serious food
shortagesoccurinfrequently
and onlyat extremelyhigh O323 0
larval densities. Moreover, even in this extremecir22 cumstance,the larvae can still surviveat the expense a.
E 21of body size and fecundity,as was observed on Cape
-A
20
BretonIsland, Nova Scotia, in 1977 and 1978 (Piene
19
et al. 1981). A. W. Thomas (personal communication) o
observedthatmothsthatwere produced fromstarved
18 larvae could be as small as one-fifthof the normal
17weightbut stillnot show any noticeableweaknessand
301seem as vigorousas those produced fromwell-fedlar* 40vae. Probably,budwormsmaintaintheirphysiological
c 50_vigorat the expense of body size to cope witha highdensitysituationlastingas long as 10 yrand occurring E 60_L,
,
,,
.I
, ..I
...
I
as frequentlyas once every30-40 yr.
50
55
1945
60
65
70
Duringthelate 1950s, thesurvivalofold larvae (H3)
Year
was stillmuch higherin the heavily damaged K plots
than in the littledamaged G plots (Figs. 4-7). NeverFIG. 23. Yearlyfluctuations
in precipitation
(inverted
and meandaily
theless,thepopulationsin all plotsdeclinedin parallel. scale),meandailymaximumtemperature,
relativehumidity
(inverted
scale)between1 June
Evidently,food shortagewas neithera primarynor a minimum
and
15
at
the
Green
River
field
July
station.
Horizontalline
universal cause of population decline. This is not an
in eachgraphindicatesaverage.
isolated observation.All populations in New Brunswick declined in the late 1950s and early 1960s (Fig.
2) regardlessof defoliationand tree mortalityat the influenceon the survivalof feedinglarvae, as was prestandlevel. Thus, budwormoutbreakcyclescannotbe viously thought.
adequately explained by habitat destruction-regener- As alreadyshown,fluctuationsin the survivalof old
ation cycles,as postulatedin thetask-forcereport(Bas- larvae (H3) about the downward trend of the 1950s
kerville 1976).
were influencedby the timingof the sample collection
4. Influenceof weather.-Some earlier analyses at the beginningof the stage concerned. Eliminating
(Wellingtonet al. 1950, Greenbank1956, 1963a, Mor- framingbias by combining H3 with H2 results in a
ris 1963b) yieldeda climatic-control
hypothesis:a dry, smootherdecliningtrend,particularlyin plot G4 (Fig.
warm summerfavorsthe developmentof the feeding 17). If the survival of larvae was much influencedby
larvae, and so a series of favorableyears allows pop- weather,the compensationof H2 and H3 is incompreulationsto increase.(A wet,cool summerproducesthe hensible. Althoughtemperatureand precipitationexoppositeresult.)Greenbank(1956 [Fig. 2], 1963a [Fig. hibit a patternof oscillation if smoothed by taking
3.2]) took 4- or 5-yrmoving averages of the average moving averages,the larvae in the Green River area
precipitationand the average daily range of tempera- could notpossiblyrespondto thesmoothed(bymoving
ture in June and July(the intervalcoveringa major average)patternof the averageweatherover the provpart of the larval feedingperiod in the northernpart ince and ignorethedetailed,muchmoreirregularyearof New Brunswick)and showed an on-average dry, ly fluctationat theGreenRiver station(Fig. 23), where
warmperiod between 1945 and 1949, an intermediate therewas no consistentdry,warmperiodbetween1945
conditionbetween 1950 and 1955, and an on-average and 1949.
In fact,fluctuations
in log larval survivalrates(H2 +
wet,cool period between 1956 and 1960. The pattern
appeared to coincide withtheriseand fallofbudworm H3; Fig. 17) are notwellcorrelatedwithweatherrecords
populationsin theprovinceoverthesame period.There in Fig. 23. Althoughsurvivalin plot G5 between 1951
were also several on-averagedry,warm years around and 1957 is vaguelycorrelatedwithmean daily max1910, which coincided withthe well-knownoutbreak imumtemperature,
thisis probablycoincidental.First,
ofthe same period (see Fig. 3). However, anothersuch the distinctlylow survival rate in G5 in 1951, which
favorableperiod around 1925 was associated withlow coincided witha low mean temperatureforthatyear,
populationsin theprovince.Aftercarefulexamination, was likelya local phenomenonratherthan an effectof
I have foundno evidence thatweatherhas much of an the prevailingwet, cool weatherof that year,because
450
T. ROYAMA
23 ,22
-
E 21 -0-4
4W
0
19
(U
18
Ecological Monographs
Vol. 54, No. 4
30_
o1
~~~~~0
70~
1946 48 50 52 54 56 58 60 62 64 66 68 70
Year
in meandailymaximumtemperature
FIG.24. Comparisonbetweentheyearlyfluctuation
(0) duringthelarvalfeeding
inmeandailyminimum
relative
period,1Juneto 15Julyandthefluctuation
humidity
scale)during
theestimated
(0, inverted
mothperiod(cf.Fig. 12) in lateJulyto earlyAugust,recordedat theGreenRiverfieldstation.
itdid notinfluencethesurvivalin plot G4. Conversely,
the even worse weatherin 1950 did not have any adverse effecton survivalin any plot,includingG2. Furthermore,an intensivestudyby dailysamplingin 1977
at a firstandnearFredericton(data on fileat Maritimes
Forest Research Centre) revealed an extremelyhigh
larval survival rate, despite the unusually wet, cool
summerof thatyear.
To compare survivalrateand weatherover a much
longerperiod,we can use the yearlyfluctuationin the
log rate of change in larval density(R3) shown in Fig.
8. Simple correlationshows some degreeofassociation
betweenthe temperaturefluctuationin Fig. 23 and the
in R3 about itsbasic oscillation.
secondaryfluctuations
This association, however, does not imply a causal
relationship.As alreadyshown,the secondaryfluctuation in R3 is due largelyto a fluctuationin the log E/
M ratio (H5), which is determinedin the moth stage
in late Julyand earlyAugust,and which shows a good
correlationwithmean dailyminimumrelativehumidityduringthatperiod. There happened simplyto be a
verygood correlationbetween the mean daily maximum temperatureduringthe feedingperiod in Juneto
the early part of Julyand the mean daily minimum
relativehumidityduringthe moth period in late July
to earlyAugust(Fig. 24).
Another example of spurious relation is a coincidence in trendbetweenmean daily minimumrelative
humidity(Fig. 23; invertedfor ease of comparison)
and R3 (Fig. 8) between 1953 and 1970. However, the
two seriesdo not agree at all in the previous outbreak
period between 1946 and 1952.
Fig. 25 shows the annual fluctuationin mean daily
maximumtemperatureduringtheapproximateperiod
of larval feedingin various parts of New Brunswick
fromas many stations as had records for the 1870s
onward. The larval feedingperiod differsamong the
areas wherethe weatherstationsare located (see Fig.
26). Usually, budwormsdevelop in the province earliest around Fredericton,wheremost larvae feed usu-
ally between 15 May and 30 June.In the Green River
studyarea, the developmentis 2 wk behind many
otherpartsof the province.Therefore,the period over
which the average temperaturewas calculated in Fig.
25 is adjusted accordingly.One of the bases for the
adjustmentis thephenologyof springbudbreakin balsam fir,shown as a contourmap in Fig. 26.
Over theperiod covered by the temperaturerecords
in Fig. 25, therewere fourknown province-wideoutbreak periods at about the times indicated by the arrows (cf. Fig. 3). As we see, thereis no particularpattern, such as a succession of warmer summers,
associated withthe initiationof these outbreaks.Further,to comparewiththeargumentoftheearlierworkers alreadycited,I took as an example the 5-yrmoving
averagesin theChathamweatherdata ofFig. 25, which
by themselves cannot be distinguishedfrom a pure
randomseriesby a simpleruntest.The resultantmoving-averageseries (Fig. 27) tends to oscillate because
of positive autocorrelationsthat do not exist in the
originalseries (details in Appendix 5). Again, thereis
no particularassociation ofthefouroutbreakswiththe
"smoothed" weatherchanges,except fora vague tendencyforsome yearsof on-averagecooler weatherfollowing an outbreakthat mighthave been associated
withthedeclineofthebudwormpopulation.This point
will be discussed in the section on the "fifthagent."
(Oscillations could be created artificiallyby taking
movingaverages of a pure random seriesof numbers;
it could be misleading to compare such an artificial
oscillationwitha populationoscillation[see Appendix
5].)
In his key-factor
analysis,Morris(1 963b) foundthat
therehas been a consistentupwardtrendsincethemid1920s in mean daily maximumtemperature(recorded
in theCityofEdmundston, 50 km southoftheGreen
River station)duringthemain partofthelarvalfeeding
period, which in the Green River area usually falls
between 1 Juneand 15 July(Morris 1963b: Fig. 18.2).
I findthe association to be spurious, however. The
SPRUCE BUDWORM
December 1984
20
.
25-
25
25
20-
25-
20[
I
1880
Sussex region; in Bathurst,there was even a slightly
decliningtrend(Fig. 25). Nevertheless,the population
trendwas much the same everywhere(Fig. 2).
I have arguedthatweatheris unlikelyto be a direct
cause of budwormpopulation oscillationsand, hence,
of outbreaks.However, my argumentsdo not exclude
possible weatherinfluenceson larval survival.For instance,late frost,whichis notinfrequentin New Brunswick, mightkill buds and thus cause high mortality
among younglarvae, thoughI have seen no concrete
evidence. Near the northernlimit of the budworm,
such as at higherelevation on the Gasp6 Peninsula in
in
Quebec, accumulatedheat unitsmay be insufficient
some years for complete larval development (Blais
1958). Conspicuous dips in the survival rate of old
larvae (Fig. 17) mightindicatesome localized weather
hazards, because the dips were sporadic, did not coincide in yearsamong plots, and leftno effecton survival in the followinggeneration.Weathermightalso
act throughthe efficacyof diseases. I shall discuss this
in the followingsection.
5. Thefifthagent.-The last ofthe mortalityfactors
to be discussed is a complex of viral and protozoan
diseases and "death fromunknowncauses."
Neilson (1963) found microsporidiosesand granulosis to be the most prevalentprotozoanand viral disin theGreenRiverarea. Otherviral
eases, respectively,
diseases, such as nuclear and cytoplasmicpolyhedroses, and bacterialand fungaldiseases were infrequent.
Between 1954 and 1958, Neilson (1963) collected
weeklysamples of budwormlarvae in plot K2, beginningfromthe thirdinstarand lastinguntil 80% pupation, rearedeach collectionof larvae in the laboratoryfor 1 wk, and examined dead larvae fordiseases.
He foundno apparentsymptomsof disease in a large
proportionoflarvae thatdied in the laboratory.More1980 over, because all pathogens that were identifiedby
Neilson were of low virulence,it is not certainifthose
J
VAX:V\FJr
MVJ':"
'."V\\
/
20
25-
.20
451
1900
1920
Year
940
1960
FIG. 25. Yearlyfluctuations
in themeandailymaximum
_-i\Dalhousie
Green
temperature
during
theapproximate
periodoflarvalfeeding,
1114
River.
sincethelate 1800s in variouslocationsin New Brunswick.
*e
15-18
r0
>Bathurst
Fromtop:Fredericton
(15 Mayto 30 June),Sussex(15 May
Edmundston
15-18 11-14
to 30 June),Chatham(15 Mayto30 June),Chatham(25 May
Grand
to 10 July),Bathurst(Dalhousie,-----;20 May to 5
Falls
Chatham
July),
GrandFalls(15 Mayto 30 June),Edmundston
(1 June
to 15 July),SaintJohn(1 Juneto 15 July).Data are taken
7-10
fromthe MonthlyRecord,meteorological
observations
in
easternCanada, Canada Department
of the Environment.
36
The arrowsin thetopgraphindicatetheoccurrence
offour
Frederion
J12
province-wide
outbreaks
ofthesprucebudworm
takenfrom
Fig.3.
upward trendin temperaturesduringthe feedingperiod, used in Morris's analysis,was due to an upward
trendin Julytemperatures.In manypartsof theprovince,thebudwormlarvae shouldhave completedtheir
feedingby the end of June,and thereis no such trend
in the temperaturesof May and June,except in the
516
7-0 Saint John
FIG. 26. PhenocontoursofNew Brunswick,numeralsrepin timingof springbudbreakof balsam
resentingdifferences
fir,Abies balsamea, in days later than that in Fredericton.
Unpublishedmap by ForestInsectand Disease Survey(Maritimes Forest Research Centre).
T. ROYAMA
452
Ecological Monographs
Vol. 54, No. 4
0)1
? 202{
E 19 _
9
I
I
I
I
I
1888
1890
1900
1910
1920
I
1930
I
1940
I
1950
I
1960
I
1970
I
1980
Year
from15 May to 30 Junein
FIG. 27. Five-yearmovingaveragesof theseriesof meandailymaximumtemperatures
in themoving-average
causedbypositiveautocorrelations
(Fig.25), showing
an oscillation
series,
NewBrunswick
Chatham,
sprucebudworm
outbreaks
takenfromFig.3.
in theoriginalseries.Arrowsindicatefourprovince-wide
notexisting
pathogens actually killed the larvae bearing them. right-handside of Eq. 5 in whichq now representsthe
mortality.Note thatthe combined effectis
Therefore,I treatthis inadequatelyunderstoodcom- fifth-agent
plex of mortalityfromdiseases and unknowncauses the union p + q - pq ratherthan the simple sum p +
as one category,the "fifthagent, or Neilson's syn- q, because thepq proportionof larvae could have been
parasitizedas well as "diseased" (fordetails,see Roydrome."
For severalreasons,it is unlikelythatthe fifth
agent ama 198 lb).
occurredonly duringlaboratoryrearing.First,spruce
Clearly, the gross field mortality(l00qj) and the
budwormlarvae are well knownamong entomologists combined (union) parasitismand fifthagent are not
as easy to rearin thelaboratory,and, ofcourse,Neilson only in the same magnitudeforthe stagesconcerned;
took the ulmost caution in rearinghis larvae. Second, theiryearlyfluctuations
are also similar.In otherwords,
Neilson took weeklysamples, reared the larvae indi- thegrossfieldmortalityin K2 in thoseyearswas mostly
viduallyfor1 wk,and obtainedconsistentresults.The attributableto parasitismand the fifth
agent.(The calthird and most interestingreason is a similarityin culatedunion ofthesetwo factorssometimesexceeded
frequencybetweentotal fieldmortalityand the com- the 100q. values, because the factorswere estimated
bination of fieldparasitismand fifth-agent
mortality independently.)Since I have raised all conceivable
in Neilson's study.This suggeststhat the fifthagent mortalityfactorsand have eliminatedunlikelycauses,
was also operatingin the field.
the fifthagent combined withparasitismwould seem
In Tables 4 and 5, I list grossfieldmortality(l00q.
to be the only possible drivingforceof oscillationsin
of the lifetables) and parasitismas well as fifth-agentthe budwormpopulation.
mortality,as determinedby Neilson in samples taken
Currently,E. Eveleigh and I are conductingvery
fromplot K2; Table 4 is forold larvae, and Table 5 is intensivefieldstudiesin a firstandheavilyinfestedby
forpupae. The gross mortality,100q, in Table 4 is budwormnear Fredericton.So far,we have foundthat
relatedto the survival of old larvae, H3 in Fig. 7c, by mortalityin feedinglarvae has been almost totallyatq_ = 1 - exp(H3). In the last column of each table, I tributableto the 50-60% parasitism,which has been
have combined parasitismand the fifthagent by the increasingonly slowly in the last 3 yr. This rate of
parasitism,thoughhigherthan those observed in the
TABLE 4. Totalstage
mortality
(100q_),
parasitism,
andmor- Green River area duringthe 1950s (Table 3), is not
talitydue to thefifth
agent,in old larvaefromplotK2 in highenoughto reducethe budwormpopulations.The
GreenRiverarea.
operation of another agent is essential forthe populations to decline fromthe currentoutbreaklevel.
Unionof
Some diseases, like typical insect parasitoids, can
parasitism?
and fifth build up over several generationsas the host populaIOOq* ParasitismtFifthagentt agent
Year
tionincreases,to induce a host-diseaseoscillation(Anderson and May 1979), thoughthe role of diseases in
Percentage
54
63
1954
69
19
thebudwormsystemis not as certainas theAnderson14
36
1955
31
26
May model. Potentiallyimportantmicrobials in the
57
76
1956
18
80
budworm are summarized in Dimond (1974)
spruce
87
1957
49
57
1611
and Burke(1980), but therolesofmicrobialsin ending
84
34
66
1958
78
a budwormoutbreakhave notbeen documented.Some
* log(l -q_) = H3 in Fig. 7.
species of Microsporidia,thoughof low virulence,are
t Same as in Table 3 (bottomrow).
: Sum of"totaldiseased"and "unknown"determined
by common protozoan parasites of budworm that have
in Neilson(1963: Table 38.5).
laboratory
rearing
? Union= p + q - pq, wherep = proportion
parasitized the propertiesof a second-orderdensity-dependent
mortalityfactorbecause theyspread by oral transmisand q = proportion
to thefifth
succumbing
agent.
forbytheKI data.
sion among feedinglarvae withina season, and then
11Substituted
December 1984
TABLE
5. Same as Table 4 but forthe pupal stage.
Year
l00q*
453
SPRUCE BUDWORM
Union of
parasitism
and fifth
agent
Parasitismt Fifthagent
34
20
18
42
22
17
5
26
37
30
9
42
51
35
4
54
- qx) = H4 in Fig. 7.
t C. A. Miller(MaritimesForestResearch Centre,personal
1954
1955
1956
1957
* log(l
communication).
are transmittedtransovariallyto the next generation
(Thomson 1958). Thomson (1960) and Wilson (1973,
1977) observedsteadyincreasesin therateofinfection
by Microsporidia over several generationsduringthe
1950s and 1970s in Uxbridge,Ontario. The host populations,however,were not monitoredquantitatively
in eitherstudy.
In his experiment,Neilson (1963) found that both
diseased and "undiseased" deaths were inverselycorand thatthe effectof
relatedwithrearingtemperature,
was greateron starvedlarvae thanon welltemperature
fedones. These resultsare not necessarilyinconsistent
withtheapparentlack ofrelationshipbetweenthefield
survivalof larvae and the weatherpattern,which has
alreadybeen discussed. If populationoscillationis due
factors,the influto second-orderdensity-dependent
agentsthatare not a cause
ence ofdensity-independent
ofpopulationoscillationmightnotshowclearlyin simple correlation(Royama 1981a).
Anotherpossibilityfor"unknowncauses" thatNeilson (1963) consideredwas intrinsicphysiologicalvigor,
which decreases with increasingpopulation density
(Franz 1949, Chitty1960, Wellington1960) through
endocrinological, behavioral, or genetic changes
(Christianand Davis 1964,Pimentel1968,Krebs 1971).
No positive evidence forthese mechanismshas been
reportedforbudworm population dynamicsas faras
I am aware,thoughthepossibilitycannotbe excluded.
correlatedwith the fluctuationin H5 (see Analysis of
life-tabledata: climaticinfluenceon E/M ratio). Thus,
the R3's distinctlyabove the smoothed trendline in
Fig. 8 (marked with arrows) indicate moth invasions
in those years. Clearly,invasions were frequent,and
theyseem to be as frequentduringthedecreasingphase
of the population oscillation as duringthe increasing
phase. (The graphafter1972 in Fig. 8 is not a reliable
indicatorof invasions, because it is based on the averageegg-massdensitydeterminedfromsmall samples
taken fromsample points scatteredover a wide area;
the averages probably do not give resolutionas high
as did intensivesamplingat a particularplot.)
It is particularlyimportantto note that duringthe
decliningphase in plot G4 the population increased
each springfollowinga moth invasion the previous
fall,as in 1954, 1957, and 1961 (Fig. 1), but that the
invasions did not reversethe overall decliningpopulation trend,even when the local food supplywas still
plentiful(forfurtherdiscussion,see Synthesis:amplitude of oscillationsand outbreakfrequency).In view
of the facts that the population trend was the same
over wide areas (Fig. 2) and thatgains of extraeggsin
a local population (as in G4, Fig. 8) were far more
frequentthan occurrencesof outbreaks,the idea that
moth invasions initiateoutbreaksis not as attractive
as I once thought(Royama 1977, 1978).
SYNTHESIS OF BUDWORM POPULATION
DYNAMICS
Translatingthe resultsof the foregoinganalysesinto
a simple time-seriesmodel allows me to explain the
followingfeaturesof sprucebudwormpopulation dynamics: synchronyof oscillationsbetween local populations,frequencyand spread of outbreaks,regularity
of populationcycles,and maintenance
and irregularity
population oscillationsunof local density-dependent
der perturbationfrommoth dispersal.
I consideran idealized situationin whichbasic probabilistic properties of population processes do not
change in time, so that even a very simple model,
necessitatedfromour limitedknowledge,can provide
Frequencyof mothinvasions
insight.We can make the above idealized situation
Some ecosystemmodels (e.g., Petermanet al. 1979) compatible with actual population processes by carehave assumed thatif food (foliage)is plentiful,spruce fullyselectingthe spatial unitsin whichwe definepopbudworm outbreakscan be "triggered"by mass in- ulations.
If we were to consider the population process in a
moths fromoutside, because
vasions of egg-carrying
the invaders upset the assumed endemic equilibrium very small foreststand, we would findthat a severe
state of local populations. However, this assumption outbreakmightdestroythe stand, and the budworm
populationwould thenbecome extinct.Subsequentreis not substantiatedby the Green River data.
In plot G4, extraeggsgained fromimmigrants(in- generationand growthof a new foreststandwould not
of the local populationprocess.
dicated by E/M ratios much greaterthan the mean ensurethe stationarity
little
have
knowledgeofthe influenceof
we
Moreover,
occurredin 1946, 1947, 1949, 1953,
potentialfecundity)
1955, and 1956 (Fig. 10, top graph). The high value forestregenerationprocesses on the growthof a budof R3 (the log rate of change in larval density)in Fig. wormpopulation.If,on the otherhand,we considered
8 fortheyears 1956-1972 indirectlyindicatesthe gain too largea geographicalarea, thenenvironmentalhetof extraeggs,because the secondaryfluctuationin R3 erogeneity,such as differencesin weather patterns,
about its principaloscillation(smooth curve) is highly would probablybe too high forsimple models to de-
454
T. ROYAMA
scribe the population processes without undesirable
complications.
Thus, I consider populations in areas large enough
that changes in some local stands withineach area in
one way over time are compensatedforby changesin
the other way in other stands withinthe same area.
Therefore,the average characteristicsof the area as a
whole do not change drasticallyin time. An area as
large as one block on the map in Fig. 2 is probablya
convenientsize formy argument(thougha fewlargescale outbreaks,such as the recentone on Cape Breton
Island, Nova Scotia, may destroyforestsover a much
largerarea). I also consider that budworm densityis
measured on the foliageof livingtrees,so as to avoid
complicationsarisingfromthe effectof treemortality.
A simplemodel
Let us approximatethe dynamicsof budwormpopulations by a second-orderdensity-dependent
process
of the generalform
Rt =J(N, N, 1) + zt,
(6)
where Nt is the log population densityof the tth generation(it need not specifythe stage),and zt is the net
effectof all density-independent
factorsinvolved during the tth generation.Rt = Nt+ - Nt, as in Eq. 3. I
now equate the functionf in Eq. 6 to the densitydependentcomponent of the log generationsurvival
rate (Hg) in Eq. 2, and equate the log E/M ratio (H5),
combined withthe temperature-dependent
efficacyof
the fifthagent, to major elements of the density-independenttermz.
Because the functionf in Eq. 6, which is probably
nonlinear,is difficultto determinefromour limited
knowledge,I further
takea linearapproximationofthe
functionforsimulationpurposes;thatis, I use the linear second-orderautoregressivemodel
Rt=
aONt + aIN,1
+ zt,
(7)
Ecological Monographs
Vol. 54, No. 4
ably chosen. Simulationsthatuse this model demonstrateMoran's idea.
In Fig. 28, I generatedthreesample series by Eq. 7
withthe same ao and a, values that are conveniently
chosen for simulations.The density-independent
z's
in each seriesare uncorrelated(zero autocorrelations)
randomnumbers,uniformly
distributedin theinterval
(-0.5, 0.5). The series a and b are startedwith an
identicalinitialstate(N1, N2),but the z's are independentlygeneratedand so are uncorrelatedbetweenthe
two series. These series simulate a situationin which
two local populations that have a common densitydependent(endogenous) structureare under mutually
independentclimatic(exogenous)influences.We see a
strongresemblancein theircyclicpatternsdue to their
common endogenousstructure,
but thepopulationsdo
not oscillatein unison,because ofthe independentexogenous influences.They come into synchronyoccasionally,but only by coincidence.
Seriesc in Fig. 28 has thesame endogenousstructure
(identicala-parametervalues) as the othertwo series.
The distributionof the density-independent
z, termis
also the same as in the othertwo series,exceptthat zt
in seriesc is correlatedwithztin seriesb; thecorrelation
coefficient
is t0.7. Althoughseriesb and c werestarted
completelyout ofphase, theycame intophase quickly,
and remained in phase thereafter.This suggeststhat
local budworm populations that oscillate independently(due to density-dependent
generationsurvival)
can be synchronizedunder the influenceof nonoscillating but correlatedweather (among localities) that
governs the E/M ratio and, probably,the efficacyof
the fifthagent. Well-correlatedweatherpatternsover
New Brunswickare exemplifiedby the annual fluctuations in temperatureshown in Fig. 25. Nonetheless,a
degree of asynchronyalways exists between series b
and c. This is analogous to an increase in budworm
populationsin thesoutheasterncornerthatwas slightly
earlierthan in northernareas of New Brunswick(Fig.
2).
in which ao and a, are constant. Note that the log
survivalrate (Hg) is nonpositive,but the above linear
Amplitude
ofoscillations
and
approximation mightviolate this constraint.Thereoutbreak
frequency
fore,I restrictmost of my argumentsto a qualitative
level, so as to remainwithinthe realm of thisapproxThe simulated populations in Fig. 28 cycle fairly
imation.
regularly,because their second-orderdensitydependence yields periodic autocorrelations.However, the
and
Synchronized
populationoscillations
amplitude of an oscillation varies considerablyfrom
theroleofclimate
cycle to cycle under the influenceof the density-inMoran (1953), in his statisticalanalysis of the Can- dependentz term.An oscillationthat happens to exada lynx(Lynx canadensis) cycles,proposed the idea ceed thedottedline in each graphof Fig. 28 represents
thatdensity-independent
climaticinfluences,if corre- a hypotheticaloutbreak.We see then that the occurlated betweenlocalities,could synchronizelocal pop- renceof outbreaksgreatlydepends on the random naulations that are oscillatingindependentlybecause of tureof the E/M ratioas a major elementofthe z term.
factorsintrinsicto each population. This important
The periodicityoftheautocorrelationfunctions(coridea, however, did not attractmuch attentionfrom relogram)of a stationaryautoregressivetime series is
ecologists.As reviewedin Royama (1977, 1981a), the knownto be uninfluencedby temporallyuncorrelated
autoregressivemodel of Eq. 7 can generateoscillations exogenousperturbations(zt in Eq. 7). This impliesthat
of various lengths,if the values forao and a, are suit- theaveragelengthofa local budwormpopulationcycle
December1984
455
SPRUCE BUDWORM
larvalsurvival,
is determinedbythedensity-dependent
at random fromyear
not by the E/M ratio fluctuating
to year. Frequent, high E/M ratios can enhance the
amplitude of an oscillation to an outbreaklevel, but
only when the population is in an upswingphase of a
cycledue to highlarvalsurvival.High E/M ratioswould
not,however,readilyreversethepopulationtrend,once
larval survivalhas starteddecreasing;highE/M ratios
were observed in 1954, 1957, and 1961 on plot G4,
but the population decreased, nevertheless(Fig. 1).
Thus, the seed of an outbreaklies in the intrinsicdenmost likelyin the survivalof
structure,
sity-dependent
old (feeding)larvae, while moth invasions (high E/M
so to speak.
ratios) act only as fertilizers,
Notice thatnot all peaks in the seriesb and c in Fig.
28 exceededan outbreaklevel simultaneously,and that
outbreakshappened to occur more oftenin series b
than in series c. In otherwords,even if the phases of
population oscillations are well synchronizedamong
localities,theamplitudesneed notbe correlatedas well.
Further,outbreakshappened to occur more regularly
in the latterhalf of series b than in the earlier half.
These resultsin thesimulationmay explaindifferences
in the outbreakfrequencyacross easternCanada from
Ontario to Newfoundland,such as the fairlyregular
occurrencesof outbreaksin the past few centuriesin
New Brunswickand Quebec (Fig. 3) and the rather
sporadic ones in otherregions(Blais 1965).
A particularlyinstructivelesson of the simulations
is thatan alternationbetweenintervalsof regularand
sporadic outbreaksdoes not necessarilyimply some
fundamentalchangesin the environmentalconditions
or in the structureofthepopulationprocesses.Simply,
therandomvariationin the E/M ratioalone can cause
such alternationsin population cycles.There is a possibility,thoughnot highlycredible,thatthe nonlinear
process of the actual budworm population dynamics
may exhibitstable oscillations,such as limitcycles.If
so, a rathermoreregularoccurrenceofoutbreakscould
be expectedthanfromthepresentsimulations,because
the simple linear model employed here is unable to
generatelimitcycles.
Initiationand spreadofoutbreaks
Sprucebudworminfestationmaps in easternCanada
(Brown 1970, Kettela 1983) mightappear to support
a widespreadnotionthatoutbreaksbeginat a fewscatteredpoints,or 'epicenters,'thenspread outwards,infestingsurroundingareas through moth dispersal.
However, Stehr(1968) considered,in addition to the
above notion, a second possibilitythat an epicenter
mightbe "merelythe spot at which a generaland alreadywidespreadpopulationsurfacesfirst,"but he admittedthat"we actuallydo not know today which of
structuresapplies to the epithese radicallydifferent
centersof the sprucebudworm."
Close inspectionof the egg-masssurveymap (Fig.
Budworm pop2) supportsthe second interpretation.
a
b
z
C
0
C
0
50
100
150
200
250
300
Generation, t
popdensity-dependent
FIG.28. Simulatedsecond-order
In each series,300 points(N1, N2, . . .
ulationoscillations.
by Eq. 7 (R, = a0Nt+ a1N11 + z1) with
N300)are generated
are(N1= 1,N2=
ao = 0.80anda, = -0.89. Initialconditions
2) in both series a and b, and (N1 = -1, N2= -2) in series
random
uncorrelated
c. The z's in eachseriesaretemporally
in theinterval
(-0.5, 0.5). z,
uniformly
distributed
numbers
withz,in seriesa, butis correlated
in seriesb is uncorrelated
a
withz, in seriesc. Dottedline in each graphrepresents
see
outbreaklevel. For detailedexplanations,
hypothetical
andtheRole
Oscillations
Population
Synchronized
Synthesis:
ofClimate.
ulations were in theirtroughsby the early 1960s, and
startedincreasingagain thereafterjust about everywherein New Brunswick.However, in the centralregion (i.e., blocks B3, B4, C3, C4, and C5 in Fig. 2) the
troughpopulationsweresomehowmaintainedat much
higherlevels than in any otherareas of the province.
Consequently,when all populations in the province
increased again in the early 1970s, an outbreaklevel
was reached in the centralregionsooner than in surroundingregions.The troughsofthesoutheasternpopulations (blocks A4, A5, B5, and B6 in Fig. 2) were
just as low as those of the populations in the northwestern corner, but the southeastern populations
somehowincreasedslightlyearlierand reachedan outbreak level sooner. On infestationmaps, these areas
mightlook like "epicenters."
To summarize,althoughmoth immigrationsmight
acceleratethe increasein local populations and create
outbreaksearlier or more frequently,moth dispersal
T. ROYAMA
456
Ecological Monographs
Vol. 54, No. 4
In thissection,I discuss (1) Morris'skey-factor
modis unlikelyto act like a vector carryingan infectious
disease. Rather,dispersalacts like a fertilizerto stim- el, (2) Watt's (1963) analysis of old (large) larvae, and
ulate the seed of an outbreak(survivalof local larvae) (3) theconceptofdichotomousendemicand epidemic
budwormpopulations,or the double-equilibriumthethathas already startedgrowingin everylocality.
oryof outbreakprocesses.I use my notationsthroughpopulation
Maintenanceofdensity-dependent
out.
underperturbations
oscillations
frommothdispersal
Morris's key-factor
model
The key-factor
model of Morris (1 963b) is a linear,
A comparison between the simulated populations
autoregression,a special case of Eq. 7 in
(Fig. 28) and egg-massfluctuations(Fig. 2) reveals a first-order
namely that the sec- whicha, = 0. Morrisused thelog initialdensityof old
subtle but importantdifference,
ondary fluctuationsabout the principaloscillation in larvae (N3 in Table 1), regressedN3,+I on N3t,and
the actual populationslook like sawteethas compared estimatedthe coefficientof N3, (ao in Eq. 7) by least
with the smootherappearance of the simulated pop- squares to obtain do = -0.24. He thenfoundthatthe
ulations. Errorsfromsmall samples in the egg-mass residuals,as estimatesofthe z's, werehighlycorrelated
surveymay contributeto the sawtooth-likesecondary withthe mean daily maximum temperature,T (in 0F)
but thesefluctuationsmay primarilybe a between 1 Juneand 13 July,whenmuch larval feeding
fluctuations,
occurs in the Green River area. Based on this regresresultof strongperturbationsfrommoth dispersal.
Using the autoregressivemodel (Eq. 7), we can sim- sion, Morris formulatedhis key-factormodel:
ulate strongperturbationsfrommoth dispersal by a
(8)
R3t =-0.24N3t + 0.18Tt - 10.99.
largevariance of z. Changes in the variance,however,
influencetheamplitudesofoscillationsbut do not pro- Using the temperaturerecords fromthe City of Edduce sawtooth-likefluctuations(Royama 1979). Eq. 7 mundstonsince 1925, Morris's backward simulation
can produce rapid fluctuationsin densityif the a-pa- with Eq. 8 yielded an oscillation that peaked around
rametervalues are changed,but this tends to obscure the late 1940s and more or less coincided with the
the oscillatorypatternof populationcycles.The N's in observed outbreakof thatperiod (Fig. 18.2 in Morris
Eq. 7 are local population densities, so the density 1963b).
The apparentinfluenceof Tton R3t in Eq. 8 is spudependence of the model is maintainedonly by local
factorssuch as the parasitoid complex, which is un- rious,however,fortwo reasons. First,as discussed in
likelyto migratewithdispersingbudwormmoths.Un- Analysis:influenceofweather,the rise and fallin temder thisassumption,the model would not produce the peraturesrecordedin Edmundston duringthe above
period did not occur everywherein the province,exdesired effect.
If, however, the density-dependentoscillations in cept in Sussex, over the two centuries(Fig. 25) and
budworm populations are caused largelyby the fifth cannot explain the province-widebudworm oscillaThe fifth tions (Figs. 2 and 3). Second, as discussed in Analysis:
agent, the situation can be quite different.
agent,be it of disease or of physiologicalorigin,would influenceof weather,R3 was onlyindirectlycorrelated
travel with its carriers,the dispersingmoths. If local with T, because: (1) T was correlatedwith the mean
populations oscillatein unison,underthe mechanism dailyminimumrelativehumidityduringthemothseadiscussed in Synthesis:synchronizedpopulation oscil- son (Fig. 24), (2) the mean daily minimum relative
lations and the role of climate, the incidence of the humidityinfluencedthe log E/M ratio H5 (Fig. 11),
fifthagent should coincide among these populations. and (3) H5 was correlatedwithR3 (Figs. 9 and 13).
Morris himselfwas not satisfiedwiththe simulated
theagent,among
Then,theexchangeofmoths,carrying
local populations can cause sawtooth-likesecondary patternof oscillationin his Fig. 18.2 (Morris 1963b),
fluctuationswithoutmuch influencingthe basic oscil- and so proposed an alternative double-equilibrium
process of the theory.To discuss this theory,however, I must first
lation caused by the density-dependent
review Watt's (1963) analysis of survival of old (his
populations as a whole.
large) larvae, because his resultserved as supportfor
COMMENTS ON SOME OTHER ANALYSES AND
Morris's theory.
THEORIES
Watt'sanalysis
There are two major problems with analyses by
earlier authors: theirtreatmentof density-dependent Watt(1963: Fig. 10.4) regressedthelog survivalrate
population parametersas firstorder, and of autore- H3 (log of his SL) on log densityN3 (log of his NL).
population processes Data takenfrommany studyplots in the Green River
gressive-typedensity-dependent
as regressionsof independentparameters.These can area were pooled in his analysis. He then divided the
seriouslymislead ifthe processesanalyzed are, in fact, densityspectruminto six intervals,calculated the avsecond or higher order (Royama 1977, 1981a); the eragesurvivalratein each interval,and fitteda regresconcept of high-orderdensity dependence was not sion curve throughthese averages (Fig. 10.5 in Watt
1963). Watt found"a tendencyforSL to increasewith
known20 yr ago.
SPRUCE BUDWORM
December 1984
457
comprisedfractionsof many such oval trajectoriesbecause in no one plot did observationscover one whole
00
OLe
population cycle.
>0
In many plots,observationswere made roughlybetweenpeak and troughdensities.As a result,the data
fromthese plots formedthe lower rightquarterof an
0)
oval trajectory.
These includedplotsK1 and K2, which
Cy$O
0:
had extremelyhigh peak densities.These data points
comprisean upper section of the densityspectrumin
log density
Watt'sFig. 10.4. In otherplots,observationsweremade
FIG. 29. A schematic
illustration
of therelationship
be- several years afterpeak density,when low survival
tweenthesurvivalof"largelarvae"andtheirinitialdensities rates were accompanied by medium to low densities,
in Watt's(1963) Fig. 10.5. For explanations,
see Synthesis: so that theirdata points formeda bottom section of
Watt'sanalysis.
the oval trajectories.These comprise the medium to
lowersectionsofthedensityspectrumin Watt's figure.
NL up to about NL = 120, afterwhich SL fallsagain." Onlyin twoplots,G4 and G5, did observationsinclude
This curious density-dependentrelationshipresulted the increasingphase of oscillations,so that theirdata
fromfitting
a first-order
model to a second-orderpro- pointsformedall but the lowerleftquarterof the oval
cess and pooling time-seriesdata taken from many trajectories.Thus, average survivalratesin theseplots
different
plots.
were comparativelyhigh. Their data points comprise
As I have deduced, budwormpopulations oscillate a middle to upper part of the densityspectrumin the
because thesurvivalrateofold larvae oscillates.Need- figure.
less to say, the survival rate tends to be highestat
I have idealized the above situationin Fig. 29. It
medium densitieswhen the population is fastincreas- would be misleadingto draw a singleregressioncurve
ing, and lowest when it is collapsing. Survival is in- throughthe data points pooled withoutregardto the
termediatebothwhenthepopulationis arounditspeak cyclicsurvivalof larvae. Populations in different
plots
and when it is around its trough.Thus, withan oscil- did not oscillate with similar amplitudes. In the K
lating second-orderpopulation process, H3, plotted plots, forexample, peak densitieswere veryhigh beagainstN3,in time-seriesdata froma given plot tends cause the larval survivalwas somehow veryhighdurto yield an oblong circularpattern,thoughsomewhat ingthepopulationincrease.In theG plots,on theother
irregularbecause ofrandomfactors.Since Wattpooled hand, the larval survival rates were not as high,and
all data taken frommany study plots, his Fig. 10.4 peak densitiesstayedcomparativelylow. Thus, higher
survivalratesproduce higherpeak densities,and then
1OO
Co
0=
E0
"E50
~~~~~
31. .l
0
1945
1950
1955
1960
1965
1970
1975
1980
Generationyear
FIG.
30. The same as Fig. 1, but density(number/M2 of foliage)is plottedon a linear scale.
458
T. ROYAMA
Ecological Monographs
Vol. 54, No. 4
fromendemicto epidemic statesoccurswhenweather
favorslarval survival duringthe feedingstage. Conversely,a transitionfromepidemic to endemic states
in the model is dependent on heavy defoliationand
resultantfood shortage.However, as I have arguedin
ofendemicand
Dichotomy
detail,the survivalof feedinglarvae does not seem to
the
populations:
epidemic
respond sensitivelyto weatherchanges (unless, possitheory
double-equilibrium
bly, the larvae are "diseased"), and food shortageis
process,i.e., a, = 0 not a universalcause of population decline.
density-dependent
A first-order
Third,Morrisconsideredthathis reproductioncurve
in Eq. 7, willnotcause thepopulationto oscillateunless
factorsinvolved, z in Eq. 7, along the450 line was ofthe same formas the survivalthe density-independent
oscillate (Royama 1981a). Thus, fittinga first-order densitycurve of Watt's Fig. 10.5; both curvesrise first
model to an oscillatorydata serieswillnecessarilyyield and then fall as densityincreases. Morris argued that
an oscillatoryseries of residuals and would lead one Watt's curve did not rise towardthe lower end of the
fac- densityspectrumonlybecause thedata did not include
to look forsome oscillatorydensity-independent
low densitysituations.However,as already
sufficiently
tors.
curve does not implya causal effect
Watt's
discussed,
Morris (1963b) noted that his key-factormodel
survival
and, therefore,is irrelevantto
on
of
density
simwith oscillatingtemperaturedid not adequately
ulate an endemicstateofbudwormpopulationsduring the question of shape in Morris's reproductioncurve.
Thus, thereis no reason to assume the dichotomy
the 1930s. Therefore,while stillmaintaininghis modendemic and epidemic equilibrium states nor to
of
properties,Morris nonlinearizedit in
el's first-order
a model on that assumption. My hypothesisof
build
on
of
N,
regression
such a way thata curvilinear
N,+1
(knownas Ricker's [1954] reproductioncurve) crosses a second-orderdensity-dependentprocess with only
the 450 line (on which N,+1 = N,) at two points from one equilibriumpoint is consistentwiththe evidence
above (Fig 18.3 in Morris 1963b), formingtwo locally and more parsimonious for describingthe dynamics
stableequilibriumpoints.In betweenthesetwo points of sprucebudwormpopulations.
thereproductioncurvecrossesthe450 line frombelow.
ACKNOWLEDGMENTS
This is an unstable equilibriumpoint, or a "release"
ServicecontribtheCanadianForestry
from
people
Many
point,above whichthepopulationincreasesto theupofthispaper.
thecompletion
to
and
indirectly,
directly
uted,
overshoots,
per equilibrium point. If the population
the
oftheGreenRiverProjectprovided
Alloriginal
members
an epidemicor an outbreakmay result.However,after life-table
CharlesA. MillerandDavid 0.
data.In particular,
sharedtheirfirst-hand
freely
bothnow retired,
yearsof defoliationand subsequentdestructionof the Greenbank,
AnthonyW. Thomasspenthis
and experience.
forest,the population recedes to a lower level, where knowledge
the
withmeduring
andinvolveddiscussions
itis again withintheendemicequilibriumregion.Mor- timeinfrequent
last fewyearsand also providedsome of his unpublished
ris consideredthatthe endemic equilibriumcould be data.DiscussionswithJacquesRegniereresulted
in thedismaintainedby predators(e.g., birds and spiders) and coveryof the framing
survivalratesin
bias in estimating
parasitoids.However, he thoughtthat even the com- youngand old larvae.HaroldPieneand David A. MacLean
defoliation
on theimpactofbudworm
bined effectof these naturalenemies would not stem providedinformation
on thehosttrees.EdwardG. Kettelaprovidedhisegg-mass
a rapidincreaseofbudwormpopulationsundera series data. GrahamPage,Eldon Eveleigh,David MacLean,and
offavorableweatherconditions,and, hence,that"pop- TonyThomasreadthemanuscript.
I oweMichaelL. Rosenof
ulation release" would occur sooner or later. I once zweig,University
ofArizona,StuartL. Pimm,University
thanksfortheircomreferee
and an anonymous
supportedthis theoryand even generalizedit to the Tennessee,
second-orderlevel (Royama 1977, 1978), but after ments.Finally,I thankDonald Strongforhis mostuseful
themanuscript.
adviceon improving
carefulexamination,I have abandoned theidea forthe
followingthreereasons.
LITERATURE CITED
First,the apparentexistenceof an endemic statebebiology
R. M.,andR. M. May. 1979. Population
Anderson,
tweenthetwo recentoutbreaksin theGreenRiver area
diseases.Nature(London)280:361-367.
ofinfectious
is mainlydue to poor data resolutionat low densities Balch,R. E.,andF. T. Bird. 1944. A diseaseoftheEuropean
(Htg.),and its place in
Gilpiniahercyniae
sprucesawfly,
when these are plottedon a linear scale (Fig. 30). The
25:65-80.
in
Agriculture
Science
control.
natural
(Fig.
scale
a
logarithmic
on
when
plotted
same data,
forevaluation
G. 1976. Reportofthetask-force
Baskerville,
1), give higherresolutionand show no clear signof an
fortheCabinet
prepared
controlalternatives,
ofbudworm
endemicequilibrium;thepopulationsimplydecreased
ProvinceofNew
on EconomicDevelopment,
Committee
Fredericton,
and thenincreasedwithoutany sign of negativefeedofNaturalResources,
Department
Brunswick.
Canada.
New Brunswick,
back. There is no reason to believe that this Green
ofthecurrent
ofthedestruction
River situationwas exceptionalamongthelow-density Blais,J.R. 1953. Effects
and habitsof
ofbalsamfiron thefecundity
foliage
year's
situationsbetween outbreaksover the past two cen85:
CanadianEntomologist
ofthesprucebudworm.
flight
turies(reconstructedin Fig. 3).
446-448.
on
bysprucebudworm
ofdefoliation
1958. Effects
Second, Morris's model assumes that a transition
some second-orderdensity-dependentmortalityfactorseventuallyreducethesurvivalrate.Thus,thecauseand-effectrelation is reversed between Watt's interpretationand mine.
December 1984
SPRUCE BUDWORM
459
ReportDPC-X-14,CanadianForofbalsamfirandwhitespruce.
America.Information
atbreastheight
radialgrowth
34:39-47.
estryService,Ottawa,Ontario,Canada.
Chronicle
Forestry
studiesin theconifdata Kendeigh,
S. C. 1947. Birdpopulation
* 1962. Collectionand analysisofradialgrowth
Onoutbreaks. erousforest
a sprucebudworm
outbreak.
biomeduring
fromtreesforevidenceofpastsprucebudworm
of Lands and Forests,Divisionof Re38:474-484.
tarioDepartment
Chronicle
Forestry
in thepastthree
outbreaks
search,BiologicalBulletinNumber1.
. 1965. Sprucebudworm
in theLaurentide
Park,Quebec.ForestScience Krebs,C. J. 1971. Geneticand behavioralstudieson fluccenturies
Pages243-256 in P. J.denBoer
volepopulations.
tuating
11:130-138.
oftheadvanced
ofeastern
insusceptibility
and G. R. Gradwell,editors.Proceeding
1968. Regionalvariation
on dynamicsof numbersin populations
attackbasedon history studyinstitute
tobudworm
NorthAmericaforests
The Nether44:17-23.
(Oosterbeek,1970). PUDOC, Wageningen,
Chronicle
Forestry
ofoutbreaks.
lands.
ofbalsamfirin relation
1979. Rate ofdefoliation
ofsprayapplication. Loughton,
B. G., C. Derry,and A. S. West. 1963. Spiders
attackandtiming
to sprucebudworm
and thesprucebudworm.In The dynamicsof epidemic
ofForestResearch9:354-361.
CanadianJournal
Societyof
ofspruce
representation
sprucebudwormpopulations.Entomological
Brown,C. E. 1970. A cartographic
in
CanadaMemoir31:249-268.
(Clem.)infestation
fumiferana
budwormChoristoneura
reviewofthespruce,
M. E. 1968. A literature
easternCanada, 1909-1966. CanadianForestryService McKnight,
UnitedStatesForest
budworms.
and 2-year-cycle
western,
Number1263:1-4.
Publication
infecting ServiceResearchPaperRM44.
Burke,J.M. 1980. A surveyofmicro-organisms
a sprucebudwormpopulation.Pages 1-9 in Information Miller,C. A. 1955. A techniqueforassessingsprucebudCanadianJourcausedbyparasites.
wormlarvalmortality
Canada,CanadianForReportFPM-X-37,Environment
SaultSte.
nal ofZoology33:5-17.
Institute,
estryService,ForestPestManagement
of
thefecundity
1957. A techniqueforestimating
Marie,Ontario,Canada.
CanadianJourofthesprucebudworm.
populations
natural
D. 1960. Populationprocessesin thevoleandtheir
Chitty,
nal ofZoology35:1-13.
CanadianJournalofZoology
relevanceto generaltheory.
ofsprucebudwormpop1958. The measurement
38:99-113.
behavior
duringthe firstand secondlarval
ulationsand mortality
J.J.,andD. E. Davis. 1964. Endocrines,
Christian,
ofZoology36:409-422.
Science146:1550-1560.
instars.CanadianJournal
andpopulations.
in
proportion
1963a. The analysisofthefecundity
Dimond,J. B. 1974. Statusof microbialsforcontrolof
ontheSpruce
ofSymposium
area. In The dynamicsof epidemicspruce
Proceedings
theunsprayed
sprucebudworm.
PubSocietyof Canada
UnitedStatesForestServiceMiscellaneous
budwormpopulations.Entomological
Budworm.
lication1327:97-102.
Memoir31:75-87.
des ZuIn The
Grundlagen
1963b. Parasitesand thesprucebudworm.
Franz,J. 1949. Uberdie genetischen
EnUraus innerem
einerMassenvermehrung
sammenbruchs
dynamicsof epidemicsprucebudwormpopulations.
3:228-260.
Entomologie
SocietyofCanadaMemoir31:228-244.
angewandte
sachen.Zeitschrift
fuir
tomological
birdcensus
Gage,S. H., andC. A. Miller. 1978. A long-term
impactof sprucebudwormon
1977. The feeding
balsam firhabitatsin north- balsamfir.CanadianJournal
in sprucebudworm-prone
ofForestResearch7:76-84.
ReportM-X-84, Miller,C. A., D. C. Eidt,andG. A. McDougall. 1971. PreInformation
westernNew Brunswick.
Canadian
ofFisheriesand theEnvironment,
Department
CanadaDepartment
development.
sprucebudworm
dicting
FredForestResearchCentre,
Forestry
Service,Maritimes
CanadianForestry
SerandtheEnvironment,
ofFisheries
Canada.
New Brunswick,
ericton,
ResearchNotes27:33-34.
vice,Bimonthly
D. 0. 195-6.The roleofclimateand dispersal Miller,C. A., and T. R. Renault. 1976. IncidenceofparaGreenbank,
in theinitiation
of outbreaksof the sprucebudwormin
sitoidsattacking
endemicsprucebudworm(Lepidoptera:
1. The roleofclimate.CanadianJournal Tortricidae)populationsin New Brunswick.Canadian
New Brunswick.
ofZoology34:453-476.
108:1045-1052.
Entomologist
of theoutbreak.In The Miller,C. A., and T. R. Renault. 1981. The use ofexperi1963a. The development
larvalmortality
at
dynamicsof epidemicsprucebudwormpopulations.Ento assessbudworm
mentalpopulations
SocietyofCanada Memoir31:19-23.
tomological
ReportM-X-115,Environment
Information
lowdensities.
1963b. The analysisofmothsurvivalanddispersal Canada,CanadianForestry
ForestReService,Maritimes
ofepidemicspruce
area.In Thedynamics
intheunsprayed
Canada.
New Brunswick,
searchCentre,
Fredericton,
Societyof Canada Mitchell,
budwormpopulations.Entomological
ofsprucebudworms
by
R. T. 1952. Consumption
Memoir31:87-99.
50:
ofForestry
forest.
Journal
birdsin a Mainespruce-fir
andR. C. Rainey. 1980.
D. O., G. W. Schaefer,
Greenbank,
387-389.
mothflight
and Mook,L. J. 1963. Birdsand thesprucebudworm.In The
Tortricidae)
(Lepidoptera:
Sprucebudworm
fromcanopyobservations, dynamicsof epidemicsprucebudwormpopulations.
dispersal:new understanding
EnSocietyofCanadaMemEntomological
radar,andaircraft.
SocietyofCanada Memoir31:268-271.
tomological
oir 110.
analysisof theCaMoran,P. A. P. 1953. The statistical
and meteorology.
Henson,W. R. 1950. The meansofdispersalofthespruce
nadianlynxcycle.II. Synchronization
ofForestry,
Yale UniofZoology1:291-298.
Dissertation.
budworm.
Department
Australian
Journal
USA.
New Haven,Connecticut,
versity,
Morris,R. F. 1954. A sequentialsamplingtechniquefor
ofZoology
CanadianJournal
Hudak,J.,and A. G. Raske,editors.1981. Reviewofthe
eggsurveys.
sprucebudworm
control 32:302-313.
sprucebudwormoutbreakin Newfoundland-its
of techniquesforforest
basedon theCanaand forest
1955. The development
implications,
management
reference
to thespruce
and
withparticular
Servicesubmission
totheNewfoundland
dianForestry
insectdefoliators,
andmanofZoology33:225-294.
onforest
protection
LabradorRoyalCommission
CanadianJournal
budworm.
datainstudies
ofmortality
1957. Theinterpretation
ReportN-X-205,Newfoundland
agement.Information
89:49Service,DeForestResearchCentre,CanadianForestry
on populationdynamics.CanadianEntomologist
St. John's,Newfoundland, 69.
oftheEnvironment,
partment
Canada.
,editor. 1963a. The dynamicsof epidemicspruce
ofsprucebudhistory
Kettela,E. G. 1983. A cartographic
Societyof Canada
Entomological
budwormpopulations.
from1967 to 1981 in easternNorth
wormdefoliation
Memoir31.
460
T. ROYAMA
EcologicalMonographs
Vol. 54,No. 4
* 1963b. The development
of predictive
equations "dispersalof forestinsects:evaluation,theoryand manforthesprucebudwormbased on key-factor
analysis.In
agement
Conference
implications."
Office,
Cooperative
ExThe dynamicsofepidemicsprucebudwormpopulations. tensionService,Washington
StateUniversity,
Pullman,
Entomological
SocietyofCanada Memoir31:116-129.
USA.
Washington,
* 1963c. Predation
. 1981a. Fundamentalconceptsandmethodologyfor
andthesprucebudworm.
In The
dynamicsof epidemicsprucebudwormpopulations.
theanalysisofanimalpopulation
Endynamics,
withparticular
tomological
reference
to univoltine
SocietyofCanada Memoir31:244-248.
species.EcologicalMonographs
51:
Morris,R. F., W. F. Cheshire,
C. A. Miller,andD. G. Mott. 473-493.
* 1981b. Evaluationofmortality
1958. The numerical
responseof avian and mammalian
factors
in insectlife
predatorsduringthe gradationof the sprucebudworm. tableanalysis.EcologicalMonographs
51:495-505.
Ecology39:487-494.
Stehr,
G. 1968. On someconcepts
inthepopulation
biology
ofthesprucebudworm.
Morris,R. F., and D. G. Mott. 1963. Dispersaland the
Proceedings
oftheEntomological
sprucebudworm.In The dynamicsof epidemicspruce SocietyofOntario99:54-56.
budwormpopulations.
Entomological
Societyof Canada Swaine,J. M., and F. C. Craighead.1924. Studieson the
Memoir31:180-189.
sprucebudworm
(Cacoeciafumiferana
Clem.).CanadaDeMott,D. G. 1963. The analysisof the survivalof small partment
of Agriculture
TechnicalBulletin(new series),
larvaeintheunsprayed
area.In Thedynamics
ofepidemic Ottawa,37.
sprucebudwormpopulations.Entomological
Societyof Thomas,A. W.,S. A. Borland,andD. 0. Greenbank.1980.
CanadaMemoir31:42-53.
Fieldfecundity
ofthesprucebudworm
(Lepidoptera:
TorNeilson,M. M. 1963. Diseaseandthesprucebudworm.
tricidae)as determined
In
fromregression
relationships
beThe dynamicsofepidemicsprucebudwormpopulations. tweeneggcomplement,
forewinglength,
andbodyweight.
Entomological
CanadianJournal
SocietyofCanada Memoir31:272-287.
ofZoology58:1608-1611.
I. 1971. Aspectsofmating
Outram,
inthesprucebudworm, Thomson,H. M. 1958. Some aspectsoftheepidemiology
ofa microsporidian
Choristoneurafumiferana(Lepidoptera: Tortricidae).Caparasiteofthesprucebudworm,
ChornadianEntomologist
103:1121-1128.
istoneurafumiferana.
CanadianJournal
ofZoology36:309. 1973. Sprucebudwormmothdispersalproject, 316.
N. B. 1973:morphometric
Chipman,
andreproductive
1960. Thepossiblecontrol
staofa budworm
infestation
tusofthesprucebudworm
moths.File Report,Maritimes by a microsporidian
disease.Canada Department
of AgForestResearchCentre,
riculture,
Fredericton,
NewBrunswick,
Ottawa,Bimonthly
CanProgress
Report16(4):1.
ada.
Tothill,J.D. 1922. Noteson theoutbreaks
ofsprucebudPeterman,
R. M., W. C. Clark,andC. S. Holling. 1979. The
worm,foresttentcaterpillar,
and larchsawflyin New
dynamicsof resilience:shifting
Proceedings
stability
domainsin fish Brunswick.
oftheAcadianEntomological
Soand insectsystems.
cietyfor1922.8:172-182.
Pages321-341 in R. M. Anderson,
B.
D. Turner,
andL. R. Taylor,editors.
Population
dynamics: Watt,K. E. F. 1963. The analysisofthesurvivalof large
the20thsymposium
larvaeintheunsprayed
oftheBritish
area.In Thedynamics
EcologicalSociety,
Lonofepidemic
don,England.
sprucebudwormpopulations.Entomological
Societyof
Piene,H., D. A. Maclean,and R. E. Wall. 1981. Effects
CanadaMemoir31:52-63.
of
sprucebudworm
causeddefoliation
on thegrowth
ofbal- Wellington,
W. G. 1960. Qualitative
changesinnatural
popsamfir:experimental
designandmethodology.
Information ulationsduringchangesin abundance.CanadianJournal
ReportM-X-128,Environment
Canada,CanadianForest- ofZoology38:289-314.
ryService,Maritimes
ForestResearchCentre,
Fredericton,Wellington,
W. G., J. J. Fettes,K. B. Turner,and R. M.
New Brunswick,
Canada.
Belyea. 1950. Physicaland biologicalindicatorsof the
Pimentel,
D. 1968. Populationregulation
andgeneticfeed- development
ofoutbreaks
ofthesprucebudworm.Canaback.Science159:1432-1437.
dianJournal
ofResearchD 28:308-331.
Renault,T. R., and C. A. Miller. 1972. Spidersin a fir- Wellington,
W. G., andW. R. Henson, 1947. Noteson the
spruce
biotype:
andinfluence
abundance,
onspruce effects
diversity,
ofphysicalfactors
ofthesprucebudworm,
Chorisbudworm
densities.
CanadianJournal
ofZoology50:1039toneurafumiferana
(Clem.).CanadianEntomologist
79:1681046.
170.
Ricker,W. E. 1954. Stockand recruitment.
Journalofthe Wilson,G. G. 1973. Incidenceof microsporidia
in a field
FisheriesResearchBoardofCanada 11:559-623.
ofsprucebudworm.
population
CanadaDepartment
ofthe
Royama,T. 1970. Factorsgoverning
thehunting
behaviour Environment,
CanadianForestry
Service,Bimonthly
Reand selectionof foodby the greattit (Parus majorL.).
searchNotes29:35-36.
ofAnimalEcology39:619-668.
Journal
1977. Observations
on theincidenceratesof No* 1971. Evolutionary
significance
of predators'resema fumiferana
in a sprucebudworm
(Microsporidia)
sponseto local differences
in preydensity:a theoretical (Choristoneurafumiferana)
(Lepidoptera:
Tortricidae)
popstudy.Pages344-357inP. J.denBoerandG. R. Gradwell, ulation.Proceedings
oftheEntomological
Societyof Oneditors.Proceeding
oftheadvancedstudyinstitute
on dytario108:144-145.
namicsofnumbers
inpopulations
(Oosterbeek,
1970).PUDOC, Wageningen,
The Netherlands.
. 1977. Populationpersistence
and densitydependence.EcologicalMonographs
47:1-35.
APPENDIX 1
1978. Do weather
factors
influence
thedynamics
of
GENERALIZATION
OFEQ. 4
sprucebudworm
populations?
CanadaDepartment
ofFisheries and Environment,
Canadian ForestryServiceBiMigration
and mortality
of mothsoccuroverthe entire
monthly
ResearchNotes34:9-10.
adultperiod,say,k days.Also,theaveragenumberofeggs
1979. Effect
ofadultdispersalon thedynamicsof carriedbya mothin anyone daytendsto decreasetoward
local populations
ofan insectspecies:a theoretical
inves- theendoftheperiod,eitherbecausetheaveragefecundity
of
tigation.
Pages79-93 inA. A. Berryman
and L. Safranyk, a mothtendsto decreaseas itsdateofemergence
getslater
editors.Proceedings
ofthesecondIUFRO conference
on in theseason,orbecausea mothlaysitseggsin batchesover
December 1984
SPRUCE BUDWORM
461
severaldays,during
whichbatchsizedecreases.The product
APPENDIX 3
ofthetwok-element
fip,is thentakentobe thescalarproduct
"CORRELATION"
BETWEEN E/M RATIO AND DENSITY
vectors
fi and Pi, in whichthePth elementsoff and Pi are,
Consider a pair of consecutive points in the series of N1,
respectively,
the mean numberof eggsstillcarriedby the
mothsin theploton day i and themeanproportion
ofthat (log egg density,Fig. 9d), e.g., N, and N,+1 (stage subscript
numberlaid in the plot. The productyieldsthe weighted one is dropped untilneeded). Take the differenceN,?1 - N,
averageof theeffective
preemigration
ovipositionoverthe and writethis ANt,and furthertake the differenceof differences AN, - AN,, and writethis A2Nt,i.e.,
A2Nt= ANt+ N-1.
(A 1)
betakentobea matrix
representation
oftheweighted
average Now connect, by a line,Nt_=Nt-2N,
to
1
N, and N, to N,+1 and
N,
k
observe if the line NN?+ 1 'swings'clockwiseor anticlockwise
canbe represented
f2p2m.Thus,thisgeneralsituation
A
by in relationto
N, 1N,.A clockwise swing means that AN, is
ill
less than AN,-,, or A2N, is negative;a positive A2N, indicates
Eq. 4 without
changesin itsform.
an anticlockwiseswing.Next, observe that as NN,+1 in Fig.
9d swingsclockwiseor anticlockwise,the correspondingsegAPPENDIX 2
ment HtH+?1 in Fig. 9c tends to swing otherwise;a better
MORTALITYOF MOTHSANDAVERAGE
example is given in a simulationin Royama (198 la: Fig. 6).
OVIPOSITION
RATE
In otherwords, A2N, and A2H, tend to have opposite signs,
A femalemothnormally
laysitseggsoverseveraldaysand, or the covariance betweenthemis negative.I show how this
ifshediesyoung,
has moreunlaideggs.Thomasetal. (1980) happens on theassumptionthatH5,(log E/M ratio)is a series
collecteddeadand dyingmothson droptraysand examined of uncorrelatedrandomnumbersgeneratedindependentlyof
thenumber
ofeggsstillretained
bythem.Collection
wasmade N1,(log egg density)and of N5,(log moth density).
k
periodofkdays,i.e., zf tip1i.Theproductf2p2m
canlikewise
ill
themothperiodin2 yratthreestudyplots.Since
dailyduring
thefullcomplement
ofeggsofa femaleis highlycorrelated By the definitionh5,= nlt+l/n5tgiven in Table la, H5t =
withherwinglength,
itis possibleto estimate
theproportion Nl t+ - N5. Then, H5tshould be positivelycorrelatedwith
ofeggsalreadylaid by thedead females.Femalesthatdied Nlt+l, because H5t is independentof N5tby the above asearlyin theseasonhad laid onlya fraction
oftheirfullcom- sumption.Also, in Eq. A1, A2Nt contains Nt+1 - 2N, and
and theaverageproportion
plement,
of eggslaid increased A2Ht likewise contains -2Ht + Ht-1. It followsthat the coforthe1st 10 d or so in eachseason.Onlyafter2 wk variance between A2Nt and A2Ht would be negative,unless
steadily
or moreintothemothseasonhad mostofthedead females the covariance betweenNt+1and Ht-1 is verylarge,which is
laidmostoftheirfullcomplement
ofeggs.In thethreeplots, unlikely.This explains why H5tH5,t+land N1tN1,t+ltend to
theaverageovipositionrateswere70, 80, and 90% of the swingopposite ways. But, if this happens all the time, it is
potential
The calculation
fecundity.
did notconsidermoths, obvious that H5tis inverselycorrelatedwith Nlt when both
ifany,thatwerepreyeduponbybirds,et cetera.The actual seriesfluctuatewithouttrend,even thoughH5twas generated
completelyindependentof N1t.
ovipositionratecould therefore
be even lower.Moreover,the
femalesthatdied earlyweremorelikelyto have emerged
APPENDIX 4
locally, and the females that died later probably included
immigrants.Therefore,even ifno emigrationtook place, and
ESTIMATION
OF BIAS IN H2
in conjunction
withbirdpredation,
theeffective
oviposition Let "2 be an estimateof H2 adjusted to the zero deviation
rateofthelocalfemalescouldbe loweredto therangeof60- of the date sampled, and let Z(D) be the adjustmentterm,
80%. However,theratewouldnotbe muchlower,because such that
females
lay;50% oftheireggsusuallywithin
2 d after
mating
H2 = H2 + Z(D),
(A2)
(Outram1973),whichoccursmainlywithin
a dayofeclosion
(Outram 1971). Heavy mortalitywithinthese firstfew days
in which D is the deviation in days, shown as 0 in Fig. 19;
Z(O) = 0 by definition.We wish to estimate Z(D). One way
ofadultlifewouldbe unusual.
02
-
(U
E
0
(U
00~~~
0
-2
OA
M
0
0
0
.
A~~~~~~~~~~~~
0~~~~~~~~~~~~
-4
-3
-15 -10
-5
0
5
10
15
N
20
D, relative timing of L3 sampling (days)
FIG. Al. A graphical
methodofcalculating
corrected
survivalrateofyounglarvae(H2)in Fig.20. D is therelativetiming
ofL3 sampling
in days(Fig. 19),and Z(D) is theadjustment
termdefined
in Eq. A2 in Appendix4. For explanations,
see
Analysisbystagesurvivalrates.
462
T. ROYAMA
EcologicalMonographs
Vol. 54, No. 4
notrend)
uncorrelated
randomseries(hence,
a completely
a 0 in Fig. from
to do thisis to regress
H2 on D; thatis, to regress
knownas theSlutzky
curve tendstoexhibita pattern
ofoscillation,
19against
thecorresponding
0 ineachplot.A regression
is curvilinear, effect.
was drawnbyeyein Fig.Al. The regression
Thisis becausein an h-pointmoving-average
series,
presumably
becausethelaterthedatein relationto theref- twopointsthatare k pointsapartfromeach otherareposiwitheachotherfork < h, sincetheyshare
erencepoint(i.e.,themid-datebetweenthepeakL3 and L4 tivelycorrelated
stages),thesteepertheslopeof populationdecline(cf.Fig. h - k pointsin theoriginalseriesin common.Thistendsto
seriesto
forthederivedmoving-average
curveis takento be the resultin a tendency
18),and viceversa.Thisregression
uncorofthepointforD = 0 stayon one sideofthemeanlevel(setbytheoriginal
function
Z(D), so thattheprojection
overtotheother
on a vertical
axisgivesZ(O) = 0. Thus,Z(D) foranygivenD relatedseries)forsometimebeforecrossing
of
givestheimpression
can be readon theright-hand
axisin Fig.Al. H2 forthatD sideofthemeanlevel.Thistendency
theoscillations
haveno fixed
an oscillatory
However,
pattern.
is thengivenbyEq. A2.
periodicity.
APPENDIX 5
oscillations,
ontheotherhand,aremorelike
Thebudworm
density-deperiodic"or "pseudoperiodic"
a "stochastically
A NOTE ON MOVING-AVERAGE SERIES
coefficients
havea fixed
processwhoseautocorrelation
A trendina timeseries,ifany,canbe mademoreapparent pendent
whenplottedagainsttimelags;i.e., thedistance
length,a periodicity
by takingthemovingaveragesof an appropriate
The patternof
The methodis ef- betweentwo timepointsto be correlated.
methodknownas smoothing
or filtering.
(Fig.28)givesa much
bythismechanism
generated
in bringing
fective
outa truetrend.Cautionis needed,how- oscillation
series
thismethod,becausean artificial
trend more"regular"appearancethanthemoving-average
ever,in employing
records(Fig.27).
can be created.A seriesof h-pointmovingaveragestaken ofweather