Directional Selection and Clutch Size in Birds
Author(s): Fred Cooke, Peter D. Taylor, Charles M. Francis and Robert F. Rockwell
Source: The American Naturalist, Vol. 136, No. 2 (Aug., 1990), pp. 261-267
Published by: University of Chicago Press for American Society of Naturalists
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Vol. 136, No. 2
The AmericanNaturalist
August 1990
NOTES AND COMMENTS
DIRECTIONAL SELECTION AND CLUTCH SIZE IN BIRDS
heritability
(Perrinsand
Clutchsize has been shownbothto have significant
Jones 1974; van Noordwijket al. 1981; Flux and Flux 1982; Boag and van
selectionto
Noordwijk1987;FindlayandCooke 1987)andtobe underdirectional
ofbirds(Nur 1984;Boyceand Perrins1987;Rockincreasein manypopulations
studieson wild
well et al. 1987;Gibbs 1988).Nevertheless,severallong-term
have failedto findanyevidenceforevolutionofa largerclutchsize
populations
withtime(Boyce and Perrins1987;Rockwellet al. 1987;Gibbs1988).Priceand
forthisapparentdiscrepancy
and conLiou (1989)reviewedearlierexplanations
ofthephenomenon.
They
cludedthatnoneis adequateto explainthegenerality
based on themodelofPriceet al. (1988).
developed,instead,a newexplanation
Price and Liou (1989) suggestedthatdirectionalselectionoperateson a cortrait(nutritional
determined
state).In theirmodel,the
related,environmentally
ofclutchsize couldalso be subjectto selection,but,ifclutch
geneticcomponent
size is notevolving,thisselectionmustbe nondirectional
(e.g., normalizing).
thepotentialimportance
oftheirmodel,we wouldliketo
we affirm
Although
forthelackofapparentresponseto selection
explanation
pointoutan alternative
ofthegenotype
may,infact,be
actingon clutchsize. We suggestthatcomponents
butthephenotypic
maynotchangebecause
expressionofthegenotype
evolving,
it dependsnot onlyon the individual'sgenotypebut on the deviationof that
Ifthepopulation
meanis changing
with
fromthemeanofthepopulation.
genotype
which
time,thiscan be considereda changein the individual'senvironment,
necessarilyaffectsthe responseto selection.We suggestthatsuch a situation
couldarisenotonlyforclutchsize butformanyothertraitscloselyassociated
withfitness.
fromthe standardunivariateequationof
We develop this conceptstarting
value,P, as
quantitative
genetics,whichdecomposesthephenotypic
P = G + E,
theeffects
ofdominance,
whereG is theadditivegeneticvalue,andE represents
ThevaluesG andE areassumedto
interaction
betweenloci,andtheenvironment.
Am. Nat. 1990. Vol. 136, pp. 261-267.
? 1990 by The Universityof Chicago. 0003-0147/90/3602-0011$02.00.
All rightsreserved.
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262
THE AMERICANNATURALIST
withthepopulationmean,E, equal to zero. Underthismodel,if
be independent,
remainsconstant,thechangein meanphenotype
in responseto
theenvironment
selection,R, is givenby
R = h2S,
(1)
betweenthe meansof the
(the difference
whereS is the selectiondifferential
of thetrait,
selectedand the unselectedpopulations),and h2 is theheritability
ofG onP (Falconer1981).Clearly,ifsucha
coefficient
measuredas theregression
modelwereapplicableto clutchsize,thenpositivevaluesofbothh2andS should
resultin an increasein meanclutchsize.
of thismodelmaybe violatedin two mainways.
However,theassumptions
First,theremay be a conditionalcovarianceof G on fitnesswhenP is held
constant.This may arise if selectionis also operatingon othertraitsthatare
withthetraitunderobservation.
maychange
correlated
Second,theenvironment
can involveeithergeneticor environmental
correlawithtime.The firstsituation
tionsand maybe treatedwiththe multivariate
approachof Lande and Arnold
(1983).Thiscase includesthemodelofPriceand Liou (1989)and was discussed
ofchangesintheenvironment,
bythemindetail.Herewe consideronlytheeffect
does
not
first
situation
that
the
apply.
assuming
theresponse,R, is notgivenby equation(1) butby
Withthisassumption,
R = h2S + AE,
(2)
component
overone generawhereAE is thechangein themeanenvironmental
of AE is well recognizedwhenE refersto the physical
tion.The significance
or derivesfromthe behaviorof a predator,prey,or competitor
environment
levelsintheenvironment
change,we
species.Forexample,iftheaveragenutrient
expectan effecton theresponseto theselectivepressureson clutchsize. Most
to estimatethe effectsof selectionwatchfor
studiesthattake measurements
trendsin anyofthesefactorsthatextendovertheperiodofthestudy.
oftheenvironment
Here we pointoutthatsomecomponents
maychangein a
mannerbutnotbe readilyobserved.In particular,
theenvironment
of
systematic
an individualincludesothermembersof thesamepopulation.Supposethatthe
environmental
E, is partlydetermined
bythemeanvalueofanother
component,
thatis evolving:as itsmeanvaluechanges,themean
traitinthesamepopulation
valueofE changes.
withan
The relevanceof thisconceptto clutchsize can best be illustrated
example.FollowingPriceandLiou (1989),we assumethatclutchsize dependsat
statusofthefemale.Evidencefromtheliterature
on
leastpartlyon thenutritional
and
this
Maclnnes
severalspeciessupports assumption
1978;Dijkstraet
(Ankney
al. 1982;Hussell and Quinney1987;Arceseand Smith1988).However,unlike
statusaffectsfitnessin any
Priceand Liou, we do not assumethatnutritional
otherway-that is, fitnessdependsonlyon clutchsize. We can thendevelopa
simplemodel,in whichwe supposethatclutchsize, P (numberof eggs),is the
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NOTESAND COMMENTS
263
productofthreefactors,
P = PIT2EO,
effecby theforaging
wherePI (numberof eggsper unitof area) is determined
size, and Eo is a random,
tivenessof the parent,T2 is the parentalterritory
(additionalfactorscouldbe addedto themodel,such
component
environmental
the
affecting
allocatedto eggs,without
ofnutrients
intheproportion
as variation
model,
thatfollow).For convenience,we use a multiplicative
basic arguments
additiveformu(thestandard
offitness
forcomponents
whichis oftenappropriate
of bothsides of the equation).We
lationcan be derivedby takinglogarithms
ofphysicalandbehavioral
bya largenumber
further
assumethatT2is determined
forconvenience,underthe name of aggrestraits,whichwe collecttogether,
sivenessand denoteby P2. Since, in a fixedregion,thetotalarea availablefor
A, mustremainconstant,
territories,
T2 =
(AIN) P2/P2,
whereN is populationsize. If we now decomposebothof the traitsPi in the
as
standardway,Pi = GiEi,thenclutchsize can be written
P
GE,
(3)
withG = G1G2 and E = EOE1E2AINP2.Thus, it is clear that,even if the mean
subcomponents
value of each of the environmental
(Ei) remainsone in each
E will changein responseto changesin P2. If P2 increasesin the
generation,
shiftin one of its
populationas a resultof, forexample,some evolutionary
thenP2 increasesandE decreases,makingAE
behavioralstrategies,
component
changeoccurs,ifPi does not
in equation(2) negative.Whilethisevolutionary
withR = 0 andforh2S
evolve,itis possibleforclutchsize,P, tobe at equilibrium
to be positive.
valueofP is affected
byP2 intwodifferent
In theexampleabove,theindividual
thepopulavalueofG2 andnegatively
through
bytheindividual
ways,positively
tionmeanF2 (whichequals G2ifE2 is zero).Onlythesecondoftheseis neededto
producea nonzeroAE and gettheabove effect.
At any timetheremustbe manytraitsin the processof evolving,whether
of an inter-or
or to theongoingeffects
to changesin theenvironment
adjusting
Such
traitscan
Valen
fashion
in
a
Red
1973).
armsrace,
(van
Queen
intraspecific
as clutch
such
affect
fitness
and
often
on
have
an
effect
to
characters,
be expected
size (P)
clutch
the
If
individual
with
fitness.
correlated
that
are
closely
size,
traits
in the
of
such
of
a
number
level
of
on
the
development
average
depends
the
of
P
is
a
function
of
the
environmental
then
(E)
component
population,
a
we
see
as
of
them
for
as
of
these
evolves,
means
any
long
and,
traits,
population
changein E.
systematic
Thisgeneralizedmodelcouldexplain,in part,theabsenceofobservedevoluForexample,in
studiesofbirdpopulations.
tionofclutchsize inseverallong-term
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264
THE AMERICAN NATURALIST
WoodsnearOxford,thereis
ofgreattits(Parus major)at Wytham
thepopulation
of clutchsize (Perrinsand Jones1974) and directional
heritability
significant
selectionforgreaterclutchsize (Boyce and Perrins1987),buttherehas beenno
increasein meanclutchsize withtimeas wouldbe expectedif
corresponding
equation(1) applied.Clutchsize, bothintermsofthenumberofeggsthatcan be
laid and thenumberof youngthatcan be raised,dependson theabilityof the
quality.As a result,
whichinturndependsonterritory
parentstogathernutrients,
territories
lay largerclutchesand raise moreyoung.
birdswithbetter-quality
Thus,thereis selectionforbirdswiththebestabilityto competeforterritories.
theaverageabilitytoacquiregoodterritories
However,as shownabove,although
quality,and hence the average
(P2) increaseswithtime,the averageterritory
clutchsize, does notchangeifthepopulationremainsconstant.
birds,whichwe can illustrate
A similarmodelcan also applyto nonterritorial
usingas an examplethe populationof lessersnowgeese (Ansercaerulescens)
on
at La PerouseBay inManitoba.In thiscolony,theselectiondifferential
nesting
decreaseinlongevity
or
clutchsize is 0.33 eggs,withno evidencefora correlated
of0.2
of fitness(Rockwellet al. 1987).Based on a heritability
othercomponent
(Findlayand Cooke 1987),thepredictedresponse,usingequation(1), shouldbe
should
generations,
which,allowingforoverlapping
0.07 eggs per generation,
in
an
averageincreaseinclutchsize of0.20eggsoverthe20 yrofthe
haveresulted
and systematic
study(Rockwellet al. 1987).In fact,therehas beena significant
decreasein meanclutchsize withtime(Cooch et al. 1989).Clutchsize in snow
withthenutrient
reservesofthelayingfemalewhen
correlated
geese is strongly
she arrivesat thebreedingground(Ankneyand Maclnnes1978).Mostof these
whentheyfeed in large
are acquiredby the birdsduringmigration,
nutrients
flocks.Clearly,selectionacts on femalesto improvetheirabilityto competefor
thuscausingan increasein P2. This couldlead to no changein mean
nutrients,
clutchsize, despitea positiveh2S. However,the snowgoose exampleis comwithtime.A
plicatedby the factthatthe colonysize (N) has been increasing
changein eitherP2 or N affectsE (eq. [3]), and thuseithercould providean
forthelackofan increase(orevena decrease)inmeanclutchsize,F,
explanation
in spiteofa positiveh2S.
ofthismodelis thatthecompetitive
abilityofbirdshas
Onepossibleimplication
withtime,such thatmodernbirdsshouldbe
been improving
systematically
ago. This hysuperiorto birdsfromseveralhundredgenerations
competitively
because new mutations
arisecontinually
pothesisis not,in fact,unreasonable,
the environment
(Hill and Keightley
thatmayallow novel ways of exploiting
even
measure
it
be
to
thisbycomparing
the
short
possible
term, may
1988).Over
mother
overa periodof,for
fromthesamemonogamous
ofdaughters
thefitness
foreffectsdue to age. Even over sucha short
example,10 yr,aftercorrecting
in the populationmean of a
improvement
period,theremightbe a sufficient
willhave lowerfitness.
numberoftraitsthatthelateroffspring
overtimeis nota
It is worthnoting,
improvement
however,thatthissystematic
ability(P2) are
necessaryconsequenceof themodel.Traitssuchas competitive
determined
by thedeviationof manyothertraitsfromtheiroptimalvalues.The
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NOTESAND COMMENTS
265
competitive
individuals
thatmostcloselyapproachtheseoptimahavethegreatest
inthebioticorphysicalenvironment
ability.Randomfluctuations
mayalterthese
optimalvalues;thus,thepopulationevolvescontinuously
to trackthesefluctuations.For example,competitive
abilitymaybe influenced
by resistanceto paraof
sites.Changesintheparasitecommunity
(possiblyinresponseto theevolution
theorganism)altertheoptimalcombination
of traitsproviding
resistanceto the
in
parasites,which,in turn,affectcompetitive
ability.Continuous
improvements
resistanceare necessaryeven to maintain
a constantparasiteload, as suggested
by theRed Queen hypothesis
(van Valen 1973).Similarly,
supposethatforaging
is a functionof deviationfromthe optimalbill size. The population
efficiency
iftheoptimalbillsize
couldbe continuously
evolvingto approachthisoptimum
withchangesin thevegetation.
fluctuates
we suggestthattheabilityto acquirenutrients
influences
clutchsize,
Although
withthismodelthatclutchsize necessarily
increasescontinuwe arenotimplying
nutrients.
ouslyin the presenceof unlimited
Large clutchescould have lower
iftheparentscannotadequatelyincubatetheeggsor raisetheoffspring
fitness
or
In addition,
environmental
ifthenestssuffer
constraints
maylimit
highpredation.
thetotalnumber
ofeggsthatcan be
thetimeavailableforegglaying,thuslimiting
factorssuchas theabilitytoacquirenutrients
maybe
laid.Furthermore,
although
selectionreunderselectionto increase,otherfactorsmaybe underdifferent
theproportion
of availablenutrients
algimes.For example,genes controlling
selectionbecause sufficient
locatedto eggproduction
maybe undernormalizing
andcaringforthe
reservesmustbe retainedfortheparentsto surviveincubation
young.
Althoughthismodelhas been developedwiththe exampleof clutchsize in
othercomponents
of
birds,it is potentially
applicableto manytraits,including
fitness.For example,considerthe matingsuccess of males in a populationin
whichfemaleschoose mates.The matingsuccess of a male(P) dependson the
value of variouscharactersthatfemalesfindattractive(P2). Charactersthat
ina
ofa maleare underdirectional
increasetheattractiveness
selection,resulting
of other
of males(withintheconstraints
continualincreasein theattractiveness
successofa maledependsnotonlyon his
ofselection).
forms
However,themating
oftheothermalesinthe
ownattractiveness,
P2, buton theaverageattractiveness
population,
P2. As a result,theaveragematingsuccessP does notchangeas P2
evolvesbutdependsonlyon thenumberofmalesandfemalesin thepopulation.
ofthemodelsdescribedbyFisher
Thismodelis, inmanyrespects,an extension
(1930) and Wright(1949) forfitnessitself.Accordingto Fisher'sfundamental
theoremof naturalselection(Crowand Kimura1970,pp. 206-225),anygenetic
A numberofimportant
infitness
resultsinan increaseinmeanfitness.
variability
whichwe
are necessaryforthisto hold. One set of assumptions,
assumptions
makehere,includesrandommatingand absenceofoverdominance,
epistasis,or
is a lack of frequency
linkageeffectson fitness.Anotherimportant
assumption
size (P) withfitness,
if
In
we
clutch
our
dependence(Wright
1949).
model,
identify
should
followFisher's
and
is
fitness
absolute
(P1P2EO) frequency-independent
fitnessP =
but
relative
is
when
there
theorem,increasing
geneticvariance;
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THE AMERICANNATURALIST
266
and should
measured,is frequency-dependent
P1T2E0,whichis whatis typically
be unchanged.
ACKNOWLEDGMENTS
We wouldliketo thankthemembers
oftheEcologyand Evolutionary
Biology
E. G. Cooch,H. L. Gibbs,D. B. Lank,
groupat Queen's University,
particularly
on theideas in thispaper.M.
and G. C. Williamsfordiscussionand comments
A. van Noordwijk,and twoanonymous
reviewers
Kirkpatrick,
providedseveral
thathelpedto improvethemanuscript.
suggestions
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NOTES AND COMMENTS
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N.J.
FRED COOKE
DEPARTMENT OF BIOLOGY
QUEEN'S UNIVERSITY
KINGSTON, ONTARIO K7L 3N6
CANADA
PETER
DEPARTMENT OF MATHEMATICS AND STATISTICS
QUEEN'S UNIVERSITY
KINGSTON, ONTARIO K7L 3N6
CANADA
CHARLES
D.
TAYLOR
M.
FRANCIS
DEPARTMENT OF BIOLOGY
QUEEN'S UNIVERSITY
KINGSTON, ONTARIO K7L 3N6
CANADA
ROBERT F. ROCKWELL
OF
BIOLOGY
DEPARTMENT
CITY COLLEGE OF NEW YORK
NEW YORK, NEW YORK 10031
DEPARTMENT OF ORNITHOLOGY
AMERICAN MUSEUM OF NATURAL HISTORY
CENTRAL PARK WEST AT 79TH STREET
NEW YORK, NEW YORK 10024
SubmittedMarch 6, 1989; Revised June23, 1989; Accepted October 29, 1989
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