The Auk 111(1):115-123, 1994
LIFE-HISTORY CONSEQUENCES OF AVIAN
BROOD REDUCTION
DOUGLAS W. MOCK • AND L. SCOTT FORBES2
•Department
of Zoology,Universityof Oklahoma,
Norman,Oklahoma
73019,USA;and
2Department
of Biology,Universityof Winnipeg,
515 PortageAvenue,
Winnipeg,ManitobaR3B 2E9, Canada
ABSTP•CT.--Studiesof avian brood reduction characteristicallyfocus on the short-term
consequences
of hatching asynchronyfor offspring(e.g. number and sizesof fledglings),
but a truly comprehensive brood-reduction theory needs to incorporate long-term fitness
effectsfor parentsif trimming family sizeleadsto lessenedparentaleffortthereafter.A simple
model showsthat a brood-reductionstrategyis more likely to be favored by natural selection
when early lossesof one or more brood members in poor years (expedited by parental
manipulationof hatchingasynchrony)leadto significantlydiminishedparentalwork levels.
Field workers should designexperimentsto assess
the effectsof brood reductionon parental
work levels, parental survivorship, and/or future fecundity; they could do so simply by
borrowing the experimental field techniques already employed in studies of avian reproductive costs.Received9 February1993, accepted10 May 1993.
DAVID LACK(1947, 1954) suggestedthat parent birds may createmore offspring than they
can normally rear as a hedge againstuncertain
food. By starting incubation before laying has
been completed,parentshandicaplast-hatched
offspring, facilitating their selective elimination if food provesshort.Conversely,when food
is bountiful, the full brood may be reared.
Lack's hypothesis has attracted considerable
attention in recent years. Field testsare easily
performed,usuallyinvolving experimentalma-
important conceptual development, it was
quickly recognizedasbeing incomplete.In part,
its failure
variation
1966a, b, Charnov and Krebs 1974).
Although Lack's hatching-asynchronyhypothesis (usually called the brood-reduction
hypothesis,following Ricklefs 1965) predates
his clutch-size model, it has not undergone
similar scrutiny and amendment. Indeed, the
brood-reductionhypothesisper se receivedlittle formal theoreticalattention until relatively
recently (Ternroe and Charnov 1987, Forbes
1991a,b, Forbesand Ydenberg 1992,Pijanowski
intervals followed by measurementof the consequencesfor number and quality of surviving
offspring. The results of such work appear uneven and have spawned considerablecontroversy (Clark and Wilson 1981, Amundsen and
Stokland 1988, Magrath 1990, Amundsen and
Slagsvoid 1991, Pijanowski 1992, Konarzewski
Experimentson the value of hatching asynchrony have focusedmostly on how differing
reproductive strategiesaffect recruitment from
the current brood. In this regard they parallel
the literature on another classicLack hypothesis,his model of optimal clutch size. There he
suggestedthat parent birds should not maximize the number of nestlings in each breeding
attempt, but rather should maximize the number of offspring surviving to recruit into the
breeding population (Lack 1954, 1966, 1968).
Fundamental to this argument is a trade-off between the number and quality of offspring in
a given brood. Although few would argue that
Lack's clutch-size model did not represent an
for all observed
inspired refinements of the basic model, most
notably recognitionthat parental reproductive
costsmay favor smaller clutch sizes (Williams
nipulation of the normal pattern of hatching
1993, Forbes and Mock 1994).
to account
1992, Konarzewski 1993). These contributions
have added much-needed mathematical rigor
to the original argument, while exploring the
roles of environmental variability, sibling rivalry, predation, and egg failure, aswell as the
costof tracking variable resourceson the evolution of brood-reduction strategies.
Not surprisingly, field studies of hatching
asynchronyand brood reduction have maintained
the same short-term
focus. Lack's brood-
reductionhypothesisis characteristicallytested
by perturbing the degree of hatching asynchrony (the presumedparental manipulation),
then assessinghow broods with trimmed (and
sometimesexaggerated)hatching spreadscompare with sham-manipulatedcontrol broodsin
termsof fledgling production.The rationalefor
this protocol is simple: the Lack argument predicts that synchronized broods should exhibit
115
116
Moc•c ^•li• FORI•œS
greater nestling mortality and/or lower fledging mass (parents being less able to satisfy
demandsof evenly matchedsiblingsduring periods of food shortage) than normally asynchronous broods (reviewed in Magrath 1990;
Amundsen and Slagsvoid1991,Pijanowski1992,
Konarzewski 1993).
One problem with this approachis that, while
hatchingasynchronycertainly facilitatesbrood
reduction
when
food is short, it also has the
potential to trigger brood reduction unnecessarily, when food is relatively abundant, which
led Amundsenand Slagsvoid(1991)to question
whether such a brood-reduction pattern is
adaptive or maladaptive. Most recently, Pijanowski (1992)pointedout that deleteriousbrood
reduction may be an unavoidable cost of a
mechanism needed for tracking variable food,
a cost that is repaid when food is short.
In general the life-history consequencesof
avian brood-reduction strategiesremain virtually unexplored. For example, the effectsof manipulating hatching asynchrony on the future
successof parents have not been measured directly. The closestindirect approximations of
this dimension have involved measuring parental effort during the period of offspringprovisioning. Of the 30 experimental field studies
reviewed by Amundsen and Slagsvoid(1991),
only three measuredparental delivery rates
(Fujioka 1985, Gibbons 1987, Mock and Ploger
1987); the rest tacitly assumedparental effort to
hold steady.
Only modestempiricalconsiderationhasbeen
given to the postfledgingsurvival of the offspring themselves. Husby (1986) found that
postfledgingsurvivorshipof Black-billedMagpies (Picapica)declined when the normal course
of brood reduction was thwarted by replacing
dying or ejectedchicks.He suggestedthat early
brood reduction diminished the parents' burden, thus enhancingthe quality of subsequent
[Auk, Vol. 111
to broodswith normal asynchrony,which presumably helped the synchronizedchicksgrow
as rapidly as the privileged senior members of
control (normal) broods(Fujioka 1985). In a Tex-
as colony, although Cattle Egret parents similarly brought more food (againabout30%more)
to artificially synchronous and asynchronous
broodsthan to broodswith normal asynchrony,
fledging successwas highest in broods with
normalasynchrony(Mock and Ploger1987).The
natural (1.5-day) hatching interval apparently
promoted higher reproductive efficiency
(fledged chicksper unit of food) for the parents
than either a doubled interval (3 days) or complete hatching synchrony(0 days).
The roles of offspring synchronyon begging
competition and on parental responsesremain
little explored, but may be a key dynamic. Of
direct interest is Smith and Montgomerie's
(1991) study of nestling American Robins(Turdus migratorius),confirming the game-theory
prediction that offspring escalatebegging intensity to the level of their siblings(Parkerand
Macnair 1979,Harper 1986).Also,Slagsvoidand
Lifjeld (1989) reported that the body massof
female (but not male) Pied Flycatcher (Ficedula
hypoleuca)parents with asynchronousbroods
was heavier at the end of the nestling period
than that of motherswith more synchronized
broods,perhaps reflecting reducedwork levels.
Considerably more data underscore the relationship between offspring size at fledging
and their probability of recruitmentasbreeders.
Becauseeven slight incrementsof fledging mass
sometimes correlate with significantly enhanced long-term survivorship (Perrins 1964,
Gustafsson and Sutherland
1988, Smith et al.
1989, Magrath 1991), one is tempted to infer
that larger size is generally better. However,
becausethe effect of fledging masson offspring
fitness logically must be a decelerating function, identifying the precise functional relaparental care. Gibbons (1987) found that hatchtionship between body massand postfledging
ing asynchrony acceleratedthe onset of brood survivorship is key to measuring the relative
reduction in Jackdaws(Corvusmonedula),theresuccessof different brood-reductionstrategies.
by truncating "wasted" parental investment. Ideally, the effectsof hatching asynchronyon
Hahn (1981) similarly argued that hatching offspring via variation in offspring size at inasynchrony promotes early brood reduction, dependence(which may occur well after fledglesseningthe costof sibling rivalry in Laughing ing) would be measureddirectly by following
Gulls (Larusatricilla), although she addressed offspring until they recruit into the breeding
population.
only the benefits for current reproduction.
In Japan, Cattle Egret (Bubulcusibis)parents
Collectively, these results suggesta life-hisbrought considerably more food (about 30% tory dimension to Lack'sbrood-reductionhymore) to artificially synchronizedbroods than pothesis, the potential effectson the future re-
January1994]
BroodReduction
andLifeHistory
productive potential of parents. Some
explanationis requiredfor the factthat in many
brood-reducingspecies,parentsappear to expend submaximaleffort, even while somemem-
bersof the their current brood are dying. That
parents are, in a sense,withholding critical resources is evidenced by their demonstrated
117
serve parental interests.Here we offer a layered verbal argument, a conceptualmodel (presentedmore
formally in Appendix) that explores how parental
costsof reproductioncan affect the payoffsavailable
from this parental strategydichotomy (brood reduction vs. brood survival).
Our model can be summarized verbally as a fivepoint argument: (1) We use parental lifetime reproability to increasefood deliveriesdramatically ductive success(LRS) asour surrogatefor fitness(eq.
under some experimental circumstances;even 1 in Appendix);we assumethat any behaviortending
if they are being "tricked" (at the proximate to increaseLRS will be favored by selection.(2) LRS
level) by the testprocedure,their enhancedper- is the product of two factors,averageannual reproformancebetraysa higher investmentcapacity duction and averageannual survival (eq. 2-4 in Apin the short run. Here we presenta verbal and pendix). This tacitly assumesno variation in repromathematicalmodelthat revisesLack'shypoth- ductive successor survival as a function of adult age
esisto incorporate these parental patterns, and
use it to explore the consequencesfor broodreduction strategies.
(see Gustafssonand P•irt 1990). (3) Both of these factors (annual reproductive successand survival) depend, in turn, on two other facetsof interest: (a) the
proportion of "good" versus"bad" years;and (b) the
parental strategy being used (brood reduction vs.
brood survival). This is spelled out in eq. 5-8. (4) In
We explore two parental reproductivestragegies, comparing these two parental strategies, then, the
brood reduction option is favored if the LRS realized
which we shall refer to as brood survival and brood
reduction.Under the former,all offspringare created by adopting it is greater than that obtainable via the
equal (i.e. they are identical in size and hatch simul- brood-survival alternative (inequality 9). (5) The
A MODEL
taneously)andoneimaginesthatparentsareattempting to raiseall brood membersto independence.This
idealizedstrategyapproximatesthe patternof synchronoushatchingobservedin manybirds(although
in somespeciessiblingsdevelopvariouscompetitive
asymmetriesthereafter). By contrast,under a broodreductionstrategy,disparitiesin the timing of hatching and/or egg size result in mismatchesand, hence,
a competitivehierarchyamongbroodmembers.Here
the parentsare viewed asleavingopen the option of
a downward adjustmentin family size at somepoint
in the rearing process.
Therearemanyvariationson thethemeof hatching
spread.Perhapsthe mostcommonavian pattern, observed in many passerines,is intermediate: incubation commences
with the penultimateegg, resulting
in the final chickhatchinga day or two after its elder
siblings("semiasynchrony"
of Mock and Schwag-
brood-reductionstrategy,thus,canbe favoredby two
routes:it canwin outright (if badyearsaresocommon
that facultativepruning of family sizeactuallyyields
the higher average annual reproduction success)or
it can win in the long run by delivering a proportional
gain in adult survivalthat compensates
fully for any
short-termlossesin annual reproduction(inequality
10).
MODEL ANALYSIS
A simple numericalanalysisof the model can
illustratetheargument'spropertiesgraphically.
The reproductivesuccess
of parentsadoptinga
brood-survivalstrategyin a good year was set
at unity; presumably this delivers the best possible annual success. We assumed that the next-
meyer 1990). Often, the last-hatchedchick in such a best scorewould also occur during favorable
broodsuffersrelatively retardedgrowth and/or ele- conditions(by parents playing the brood-revated prefiedging mortality. More extremepatterns ductionstrategy),but that bad-yearconditions
of hatching asynchronyalso occur. For example, give an advantageto brood-reducingparents.
Green-rumped Parrotlets (Forpuspasserinus)lay In the Appendix model'sterminology,w(s, g)
clutchesof 5 to 10 eggsthat hatchover an average > w(r, g) > w(r, b) > w(s, b). The values for
span of 8.7 days (Beissingerand Waltman 1991). In
any case,it is beyond the scopeof our present treatment to considerthe effectsof differing magnitudes
theseparameters(seeFig. 1 legend) were chosen so that the payoffsfor brood reductionand
broodsurvivalare identicalwhen goodand bad
of offspringasynchrony.Rather,we simplycontrast
synchronous
and asynchronous
offspringstrategies years are equally probable (the probability of
goodyears,P, is 0.5), if we ignore parentalsurin a dichotomous
fashion.
Lack (1947, 1954) surmised that a measure of hatch-
ing asynchronyshould facilitate adaptive brood reduction during periodsof food shortage.Insofar as
asynchronyisunderparentalcontrol,itsdegreeshould
vival costs (i.e. brood survival is favored when
good years predominate [P > 0.5]; brood re-
ductionfavored when bad yearspredominate
[P -< 0.5]). We now examine the effect of a sur-
118
MOCK^NO FORI•ES
and brood survival yielded equivalentfitness
as the penalty for adoptinga brood-survival
1.00.9÷
'•o.8.
[Auk, Vol. 111
o.•
strategyin a bad yearrosefrom zero (Fig. 1).
Across all levels of maximum adult survival, the
level of P at which brood reduction and brood
survivalyield equivalentfitnessrosesharplyas
this penalty declined.That is, a steepincrease
in the frequencyof good yearsis required to
-• 0.4.
sustain a brood-survival strategy if there is a
significantpenaltyfor usingthatstrategyin bad
years.
0.2.
In the secondanalysis,we examinedthe relative fitnesspayofffor broodsurvival(Ws)ver0.0
0.5
016
017
0'.8
0'.9
1.0 susthat for brood reduction (WR)acrossvarying
frequencies
of goodyears.A simpleratio,Ws/
Proportion
of GoodYears
Fig. 1. Proportionof goodyears,P, requiredto
sustaina brood-survivalstrategy,given that parents
incur a mortality penalty for using that strategyin all
(1 - P) bad years. Four levels of maximum adult
survival are shown (0.5, 0.75, 0.90, and 0.95), values
that are realized only if all years are good (P = 1).
The survivalpenaltiesf(s, b) < f(s, g) = f(r, b) = f(r,
g) are thoseusedin Appendixeq. (9). Isoplethsindicatecombinationsof good-yearfrequencies(P) and
survivalpenalties(•s, b])at whichthe parentalstrategiesof broodreductionand broodsurvivalyield
equivalent fitnesses.Expectedrecruitmentparameter
valuesusedin generatingthesecurvesare:w(s, g),
for brood-survivalstrategy in good years, set at 1.0
(seetext); w(r, g), brood-reductionstrategyin good
WR, combines the payoffs, such that values
greater than 1.0 representan advantagefor
brood survival
and those less than 1.0 indicate
brood reduction'ssuperiority.Two levels of
maximumsurvival(fir, g] = f[s,g] = fir, b])were
examined: 0.95 (an annual survival rate corre-
spondingto long-livedseabird)and 0.50 (correspondingto short-livedpasserine).
Five levels of additive mortality costswere examined
for parentsusing the brood-survivalstrategy
duringbadyears(calculationexplainedin Fig.
2 legend).
Thisanalysisrevealstwo mainpoints(Fig.2).
First,broodsurvivalis lesslikely to prevailwhen
years,0.9;w(r,b)brood-reduction
strategy
in badyears, goodyearsarerare(i.e.when P is low). As the
penalty for choosingthe wrong (=brood-survival) parentalstrategyin a badyear(i.e.f[s,b])
declines,goodyearsneed not be sofrequentto
frequencyof badyearsrequiredto keepfitnesspayoff sustainthe brood-survivalstrategy.That is, the
0.6; and w(s, b), brood-survivalstrategyin badyears,
0.5. As the adult survival penalty for playing brood
survival in bad yearsdeclines,there is a sharprise in
of broodreductionashigh asthat for broodsurvival.
threshold value of P (where fitnessesfor brood
reduction and brood survival are equivalent)
vival penaltyimposedupon parentshavingthe
rises. Second, long-lived parents may pay an
misfortune (in the context of our model) to adopt
especially
steepfitness
penaltyforadoptingthe
survivalstrategyin badyears.Conversely,
such
penaltiesarelessimportantwhenadultsurvival
is low anyway.As BobDylan put it succinctly,
"when youain't got nothin'yougot nothin' to
a brood-survival strategy in a bad year.
For simplicity,we assumethat parental survival is compromisedonly by attempting the
labor-intensive brood-survival strategy when
conditions are bad--formally, when f(r, g) =
lose."So, short-lived parents(e.g. small passer-
f(s,g) = f(r, b) > f(s,b).Fourlevelsof maximum ines)arelikely to find additionalmortalitymore
annual parentalsurvivalwere examined(0.50, affordable than parents of longer-lived taxa
0.75, 0.90, and 0.95), bracketing the range of
adult survival rates for most birds (Lack 1966,
Botkinand Miller 1974).The penalty to parents,
(seabirds,large raptors,herons,etc.).
DISCUSSION
expressed
asa mortalitycostfor employingthe
brood-survival strategy in lean times, was ex-
Severalgeneralfacetsof parentalstrategyin
amined asdeparturesfrom thesemaximumval-
an uncertain world merit special consideration:
(1) the potential penalty parentsmay pay for
In the first analysis,we calculatedthe pro- being overly conservativewhen conditions
portion of goodyearsat which broodreduction proveto be good(e.g.hatchingasynchronously
ues.
January
1994]
Brood
Reduction
andLifeHistory
and sufferingunnecessaryoffspringlosses);(2)
the potential current-broodbenefit parentscan
reap from the samemeasurewhen conditions
prove bad; and (3) the benefits that asynchrony
can confer to parental survivorship.As the first
two have been explored extensively, both theoretically (Temme and Charnov 1987, Pijanowski 1992, Konarzewski 1993) and empiri-
cally(e.g.seereview by Magrath 1990),we shall
focus on the third.
119
1.2Maximum
Parental
Survival
= 0.95
1.o
•
Brood
S• rvival
Favored
Bro
Reduction
Favored
o.8-
0.4-
Where the effectsof variation in parental effort between
brood-reduction
and brood-sur-
vival strategiesare ignored, brood reduction is
0.2
,
0.0
0.5
1.0
favoredby selectiononly when the net effects
on recruitment from the current brood are positive (i.e. the left-hand side of Appendix eq. 7
1.2Maximum
Parental
Survival
= 0.50
of decreased work
levels associated with
off-
spring asynchronyare considered,we seethat
sucha strategycan be favored,even when the
net effects on recruitment
Bf
Brood
Su•,ival
Favored
is greater than 1.0). However, when the effects
1.0
B•ood
•
©o.sJ
c
Reduction
Favored
from the current brood
are negative, so long as this costis counterbalanced by enhanced parental survivorship.
Moreover, the simple numerical analysissuggeststhat associatingeven slight mortality costs
to a brood-survivalstrategymay have dramatic
effectson the relative payoffsfor brood-reduction versus brood-survival strategies, particu-
larly in taxawith normally high adult survival
rates.
The framework developed here suggeststwo
further questions.First, how hard should parents work under differing environmental conditions?Second,how do differencesin parental
work levels influence a parent's opportunities
for future reproduction?
No detailed empirical information existsrel-
evant to the first question. Certainly, parents
are known to abandon broods entirely when
conditions are disastrous(e.g. Kahl 1964), but
it would be of great interest to know if parents
adjusttheir effortson a continuousscale,working somewhatharderwhen food is moderately
short (e.g. Wright and Cuthill 1989). If so, do
parental costsof asynchronymanifest themselvesonly under bad conditions?Alternatively, do differencesin work levelsbetween synchronousand asynchronousstrategiesextend
across all food conditions?
•o.6.
0.4-
0.2
0.0
0.5
1.0
Proportionof GoodYears
Fig. 2. Relative fitnessesof brood-survivaland
brood-reductionstrategies(W•/W,•) with respect to
the proportionof good years(P) and the adult survival penalty paid by parentstrying brood-survival
strategyin bad years.When this relative fitnessratio
is greaterthan 1.0 brood survival is favored (upper
zones);when lessthan 1.0,brood reduction is favored
(lower zones).Top panel showscasewhere maximum
survival for parentsis very high (0.95, comparableto
that reported for large raptorsand seabirds),while
bottompanel showsparentalsurvivalrate typical of
passerines(0.50).The five curvesin eachfigure representimpactsof various mortality penaltieson parents endeavoringto use the brood-survivalstrategy
in bad years(i.e. f[s,b]),namely0.0 (no penalty),0.01,
0.02, 0.04, 0.08, and 0.16. These penaltiesare subtracted from maximum adult survivorship value (e.g. a
passerineincurringa penalty of 0.08 for trying the
brood-survivalstrategyin a bad year achievesa net
survival rate of 0.5-0.08 = 0.42). In both panels, increasedsurvival penalties enhance attractivenessof
brood reduction,but this is especiallytrue in the up-
The secondquestionhas not been addressed per graph (long-lived parentshave more to lose).In
directly either, although useful inferencescan general,asthesepenaltiesrise,the proportionof good
required to sustaina brood-survivalstrategy
be drawn from the burgeoning literature on years
increases.
clutch size and costsof reproduction(e.g. Williams 1966a, b, Charnov and Krebs 1974, Good-
120
Mooc ANDFORBES
man 1974, Nur 1984, 1988, Reid 1987, Gustafsson and Sutherland 1988, Linden and Moller
1989,Dijkstra et al. 1990,Magnhagen 1991,Hochachka 1992). Parents with experimentally increasedclutcheswork harder, which may result
in reduced parental survivorship and/or future
fecundity. Whether increased parental work
levelsassociated
with offspringsynchronyyield
similar
effects remains
to be established.
Exploring stochasticsystems, such as the
brood-reduction mechanismproposedby Lack,
presents formidable challenges to field workers. Without knowledge of the explicit rela-
[Auk, Vol. 111
enlargement experiments is that the manipulation may render the brood-reductionmechanism impotent. The adding of offspring is likely to have a greater relative impact on small
broods than on large broods (see O'Connor
1978). For example, increasing a sibship from 2
chicks to 3 createsroughly a 50% jump in total
brood needs,while increasingfrom 9 to 10 adds
only 11%. If a brood-reduction strategy were
pre-set for an expected range of supply/demand ratios, an experiment grossly exceeding
that range might easily produce dramatic, but
totally spurious, results.
tionship between the food supply/demand dynamic and the optimum clutch size, short-term
CONCLUSIONS
studies can generate results that appear to be
A life-history framework adds an important
firmly in supportof, or equally antagonisticto,
Lack's hypothesis. The chief benefits of brood dimension to the study of avian brood reducreduction are realized only when food is short tion, but it also makes the task for field workers
relative to brood needs,which may themselves more complex. It is increasingly clear that fitvary stochastically (e.g. due to capricious nessestimatesbasedsolely on short-term studweather; Sullivan and Weathers 1992). A comies (e.g.assessing
only success
of current brood)
prehensivetestof the brood-reductionhypoth- are inadequate. They cannot accountfor potenesis requires simultaneous proof that food is tially important effects of intrabrood differindeed both short and unpredictable (lest par- encesin nestling condition on the recruitment
ents make the necessaryadjustmentsto clutch prospectsfor individual offspring (see reviews
size). At present, it is customary merely to as- in Smith et al. 1989, Magrath 1991), nor can they
sume these conditions (but see Magrath 1989). accountfor effectson parentalsurvivorshipand/
Accordingly, reliance on natural variation in or future fecundity. The latter set of problems
food supplies to provide critical tests of the is easily addressed,however, by adopting the
brood-reduction hypothesis is risky in short- field techniques employed in studies of avian
term studies,although suchproblems diminish reproductive costs (e.g. Nur 1984, Reid 1987,
Gustafssonand Sutherland 1988, Dijkstra et al.
over the courseof long-term studies.
Experimental enlargement of brood size is 1990, Martins and Wright 1993).
In short, brood reduction represents but one
one techniqueusedto dodgethe tricky issueof
measuring the relationship between food sup- mechanismfor matchingvariable food supplies
plies and brood demands, the rationale being and demands, with parental effort being an inthat food shortage is more likely for larger tegral component of such systems(at least for
broods.While this assertionis undoubtedlytrue care-providing taxalike birds). Insufficient food
on average, brood enlargement by no means may imposecostsfor either parentsor offspring
guaranteesthe desired effect. Parents may still (or both). The extent to which hatching asynbe able to compensateby escalatingtheir efforts chrony provides relief to parents during periso as to meet the food demands of enlarged ods of food shortageby facilitating early brood
broods in a good (or even average) food year. reduction, however, remains little explored. We
Thus, parents may confound such experiments see this as a natural, albeit somewhat overdue,
by stepping up the rate of food deliveries to extensionof Lack'soriginal ideason clutch size
enlarged broods(seereview in Martin 1987) or and brood reduction; addressing these issues
by transferringthe intended costsof food short- will require the study of avian brood reduction
fails to themselves(e.g. by drawing down fat to be woven into the fabric of research on rereserves). Unless one takes the extra trouble to productive costsand clutch-size optimization.
assessparental effort and body condition, cau- Doing so will be an essential step in the detious interpretation must prevail.
velopment of a comprehensive,stochastictheA further disquieting feature of brood- ory of avian clutch size.
January1994]
Brood
Reduction
andLifeHistory
ACKNOWLEDGMENTS
121
parental investmentin the Jackdaw.J.Anim. Ecol.
56:403-414.
Thispaperwaspreparedunderpartialsupportfrom GOODMAN, D. 1974. Natural selection and a cost ceilthe NationalScience
Foundation(USA)(BSR9107246)
ing on reproductive effort. Am. Nat. 108:247-268.
to D.W.M. and NaturalScienceand EngineeringRe- GUSTAFSSON,L., AND W. J. SUTHERLAND. 1988. The
searchCouncil(Canada)to L.S.F.We thankT. Lamey,
costsof reproduction in the Collared Flycatcher
C. Lamey,T. Woser,B. Pijanowski,W. Hochachka,E.
Ficedula albicollis. Nature 335:813-815.
Licat,and especiallyP. Schwagrneyer
for comments GUSTAFSSON,L., AND t. PXRT. 1990. Acceleration of
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[Auk, Vol. 111
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(1)
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(3)
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Survivorshipof parentsto yearx, l(x), will be some
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On average,parentalsurvivorship
to yearx will be
1966a. Adaptation and natural se-
l(x) = f(i, g)•t'f(i,b)•'
lection. Princeton Univ. Press, Princeton, New
(4)
Substituting
equations(3) and (4) into equation(2)
Jersey.
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'"
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yields
E[LRS]
= • {w(i,
g)P
+ w(i, b)(1 - P)lf(i, g)"'f(i, b)'•.... , (5)
which rearrangesto
APPENDIX. The formal
model.
Becausethe strategiesof interest are behavioral
phenotypesof the parents,we use expectedlifetime
E[LRS]= [w(i, g)P
+ w(i,
b)(1
- P)]• f(i,g)•?f(i,
b)'•''".(6)
January1994]
Brood
Reduction
andLifeHistory
The secondterm on the right-hand side of equation
(6) is the sum of a geometricprogression.As n -->
this convergesto
resented as i in equation (8)], denoting the broodreduction
alternative
ternative
as s. Brood
brood
• f(i,g)'"f(i,
b).....' = 1/[f(i,
g)"f(i,
b)•'"']. (7)
Of course, parents do not live forever (as n =
implies), but this approximationintroducesonly a
small
error
because the terms
on the left-hand
side
of equation(7) becomevery smallasn increases.
Such
an allowancehasthe advantageof greatlysimplifying
the algebra.
Substitutingequation (7) into equation (6) yields
E[LRS] =
w(i, g)P + w(/, b)(1 - P)
1 - f(i, g)"f(i, b)....
(8)
We can now substitutefor the parentalstrategy[rep-
123
survival
as r and the brood-survival
reduction
will
be favored
alover
when
w(r, g)P + w(r, b)(1 - P)
1 - f(r, g)"f(r, b)I'
>
w(s, g)P + w(s, b)(1 - P)
I - f(s,X)"f(s,b)•' "• '
(9)
which rearrangesto
w(r, g)P + w(r, b)(1 - P)
w(s, g)P + w(s, b)(1 - P)
>
1 - f(r, g)"f(r, b)•'
I - f(s,X)•f(s,b)•' •,'
(10)