Clutch Sizes That Maximize Annual Fecundity of Multiple-Brooded Birds

The Auk 118(4):973-982, 2001

HOW MANY BASKETS? CLUTCH SIZES THAT MAXIMIZE ANNUAL FECUNDITY OF MULTIPLE-BROODED BIRDS

GEORGE L. FARNSWORTH • AND THEODORE R. SIMONS CooperativeFish and Wildlife Research Unit, Departmentof Zoology,North CarolinaState University, Raleigh,North Carolina27695, USA

ABSTRACT.--Wedeveloped deterministic models on the basisof nest survival rates and renestingbehavior capable of predicting annual fecundity in birds. The modelscalculate probabilitiesof fiedgingfrom oneto four nestswithin a discretebreeding season. We used thosemodels to addresstheoretical issues related to clutch size. In general,birds require at least one day to lay an egg, and many speciesdelay incubationuntil their entire clutch is laid. Becauseit takeslonger to completea larger clutch,and fewer suchclutches can fit into a limited breedingseason, there exists a clutchsize for whichannual fecundity is maximized. We asked,for a givenamount of reproductiveeffort (i.e. a setnumber of eggs),does the age- old maxim "don't put all your eggsin one basket" apply? If so, in how many "baskets" shoulda nestingbird placeits eggs?The answerdepends on both likelihoodof nestpredation and length of the breedingseason. Those results are consistentwith the observed increasein clutchsize with latitude (shorterbreeding season length) and largerclutch sizes characteristicof cavity-nestingspecies (with highernest survival rates). The modelsalso predict that the size of replacementclutches should decrease as the breeding season progresses, and that intraseasonaldecline in clutchsize shouldbe more pronouncedwhen the breeding seasonis short.Received 24 January2000, accepted24 April 2001.

ECOLOGISTSHAVE BEEN fascinated by factors vival rate of nests and the trade-off between constrainingavian clutchsize for more than 50 clutchsize and predationrisk. He estimatedfe- years. Lack (1947, 1954) proposedthat clutch cundity (?) as, size should reflect maximum number of young F = ns'•+L (1) that adults can raise. Most discussionsof optimal clutch size in birds have centered on pro- where n representsthe clutchsize, L is the num- ductivity of a single clutch of eggs,but some ber of days of incubationneeded to hatch the have looked at the influence of clutch size on eggs,and s is daily nest survival rate. We have lifetime reproductive success(for a recent re- changedPerrins' notation slightly to matchno- view, seeMonaghan and Nager 1997).Another tation used in our models.By taking the partial important measure of productivity is annual derivativewith respectto n, Perrinsrelated op- fecundity becausemany speciesattempt to nest timal clutchsize to daily survival rate of nests: more than once within a limited breeding sea- -1 son. In those species,length of the breeding (2) seasonmay be an important constraint on an- F/opt= ln(s) nual productivityleading to selectionon clutch For example,with a daily nest survival rate of sizes that maximize annual fecundity. 0.95, the predicted optimal clutch size is 19.5 Many birds lay one egg a day until their eggs. clutchesare complete and then begin incubat- The optimum predicted by Perrins' model ing. That means that larger clutchesare ex- would be reduced if daily nest survival rate posed to predatorsfor a longer period of time. were modeledto decreasewith larger clutches. For many species,predation usually resultsin Skutch (1949) hypothesized that larger broods loss of the entire clutch or brood (e.g. Wood have higher predation rates due to increased Thrush, Hylocichlamustelina; Farnsworth 1998). activity at the nest.He reasonedthat in altricial Perrins (1977) related optimal clutch size di- birds, more begging chicksand more frequent rectly to risk of predation.He proposeda math- feeding trips by adults could attract attention ematicalmodel based on a constantdaily sur- of predators. There has been some empirical supportfor the mechanismsof that hypothesis l E-mail: [email protected] (Mullin and Cooper 1998, Martin et al. 2000),

973 974 FARNSWORTHAND SIMONS [Auk, Vol. 118 but others have failed to find that (Roper and we investigatehow intraseasonalvariation in Goldstein 1997). Ricklefs (1977) developedan clutchsize may affect annual fecundity. optimalclutch-size model for singlenesting at- Other models have been developedto esti- tempts that incorporatedlower nest survival mateannual fecundity in multiple-broodedbird for larger clutchsizes. He concludedthat even species(Ricklefs 1970, Peaseand Grzybowski with higher predation rates on larger clutches, 1995),but thosehave not been appliedto ques- that alone was not likely to be a major factor tionsof optimal clutchsize. Ricklefs(1970) de- determining evolutionof clutchsize. velopeda modelthat convertedestimates of nest Departing from traditional inquiries about survival,season length, and renestingbehavior clutchsize at which fecundity of a singleclutch into estimatesof annualfecundity. It assumeda is a maximum, someinvestigators have exam- constantrate of nest initiation throughoutthe ined how clutchsize may affect lifetime repro- breedingseason. That rate was setequal to rate ductivesuccess. Lima (1987)developed a mod- of nest termination,keeping the number of ac- el in which an increase in clutch size was tive nestsat equilibrium.In this model,survival associatedwith an increasein predationrisk to rate of nestsdetermined the proportionof suc- nesting femalesas well as to their dependent cessfulnests and the averageduration of a nest- chicks,thus reducingher future reproductive ing attemptbecause higher predation rates in- potential.That modelshowed that underhigh creaseproportion of neststhat fail early in the nest-predationrates, smaller clutchsizes were nestingcycle. The resultingmodel calculated a more productive than larger clutchsizes. Mur- constantnumber of fledglingsproduced per day ray (1979)used an interestingapproach to evo- for a large population(see also Ricklefsand lution of clutch size by assumingthat females Bloom1977). Pease and Grzybowski(1995) de- are selected to produce the minimum clutch velopedan approachthat incorporated pulses of size necessaryto replacethemselves based on nestingactivity by allowing the numberof ac- the Euler-Lotkaequation. That model has pre- tive neststo fluctuatethroughout the breeding dicted clutch sizes close to those observed for season.Their modelapplied instantaneous rates at least two species(Prairie Warbler[Dendroica of nestpredation and brood parasitism in a con- discolor];Murray and Nolan 1989,and Florida tinuous-timemodel adaptedfrom VonFoerster Scrub-Jay[Aphelocoma coerulescens]; Murray et equations.The model does not assumea con- al. 1989), but the model also requires the as- stant rate of nest initiation throughout the sumption that larger clutchesincur a larger breedingseason. Our approachis basedon a survival cost to the female,reducing her pros- discrete-timeprobability model, roughlyanal- pectsfor future breedingsuccess. ogousto a specialcase of the modelof Peaseand All of those studieshave investigatedinflu- Grzybowski (1995) with constantparameters enceof clutchsize on either fecundity of a sin- and no parasitism.However, our model is ca- gle nestingattempt or lifetimefecundity of a fe- pable of limiting number of eggs a female can male. In this paper, our goal is to investigate lay per season;previous models have not in- the relationshipbetween clutchsize and a fe- cluded that potentially important constraint. male'sannual fecundity.We soughtto begin by Birds do not have unlimited resources(includ- using a minimum number of assumptions.We ing a limited time remaining in the breeding describe here two mathematical models that season),and that limitation may have implica- are capableof incorporatingthe renestingbe- tions for evolution of clutch size. havior of multiple-brooded species. These models do not invoke mechanisms that have di- MODEL DESCRIPTIONS rect negative effectson larger clutchessuch as thoseemployed by Ricklefs(1977), Lima (1987), Our approach is based on the assumption and Murray (1979). This approachprovides a that a nestingfemale will renestafter her nest new framework for testing ideas about clutch fails or she fledgesa brood, provided there is size. We use the models to find clutch size at enoughtime remainingin the breedingseason which annual fecundityis a maximum.We ex- to fledge anotherbrood (for a list of parame- amine how that optimal clutch size changes ters,see Table 1). The logicalformulation of the with changesin both the length of breeding model is as follows.A breeding femalebegins seasonand survival rate of nests.Additionally, the seasonwith an initial nesting attempt.She October2001] ClutchSize in RenestingBirds 975

TABLE1. Parametersused to calculateannual fecundity in multiple-broodedbird species.

Param- eter Value(s) Explanation L 25 days Lengthof nestingcycle from the time the last egg is laid to the time all chicks leave the nest d 8 days Number of daysbetween failure of one nest and first egg of subsequentnest D 14 days Numberof daysfrom a successfulnest to the first eggof subsequentnest t 60, 90, 120 days Length of breedingseason s 0.93, 0.95, 0.97 Daily nest survival rate n 1 to 30 eggs Clutch size rn 2,3,4 Maximum number of nesting attemptsper season

lays one egg each day until her clutch is com- all the independentways to attempt the ith plete. The nest is subjectto a constantproba- brood with a maximum of m nestingattempts. bility of predationevery day from the day the The annual fecundity is simply the product of first egg is laid. If the first nest fails, and there clutch size (n) and the sum of Pcfrom i to m. is enoughtime remainingin the breedingsea- Because P, represents the probability of son to complete another nest, the female will fiedgingat leasti nests,probability of failing to renesta set number of days later. Similarly, if fledge any young is i - P•. The probability of the first nest successfullyfledges young, and fiedgingi and only i nestsis P, - P,+•.Thus var- enough time remains in the season,the female iance of seasonalfecundity is will renesta setnumber of dayslater. The same rules apply any time a nest'sfate is determined, with an additional restriction that females are (•f2= • (El _ p,+l)(iFl _ F)2 (5) i=0 limited to a fixed maximum number of nests per season.The restriction on the maximum Model 1 assumptions: number of nesting attemptswas necessaryto 1. Clutch size is constant for all nests. evaluateannual fecundity for different strategies of laying the samenumber of eggswith a 2. A female nestsup to rn times if there is time uniform clutch size (e.g. three clutchesof four remaining in the breeding season. 3. Daily nest survival is constantand indepen- eggseach vs. four clutchesof three eggseach). dent. Nest survival doesnot vary during the Model /.--This model calculatesthe proba- breedingseason, for different nest stages,or bility of successfullyfledging one or more for different nests. broods (P) and the resulting annual fecundity 4. All eggs hatch and all chicksfledge in suc- (F) when the clutchsize (n) is constantthrough- cessful nests. out the season: 5. There is no adult mortality during the breeding season. P,= s"*L • R,,j (3) 6. The time it takes to initiate the subsequent nesting attempt doesnot vary.

= n P, (4) Model2.--We relaxedthe assumptionof con- •=1 stantclutch size to examinepossible advantag- The term sn+L is the probability of fiedging a es of having differentclutch sizes during the brood, and R,.i representsthe probabilitythat season.We allowed each of four possiblenest- therewill be enoughtime remainingin the sea- ing attemptsto have a different clutch size (n• sonfor the jth nest to fledge the ith brood. For to n4).All other assumptionsabove still apply example,RL3 is the probability the first two at- to that model.With that approach,it is no lon- tempts fail with enough time remaining to ger useful to have the parameter m or to cal- completea third nestingattempt. R,.j incorpo- culateP, becauseclutch sizes will vary with dif- rates the ability to renest as well as the con- ferent ways a female can fledge i broods. The straintsof the limited breeding season(see Ap- new estimate of annual fecundity can be cal- pendix for detailed calculations). The culated directly as: summation7Z•,R,.j is thesum of probabilities of 976 FARNSWORTHAND SIMONS [Auk, Vol. 118

um clutches, or four small clutches. We asked: j •,j for a given level of reproductiveinvestment, •=l j=• measured as the total number of eggs laid, The nestingcycle (n• + L) now dependson which strategyyields highestannual fecundi- clutch size of a particular nesting attempt be- ty? Resourcesavailable to a breeding female causeit takesone day to lay eachegg of the jth are limited, and it is reasonable to assume that clutch (n•). The expectednumber of chicks thoselimits constrainnumber of eggsa female fledged from the jth nesting attempt is the can lay (sensuMilonoff 1989). Using the same productof the clutchsize (n) and probability valuesfor daily survival rate (s = 0.95), we ex- the nest will survive for the length of the jth amined expected fecundity for a female re- nestingcycle (n• + L). The calculationsof R,,•in strictedto laying a maximumof 12 or 24 eggs model 2 incorporatean approximationfor the with a breedingseason length (t) of 60, 90, and probability of renesting (see Appendix for 120 days.We used the samemodel parameters details). to examine effect of different nest survival rates on optimal clutchsize. Using the moderatesea-

METHODS son length (t = 90 days),we examinedannual fecundityfor daily nestsurvival rates (s = 0.93, We evaluated the model for a variety of pa- 0.95, and 0.97). rameter valuestypical of natural populations. Model 2 with no limit on numberof eggs.--We For all models tested, we used the same values computedthe optimal strategyfor eachof the for three parameters(Table 1). The value used nine combinationsof seasonlength and nest for L (25 days) is realisticfor a taxonomically survival rate in the absenceof any limitation on diversearray of bird species,including preco- total number of eggs.We testeda broad range of combinations of clutch size for each of the cial as well as altricial species.For precocial species,L canbe definedas length of time from four nestingattempts. onsetof incubationto hatchingof the eggs(e.g. Model2 with limitednumber of eggs.--In a sim- for Northern Bobwhite [Colinusvirginianus], L ilar manner,we comparedexpected annual fe- = 24 days,and Mallard [Anasplatyrhynchos], L cundity from differentstrategies of laying a set = 26-29 days;Baicich and Harrison 1997).For number of eggs without the restricting as- altricialspecies, L representsaddition of thein- sumptionthat all clutchesare the samesize. cubationstage and the nestlingstage (e.g. for Carolina Wren [Thryothorusludoviscianus], and RESULTS Wood Thrush, L = 26 days;Baicich and Harri- son 1997).The valuesused for the renestingin- Model1 with no limit on numberof eggs.--Un- tervals (d = 8 and D = 14 days)are typical for der the assumptionsof model I with no addi- speciesthat renest quickly such as the Prairie tional constraints, there exists a maximum ex- Warbler and Black-cappedVireo (Vireoatricap- pected annual fecundity of 5.13 chicks at a illus;Pease and Grzybowski 1995). The values clutchsize of 13 eggs(Fig. 1) when the season for breeding seasonlength (t) and daily nest was 90 days long and survival rate was 0.95. survival rate (s) were chosen to represent a Probability of fledging at least one nest was range of possibilitiesin order to examine 0.375, and probability of fledging two nests trendsin optimal clutchsize. was 0.020. Peak annual fecundity from single- Model 1 with no limit on numberof eggs.--We brooding alone was 5.02 chicks,which oc- computedannual fecundityfor a hypothetical, curred at a clutchsize of 16 eggs.Both proba- multiple-broodingspecies with a breedingsea- bility of fledgingzero chicks(e.g. 1 - P• = 0.625 son (t) of 90 daysand a daily nest survivalrate for n = 13 and I - P• = 0.686 for n; 16) and (s) of 0.95. We allowedbreeding females to at- the variance(e.g. cr2; 47.2 for n = 13 and cr2; tempt a maximum of four nests,and we varied 55.1 for n = 16) was higher for larger clutches. the clutchsize from 5 to 20 eggs. Model 1 with limited numberof eggs.--When Model 1 with limitednumber of eggs.--Tofur- number of eggswas limited, smaller clutches ther examine trade-offs between clutch size and were more productivethan large clutchesfor annual fecundity,we compareddifferent nest- both long breeding seasons(Fig. 2) and low ing strategies:two large clutches,three medi- survival rates (Fig. 3). With a seasonallimit of October2001] ClutchSize in RenestingBirds 977

• Clutch size = 3 eggs broods brood MultipleOnly one -11- Clutch size = 4 eggs possible possible -.0-- Clutch size = 6 eggs

, 5 10 13 15 20 Short(60 days) Medium(90 days) Long(120 days)

Clutch Size

F•G. 1. Expected annual fecundity versus clutch size for a bird with seasonlength (t) of 90 days,and daily nest survival (s) of 0.95. The dotted line represents the optimal clutch size. This occurs at the maximum clutch size for which double-broodingis •"•"• -•-Clutch size=6eggs possible(13 eggs). -I1- Clutch size = 8 eggs ß.0-- Clutch s•ze = 12 eggs

Short(60 days) Medium(90 days) Long(120 days) 12 eggs,a clutchsize of 6 eggs(2 clutches)produced the maximum number of fledglings Breeding Season Length when the seasonlength was 60 days long (F,=6 = 2.05, F,=4 = 1.73, F,•=3 = 1.40). A clutch size FIG.2. Annual fecundityversus season length for of 4 eggs (3 clutches)produced the maximum different ways to lay a maximum of (A) 12 eggsand when the seasonwas 90 dayslong (F,=6= 2.45, (B) 24 eggs. Daily nest survival was constant(s = 0.95). Triangles represent a maximum of rn = 4 F,=4 = 2.51, F,-3 = 2.25). And a clutch size of 3 clutches,squares rn = 3 clutches,and circlesrn = 2 eggs (4 clutches)produced the most fledglings clutches. Annual fecundity is higher for smaller when the seasonwas 120days long (F,=o= 2.45, clutch sizes as the length of the breeding season F,=4 = 2.71, F,,_3= 2.72). When the breeding increases. seasonlength was held constantat 90 days to investigateeffect of survivalrate, maximum expected fecundity was achievedwith a clutch size of 4 eggs (3 clutches)at survival rates of 0.93 and 0.95. A clutchsize of 6 eggs(2 clutch- clutchsizes were moreproductive when breed- es) was most productive with a nest survival ing seasonswere long (Table2). rate of 0.97. A similar result was achieved when Model 2 with limited numberof eggs.--When total number of eggsa female could lay was re- total number of eggslaid was restrictedto ei- strictedto 24 eggs.With a shortseason, the best ther 12 or 24, the sametrend in optimal clutch strategywas to lay two clutchesof 12 eggs.A size was apparent (Table 2). Longer seasons moderatebreeding season favored three clutch- and higher levels of nest predation favored es of 8 eggs, and a long seasonfavored four more nesting attemptswith fewer eggsin each clutchesof 6 eggs.When the seasonlength was clutch. When breeding seasonwas short and held at 90 days, the largest clutchsize (n = 12, levelsof nest predationwere low, the mostpro- m = 2 clutches)was most productive at the ductive strategyhad large initial clutchesand highestsurvival rate (s = 0.97) and the smallest small replacementclutches with no eggs re- clutchsize (n = 6 eggs,m = 4) was most pro- servedfor the third or fourth nestingattempt. ductive at the lowest nest survival rate (s = In general, longer seasonsfavored clutchesof 0.93). more uniform size. The two scenarios with the Model2 with nolimit onnumber of eggs.--Larg- longest seasonand lowest survival had maxi- er clutcheswere more productive when nest mum productivity when clutchsizes were uni- survival rates were high, and more uniform form (n• = //2 = n• = n4). 978 FARNSWORTHAND SIMONS [Auk, Vol. 118

TABLE2. Nesting strategiesthat maximize annualfecundity. Total number of eggslaid per year was unlimited or restrictedto either12 or 24 eggs.For each combination of seasonlength and daily nestsurvival rate, we report the most productivecombination of clutchsizes (n•-n4). Optimal clutcheswere smallerand more uniform throughoutthe seasonwith longer seasonsand lower nest survival.

60 daysseason 90 day season 120 day season Daily nest survival n• //2 //3 //4 //1 //2 //3 //4 //1 //2 //3 //4 Unlimited number of eggs per season 0.93 14 10 6 3 13 13 11 9 14 13 13 12 0.95 19 11 6 3 19 17 13 9 18 18 16 13 0.97 33 12 7 3 33 22 15 10 28 28 17 15 Number of eggs limited to 12 per season 0.93 6 5 1 0 4 4 3 1 3 3 3 3 0.95 8 4 0 0 5 5 2 0 4 3 3 2 0.97 11 1 0 0 6 6 0 0 4 4 4 0 Number of eggs limited to 24 per season 0.93 11 9 4 0 7 7 6 4 6 6 6 6 0.95 14 8 2 0 9 9 5 1 7 7 6 4 0.97 18 6 0 0 12 11 1 0 9 6 6 0

DISCUSSION enoughto increasethe expectedannual fecundity abovethat producedby larger clutches.A We developedmodels to predict clutchsizes 90 day seasonwas not long enoughto allow that maximize annual fecundityof birds capa- double-broodingfor clutches> 13 eggs.Annual ble of renestingwithin a limited breedingsea- fecundity from clutchesof 16 eggs(F = 5.02, •r2 son. The advantageof that approachis that the = 55.1) was closeto that for 13 eggs(F = 5.13, measureof annual fecundity is more ecologi- •r2 = 47.2), but larger clutcheshad a higher cally relevantthan fecundityof a singlebrood probability of complete reproductive failure for such bird species.Other investigationsof (fledge zero young for the whole season)and optimal clutchsize have invoked compensatory higher variance.In that case,the most produc- mechanismsthat havedirect negative effects on tive strategywas alsothe saferstrategy. It may fitness value of larger clutches,either by in- be beneficialfor a femaleto employa bet-hedg- creasingpredation rates on larger clutches(e.g. ing strategy by laying eggs in several small Ricklefs1977) or by reducingfuture reproduc- clutches,increasing the probabilitythat at least tive potentialof adults(e.g. Lima 1987,Murray one of the nestswill fledge young. 1979). Although we do not dispute those po- That model alsoproduced interesting results tential mechanismsmay be importantfor many species,it is important to understand how the when we limited number of eggs a female optimal clutch size varies without thosemech- could lay annually. The age-old maxim, "don't anisms. Our approach should serve as a new placeall your eggsin onebasket," presents the framework in which to test those and related question:in how many "baskets"should a fe- ideas. male place all her eggs?For a nestingbird, the Applying a model with uniform clutchsize answerappears to dependon both the length (model 1) to a hypotheticalmultiple-brooded of the nestingseason and survival rate of nests. bird species,we found that the selectivepres- Shorterseasons (Fig. 2) and higher nestsurviv- suresof nestpredation and seasonlength alone al rates(Fig. 3) favor a nestingstrategy of few- can produce clutch sizes typical of many spe- er, larger clutches.Although absolute fecundity cies of precocial birds. When the only con- estimatesare sensitiveto values of the param- straint on the productionof eggswas a limit of eters used, the predicted trends are not. With a four nestingattempts per season,the predicted breeding seasonof 120 days, a clutch size of optimal clutchsize was 13 eggs(Fig. 1). In that three eggs is only slightly more productive case, even though probability of successfully than a clutchsize of four eggs(Fig. 2A). How- fledging two broods was only 2%, it was ever, for even longer breeding seasons,the fe- October2001] ClutchSize in RenestingBirds 979

,Q and nonbreedingseason productivity of the en- vironment.A harsh nonbreedingseason allows the few survivorsaccess to a rich food supply during the breeding season. That seasonal abundanceallows birds to lay large clutches 2, ß•' ' • Clutchsize = 3 eggs and raise large broods(Ricklefs 1980). The sea- -r•- Clutchsize = 4 eggs sonality hypothesisaccounted for latitudinal -'•).. Clutchsize = 6 eggs trendsbut failed to explaindifferences between

o cavity and open-cup nesters. Martin (1993) ß o proposed that the large clutch sizes observed O.93 O.95 0.97 for cavitynesting species was not due to higher nest-survival rates, but was instead due to the

¸ need for nonexcavatingspecies to maximize 7 their fecundityfrom limited nest sites.In general,nonexcavating species have larger clutches 5 than those speciesthat excavatetheir own cav-

4 ities. Our models predict both trends in clutch

3 Clutch size = 8 eggs sizeas a functionof breedingseason length and nest survival rate. Larger clutchesare favored 2 Clutchs•zesize= 612 eggseggs as breeding seasonlength decreases(as with

o increasinglatitude, Fig. 2) and as nest survival O.93 O.95 O.97 ratesincrease (as for cavity nests,Fig. 3). Perhaps the most interesting result of our Daily Survival Rate model is that althoughsmaller clutch sizes will FIG. 3. Annual fecundity versus daily nest sur- neverachieve the maximumfecundity possible vival for differentways to lay a maximumof (A) 12 with larger clutches,the constraintsof season eggsand (B) 24 eggs.Season length (t = 90 days), length and nest survival can make smaller nestingcycle (L = 25 days), and renestingintervals clutchesmore productive on averagethan larg- (d = 8 and D = 14 days) were held constant.Trian- er clutches.For example,in Figure 2B, with a glesrepresent a maximumof rn = 4 clutches,squares seasonlength of 120days, there is enoughtime rn = 3 clutches, and circles rn = 2 clutches. Annual to raise two broods of 12 eggs(solid circles)but fecundityis higherfor larger clutchsizes as the daily not enoughtime to raise three broodsof 6 eggs survival of nests increases. (solidtriangles). Thus, the maximumfecundity is 24 chickswith the larger clutchsize, but the maximumfecundity is only 12 chickswith the cundity of a strategy employing three-egg smallerclutch size. It appearsthe probability of clutchesoutpaces that for four-egg clutches. completingtwo attemptsof 12 eggsis too low Thus the trendis clear:longer breeding seasons to compensatefor the chanceof fiedging zero favor more attemptsof smallerclutches. chicks.Even when a femaleis capableof laying That result may help to explain two well- 24 eggs,she is betteroff trying to raiseonly 12 documented trends in clutch size. Clutch size chicks (6 at a time), and saving the other 12 generallyincreases with latitude, and species eggs for renesting after nests fail. In fact, the that nest in cavitieshave larger clutchesthan model predicts that -23% of the time, females open-cup nesters (Lack 1947, Klomp 1970). with a clutchsize of 6 eggswill not lay themax- Lack suggestedthe increasein clutchsize with imum of 24 eggsper season. latitude reflected increasingbreeding season We also found interestingpatterns when we day length and, hence,more foragingtime for allowedclutch size to vary during thebreeding birds nesting farther north. However, that ex- season(model 2). Milonoff (1989, 1991) exam- planation failed to account for a similar in- ined effect of different sizes of replacement crease in clutch sizes of nocturnal owls. Anoth- clutcheson annualfecundity, and showedthat er theory to explain the trend was offeredby higher predation rates favor smaller initial Ashmole (1963), who proposedthat clutchsize clutchesfor precocialbirds capable of renesting was determinedby differencesin the breeding onceor twice.When the first nestis morelikely 980 FARNSWORTHAND SIMONS [Auk, Vol. 118 to fail, a female should save more resources for A½KNOWLEDGMENTS renesting. Our results agree with the predic- We thank Jeffrey Brawn, Steve Ellner, JamesGil- tions of Milonoff's renesting hypothesis and liam, Martha Groom,Kate Lessells, Jeremy Lichstein, extendthe approachto examineeffects of a lim- JuanManuel "Pajaro" Morales,Ian Newton, Sumita ited breeding seasonand multiple-brooding. Prasad, Robert Ricklefs, Vanessa Sorensen, and Allowing clutchsize to vary during the breed- anonymousreviewers for their thoughtfulcomments ing seasonproduced a trend toward smaller on earlier versionsof this manuscript. and more uniform clutchesas breeding season length and nest predation rates increased(Ta- LITERATURE CITED ble 2). Shorter breeding seasons,lower nest predation rates, or both favored fewer nesting ARCESE,P., AND J. N.M. SMITH.1988. Effects of pop- attempts,larger initial clutches,and smallerre- ulation density and supplementalfood on replacementclutches. Slagsvoid (1982) described productionin SongSparrows. Journal of Animal Ecology57:119-136. a similar patternwith empiricaldata. He found ASHMOLE,N. P. 1963. The regulation of numbersof that specieswith short breeding seasonsand tropical oceanicbirds. Ibis 103b:458-473. low nest-predation rates in Switzerland typi- BAICICH, P. J., AND C. J. O. HARRISON. 1997. A Guide cally exhibited seasonaldeclines in clutchsize. to the Nests,Eggs, and Nestlingsof North Amer- We acknowledgethat factorsother than sea- ican Birds, 2nd ed. AcademicPress, San Diego, sonlength and nest survival ratescan influence California. avian clutch size (see reviews by Monaghan FARNSWORTH,G. L. 1998. Nesting successand sea- and Nager 1997, Klomp 1970). In addition to sonalfecundity of the Wood Thrush,Hylocichla the ideas involving direct costsassociated with mustelina,in Great Smoky Mountains National Park. Ph.D. dissertation, North Carolina State large clutches, such as those proposed by University,Raleigh. Skutch(1949), Lima (1987), and Murray (1979), FOSTER,M. 1974. A model to explain molt-breeding other constraints on optimal clutch size are overlap and clutchsize in sometropical birds. likely. For example,field studieshave demon- Evolution 28:182-190. strated effects of supplemental feeding and KLOMP, H. 1970. The determination of clutch-size in maternal effectson clutchsize (e.g. Arseceand birds. A review. Ardea 58:1-124. Smith 1988, Schluter and Gustafsson 1993, Na- LACK,D. 1947. The significanceof clutch-size.I and ger et al. 1997). Renestingintervals are proba- II. Ibis 89:302-352. bly not independent of clutch size as we as- LACK,D. 1954. The Natural Regulation of Animal Numbers. Clarendon Press, Oxford. sumed in our models. in Great Tits (Parus LIMA, S. T. 1987. Clutch size in birds: A predation major), renesting intervals increased when perspective.Ecology 68:1062-1070. clutcheswere artificially enlarged,presumably LOMAN, J. 1982. A model of clutch size determination reflectinghigher costsof raising larger broods in birds. Oecologia52:253-257. (Slagsvoid 1984, Tinbergen 1987). Similarly, MARTIN, T. ]•. 1993. Evolutionary determinants of longer renestingintervals may reflect the ad- clutch size in cavity-nestingbirds: Nest preda- ditional time it takes females to accumulate re- tion or limited breeding opportunities.Ameri- serves for larger replacementclutches (sensu can Naturalist 142:937-946. MARTIN, T. E., P. R. MARTIN, C. R. OLSON,B. J. HEI- Loman 1982). Other factors,such as molt, may DINGER, AND J. J. FONTAINE. 2000. Parental care also influence amount of time available for and clutch sizes in North and South American breeding. Tropical species may extend the birds. Science 287:1482-1485. breeding seasonby overlapping molting and MILONOFF,M. 1989. Can nest predation limit clutch breeding, allowing many nesting attempts size in precocialbirds? Oikos 55:424-427. with small clutches(Foster 1974). Although in- MILONOFF,M. 1991.Renesting ability and clutchsize corporationof those factorsmay make models in precocialbirds. Oikos 62:189-194. more realistic, we do not believe that our sim- MONAGHAN,P., AND R. G. NAGER.1997. Why don't plifying assumptionsalter the fundamentalre- birds lay moreeggs? Trends in Ecologyand Evo- lution 12:270-274. lationship between clutch size, length of the MULLIN,S. J., AND R. J. COOPER.1998. The foraging breeding season,and nest survival rates. Ex- ecology of gray rat snake (Elapheobsoleta spilo- amining dynamics of more complex models ides)--Visual stimuli facilitate location of arbo- should provide valuable insights into the fac- real prey. American Midland Naturalist 140: tors constrainingannual fecundity in birds. 397-401. October2001] ClutchSize in RenestingBirds 981

MURRAY,B. G. 1979. Population Dynamics: Alter- T,,j = t- (j - i)d - (i- 1)D - ic. (7) native Models. Academic Press, New York. MURRAY, B. G., AND V. NOLAN. 1989. The evolution The probability of attemptingthe jth nest, which, if of clutch size. I. An equationfor predicting successful,would fledge the ith brood, can then be calculated as: clutch size. Evolution 43:1699-1705. MURRAY, B. G., J. W. FITZPATRICK,AND G. E. WOL- FENDEN. 1989. The evolution of clutch size. II. A =Is 0 ')' (1 - s)•-'G,,j,T,,•-> 0 test of the Murray-Nolan equation.Evolution 43: R,,•[0, elsewhere,(8) 1706-1711. where c is the length of the breedingcycle (c = n + NAGER, R. G., C. ROEGGER,AND A. J. VAN NOORD- L). R,,•sums the probabilitiesof all the possibleways WIJK.• 997. Nutrient or energylimitation on egg to succeed i - i times and fail j - i times, with formation:A feedingexperiment in Great Tits. enough time remaining in the breeding seasonto Journalof Animal Ecology66:495-507. completeanother nest. If T,,jis <0, thenR,,j = 0 be- PEASE,C. M., ANDJ. A. GRZYBOWSKI.1995. Assessing causethe breeding seasonis too short to accommo- the consequencesof brood parasitismand nest date i completenesting cycles and the renestingde- predation on seasonalfecundity in passerine laysassociated with fiedgingi - i broodsand failing birds. Auk 112:343-363. j - i times.If T,,•-> 0, G,,•accounts for all the possible PERRINS,C. M. 1977.The role of predation in the evo- independent ways to renest within the limited sea- lutionof clutchsize. Pages 181-191 in Evolution- son.When a femalehas not failed in any nestingat- ary Ecology (B. M. Stonehouseand C. M. Per- tempt (j = i, i = i to 4), rins, Eds.). University Park Press, Baltimore, Maryland. G,,j= i (9) RICKLEFS,R. E. 1970. The estimation of a time func- All femaleswith enoughtime left in the seasonwill tion of ecologicaluse. Ecology 51:508-513. renestwith a probability of one. When a female fails RICKLEFS,R. E. 1977. A note on the evolution of clutch onceduring the breeding season(j = i + 1, i = i to size in altricial birds. Pages193-214 in Evolu- 3), tionary Ecology (B. M. Stonehouseand C. M. Perrins,Eds.). University Park Press,Baltimore, mln[T•/,c 1] Maryland. C,,j=i • sx (10) x-0 RICKLEFS,R. E. 1980.Geographical variation in clutch size amongpasserine birds: Ashmole'shypoth- Becauseone of the nestsfailed, the femalelost x days esis. Auk 97:38-49. during which that nest remained active. The sum- RICKLEFS,R. E., ANDG. BLOOM.1977. Components of mation term in Equation (10) accountsfor thoselost avian breeding productivity. Auk 94:86-96. days.Number of daysthat can be lost is limited by ROPER,J. R., AND R. R. GOLDSTEIN.1997. A test of the eitherthe lengthof the breedingseason (T,,•) or by Skutch hypothesis:Does activity at nests in- numberof days in the breedingcycle (c - 1). If the creasenest predation?Journal of Avian Biology failed nest were to have survived c days, it would 28:111-116. have fledged.When a femalefails twice during the SCHLUTER, D., AND L. GUSTAFSSON.1993. Maternal breedingseason (j = i + 2, i: 1 to 2), inheritance of condition and clutch size in the Collared Flycatcher.Evolution 47:658-667. rmmlTij,c SKUTCH,A. F. 1949. Do tropical birds rear as many G,,,=(2i- 1)b •0 (x+ 1)s •' young as they can nourish. Ibis 91:430-455. SLAGSVOLD,T. 1982. Clutch size variation in passer- + • (2c- y)sv (11) ine birds: The nest predationhypothesis. Oec- y=c ologia 54:159-169. mtn[T•/,2c2] ] SLAGSVOLD,T. 1984. Clutch size variation of birds in The x and y termsin Equation(11) representnumber relationto nestpredation: On the costof repro- of days lost during the previoustwo failed nests. duction.Journal of Animal Ecology53:945-953. Now that number of lost days are divided between TINBERGEN,J. M. 1987. Costsof reproductionin the two nestingattempts, the upper limit (other than the Great Tit: Intraseasonal costs associated with length of the breedingseason) is 2c - 2 becausenei- brood size. Ardea 75:111-122. ther of the two nests could have remained active longer than c days. The first summationterm accounts AssociateEditor: J. Brawn for all the ways theselost daysmay be divided into the two failed attemptsup to c - i days.The second APPENDIX. We defineT,,j as the maximumnumber summation term is necessaryto correct for the fact of days remaining in the breeding seasonwhen j that oncethe total numberof lost daysis greaterthan nestshave been attemptedand i nestshave succeed- c, there are fewer waysto divide thesedays between ed. Thus, two nesting attempts. Finally, when a female has 982 FARNSWORTHAND SIMONS [Auk, Vol. 118 failed three times during the breeding season(,j = 4, tion (12) is the same as that for Equations(10) and i= 1), (11). The details are more complicatedbecause the number of lost days must now be divided among mln(Tt'4'c-1)X2 -t- 3x + 2 GL4= Z SX three failed nesting attempts. x-o 2 Model 2. To allow for variable clutch sizes within a rain(T1,4,2c 2) season,we defined a new parameter,cj, as the aver- y-c age length of the nestingcycle for the first j nesting attempts.When the values for cjare used in themod- el, they are rounded to the nearestinteger because XIy2 +3y2 +2 the minimum time-step is a whole day. We substi- tuted thenew parametercj for c in Equation(7) such -- $y that: 3(y--c)2+ 3(y--2 c)+2) T,,,= t- (j- i)d- (i- 1)D - (i- 1)c•_• m•n(T1,4,3c 3)

z--2c 1 - (n, + L) (13) All the c terms in Equations (8-12) are simply re- (3C -- Z -- 3)2 + 3(3C -- Z -- 3) + 2 placedby c•_•.This is becausethe limitationdue to 2 the lengthof the season(T,,) mustinclude the length (12) of thejth nestingcycle (nj + L),but thecalculation of there-nesting limits (R,,j and G,,) is onlyrestricted by The termsx, y, and z are the total numberof dayslost the nestingcycle of the previous(j - 1) nestingat- during the three unsuccessfulnesting attemptsbe- tempts,here modeled as the averageof thosenest cy- fore attemptingthe fourth nest. The logic for Equa- cles(cj •).