Costs of reproduction: assessing responses to brood size ...

Journal of Applied Statistics, Vol. 29, N os. 1- 4, 2002, 407- 423

Costs of reproduction: assessing responses to brood size manipulation on life-history and behavioural traits using m ulti-state capturerecapture models

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BL ANDINE D OLIG EZ , JEAN CLOBERT , R ICHA RD A. PETTIFOR , 2 3 M ARCU S ROW C LIFFE , LA RS G US TAFSSON , CHR ISTOPH ER M. 4 4 1 PERR INS & RO B IN H . M C CLEERY , Laboratoire d’ E cologie CN RS -U M R 2 7625, UniversiteÂ Pierre et M arie C urie, Paris, France, Institute of Zoology, London , 3 4 UK, Evolutionar y B iology Centre, Uppsala University, Sweden and E dward Grey Institute, Oxford, UK

abstract

Costs of reproduction are fundamental trade-oþ s shaping the evolution of life histories. There has been much interest, discussion and controversy about the nature and type of reproductive costs. The manipulation of reproductive eþ ort (e.g. brood size manipulation) may alter not only life-histor y traits such as future adult sur vival rate and future reproductive eþ ort, but also behavioural decisions aþ ecting recapture /resighting and dispersal probabilities. We argue that many previous studies of the costs of reproduction may have erroneously concluded the existence or non-existence of such costs because of their use of local retur n rates to assess sur vival. In this paper, we take advantage of the moder n multistate capturerecapture methods to highlight how the accurate assessment of the costs of reproduction requires incorporating not only recapture probability, but also behavioural `state’ variables, for example dispersal status and current reproductive investment. The inclusion of state-dependent decisions can radically alter the conclusions drawn regarding the costs of reproduction on future sur vival or reproductive investment. We illustrate this point by re-analysing data collected to address the question of the costs of reproduction in the collared ¯ ycatcher and the great tit. We discuss in some detail the methodological issues and implications of the analytical techniques. Correspondence: B. Doligez, Laboratoire d’ Ecologie CNRS-UM R 7625 , UniversiteÂ Pierre et M arie Curie, 7 quai Saint Bernard, BaÃ tim ent A 7eÁ me eÂ tage, Case 237, F-7525 2 Paris, Cedex 05, France. Present address: U niversity of Bern, Institute of Zoology, Evolutionary Ecology, Baltzerstrasse 6, CH-3012 Bern, Switzerland. E-mail: blandine.doligez@ esh.unibe.ch ISSN 0266-476 3 print; 1360-053 2 online/02/010407-1 7 DOI: 10.1080 /02664760 12010884 5

© 200 2 Taylor & Francis Ltd

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1 Introduction Trade-oþ s linking life-history traits constrain their sim ultaneous evolution, and are therefore fundamental to the understanding of the evolution of life histories (Roþ , 1992; Stearns, 1992). Trade-oþ s arise when two traits are lim ited by a single resource, so that increasing one trait can only be done at the expense of the other one (Lessels, 1991). Life-history theory predicts a cost of reproduction, that is, a trade-oþ between current and future reproduction (W illiam s, 1966; Charnov & Krebs, 1974; Reznick, 1985). An increase in current reproductive eþ ort m ight aþ ect the parents’ future reproduction (i) by lowering their future survival, hence lowering the probability of future reproduction (e.g. N ur, 1984, 1988, but see Pettifor, 1993), and /or (ii) by lowering their future fecundity or probability of reproducing successfully (e.g. Slagsvold, 1984; Lessels, 1986). The experim ental testing of the costs of reproduction has often used m anipulations of the num ber of eggs or young that parents are m ade to rear. This procedure has been suggested to provide an a priori reliable means of determ ining these costs (Lessels, 1991; Roþ , 1992). U ntil now, such experim ental tests have focused exclusively on survival and reproductive traits of parents and oþ spring (see reviews in Reznick, 1985; N ur, 1990; Lessels, 1991; Roþ , 1992; Stearns, 1992).

1.1 Costs of reproduction on future adult sur vival: recapture/resighting and dispersal probability M ost ® eld studies that investigated costs of reproduction used return rates, i.e. the proportion of individuals present in year t and returning in year t + 1, as estim ates of survival rates (Clobert, 1995; M artin et al., 1995, but see Yoccoz et al., this issue). However, return rates depend on (i) the probability of surviving, (ii) the probability of returning to the study area if alive, and (iii) the probability of being recaptured /resighted if alive and present in the study area (Brownie et al., 1993; N ichols & Kendall, 1995). In m any studies, as the recapture probability is not equal to one, return rates will provide biased estim ates of survival probability (Lebreton et al., 1992, 1993; C lobert, 1995). The potential consequences of this bias have been discussed previously (M artin et al., 1995), and it has recurrently been advocated that studies attempting to estim ate survival probabilities should also estim ate recapture /resighting probabilities (M artin et al., 1995). Even when the estim ation of exact sur vival rate is not required (e.g. in com parative analyses, see M artin et al., 1995), a change in return rate m ay be due to a change in either survival or various underlying behavioural processes (C lobert, 1995). D iþ erences in return rates am ong individuals can indeed re¯ ect m ere variation in behavioural decisions in¯ uencing recapture probability (e.g. `trap dependence’ eþ ectÐ Pradel, 1993; or decisions to skip breeding, when recapture /resighting is linked to breeding status; see also Viallefont et al., 1995). M oreover, studies are often based on estim ates of local survival, not distinguishing between m ortality and dispersal (Clobert & Lebreton, 1991; N ichols & Kendall, 1995; Spendelow et al., 1995). D iþ erences in local survival rates among individuals can re¯ ect m ere variation in dispersal probability (HoÈ gstedt, 1981; Boulinier et al., this issue). T he costs of reproduction m ight be expressed not only in life-history traits, but also in behavioural traits such as the likelihood of breeding or dispersing. U ntil now, such behavioural consequences of clutch /brood size manipulations have rarely been investigated ( but see Viallefont et al., 1995).

Costs of reproduction on life-histor y and behavioural traits

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1.2 Costs of reproduction in future reproductive investment: information on environmental suitability Individuals of m any species have been shown to m odify their clutch /litter size according to the num ber of young they can raise (Individual O ptim ization HypothesisÐ Perrins & M oss, 1975; Pettifor et al., 1988; Pettifor et al., 2001). Individuals thus adjust their clutch /litter size to an estim ate of environm ental suitability or parental care ability at the tim e of young rearing (H oÈ gstedt, 1980, 1981; Slagsvold, 1984). Clutch /brood size m anipulations m ay produce a m ism atch between the num ber of young being reared and environm ental/parental conditions, and may thus induce a recalibration of such an adjustm ent rule (Lessels, 1991). This m echanism points out that changes in future fecundity in response to clutch /brood size m anipulation are likely to depend on the information gathered by individuals prior to the m anipulation, and on how this information is m odi® ed by the m anipulation. Variation in clutch /litter size m ay be partly due to individual variation in inform ation on environm ental suitability in varying environm ents (Shettleworth et al., 1988). T his information depends on individual’ s previous exp erience in the current breeding habitat (M assot et al., 1994; PaÈ rt, 1995), w hich m ay in turn depend on dispersal status. Under the Individual Optimization Hypothesis, current reproductive eþ ort before m anipulation is also exp ected to re¯ ect individual inform ation. As a consequence, studies attem pting to investigate costs of reproduction on future fecundity should account for individual variables, such as dispersal status or current reproductive eþ ort, which are likely to in¯ uence the decision to produce a given clutch /litter size the next year. 1.3 Reassessment of two experimental case studies of costs of reproduction Two previous experim ental studies have investigated potential life-histor y tradeoþ s revealing costs of reproduction in the collared ¯ ycatcher Ficedula albicollis (Gustafsson & Sutherland, 1988) and the great tit Parus major (Pettifor et al., 1988). However, neither took into account recapture /resighting and dispersal probabilities, nor included individual variables, as discussed above. In this study, we used m ulti-state capturerecapture m odels (Brownie et al., 1993; N ichols et al., 1994; N ichols & Kendall, 1995) to address this issue and attem pt to reassess costs of reproduction in these species. We focus on possible changes in four diþ erent life-history and behavioural traits following m anipulation of current reproductive eþ ort: (i) survival rate; (ii) capture probability; (iii) future reproductive eþ ort; (iv) dispersal rate (in the collared ¯ ycatcher only). We concentrate here on the m ethodological aspects of our analyses. In particular, we show how the inclusion of a behavioural variable (dispersal) can m odify the interpretation of evidence for a cost of reproduction, even when appropriate statistical techniques have apparently been employed. 2 Estim ating costs of reproduction using m ulti-state capturerecapture m odels: m ethods 2.1 The collared ¯ ycatcher study: study site and species The collared ¯ ycatcher is a sm all, hole-nesting m igratory passerine bird breeding in Europe. T he data used in this work were collected during a long-term study of a population of collared ¯ ycatchers carried out on the Southern part of Gotland,

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Sweden (57ë 10 ¢ N , 18ë 20 ¢ E), 1983 - 1996, in 13 diþ erent discrete woodlands (see PaÈ rt & Gustafsson, 1989). The study design allows the detection of individual m ovem ents between woodlands, and thus the estim ation of dispersal probabilities. Collared ¯ ycatchers lay only one clutch per year, and the m odal clutch size is six eggs, but ranges from four to eight (ver y rarely nine). E ach year laying date, clutch size, hatching date and num ber of ¯ edglings were m onitored in all nests in boxes through out the season. All adults caugh t and ¯ edglings were ringed w ith individually num bered rings. Adults were trapped and identi® ed while breeding, which im plies that adults were caugh t only when successfully breeding. T he collared ¯ ycatcher is a facultatively polygynous species, and m ales are som etim es very diý cult to trap at their secondary nests (G ustafsson, 1989). Polygyny is thus a m ajor reason for failure to capture som e of the m ales. M ore details on the study site and breeding ecology of the collared ¯ ycatcher can be found in Gustafsson (1989) and PaÈ rt & G ustafsson (1989). 2.2 M anipulations of clutch/brood size, experimental g roups, capture histories and state variables Clutch/brood size m anipulations were performed during three diþ erent periods: 1983 to 1985, 1988 to 1990, and 1992 to 1994. Because the collared ¯ ycatcher is short-lived, individuals m anipulated in these three diþ erent periods were in large part diþ erent (4.1% of m ales captured in period 1983 - 1985 were found again in 1988 - 1990, and 11.9% from period 1988 - 1990 in 1992 - 1994; these percentages were 3.2% and 9.0% respectively for females). Therefore, the three periods can be considered as three quasi-independent replicates of the exp eriment. Clutches with the sam e laying/hatching date were random ly treated in pairs, and one or two eggs/ young were m oved from one nest to the other. Birds were thus random ly assigned to one exp erim ental group: (i) increased or (ii) decreased clutch /brood size, or to the control group (no change in clutch /brood size). Some individuals have been m anipulated several tim es within each experim ental period. W hen the exp erim ental treatment they received changed between years, or when their clutch /brood size was m anipulated only on their second or third capture in the period, their capturerecapture history was cut into two (occasionally three) histories in order to account for the responses to diþ erent treatments. The ® rst history included the recapture history until the second experim ental m anipulation was perform ed (or the ® rst after a control treatm ent), and the second history included the histor y from the second m anipulation onwards (or the ® rst after a control treatm ent). The individual was removed at the end of the ® rst history as if it were not released again, i.e. lost on capture, and the second history was assigned to the new corresponding exp erim ental group. T his procedure im plicitly assum es that m emory eþ ects can be neglected. We chose this approach instead of elim inating these individuals from the analysis in an attem pt to keep the highest sam ple size possible. T he total num ber of capturerecapture histories obtained for the analyses varied from 587 to 918, depending on sex and study period. C apture- recapture histories were constructed over periods of ® ve years, beginning on the ® rst year of each experim ental period (1983, 1988 and 1992 respectively). O nly individuals that had been caugh t at least once during one of the three experim ental years were included. In our m ulti-state histories, we considered two possible state variables: (i) natural clutch size ( before manipulation when perform ed), and (ii) dispersal status. In the


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case of natural clutch size, grouping of individuals was necessary to render the analysis tractable (C lobert, 1995). Adult birds were thus assigned to one of three clutch size states as follows: state 1: clutches of less than 6 eggs (sm all clutch size); state 2: clutches of 6 eggs (m edium clutch size); state 3: clutches of m ore than 6 eggs (large clutch size). In the case of dispersal status, the state variable had two m odalities: resident or disperser. A breeding adult was considered as a disperser when (i) it was unringed when caught, or, if ringed, (ii) it had been caugh t breeding in another woodland on its last capture as a breeder (for two-year old or older individuals) or had been ringed as a chick in another woodland (for one-year old individuals, and older individuals that had not been caught as breeders previously). Any breeding bird caught in its natal woodland, or that had been caught breeding in the sam e woodland on its last capture occasion was considered as a resident. For each sex, period, and state variable considered, one set of three dem ographic param eters (i.e. one survival rate, one recapture rate and one set of transition rates) was m odelled, thus giving a total of 3 param eters 3 2 sexes 3 3 periods 3 2 state variables 5 36 diþ erent param eters investigated. 2.3 The great tit study A sim ilar exp erim ental approach was used to investigate costs of reproduction in the great tit, a non-m igratory species w hose breeding biology is sim ilar to that of the collared ¯ ycatcher. The great tit data were collected during a long-term study in Wytham Wood, near Oxford (51ë 46 ¢ N , 1ë 19 ¢ W ). The study site and general m ethods associated w ith this study are given in Perrins (1965, 1979), with speci® c details on the brood size m anipulations in Pettifor et al. (2001). Brood size was m anipulated in the years 1959 - 1964 and 1977 - 1980, w ith, in m ost cases, three or four young being removed from , or added to, random ly chosen experim ental nests, usually on or just after the day of hatching. T he sam e procedures as described for the ¯ ycatcher were applied to the great tit data, except for the assignm ent of natural clutch size classes. Clutch size is m ore variable am ong years and individuals in the great tit than in the ¯ ycatcher, the m edian being either 8 or 9 eggs, but w ith a range from 2 to 17. Adult birds were therefore assigned to one of three clutch size states as follows: state 1: clutches sm aller than the m edian clutch size for the year by two or more eggs; state 2: clutches equal in size to the m edian clutch size 6 one egg; state 3: clutches larger than the m edian clutch size by two or m ore eggs. Capture- recapture histories were constructed in the sam e way as in the collared ¯ ycatcher over the two periods of experimental brood size m anipulations, plus a further two years following the last year of m anipulation (i.e. 1959 - 1966 and 1977 - 1982). Individuals that had been m anipulated in more than one year were treated as above. M ales were not captured as breeding adults in the ® rst period, so that only fem ales were included in the analyses for this period. The num ber of capturerecapture histories obtained for analyses varied here from 498 to 525. The total num ber of sur vival, recapture and transition param eters m odelled for the great tit was 9. 2.4 Statistical methods, data overdispersion and model selection procedure M ales and fem ales were considered in separate analyses. Indeed, sex-speci® c dispersal patterns have previously been suggested to result from diþ erent behavioural mechanism s between sexes in these species (PaÈ rt & Gustafsson, 1989; D oligez

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et al., 1999). Furtherm ore, diþ erent reproductive costs m ay be exp ected between m ales and fem ales, due to their diþ erent investment in various reproductive activities (incubation and brooding by fem ales alone; incubation feeding by m ales; diþ erential young feeding and nest defence by both sexesÐ Perrins, 1979; Sheldon et al., 1997; Michl et al., 2000; see also N ichols et al., 1994). M ulti-state capturerecapture models (Brownie et al., 1993; N ichols & Kendall, 1995) were used to test the eþ ect of exp erimental clutch /brood size m anipulations on four diþ erent traits: (i) survival rate; (ii) capture probability; (iii) future reproductive investment (m easured by future clutch size); and (iv) dispersal probability. T his m ethod allows precise m odelling of the variation in the above param eters according to diþ erent relevant factors, and, in particular, perm its estim ation of state-speci® c survival and recapture probabilities, and transition probabilities between states. The m ost general m odel included (i) tim e-; (ii) experim ental group-; (iii) `pseudo-age’ - and (iv) state-speci® c survival, capture and transition probabilities. The `pseudo-age’ eþ ect was included to investigate and separate possible short-term and long-term eþ ects of clutch /brood size m anipulations (e.g. Clutton-B rock et al., 1982; Gustafsson & PaÈ rt, 1990; McCleer y et al., 1996). We considered two àge’ classes: one year after the m anipulation versus two years or m ore. M odel notation has been extended from the notation de® ned in N ichols et al. (1994). S st, a ( g) (survival probability) is the probability that a bird of experis m ental group g and age class a in state s at time t 2 1 sur vives until tim e t. P t, a ( g) (recapture probability) is the probability that a bird of group g and age class a is recaptured at tim e t in state s, given that it is alive and present at tim e t. T srt, a ( g) (transition probability) is the probability that a bird of group g and age class a in state s at time t 2 1 is in state r at time t given that the individual has sur vived from year t 2 1 to year t. We used M ARK software (W hite & Burnham , 1999) to com pute m odels’ deviance and param eters estim ates. It was not possible to include in a single analysis the two com bined state variables (natural clutch size and dispersal status) given the num ber of parameters required by such a m odel: w ith dispersal status (two possible states), the num ber of transition param eters to be estim ated was two. W ith natural clutch size (three possible states), this num ber was six. In a m odel com bining both states, the num ber of transition param eters would increase up to 30. We thus perform ed two series of analyses: (i) using natural clutch size as the state variable, we ® rst investigated the consequences of clutch /brood size m anipulation in term s of survival rate, capture probability and future reproductive eþ ort (transitions between natural clutch size classes); (ii) in a second step (in the collared ¯ ycatcher only), using dispersal status as the state variable, we investigated the consequences of m anipulation on dispersal probability (transitions between disperser and resident status) instead of future reproductive eþ ort. G oodness-of-® t (GO F) tests are not available in M ARK for multi-state capturerecapture m odels yet. We attem pted to check for data overdispersion by com puting GO F tests for the corresponding uni-state data sets (Lebreton et al., 1992; Anderson et al., 1993). We com puted TESTS 3 and 2 of the R ELEASE option of program M ARK (Lebreton et al., 1992), and ran the bootstrap procedure im plem ented in M ARK (W hite & Burnham , 1999), for the m ost general m odel for unistate data sets, i.e. including tim e, group and `pseudo-age’ eþ ects. As the bootstrap procedure cannot handle losses on capture, the extra capturerecapture histories com puted when individuals had been m anipulated several tim es (see above) were elim inated. M odel selection was based on the Akaike’ s Information C riteria


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corrected for eþ ective sam ple size (AIC cÐ Lebreton et al., 1992; Anderson & Burnham , 1994; Burnham et al., 1995; Cooch & W hite, 2000); the m odels whose AIC c value diþ ered by less than two units from the lowest AIC c model were those selected. Four diþ erent eþ ects were investigated (see above). Thus, the total num ber of diþ erent possible models including only m ain eþ ects and interactions on sur vival, capture and transition probabilities (but no additive eþ ects) was 15 3 for each sex, experim ental period and state variable considered. T herefore, it was obviously not possible to compute deviance and AIC c for all m odels. T he m odel selection procedure adopted was the following. We ® rst checked w hether the tim e eþ ect (the eþ ect of least interest here) could be elim inated by com puting deviances and com paring AIC cs of the eight most general m odels with or w ithout a time eþ ect (in interaction with the three other factors) on survival, capture and transition param eters. W hen all those tim e eþ ects that could be elim inated had been rem oved, m odel selection was continued with this sim pli® ed m odel as the reference m odel. Sim pli® ed m odels of survival probability were investigated ® rst, then capture probability w hile keeping the sim plest m odel for sur vival probability, and ® nally transition probabilities while keeping the sim plest m odels for both survival and capture probabilities. To test the robustness of this selection procedure, we com pared AIC cs of the ® nal selected m odel(s) with those of m odels in which som e of the elim inated eþ ects were re-introduced on sur vival and capture probabilities, while keeping the sim plest m odel for transition probabilities. In particular, w hen selected m odels diþ ered between periods for the sam e sex, we com puted AIC cs of the models selected in one period for the other periods (if not done previously). However, we are aware of the weakness of this m odel selection procedure, which does not allow absolute con® dence that the best possible models have been selected. We cannot rule out that some m odels not investigated here m ight have sm aller AIC cs than the selected ones. For this reason, we focus here on general results. We did not com pute any additive m odels for the reason given above (keeping the num ber of possible m odels to a tractable level). After identifying one or m ore `best’ m odels, m odels with new constraints were built when the treatm ent eþ ect was retained, to test speci® c a posteriori hypotheses about which experim ental groups diþ ered from each other.

3 Results 3.1 Validation of model selection procedures N o overdispersion was observed in any of the uni-state data sets analysed (Table 1). Therefore, the m odel selection based on AIC c values seem ed valuable (Anderson et al., 1993; Anderson & Burnham , 1994; Burnham et al., 1995). An exam ple of the m odel selection procedure described above is given in Table 2. T he tim e eþ ect could be eliminated in all cases following this procedure. W hen the state variable was natural clutch size, som e of the m odels with tim e eþ ects did not converge due to insuý cient data in view of the large num ber of param eters; their deviance m ay thus not be reliable. H owever, time eþ ects could always be rem oved when convergence was attained. Therefore, we are con® dent that tim e eþ ects did not strongly in¯ uence survival, capture or transition probabilities. Ver y often we could not discrim inate between several `best’ m odels (w hose AIC cs diþ ered by less than two units).

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Table 1 . G oodness-of-® t tests for the ¯ ycatcher data sets. (a) Results of the R ELEASE tests 3 and 2 2 (v values and associated probabilities); (b) results of the bootstrap procedure implem ented in M ARK ( probability of obtaining the observed deviance of the modelÐ p > 0.05 indicates no overdispersion of dataÐ and observed cÃ values). The num ber of sim ulations was 500 in each case (a) Test

Period

Test 3

1983 - 1987 1988 - 1992 1992 - 1996

Test 2

Tests 3 and 2 combined

M ales

v v v

1983 - 1987 1988 - 1992 1992 - 1996

v v v

1983 - 1987 1988 - 1992 1992 - 1996

v v

5

9.399, p 5 0.67 3.763, p 5 0.88 5 7.241, p 5 0.84

2 12 2 8 2 12

v

2 6 2 4 2 6 2 18 2 12 2 18

Fem ales

5 5 5 5

3.852, p 5 1.547, p 5 1.518, p 5

0.70 0.82 0.96

13.251, p 5 5.310, p 5 8.759, p 5

0.78 0.95 0.97

5 5 5

5

2 12 2 11 2 10

v v v v v v v v v

2 5 2 5 2 2 2 17 2 16 2 12

5 5 5

7.740, p 5 4.552, p 5 2.323, p 5

0.81 0.95 0.99

p5 p5 p5

0.65 0.19 1.00

11.083, p 5 11.947, p 5 2.323, p 5

0.85 0.75 0.99

3.343, 7.396, 5 0.000, 5

5 5 5

(b) Period 1983 - 1987 1988- 1992 1992- 1996

Males p5 p5 p5

0.14, cÃ 5 0.16, cÃ 5 0.95, cÃ 5

Females 1.229 1.344 0.526

p5 p5 p5

0.11, cÃ 5 0.12, cÃ 5 0.26, cÃ 5

1.118 1.336 0.726

3.2 General results: evidence for a manipulation eþ ect but not for a cost of reproduction A total of 45 survival, capture and transition param eters were m odelled across both species (36 for the ¯ ycatcher and 9 for the great titÐ see M ethods). An eþ ect of exp erim ental clutch /brood size m anipulation could be found in 13 out of these 45 param eters, although the alternative m odel w ithout m anipulation eþ ect on the param eter considered was also selected in 8 cases out of 13. A posteriori tests showed that, in 7 cases out of 13, the param eters diþ ered between m anipulated and non-m anipulated individuals, but not between individuals of the decreased and increased groups. `Decreased’ and ìncreased’ individuals diþ ered in 7 cases (the capture probability of females ¯ ycatchers in the ® rst period belongs to both categories; it did not diþ er between decreased and increased fem ales when they laid sm all clutches, but diþ ered when they laid m edium or large clutches). In only one of these seven latter cases did decreased and increased individuals diþ er as predicted by a cost of reproduction: ¯ ycatcher survival rate in the third period was sm aller for females of the increased group, and higher for fem ales of the decreased group, com pared with the control group (the state variable being clutch size) (Fig. 1(a)). However, this pattern seemed to be due to diþ erential dispersal (see below). In sum mary, the results do not provide evidence for the existence of costs of reproduction on survival or future reproductive investm ent. W hen the brood size m anipulation (i.e. group) eþ ect was retained in a selected m odel, (i) one or several alternative m odels with no group eþ ect were often selected at the sam e tim e; and (ii) except in one case, we did not obser ve the patterns predicted under costs of reproduction (i.e. reduced future adult survival rate and /or future reproductive investm ent for individuals from the increased group com pared with the control group, and vice-versa for individuals from the decreased group). N either did we ® nd a clear eþ ect of clutch /brood size m anipulation on capture and dispersal

Costs of reproduction on life-histor y and behavioural traits Table 2 . An example of the model selection procedure for collared ¯ ycatcher fem ales in the period 198 3 - 1987. The state variable is the dispersal status. In each of the sub-tables, m odels are ranked by increasing value of AIC c , and the bold lines indicate the set of `best’ m odels (lowest AIC c values, with diþ erence in AIC c s sm aller than 2). At the end of each selection step, the simplest model was retained as the starting model for sim pli® cation in the next step F irst step: checking for time effects M odel S S S S S S S S

Deviance

s a s a s a s t, a s t, a s a s t, a s t, a

s a

sr a sr a sr t, a sr a sr a sr t, a sr t, a s t, a

( g), P ( g), T ( g) s ( g), P t, a ( g), T ( g) ( g), P as ( g), T ( g) ( g), P as ( g), T ( g) ( g), P t,s a ( g), T ( g) s ( g), P t, a ( g), T ( g) ( g), P as ( g), T ( g) s ( g), P t, a ( g), T ( g)

Nb param eters

2135.917 2097.626 2104.752 2113.969 2075.407 2077.936 2082.684 2063.238

36 66 66 66 84 96 96 114

AIC c 2210.46 2238.31 2245.43 2254.65 2257.67 2288.77 2293.52 2318.24

S econd step: simplifying models of survival rate M odel s

sr

S, P a ( g), T a ( g) s s sr S , P a ( g), T a ( g) s sr S a , P a ( g), T a ( g) s sr S ( g), P a ( g), T a ( g) s s sr S a , P a ( g), T a ( g) s sr S a ( g), P a ( g), T a ( g) s s sr S ( g), P a ( g), T a ( g) s s sr S a ( g), P a ( g), T a ( g)

Deviance

Nb param eters

AIC c

2148.062 2147.762 2147.892 2146.460 2145.683 2142.063 2142.390 2135.917

25 26 26 27 28 30 30 36

2199.29 2201.08 2201.21 2201.89 2203.22 2203.82 2204.16 2210.46

T hird step: simplifying models of recapture probability M odel sr a sr a sr a

S, P, T ( g) s S, P , T ( g) S, Pa , T ( g) sr S, P ( g), T a ( g) s sr S, P a , T a ( g) sr S, Pa ( g), T a ( g) s sr S, P ( g), T a ( g) s sr S, P a ( g), T a ( g)

Deviance

Nb param eters

AIC c

2152.798 2152.579 2152.598 2152.154 2152.101 2149.968 2150.686 2148.062

14 15 15 16 17 19 19 25

2181.19 2183.03 2183.05 2184.66 2186.67 2188.68 2189.40 2199.29

F ourth step: simplifying models of transition probability M odel

Deviance sr a sr

S, P, T S, P, T ( g) sr S, P, T sr S, P, T a ( g) S, P, T a ( g) S, P, T a S, P, T ( g) S, P, T

2165.423 2162.447 2172.505 2152.798 2262.766 2271.178 2285.983 2294.811

Nb param eters 6 8 4 14 8 4 5 3

AIC c 2177.50 2178.58 2180.54 2181.19 2278.90 2279.22 2296.04 2300.83

415

416

B . D oligez et al. Table 3 .Ð

(Continued )

F ifth step: checking the selected models against other models by reinjecting

simple effects eliminated during previous steps of model selection M odel

Deviance sr a sr

S, P, T S, P, T ( g) s sr S, P , T a sr , S, Pa T a s s sr S , P , Ta s sr , , Sa P T a sr S, Pa , T (g) s sr S , P, T (g) sr S a , P, T (g) sr S ( g), P, T a s sr S, P , T (g) sr S, P, T s s sr S , P , Ta sr S, P ( g), T a s sr Sa , P , T a sr S a , Pa , T a s sr S , Pa , T a sr S a , Pa , T ( g) s sr S , Pa , T ( g) s s sr S , P , T ( g) s sr S a , P , T ( g) s sr S, P , T sr S ( g), P, T sr S, P( g), T s s sr S ,P ,T s sr S ( g), P , T s sr S , P ( g), T sr S ( g), P ( g), T s S, P , T s S, P , T ( g) s S , P, T

2165.423 2162.447 2164.916 2165.222 2165.276 2165.365 2162.247 2162.320 2162.389 2164.429 2162.447 2172.505 2164.621 2164.779 2164.860 2164.884 2164.968 2161.909 2162.023 2162.299 2162.386 2172.499 2171.511 2171.860 2172.379 2171.508 2171.674 2170.588 2200.177 2196.910 2294.634

Nb param eters 6 8 7 7 7 7 9 9 9 8 9 4 8 8 8 8 8 10 10 10 10 5 6 6 6 7 7 8 4 6 4

AIC c 2177.50 2178.58 2179.02 2179.33 2179.38 2179.47 2180.41 2180.49 2180.56 2180.56 2180.61 2180.54 2180.76 2180.91 2180.99 2181.02 2181.10 2182.11 2182.23 2182.50 2182.59 2182.55 2183.59 2183.94 2184.46 2185.61 2185.78 2186.72 2208.22 2208.99 2302.67

probabilities. Rather, the results suggest an eþ ect of the m anipulation itself, since, in m any cases, birds from the increased and decreased groups did not diþ er, but diþ ered from birds of the control group. T he results also illustrate tem poral variability in responses to factors aþ ecting life-history and behavioural traits, which is a classical result in previous studies (Nur, 1988). Indeed, the selected m odels diþ ered according to the period considered (see also Pettifor et al., 2001). 3.3 The importance of including behavioural variables: the case of dispersal probability in the collared ¯ ycatcher W hen using clutch size as the state variable, fem ale ¯ ycatcher sur vival in the third period was lower in the increased group, and higher in the decreased group, com pared w ith the control group (Fig. 1(a)). This was the only case where the obtained pattern of param eter variation matched the one predicted under a cost of reproduction. T he m odel with no group eþ ect (constant survival) was, however, also selected. W hen considering dispersal status as the state variable, for the sam e period, the diþ erence in survival rate for fem ales of diþ erent groups disappeared.


417

F ig. 1 . (a) Survival probabilities ( 6 1 s.e.) of collared ¯ ycatcher fem ales for the period 1992 - 1996 , with clutch size class as the state variable, according to experim ental treatm ent: increased clutch /brood size (increased); decreased clutch /brood size (decreased); control (see text). N 5 895. A posteriori models constraining parameters, constructed to determine which experimental groups diþ ered, showed that fem ale survival rate for the decreased group was higher than fem ale survival rate for the increased group, while fem ale survival rate for the control group did not diþ er from the two other groups. However, the alternative m odel with no g roup eþ ect on survival was also selected in this case (AIC c s of the models with and without a g roup eþ ect diþ ered by less than two units). (b) Probability for collared ¯ ycatcher fem ales to stay in their breeding area the follow ing year ( 6 1 s.e.), for the sam e period (1992 - 1996), according to experim ental treatm ent (same as in part (a)), and previous dispersal status. T he state variable here was dispersal status. Models constructed a posteriori showed that the probability of staying was lower in the increased group for resident fem ales, and higher in the decreased group for dispersing fem ales (as indicated by the asterisks); the two other probabilities did not diþ er between each other in either residents or dispersers.

In this case, fem ale dispersal probability diþ ered according to previous dispersal status and group (Fig. 1(b)), although the alternative m odel with no group eþ ect (dispersal status alone) was also selected. T he previously observed pattern in survival could, in fact, be explained by diþ erential dispersal probability between fem ales of diþ erent groups. Resident fem ales whose brood had been enlarged were m ore likely to leave their breeding patch than other fem ales, thus m ore likely to disperse out of the study area and less likely to be caught again. As a result, fem ales from the increased group had, on average, a lower local, apparent sur vival rate (Fig. 1(a)), and capture probability. Sim ilarly, dispersing fem ales whose brood size had been decreased were m ore likely to becom e resident; thus, fem ales from the decreased group had a higher average local, apparent survival rate.

418

B . D oligez et al.

4 D iscussion: current lim itations of the use of m ulti-state capturerecapture m odels D iþ erences in survival, capture and transition param eters am ong experim ental groups were often retained in our study, but these diþ erences alm ost never supported costs of reproduction. T he biological im plications of our results will be discussed elsew here. We focus here on the m ethodological issues and implications of our study, and on som e aspects of the use of m ulti-state capturerecapture m odels in evolutionary biology in general. O ur analyses were constrained by three types of lim itation: (i) technical and practical lim itations, including data lim itation; (ii) lim itations of m odelling tools; and (iii) lim itations of theoretical predictions. Below, we discuss the ® rst two issues, em phasizing the need for future work aim ed at developing the use of m ulti-state capturerecapture models for the study of evolutionar y questions to address these issues.

4.1 Technical limitations 4.1.1 N um ber of parameters to be estimated in complex models. T he use of m ultistate capturerecapture m odels perm its powerful testing of various predictions about behaviour and physiology (Nichols et al., 1994; Clobert, 1995; N ichols & Kendall, 1995), but such m odels use a large num ber of param eters. In particular, the num ber of transition param eters rapidly èxplodes’ with the num ber of states: for n states, the num ber of possible transitions between states to be m odelled is 2 n(n 2 1), i.e. is a function of n . M ultistate m odels thus require (i) com putation power, and (ii) large data sets. Com puter facilities currently available no longer lim it calculations. Conversely, the num ber of individuals in each possible cell describing transitions between states has to remain suý ciently large to allow estim ation of transition probabilities. T hus, m ulti-state m odels involving a large num ber of states (e.g. when studying m ovem ent rates between sites) require m uch larger data sets than `classical’ capturerecapture m odels. It will often be necessary to adopt strategies to lim it the num ber of diþ erent states, for instance grouping data into classes as we did here with clutch size, so as to m ake analyses tractable (Clobert, 1995; N ichols & Kendall, 1995). H owever, such lim itation m ight also constrain the biological hypotheses that can be investigated. In our case, the two state variables consideredÐ natural clutch size and dispersal statusÐ could not be included in a single analysis. W hen three diþ erent states were possible (clutch size as the state variable), convergence was already questionable or non-existent for som e of the m ost com plicated m odels (in particular those with tim e eþ ects), and estim ates of transition probabilities were in som e cases aberrant (e.g. the sum of transition probabilities from one state to all others was greater than one). It was not clear whether som e of these m odels should be kept in the analysis or rem oved, and on which criteria to base such a decision. H owever, we believe that the num ber of states that were considered here to address our biological questions was not unreasonable given our data sets. W hen addressing the question of dispersal, using site as the state variable would allow us to account for variability between sites in dispersal rate (see for exam ple M orris, 1987). However, this procedure requires far too m any states for the analysis to be tractable as soon as m ore than two sites are considered (for exam ple, here, ¯ ycatchers were caught in 13 diþ erent sites). Using site characteristics (e.g. size, or breeding pairs density) as individual covariates (Skalski et al., 1993) is another


419

way to tackle the question of site variability, but requires dynam ic covariates since individuals m ay change sites (see below). F uture developments in capturerecapture theory m ay in¯ ate this problem . For exam ple, incorporating long-term m emor y eþ ects in m odels can only increase the need for larger data sets. The Bayesian approach m ay, in turn, be a way to increase analytical power without demanding m ore param eters, owing to the use of prior inform ation (see D upuis, this issue). T he current need for such large data sets both justi® es the existing eþ orts to sam ple populations in the ® eld and calls for even m ore eþ ort in the future. 4.1.2 N um ber of possible models to be ìdeally’ run and model selection strategy. T he in¯ uence of four factors on survival, capture and transition param eters was tested here. Well-designed experim ents usually allow the num ber of factors under investigation to be lim ited to a tractable few, but a total of four factors is not uncom m on in biological ® eld studies. As emphasized above, the total num ber of possible m odels to be ìdeally’ run to determ ine the best model(s) is also very large even for a lim ited number of factors (here four), and èxp lodes’ when the num ber of factors considered increases. Indeed, in m ulti-state capturerecapture m odels, the `model landscape’ to be explored is three-dim ensional. T hus, it will often appear necessary to follow speci® c m odel selection strategies investigating a restricted subset of m odels. Future work m ight prove useful concerning the criteria and strategies to be used to allow eý cient but lim ited model selection procedures. 4.1.3 C urrent development of software: goodness-of-® t tests. Our approach to test goodness-of-® t was lim ited to ùni-state’ data sets (i.e. the diþ erent states were not considered). Thus, we could only test the absence of heterogeneity among groups for `global’ (i.e. across states) survival and capture probabilities. We did not use Q AIC c for m odel selection as tests did not reveal signi® cant overdispersion, although (i) the results of the bootstrap GO F procedure were som etim es at the lim it of recom m ended correction, i.e. p < 0.2 and /or cÃ > 1.3, and (ii) the lack of power to detect such overdispersion w ith T ESTS 3 and 2 of R ELE ASE is well known (Cooch & W hite, 2000). W ithout appropriate goodness-of-® t tests for m ulti-state capturerecapture data, we could not rule out that the data were overdispersed. T his could arise for exam ple as a result of group behaviours, in which individuals may change state non-independently from other individuals of their group (e.g. group m igration or exploration). T hese technical lim itations com bine with lim itations of the capturerecapture m odelling tools to prevent the investigation of m ore speci® c evolutionar y questions. 4.2 Limitations of modelling tools 4.2.1 Temporal patter n of state transition. C urrent m ulti-state m odels assum e that the transition from one state to another (such as dispersal m ovem ent, decision to breed, decision to lay a given num ber of eggs) occurs at the end of the tim e inter val considered to calculate survival rate (Brow nie et al., 1993; N ichols & Kendall, 1995). T his assum ption was m et here in both biological models: (i) mortality is likely to occur m ostly during the winter (non-breeding) season in birds (see HoÈ gstedt, 1981), especially in migrating species such as the collared ¯ ycatcher, and (ii) capture and assignm ent to a given state were associated here w ith breeding activity in both the collared ¯ ycatcher and great tit. W hen capture /resighting is not

420

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linked to the activity for w hich states have been de® ned, or when transition may occur at any time in the life-cycle, this assum ption is no longer m et. Tricky m odelling m anipulations m ay then be required. Separating survival and transition between states in multi-state m odels is needed to relax this constraining assumption, allow ing a generalized use of these tools, whatever the recapture /resighting design. 4.2.2 Individual covariates. G iven the technical diý culty of investigating all responses to clutch /brood size m anipulation considered here in a single analysis (see above), we used a two-step approach. A m ore general approach to account for both clutch size and dispersal status in the sam e analysis could have been to analyse separately the capture histories of dispersers and residents at the tim e when they were ® rst m anipulated, w ith clutch size as the state variable, and com pare the m odels selected for both categories of individuals. This m ethod could probably not have been im plem ented here because sm all sam ple sizes would have prevented eý cient model selection. Indeed, som e of the com plex m odels did not converge even when grouping all individuals (see above). D ispersal status could also have been included as an individual covariate. H owever, our results showed that future dispersal probability often depended on previous dispersal status, as well as on age or experim ental clutch /brood size m anipulation. Both dispersal status and reproductive investm ent are thus dynam ic states, susceptible to change over the course of an individual’ s lifetime, and could not be considered ® xed at the ® rst capture. H owever, no currently available capturerecapture m odelling program allow s individual covariates to change through tim e (i.e. dynam ic individual covariatesÐ Clobert, 1995), unless covariate values are know n or can be inferred for occasions w hen individuals are not captured. T herefore, the eþ ect of m anipulation on dispersal could not have been accounted for by using dispersal status as a covariate. N either could we investigate how natural clutch size prior to m anipulation in¯ uences the eþ ect of manipulation on dispersal probability by using clutch size as an individual covariate. The ability to incorporate dynam ic individual covariates in capturerecapture m odels is badly needed, especially when one addresses questions concerning either behavioural or physiological m echanism s underlying life-history trade-oþ s. 4.2.3 M emor y eþ ects. Further work on m ulti-state capturerecapture m odelling is also needed to include possible m em ory eþ ects, i.e. the dependence of future lifehistory and behavioural traits on previous capturerecapture history, or previous experience (e.g. exp erimental m anipulation). Such m emory eþ ects have already begun to be incorporated in m odels accounting for dependence on previous year’ s factors, i.e. a one-year tim e step (Brownie et al., 1993; N ichols et al., 1993). W hile this is likely to be suý cient for short-lived species, investigating life-history patterns and evolution in long-lived species will require m odelling m emory eþ ects over longer periods (Stearns, 1992). This raises the question of which patterns are to be expected in w hich conditions and life-cycles, a theoretical issue com pletely ignored until now. 4.3 Conclusion W ith m ulti-state capturerecapture m odels, three lim its have now been reached: (i) the data lim it (i.e. the need for larger data sets to allow powerful analysis with available tools), (ii) the m odelling tool lim it (i.e. the need to develop tools allowing


421

speci® c biological questions to be answered), and (iii) the theoretical lim it (i.e. the need for m ore speci® c predictions to be tested about which life-history traits we should expect to be aþ ected by costs of reproduction). To improve our understanding of life history evolution, we need to work further in these three m ajor research axes. F urther eþ ort should also be made to incorporate these techniques in a wider range of biological studies (both regarding the design of experim ents and the analysis of data), m any of which still largely ignore the capturerecapture approach (Clobert, 1995; V iallefont et al., 1995).

Acknowledgem ents We thank all the people that m ade this study possible, and in particular those that helped collecting data in the ® eld. We also thank B. J. T. M organ, N . G. Yoccoz and an anonym ous referee for helpful com m ents on a previous version of the m anuscript.

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