partial clutch predation, dilution of predation risk, and ...

The Auk 125(3):679–686, 2008  The American Ornithologists’ Union, 2008�� . Printed in USA.

Partial Clutch Predation, Dilution of Predation Risk, and the Evolution of Intraspecific Nest Parasitism C harlot te L. Roy N ielsen,1,3 Patricia G. Parker , 2 1

and

Robert J. G ates1

School of Environment and Natural Resources, The Ohio State University, 2021 Coffey Road, Columbus, Ohio 43210, USA; and 2 Department of Biology, University of Missouri-St. Louis, 8001 Natural Bridge Road, St. Louis, Missouri 63121, USA

Abstract.—Distributing eggs among multiple nests may have a selective advantage over laying eggs in one nest when stochastic events, such as predation, affect individuals of the same phenotype differently. However, an earlier analysis revealed that the mean fitness of such an egg-spreading strategy is equal to putting all eggs in one nest when predation destroys entire clutches. However, if predation typically results in partial clutch loss, distributing eggs among multiple nests may provide a selective advantage. We investigated the possibility that partial clutch loss could favor egg-spreading strategies by modeling mean fitness under a variety of egg-distribution strategies with partial nest predation. We found that higher fitness resulted from distributing eggs among multiple nests that contained at least as many eggs as a single nest containing the eggs of one female. The highest fitness resulted when eggs were in large clutches, because of predator-dilution effects. The fitness differences among egg-distribution strategies increased as predation rates, frequency of partial clutch loss, and the number of eggs destroyed in each partial predation event increased. We also examined the invasibility of pure and mixed parasitic and nesting strategies. Nest parasites may increase their fitness by spreading eggs among multiple nests that contain more eggs than would be present if they were nesting alone, but only a pure parasitic strategy can invade a population of nonparasites when the number of eggs laid is constrained. Received 2 July 2007, accepted 15 January 2008. Key words: dilution of predation risk, egg distribution, intraspecific nest parasitism, nesting strategies, partial nest predation.

Prédation partielle des couvées, dilution du risque de prédation et évolution du parasitisme intra-spécifique Résumé.—Distribuer ses œufs dans plusieurs nids plutôt que de les pondre dans un seul nid peut comporter un avantage sélectif lorsque des événements stochastiques, comme la prédation, affectent des individus du même phénotype différemment. Une étude a toutefois révélée que le fitness moyen associé à une telle stratégie de distribution des œufs équivaut à mettre tous ses œufs dans le même nid lorsque la prédation détruit des couvées entières. Cependant, si la prédation résulte typiquement en une perte partielle de la couvée, le fait de distribuer ses œufs dans plusieurs nids peut fournir un avantage sélectif. Nous avons étudié la possibilité que la prédation partielle d’une couvée puisse favoriser les stratégies de distribution des œufs en modelant le fitness moyen à partir d’une variété de stratégies de distribution des œufs avec une prédation partielle des nids. Nous avons trouvé qu’un fitness plus élevé était le résultat d’une distribution des œufs dans plusieurs nids qui contenaient au moins autant d’œufs qu’un nid contenant les œufs d’une seule femelle. Le fitness le plus élevé s’est produit lorsque les œufs faisaient partie de grosses couvées, en raison des effets de dilution de la prédation. La différence de fitness entre les stratégies de distribution des œufs a augmenté à mesure qu’augmentaient le taux de prédation, la fréquence de la perte partielle d’une couvée et le nombre d’œufs détruits dans chaque événement de prédation partielle. Nous avons aussi examiné l’invasibilité des stratégies de nidification et de parasitisme pur ou mixte. Les parasites peuvent augmenter leur fitness en répartissant leurs œufs dans plusieurs nids contenant plus d’œufs qu’il n’y en aurait s’ils nichaient seuls, mais seulement une stratégie pure de parasitisme peut envahir une population de non-parasites lorsque le nombre d’œufs pondus est limité. The question of whether animals should place all eggs in a single nest or disperse them among several nests (i.e., bethedging) has been discussed in the literature for more than 30 years (Gillespie 1974, Rubenstein 1982, Hopper 1999). Such within-generation bet-hedging was hypothesized to evolve when

stochastic events such as nest predation did not affect all individuals of the same phenotype (e.g., placing all eggs in a single nest) to the same extent. (Note that within-generation bet-hedging differs from between-generation bet-hedging, in which individuals with the same phenotype are affected to the same extent; see

3

Present address: Cooperative Wildlife Research Laboratory, Southern Illinois University Carbondale, mailcode no. 6504, Carbondale, Illinois 62901, USA. E-mail: [email protected] The Auk, Vol. 125, Number 3, pages 679–686. ISSN 0004-8038, electronic ISSN�� 1938-4254.  2008 by The American Ornithologists’ Union. All rights reserved. Please direct all requests for permission to photocopy or reproduce article content through the University of California Press’s Rights and Permissions website, http://www.ucpressjournals. com/reprintInfo.asp.�� DOI: 10.1525/auk.2008.07114

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— Roy N ielsen, Parker ,

Hopper et al. 2003.) For instance, among birds that lay eggs in a single nest, some individuals’ nests will escape predation, whereas the nests of others will suffer total loss. In other words, individuals with a “single nest” phenotype can either be successful or have no success for the year. On the other hand, although individuals that lay eggs in multiple nests (i.e., within-generation bet-hedgers) may also have variable success, they reduce the probability of total loss by spreading the risk among several nests (Rubenstein 1982). This within-generation bet-hedging was originally thought to confer a selective advantage by minimizing the probability of lineage extinction. However, this reasoning proved to be flawed, from an evolutionary perspective, when stochastic events result in complete clutch loss. Bulmer (1984) showed that both eggdistribution strategies had the same arithmetic mean fitness, differing only in the variance. Individuals that lay eggs in a single nest have higher variance in fitness, because they suffer total clutch loss more often than individuals that use multiple nests, but they also experience total clutch success more often. As a result, “single-nesters” have the same arithmetic mean fitness as individuals using multiple nests. However, the reduction in variance can be important in small populations, because reduced variance can increase geometric mean fitness (G; Gillespie 1974). Maximizing geometric mean fitness is important evolutionarily, because it considers fitness through time. Gillespie’s seminal papers (1974, 1975) showed that G for within-generation bethedgers is G = μ A – σ2/N where µA is the arithmetic mean fitness, σ2 is the variance in fitness, and N is breeding population size. This equation shows that variance effects are important in small populations only. For large N (e.g., N > 100), G ≈ µA. Because reduced variance does not convey a selective advantage to within-generation bet-hedgers in large populations, the ability of risk-spreading to explain the evolution of egg distribution among multiple nests has been largely dismissed in the literature when stochastic events result in total clutch loss (Hopper 1999, Hopper et al. 2003). In intraspecific parasitism, parasitizing females lay eggs in the nests of other females of the same species, and the host female incubates the eggs. Nest parasitism differs slightly from more conventional definitions of nest dispersal (i.e., laying eggs in multiple locations), in that parasite eggs are mixed with the eggs of other females. Payne (1977) hypothesized that intraspecific nest parasitism evolved as a type of bet-hedging against predators. However, until recently, within-generation bet-hedging was also dismissed as an explanation for the evolution of intraspecific nest parasitism (Bulmer 1984, Arnold and Owens 2002), using the same logic as for the distribution of eggs among multiple nests when predation affects entire clutches. However, Pöysä and Pesonen (2007) recently revisited Bulmer’s (1984) model, with the following modification: they allowed predation risk to vary among nest sites, such that some nest sites were safer than others. They found that bet-hedging, also referred to as “risk-spreading,” could favor the evolution of intraspecific nest parasitism when predation was not random. Before Pöysä and Pesonen’s (2007) study, theoretical examination of the role of bet-hedging in the evolution of egg distribution among multiple nests had considered only stochastic events that


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affect entire clutches (Gillespie 1974, Bulmer 1984, Farnsworth and Simons 2001, Hopper et al. 2003). Pöysä and Pesonen (2007) relaxed the assumption of random nest predation, but they also assumed that predation affected entire clutches. However, predation events do not always affect entire clutches. Some partially depredated nests are not abandoned and may eventually be successful, as reported for Wilson’s Phalaropes (Phalaropus tricolor; Colwell and Oring 1988), Meadow Pipits (Anthus pratensis; Halupka 1998), and waterfowl (Larivière and Walton 1998; Zanette 2002; Ackerman et al. 2003a, b). Partially depredated nests are not necessarily completely depredated later. For example, only 2 of 32 Meadow Pipit nests that were partially depredated were later totally depredated (Halupka 1998). In other cases, partially depredated nests may suffer partial clutch loss again. Ackerman et al. (2003b) reported that 30.5% of Mallard (Anas platyrhynchos), Gadwall (A. strepera), and Northern Pintail (A. acuta) nests were partially depredated at least once. Mean clutch sizes were 8.3, 9.3, and 8.6 for Mallards, Gadwalls, and Northern Pintails, respectively, with an average of 3.0, 3.9, and 3.5 eggs depredated from each nest in the first predation event (Ackerman et al. 2003b). The attending female continued to incubate 62.3% of these partially depredated nests. In Mallards and Gadwalls, 27% and 23% of partially depredated nests hatched young, respectively, producing 22% and 21% of all ducklings on the study area (Ackerman et al. 2003a). In our investigation, 22.9% of depredated Wood Duck (Aix sponsa) nests in cavities were partially depredated at least once (C. L. Roy Nielsen et al. unpubl. data), and 50% of partially depredated nests eventually hatched young. Predation by Common Raccoons (Procyon lotor) frequently resulted in partial clutch loss. A potential advantage of dispersing eggs among multiple nests in systems in which partial clutch loss occurs has not been examined. Given its prevalence, partial nest predation may prove to have important effects on populations and on the evolution of nesting strategies. Furthermore, when multiple females deposit eggs in the same location, such as in systems with male parental care (e.g., fish [Rohwer 1978, Page 1985, Unger and Sargent 1988] and some arthropods [see review in Tallamy 2001]) or intraspecific nest parasitism (e.g., waterfowl [Yom-Tov 1980, 2001; Rohwer and Freeman 1989], treehoppers [Eberhard 1986], burying beetles [Müller et al. 1990], and bees [Eickwort 1975]), the risk of egg loss during partial predation events may be diluted by the presence of eggs from other females in the nest. Thus, individuals may reduce predation risk by spreading eggs among multiple nests, or predation risk may be diluted because eggs of other females are present (McKaye and McKaye 1977, Foster and Treherne 1981). Our goal in the present study was to create a generalized model to examine how stochastic events that result in partial clutch loss, specifically partial nest predation, influence the mean fitness of individuals under a variety of egg-distribution strategies. We determined whether egg dispersal might have a selective advantage in systems where partial nest predation occurs, which could facilitate the evolution of intraspecific nest parasitism and other egg-distribution strategies (e.g., serial nests). We modeled different egg-distribution strategies with partial predation and examined the effects of predation rate, frequency of partial clutch loss, and number of eggs consumed in each partial predation attempt on the differences among egg-distribution strategies. We

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Table 1. Egg-dispersal strategies (A–E) modeled with partial predation. Scenario

Distribution

A. Nest alone B. Serially nest (or multiple nests) C. Parasitize two nests D. Lay all eggs in one nest of another female E. Nest and parasitize

10 eggs in 1 nest 5 eggs in each of 2 nests 5 eggs in 2 nests with 10 other eggs 10 eggs in 1 nest with 10 other eggs 7 eggs in 1 nest, 3 in second nest with 10 other eggs

also examined how robust our conclusions were to changes in clutch size and how predator learning affected findings. M ethods We derived expressions for arithmetic mean egg survival and reproductive success of females under each of five egg-distribution strategies (Table 1), in which eggs were distributed between one or two nests with or without eggs of other females. Specifically, the strategies included (1) laying all eggs in the same nest and nesting alone (strategy A); (2) serial nesting or nesting at multiple sites, as might occur in systems where the male provides parental care, as in jacanas (Jacana spp.) or multibrooded passerines (strategy B); (3) laying in the same nest(s) as other females, as is common in many species of waterfowl (strategies C and D); and (4) egg distribution among locations with and without eggs of others (i.e., nesting and parasitizing; strategy E). We varied the number of eggs that additional females contributed to nests to examine the effects on predation risk during partial predation events. Because Bulmer (1984) and Pöysä and Pesonen (2007) kept the number of eggs laid by each female constant for all strategies, we also kept the number of eggs laid by each female constant. Each female laid 10 eggs in all strategies and varied only in the distribution of these eggs among nests (Table 1, strategies A–E). The clutch sizes resulting from these parameters, with or without parasitism, are realistic for waterfowl that exhibit intraspecific nest parasitism; in particular, they are realistic for Wood Ducks, a species for which we have data on clutch sizes, parasitism, predation, and partial predation (Roy Nielsen et al. 2006a, b, c; Roy Nielsen and Gates 2007). We also assumed that each nest and each predation attempt were independent and that the numbers of nests and of eggs per nest did not affect predator behavior. This assumption seemed reasonable on the basis of our previous experience with Wood Ducks, in which clutch size did not affect predation (Roy Nielsen et al. 2006b; but see Fulton et al. 2004). We defined “predation rate” (a) as the daily probability that a predator would encounter a nest and destroy at least one egg. The frequency of partial clutch loss (d) was the rate at which nests found by predators were partially consumed and were not abandoned, as opposed to predation resulting in complete clutch loss. Nests that were abandoned after partial clutch loss were included with total predation, because the result was clutch failure. We defined “intensity of partial predation” (t) as the number of eggs lost to predators in each partial predation event, which can be loosely regarded as the number of eggs that predators consumed before satiation. We incorporated the possibility that predators visited nests more than once during incubation. Each nest could withstand


Final clutch size 10 5, 5 15, 15 20 7, 13

a limited number (m) of partial predation events before all eggs in the nest (n) were depredated, such that m = (n/t) – 1 rounded up to the nearest integer. (A nest of n = 10 eggs could receive m = 9 partial predation events of t = 1 egg and still have eggs survive.) We let incubation length (u) be 30 days. The number of predation events (i) at a nest was then modeled as a Poisson random variable with mean = variance = au, such that the probability of a nest receiving i events was given by

Pi = e–au(au)i/i!

(1)

Incorporating the frequency of partial clutch loss, the proportion of eggs that survived to hatch was

E(egg survival | n) =

max

∑ P d (1 – it/n) i=0

i

i

(2)

We varied parameters a, d, t, and n and calculated the mean performance of egg-distribution strategies. We let a = 0.00000001 (because the expression is undefined when a = i = 0), 0.01, 0.03, 0.06, and 1; d = 0, 0.3, 0.5, 0.7, and 1; t = 3 and 5; and n range from 5 to 20. For egg-distribution strategies that produced nests of different sizes, we let pn be the proportion of the focal female’s eggs in nests of size n, and the mean egg survival for a strategy was

E(egg survival) =

10

∑ p *E(egg survival | n) n =1

n

(3)

We evaluated the relative success of strategies on the basis of mean number of young produced. Because our goal was to determine the distribution of eggs among nests that maximized the average number of offspring escaping predation, we did not incorporate other costs and benefits of each strategy, given that such values will differ markedly among systems. Incorporating predator learning.—Some predators may return to nest sites after learning the nest location (Nilsson et al. 1991, Sønerud 1993; but see Yahner and Mahan 1999), so we used Microsoft EXCEL (MS Office XP) to simulate predator learning by increasing the probability that a nest would be found after initial nest detection (Fig. 1). Therefore, predation was no longer a Poisson process, and simulations were necessary. To demonstrate that variance effects on geometric fitness were negligible at large population sizes, we ran the simulations without predator learning for population sizes of 100 and 1,000. In simulations with predator learning, the probability that a predator would find the nest was 0.03 per day initially (as before), but after the first partial predation event, the probability that the nest would again be visited by the predator

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Fig. 1. Model of nest predation applied to each nest to simulate nest fates for 100 females under each of five egg-distribution schemes.

doubled, to 0.06 per day. For example, if a clutch contained 5 eggs of the focal female and 10 eggs of other females, eggs were depredated in proportion to their representation in the clutch of 15 eggs. A revised composition of the remaining eggs was determined, and the nest continued from the day at which the predation event occurred until hatch or total failure, but at a higher predation rate. Therefore, a partially depredated nest could later hatch without further disturbance from predators, hatch after additional partial nest predation attempts, or suffer entire clutch failure in subsequent predation events. Following each simulation, the arithmetic mean number of offspring was determined for each strategy. When a female distributed eggs in more than one nest, both nests were simulated independently and offspring number was summed across nests. We simulated nests for 100 females. Invasibility of the parasitic strategy in a population of females nesting alone.—To determine whether the parasitic strategy could invade a population of nonparasites, we compared the fitness of a new mutant parasite (when rare) with the fitness of incubating females (when common) using equation 3. For example, when a new mutant parasite using strategy E was rare, 3 eggs would be laid in a nest with 10 other eggs, producing a clutch of 13, and 7 eggs would be laid in a nest alone and not parasitized (because no other parasites exist). The fitness of the mutant parasite was then calculated using the proportion of eggs in nests of 13 (30%) and 7 eggs (70%) and egg survival from the two nests. This was then compared to the fitness of females that nested alone and were not parasitized because parasites were rare (e.g., egg survival for 10 eggs in a clutch of 10). We then determined whether a mutant using strategy A could invade a population of females using another strategy in a similar manner. In all scenarios, a nest had to be incubated to be successful and parasites only targeted nests with existing eggs. We also did not let multiple parasites target the same nests, because nests of unlimited egg number could otherwise result. R esults Effect of predation parameters on mean offspring number.—All egg-distribution strategies resulted in similar mean fitness at low rates of predation and partial clutch loss (Fig. 2A, B). However,


Fig. 2. The influence of (A) predation rate (proportion of clutches found by a predator) and (B) partial predation rate (proportion of clutches found by predators that are only partially depredated, as opposed to completely depredated) on mean offspring number resulting from different eggdistribution strategies. A–E represent strategies from Table 1. Solid lines represent results when five eggs are depredated at a time. Dashed lines represent results when three eggs are depredated at a time. In A, the partial predation rate is 0.5. In B, the daily predation rate is 0.03.

as predation rate, frequency of partial clutch loss, and intensity of partial predation increased, the differences among eggdistribution strategies became more pronounced. The maximum difference between the best (D) and worst (B) strategies was 3.7 offspring when the number of eggs depredated in each attack was 5 and partial predation rate was highest (Fig. 2B). The minimum difference among strategies was 0 when daily predation rate was either 0 or 1, which meant that partial clutch loss did not occur. Egg survival increased asymptotically as clutch size increased (Fig. 3), such that the gain in egg survival with each additional egg was greatest for small clutches (0.04) and lowest for the largest clutches (0.01). In small clutches, predation could quickly result in total clutch loss, whereas, in large clutches, a few additional eggs had much less influence on the probability that eggs of the focal female would be selected by predators in partial predation events.

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Invasibility of parasitism as a strategy in a population of females nesting alone.—Strategy A (all eggs in a clutch of 10) could not be invaded by strategies B or E (Table 3). Strategy A always had higher fitness (Fig. 3) compared with all eggs in clutches of 5 for strategy B, and a mixture of 70% of eggs in clutches of 7 and 30% of eggs in clutches of 13 for strategy E. However, strategy C (all eggs in clutches of 15) and D (all eggs in clutches of 20) could invade a population of females using strategy A. When nesting females were rare, these strategies had lower fitness (0) because parasitic eggs were laid in nests without an attending female. Therefore, a mixed, evolutionarily stable strategy (ESS) resulted. D iscussion

Fig. 3. The asymptotic nature of egg survival as clutch size increases. Mean fitness for a strategy can be determined by multiplying the proportion of eggs of each female in clutches of each size and summing across clutches.

The net result was that the best strategies were those that produced the largest clutch sizes, though the benefits of adding each additional egg diminished as clutch size increased. Predator learning.—Predator learning, as simulated by doubling the probability that a nest would be depredated after initial predation events, reduced mean offspring number by 0.9–1.1 offspring for each strategy when compared with the model without learning (Table 2). Predator learning had little effect on relative performance of egg-distribution strategies and only slightly reduced the magnitude of differences among strategies. Simulations illustrated that the influence of variance on geometric mean fitness was overwhelmed by differences in arithmetic mean fitness at population sizes of 100 and 1,000, despite the fact that variance for strategies in which a single nest was used was almost twice as high as that for strategies in which multiple nests were used (Table 2). Geometric mean fitness was less than arithmetic fitness for both population sizes (Table 2), but arithmetic mean fitness was more similar to geometric mean fitness in the simulation with 1,000 females. Nevertheless, the ranking of strategy performances was similar for populations of both 100 and 1,000 individuals (D > C > A > E > B; Table 2).

Bulmer (1984) found that different egg-distribution strategies produced the same mean fitness when entire clutches were affected by stochastic events. Our model produced the same result when stochastic events resulted in total clutch loss and predators consumed a fixed proportion of eggs. However, when predators consumed a fixed number of eggs, laying eggs in nests of other females could dilute predation risk (McKaye and McKaye 1977, Foster and Treherne 1981, Arnqvist and Byström 1991) and have important fitness consequences. Unlike in systems where predation affects entire clutches, mean offspring number differed among eggdistribution strategies in our model with partial predation. As clutch size increased, the probability that an egg was depredated in a partial predation event decreased. This is not bet-hedging, because differences in the arithmetic mean, rather than the variance, drive differences in geometric mean fitness. (Variance effects are unimportant in large populations because σ 2/N approaches zero and G ≈ µA.) Nevertheless, this finding has important implications for the evolution of intraspecific nest parasitism. In general, strategies that increased clutch size performed best because egg survival increased with clutch size. As an example, females nesting alone had higher fitness when they laid eggs in a single location (strategy A) than when they laid eggs in multiple locations (strategy B). This differs markedly from Bulmer’s (1984) conclusions when predation resulted in total clutch loss. Here, in the case with partial predation, the arithmetic mean fitness of the two strategies differed (and in large populations where variance effects are unimportant, geometric mean fitness would also differ, because G ≈ µA). Our findings suggest that females should not spread eggs among different nests if the clutch size in these nests is smaller than the clutch size obtained laying all eggs in one location. This also suggests that parasites do best if they can put all

Table 2. Arithmetic mean fitness (µA), variance (σ2), and geometric mean fitness (G) for different egg-distribution strategies when five eggs are removed per partial predation event in the simulation model with and without predator learning (n = 100) and for a population size of n = 1,000. Without learning µA, (σ2) G Scheme

(n = 100)

(n = 1,000)

A. Nest alone B. Serially nest C. Parasitize two nests D. Lay all eggs in one nest of another female E. Nest and parasitize

5.1, (22.0) 4.8 4.4, (12.3) 4.3 5.4, (10.2) 5.3 5.7, (20.2) 5.5 4.9, (12.7) 4.8

5.3, (20.5) 5.3 4.4, (13.0) 4.4 5.7, (10.0) 5.7 5.9, (20.0) 5.9 5.1, (12.0) 5.1


With learning µA, (σ2) G (n = 100) 4.0, (21.2) 3.8 3.4, (11.6) 3.3 4.3, (11.4) 4.2 4.6, (21.5) 4.4 4.0, (12.1) 3.9

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Table 3. Examination of the invasibility of strategies in populations of females nesting alone (A) or using alternative strategies (X), such as spreading eggs among nests through parasitism or serial nesting. Clutch sizes for each strategy are listed when one strategy is common and the other is rare. Mean fitness for each strategy was based on egg survival values from Figure 3, using the scenario with a predation rate of 0.03 and a frequency of partial loss of 0.5, and is presented in parentheses. (Similar patterns would be obtained with other scenarios from Fig. 3, because egg survival always increases with clutch size; thus, only one scenario is presented.) Nesting alone rare Strategy X Clutch Size A B C D E a

A 10 (5.0) 10 (5.0) 15 (5.4) 20 (5.7) 13 (5.3)

Mutant rare X

A

5, 5 (4.1) 0 (0) 0 (0) 10 (5.0)

10 (5.0) 10 (5.0) 10 (5.0) 10 (5.0)

Outcome

> > > > >

> < < >

5, 5 (4.1) 15, 15 (5.4) 20 (5.7) 7, 13 (4.8)

B cannot invade Mixed ESSa Mixed ESS E cannot invade

Evolutionarily stable strategy.

their eggs in one host nest (provided that other costs associated with the behavior are not too high). More specifically, laying all eggs in a single nest with eggs of another female resulted in higher fitness, on average, than other strategies that spread eggs among multiple, smaller nests. Furthermore, at high predation rates, strategies with small clutch sizes (B and E) performed worse than expected from dilution effects alone (Fig. 3), because the number of attacks that these clutches could withstand became important. After one attack in which five eggs were depredated, nests of females using strategy B were complete losses. Larger proportions of nests were completely lost as predation rate increased. Similar effects were apparent for strategy E, in which seven-egg clutches could withstand fewer attacks than the larger clutches of females using other strategies. Predation parameters had a large influence on the mean number of offspring and the relative fitness differences among strategies. In systems or populations where predation played a small role, egg-distribution strategies produced similar outcomes and, therefore, the selective advantages of different strategies were negligible. However, the fitness of strategies differed considerably at high predation rates, high frequencies of partial clutch loss, and substantial intensities of partial predation (Fig. 2A, B), which is consistent with findings of McKaye and McKaye (1977). The eggdistribution strategy employed became more critical as predation became a stronger selective force. However, the ranking of strategy performance remained constant over a variety of predation parameters (Fig. 2A, B). Therefore, even if predation parameters vary unpredictably among years, when all else is constant, strategy D always performed best. Invasibility of strategies.—Mutant parasites could invade a population of nonparasites only when final clutch size in the parasitized nest(s) exceeded sizes obtained by nesting alone (strategies C and D; Table 3). This occurred only when parasites used a pure parasitic strategy. Strategy E (parasitize and incubate a nest) could not invade because this mutant did not receive eggs from other parasites in the nest it incubated (because it was the only parasite when strategy E was rare in the population) and, hence, its incubated


X

clutch was smaller than that of females nesting alone. Thus, eggs in this smaller clutch would have comparatively low survival. Although a female using strategy E would have eggs in a larger, parasitized clutch and these eggs would have higher survival, this higher survival would not compensate for the lower survival of the eggs in the clutch it incubated. However, if the mutant parasite laid eggs only parasitically in nests of other females (strategies C and D) and did not incubate a nest of its own, its eggs would always be in a larger clutch when the strategy was rare and would always have higher survival than if the female had nested alone. In such cases, parasitism could invade. The benefit of parasitism was attributable not to bet-hedging but, rather, to dilution of predation risk by enlarged clutches. However, although a pure parasitic strategy (C and D) could invade a population of nesting females, it always resulted in a mixed ESS, because when nesting females became rare in the population, there were no nesting females left for pure parasites to parasitize. The success of parasites was low when nesting females were rare because pure parasites do not incubate. Our finding that a pure parasitic strategy was necessary to invade a population of nesting females was, in part, a consequence of our limitation that all females laid the same number of eggs and differed only in the distribution of those eggs. If we relax this condition and allow females to vary the number of eggs they lay, the invasibility of strategies can change. For example, if we relax the condition that females that nest and parasitize (strategy E) can lay only 10 eggs and let them lay 13 eggs (10 in their own nest and 3 parasitically), this strategy can invade. Åhlund and Andersson (2001) reported that female Common Goldeneyes (Bucephala clangula) that nest and parasitize lay more eggs than females that are pure parasites or pure nesters. However, whether the three eggs are placed parasitically or in the female’s own nest is not important with regard to egg survival in our model. Distribution of parasitism.—If parasitism can invade populations of nonparasites, why is intraspecific nest parasitism not more common among animals? The answer to this question likely lies in the costs and benefits of parasitism. Eggs may benefit from

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being in a large clutch. However, costs of being in a large clutch are also likely in many taxa. When the costs are too high, they may offset the benefits of diluted predation risk and select against such egg-distribution strategies. For example, locating nests to parasitize may be very costly (Rohwer and Freeman 1989). Such costs have been suggested to explain the disproportionate representation of intraspecific nest parasitism among colonial and cavity-nesting birds compared with birds for which nests may be harder to locate (Eadie et al. 1988, Rohwer and Freeman 1989, Beauchamp 1997). Furthermore, following nest location, hosts may resist parasites. In Wood Ducks, encounters among females are infrequent, because females visit nests only briefly (