Competition to Cannibalize and Parent-Offspring Conflict Lead To

doi:10.1111/j.1420-9101.2005.00941.x

Games among cannibals: competition to cannibalize and parent-offspring conﬂict lead to increased sibling cannibalism

J.C.PERRY&B.D.ROITBERG Behavioural Ecology Research Group, Department of Biological Sciences, Simon Fraser University, Burnaby, Canada

Keywords: Abstract game interactions; Sibling cannibalism occurs in many species, yet understanding of sibling parent-offspring conflict; cannibalism as an adaptation currently lags behind understanding of other sibling cannibalism; antagonistic interactions among siblings. Observed sibling cannibalism phe- sibling rivalry; notypes likely reflect the interaction between competitive games among trophic eggs. siblings and parent-offspring conflict. Using a game-theoretic approach, we derive optimal offspring cannibalism behaviour and parental modifiers that limit or facilitate cannibalism. The results are compared to contemporary frequency-independent analysis. With the addition of game interactions among siblings or parent-offspring co-evolution, our model predicts increased cannibalism (compared to the frequency-independent prediction), as offspring compete to eat siblings. When infertile eggs are present – strengthening competition – offspring risk eating viable siblings in order to gain access to infertile eggs, intensifying parent-offspring conflict. We use the results to make new predictions about the occurrence of sibling cannibalism. Additionally, we demonstrate the utility of trophic egg laying as a maternal mechanism to promote egg eating.

Theory for resource-based sibling rivalry (SR) has been Introduction well developed (O’Connor, 1978; Stinson, 1979; Dickins Although there is typically a high degree of relatedness & Clark, 1987; Parker et al., 1989; Godfray & Harper, among siblings, antagonistic sibling interactions are 1990; Godfray & Parker, 1992; Forbes, 1993; Rodrı´guez- frequently observed. Selfish sibling interactions may be Girone´s, 1996; Mock & Parker, 1997; Mock et al., 1998), broadly categorized by whether they involve competition and the expected limits to selfishness in resource-based for resources or cannibalism (Mock & Parker, 1997). As competition have been clearly outlined. These models an example of resource-based competition, many nest- have generally required a game-theoretic approach to ling birds compete for limited parental investment (Mock predict optimal selfishness, because it is necessary to take & Parker, 1997, and refs therein). In the extreme case, into account the strategies of other offspring in order to there may be selection to eliminate competitors via predict optimal selfishness for a sibling. As an example siblicide (e.g. O’Connor, 1978). In contrast, for cannibal- (paraphrasing Parker et al.’s (1989) remarks), consider a istic interactions, obtaining a meal (in the form of a senior nestling ‘A’, which must decide what fraction of relative) is generally the driving selective pressure. resources to leave for a junior sibling ‘C’. The usual Sibling cannibalism occurs across diverse taxa, and assumption is that if A leaves a food item, another senior illustrative species may be found within insects (e.g. sibling ‘B’ might consume that food item, rather than Michaud & Grant, 2004), other invertebrates (e.g. Iida, leaving it for the intended C. In this case, A’s best option 2003), birds (refs within Stanback & Koenig, 1992), might be to eat the item itself, rather than allowing B to Amphibia (refs within Crump, 1996) and fish (e.g. have it. Thus, the best strategy for a senior sibling to Fitzgerald & Whoriskey, 1992). adopt towards vulnerable juvenile siblings depends on what other senior siblings do. In contrast, current Correspondence: Jennifer C. Perry, Department of Zoology, University of Toronto, 25 Harbord St., Toronto, ON, Canada M5S 3G5. understanding of sibling cannibalism as an adaptation Tel.: 416-978-0387; fax: 416-978-8532; (reviewed in the following section; Eickwort, 1973; e-mail: [email protected] Crespi, 1992; Dong & Polis, 1992; Pfennig, 1997) is based

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on a ‘simple’ optimization approach (sensu Mock et al., (P + P¢). By re-stating Hamilton’s Rule (Hamilton, 1964) 1998), in which the optimal strategy (to eat a sibling or for the spread of a selfish act (Mock & Parker, 1997), not) does not depend on the actions of other siblings in sibling cannibalism is favoured when the relative benefit the same clutch. Yet it is clear that, when offspring to the cannibal exceeds the cost to the victim, weighted interact in groups, victim siblings themselves become a by relatedness – that is, when P¢ > Pr. This can be restated resource over which cannibal siblings compete (Mock as , 1998). Such competition may change the benefit et al. 0 thresholds for sibling cannibalism from the current P =P > r: ð1Þ prediction. For example, a cannibal must increase survival by at Furthermore, current models of sibling cannibalism do least 50% to profit from consuming a full sibling. not incorporate parental interests in the degree of Throughout the paper, we refer to the term (P¢/ cannibalism among their offspring. It can be optimal for P) · 100 as the relative benefit of cannibalism (RBC). parents to facilitate or to limit selfish interactions among As mentioned above, in this model of sibling canni- offspring, depending on the benefit that an offspring balism, the optimal phenotype does not depend on the receives from a selfish act towards a sibling, relative to frequency distribution of phenotypes in the population. the cost of the act for the target sibling (O’Connor, 1978). In the model, the probability of survival of the victim C, Because the thresholds for parents and offspring to PC, is equal to the probability of survival for all offspring, benefit from cannibalism differ (as described below), P*. The optimal cannibalism behaviour of A with respect parent and offspring interests may overlap or conflict. to C is then considered, using P* as the basis of the Mothers have several tactics available for managing inclusive fitness cost of eating C. However, if clutch size is cannibalism among offspring. For example, hatching increased to three and there is a second senior offspring, synchrony may limit sibling egg cannibalism (e.g. B, then the true value of PC is modified by B’s phenotype: Frechette & Coderre, 2000), whereas hatching asyn- PC now depends on the frequency distribution of chrony (e.g. Polis, 1981) and trophic egg laying (the phenotypes in the B offspring position. As the frequency production of infertile eggs as food for offspring, Crespi, of the cannibalistic phenotype in the population (f) 1992; Perry & Roitberg, 2005) facilitate egg eating. increases, PC approaches 0: Evolutionary games between two sets of family lim PC ¼ 0 members – among siblings and between parents and f !1 offspring – may, then, influence observed sibling cannibalism behaviour. This study investigates the effect of whereas, if cannibalistic phenotypes are rare, the these games on predicted sibling cannibalism behaviour. approach used above becomes approximately correct: We model the co-evolution of sibling cannibalism and lim PC ¼ P : two maternal tactics – hatching synchrony or asynchrony f !0 and trophic egg production – for managing cannibalism It is clear, then, that when siblings interact in groups of among offspring. Given the complexity of a co-evolving, more than two, the usual frequency independent analy- multiple-trait system, there is a large set of possible sis may not apply. solutions. Here, we use stochastic simulation models (Goldberg, 1989) to determine the evolved outcome. In From a parent’s perspective, sibling cannibalism pro- separate experiments, we investigate how three factors vides a net benefit when more offspring are gained from alter the expected frequency independent thresholds: (1) the increased survival of cannibals than are lost as victims a SR game; (2) the co-evolution of, or constraints on, (e.g. Crespi, 1992). With pairwise sibling interactions, parent and offspring traits; and (3) infertile eggs, which this occurs when were introduced to intensify the competitive game P0 > P: ð2Þ among siblings. We use the results to make new predictions about expected patterns of sibling cannibal- Parents favour cannibalism when the survival of ism behaviour. The study also has implications for the cannibals is at least doubled through cannibalism (when evolution of trophic egg laying. RBC > unity). The model demonstrates that parent and offspring interests may overlap or conflict, depending on intra- Current understanding of sibling cannibalism clutch relatedness and the relative increase in survival Eickwort (1973; see also Crespi, 1992; Pfennig, 1997) from cannibalism. Neither parents nor offspring benefit used Hamilton’s rule to investigate the conditions from cannibalism when RBC < r. When r < RBC < 1, it favouring sibling cannibalism. To review the argument, is in the interests of offspring to cannibalize siblings and consider a senior offspring (‘A’) with a probability of the interests of parents to prevent cannibalism. When survival, P, in a two-offspring clutch. If A cannibalizes its RBC > 1, parents and offspring agree that cannibalism junior sibling (‘C’), it receives an increase in survival, P¢, should proceed. The model also shows that, for sibling through reduced starvation risk, and has total survival cannibalism to be beneficial, a noncannibal’s probability

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of survival must be low. For example, if P > 2/3, In our simulations, individuals were represented as individuals cannot be selected to eat full siblings due to 12-byte strings of information, divided into 4-byte the constraint that (P¢ + P) £ 1. Similarly, for parents to segments (here, genes) that code for the hatching favour sibling cannibalism survival must be less than synchrony, trophic egg laying, and cannibalism lag time 50%, else eqn 2 cannot be satisﬁed. behaviours. Each individual possessed all three genes, with the cannibalism gene expressed in offspring and the The models hatching synchrony and trophic egg genes expressed in mothers. In computer simulations, we modelled sibling egg can- In interactions within clutches, each pair of haploid nibalism and maternal inﬂuence of cannibalism over parents produces one clutch of 16. The number of trophic many generations, allowing coded ‘genes’ for the behav- eggs (0–15) is determined by the mother’s trophic egg iours to evolve according to the success of the coded allele; ‘trophic’ status is assigned randomly. The remain- strategy. To describe the ecological situation of interest in ing viable offspring hatch over 16 time units, in a pattern general terms, we consider sibling interactions within determined by the mother’s allele for hatching synchrony clutches of more than two offspring, with potential egg (Table 1). For example, all offspring might hatch within cannibalism, no parental care, and dispersal of offspring one time unit, or hatching might be spread out over time. after egg cannibalism. Within a clutch, we assume that In each time unit, the hatching offspring (if any) was offspring hatch more or less synchronously, with the selected randomly. After an offspring hatches, it waits degree of synchrony under maternal control. We assume some number of time units (1–16, determined by its allele that cannibal offspring consume, at most, one egg. for ‘cannibalism lag time’) before seeking an egg to eat Cannibals may consume a potentially viable sibling, or within its clutch; victims were selected randomly from an infertile or trophic egg. Infertile eggs are produced by remaining unhatched eggs. A delay of 16 time units constraint (i.e. mothers cannot avoid producing them), permits all viable siblings to emerge. After time 16, whereas trophic eggs are produced according to a offspring may continue to consume any trophic or mother’s trophic egg gene. We assume that viable, infertile eggs present (to a maximum of one egg per infertile and trophic eggs provide equal food value. We offspring). Thus, an offspring’s opportunity to cannibalize assume that cannibals do not discriminate between depends on the availability of unhatched eggs when it viable and inviable eggs; there is apparently no such emerges and the combination of its hatch time and delay discrimination in several well-studied empirical systems time. For example, an offspring that hatches at time 5 and (e.g. Pienkowski, 1965; Baur & Baur, 1986). Mothers has a lag time of 12 will seek an egg to eat at time 17, produce only one clutch, after mating once. when all potentially viable eggs will have hatched.

Table 1 The range of hatching synchrony phenotypes tested in simulations, expressed as the number of offspring that hatch in each time period. Mothers produce clutches with the hatching pattern indicated, based on the allele they possess.

Time period

Allele value Possible cannibalism events* 12345678 910111213141516

10 16 21 115 32 1141 43 11131 54 111211 6 5 1111111 7 6 1111011 1 8 7 1111 911 1 9 8 1111 811 1 1 10 8 11111 711 1 1 11 8 11111 611 1 1 1 12 8 111111 511 1 1 1 13 8 1111114111111 14 8 1111111 311 1 1 1 1 15 8 1111111 211 1 1 1 1 1 16 8 1111111 111 1 1 1 1 1 1

Blank cells signify zeroes. *Derived for a clutch size of 16 and the condition that offspring eat, at most, one egg. Alleles closer to 16 allow maximal cannibalism at a wider range of offspring cannibalism delay phenotypes.

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For each generation, interactions within two hundred value in all individuals, and mutation was prevented clutches were simulated simultaneously and independ- within these genes. In these simulations, the cannibalism ently. When time ended (i.e. when no further hatching lag time gene evolved, while trophic egg laying was or egg eating could occur within a clutch), successfully prevented and hatching was maximally asynchronous. hatched offspring had a probability of surviving starva- Thus, offspring could potentially consume viable siblings, tion that was dependent on number of eggs consumed creating selection on the cannibalism lag time gene, with (0 or 1). From the survivors, 200 pairs of individuals were the direction of selection pressure dependent on the RBC randomly selected as parents of the next generation. value. Thus, fitness was assigned indirectly: successful alleles Next, we tested the two maternal genes when parent- made more copies of themselves and were proportionally offspring co-evolution was prevented and there were no more represented in the pool from which reproducing infertile eggs. In the second set of control simulations, we individuals were drawn. allowed hatching synchrony to evolve with cannibalism The algorithm that we used, often referred to as a lag time fixed at minimal (creating selection on mothers genetic algorithm, introduced new alleles – from which to manage cannibalism among their offspring) and to search for optimal strategies – through mutation- and trophic egg laying prevented (constraining them to crossover-like processes during reproduction. The chance respond with hatching synchrony alone). Finally, we of mutation (i.e. changing a 1 to 0 or 0 to 1) was 1% at allowed the trophic egg gene to evolve with cannibalism each byte locus. When crossover occurred (in 10% of lag time fixed at minimal and hatching at completely offspring) the parental chromosomes were spliced at a synchronous. In these simulations, mothers could not random location anywhere along the string. High rates prevent sibling cannibalism, but could facilitate egg are used to quickly generate the variation from which eating by laying trophic eggs. optimal solutions may be found (as in, e.g. Browning & After confirming that our simulations could generate Colman, 2004). For some simulation sets, we conducted the frequency-independent predictions for optimal off- replicates with mutation and crossover (MC) rates set to spring and maternal behaviours, we conducted three zero to ensure that the introduction of new alleles did not experiments (described below) that introduced game influence the results. By incorporating these two natural interactions, parent-offspring co-evolution, and intensi- selection-like processes – differential success of inherited fied competition. We compared the predicted evolutio- traits and the testing and re-testing of strategies through narily stable mean phenotypes from these models to the introduction of new alleles – the algorithm finds the those of the controls. evolutionarily optimal phenotype for each behaviour considered. Because genetic algorithms can quickly Experiment 1: a sibling rivalry game search a large strategy set, they are a valuable technique for complex co-evolutionary games (e.g. Forrest, 1993). To introduce SR, eggs were not paired as described above. To initialize simulations, a population of 400 randomly Any hatched offspring could consume any unhatched drawn strategies was created (i.e. the aforementioned egg. To ensure that the introduction of variability 12-byte strings). For each parameter set examined, we through MC did not affect the results, we ran simulations conducted five simulation runs with different random with MC rates set to 1 and 10%, respectively, or to 0%. number seeds. Simulations ran for 1000 generations; gene The response variable of interest was the optimal canni- values stabilized after approximately 100 generations. balism lag time. We compared the optimal lag time from these simulations to the first set of control simulations, in which the competitive game among siblings was preven- Control simulations: frequency independence ted. As in the first set of control simulations, both In a set of control simulations, we tested that our model maternal genes were fixed, with hatching at maximally reached the same conclusions as the frequency-inde- asynchronous and trophic egg laying prevented. pendent model (outlined in the introduction) when the In further simulations, we permitted either the hatch- assumptions were identical. ing synchrony or trophic egg laying genes to evolve with First, we tested the cannibalism lag time gene when the other genes fixed (as described for the second set of competition among cannibals was prevented, there was control simulations) and with competitive interactions no parent-offspring co-evolution and no happenstance among offspring. These simulations are used for com- infertile eggs. To prevent the SR game, we randomly parison with experiment 2. paired offspring at the beginning of within-clutch interactions. The first-hatching offspring within each pair Experiment 2: parent-offspring co-evolution could consume only the egg it was paired with; if the paired egg was not consumed, no other offspring Parent-offspring co-evolution was introduced by permit- was permitted to eat it. To prevent parent-offspring ting all three genes to evolve at once. We tested whether co-evolution, we permitted only one gene to evolve per co-evolution affected the optimal maternal and offspring simulation set. The other genes were fixed for one allele phenotypes by comparing the results of these simulations

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to those of experiment 1, in which a competitive game 16 * among siblings was present but co-evolution was pre- * * vented. 14 12 Experiment 3: happenstance infertile eggs 10 We introduced happenstance infertile eggs (i.e. unavoid- 8 able infertility, in contrast to trophic eggs under a 6 mother’s genetic control) to intensify the competitive 4 game among siblings. Simulations were conducted in Cannibalism lag time which all clutches contain such eggs (2 per clutch of 16), 2 and in which SR and co-evolution were also present. We 0 tested the effect of infertile eggs on optimal maternal and 0 25 30 40 44 50 60 75 90 100 125 offspring traits, compared to the optimal phenotypes Relative benefit of cannibalism (RBC) from experiment 2. In these (and all) simulations, offspring could consume infertile eggs after all viable Fig. 1 Optimal cannibalism lag time phenotype when there is siblings hatched, if lag times were long enough. competition among siblings to cannibalize (open squares) or when such competition is prevented (filled circles), for a range of values of relative benefit from cannibalism (RBC; i.e. the per cent increase in Statistical analyses survival from eating one egg). A delay of 16 time units before We took the evolutionarily stable mean phenotypes to be cannibalism permits all viable siblings to hatch, whereas a delay of the mean allele value of each gene for the last 200 one time unit (the minimum) means that a potentially viable sibling will be eaten. When a competitive game among offspring was generations, averaged over all individuals in the parent prevented, our simulated cannibals obeyed the 50% threshold for population and taken every 10th generation. Allele sibling cannibalism predicted from a frequency-independent appli- values and phenotypes correspond: the cannibalism lag cation of Hamilton’s Rule (see text, Eickwort, 1973; Pfennig, 1997). time allele represents the average number of time units When game interactions were introduced, sibling cannibalism that offspring wait before attempting to eat an egg; the became optimal at lower RBC values. The optimal phenotype was trophic egg allele equals the number of trophic eggs in a obtained from a population average over the last 200 generations of clutch; and the hatching synchrony allele corresponds to each simulation, when gene values had stabilized; five replicates the hatching patterns in Table 1. To test for an effect of were conducted for each combination of factor values. Least-squares treatment (in experiment 1, presence or absence of means are presented, which account for variation in optimal competition among siblings; in experiment 2, presence or cannibalism lag time caused by the other factors of the ANOVA model presented in Table 2. Asterisks indicate significant differences among absence of co-evolution; in experiment 3, presence or means (P < 0.05), based on Tukey post hoc tests. For clarity, RBC absence of infertile eggs), we included the factors RBC, values are presented as categories. treatment, and the RBC · treatment interaction in ANOVA models using the program JMP 5.0. In experiment 1, the additional factor of ‘MC’ – prevented or allowed – (Fig. 1). The maternal genes of hatching synchrony and was included, along with two-way interactions (the trophic egg laying also show different trajectories below three-way interaction term was not significant and was and above the 100% RBC threshold (eqn 2) for mothers therefore dropped from the final model). The response to benefit from cannibalism among offspring. At variables were the evolutionarily stable mean pheno- RBC < 100%, mothers limit cannibalism with synchro- types for the responding genes (for experiment 1, nous hatching (Fig. 2b). When RBC > 100%, mothers cannibalism lag time; for experiments 2 and 3, all three facilitate egg consumption with asynchronous hatching genes). We used the Tukey–Kramer post hoc tests to test (Fig. 2b) or trophic eggs (Fig. 2c). for differences between groups. Least-squares means, which account for variation in the response variable Experiment 1: sibling rivalry caused by all other factors in the ANOVA model, are presented. The addition of game interactions significantly decreased the RBC threshold at which sibling cannibalism was Results favoured (Table 2 and Fig. 1). With the addition of game interactions, average cannibalism lag times decreased The results from control simulations, in which competi- (compared to control simulations) at 40 and 44% RBC – tion among potential cannibals was prevented, match the before the 50% threshold predicted by the frequency- frequency independent prediction. As expected from independent analysis. Importantly, the interaction eqn 1, when there was no competition among offspring, between RBC and game interactions was significant the evolutionarily stable cannibalism lag time declined (Table 2): the effect of SR occurred only at 40–50% RBC sharply and significantly at RBC values above 50% (Fig. 1). At RBC values above the 50% threshold,

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cannibalism lag times were minimal with and without Table 2 The effect of the RBC (at levels 0–125%), sibling rivalry game interactions, as predicted by both models. (SR) (present or absent), and mutation and crossover (MC) (rates set Whether MC rates were set to zero or to positive values to 0 or 1 and 10%, respectively) on the average cannibalism delay (mentioned under ‘The Models’) did not affect the gene values derived from simulations. evolutionary stable cannibalism lag time (Table 2). How- Source d.f. F Ratio P ever, MC rates, in interaction with the factors RBC and game interactions, affected the evolved cannibalism lag RBC 10 394.1 <0.0001 time (Table 2). This occurred because, without MC, new SR 1 82.6 <0.0001 RBC SR 10 35.2 <0.0001 alleles were not reintroduced each generation; if a · MC 1 2.4 0.1207 RBC · MC 10 19.1 <0.0001 SR · MC 1 6.7 0.0107 (a) 16 Whole model: F33,186 ¼ 138.7, P < 0.0001.

14 * particular allele became ﬁxed, it remained ﬁxed for the 12 rest of the simulation. 10

8 Experiment 2: co-evolution vs. constraints on traits * 6 Whether maternal and offspring traits co-evolved, or evolved independently while other traits were fixed, Cannibalism lag time 4 significantly affected the evolutionarily stable behaviours for both mothers and offspring (Fig. 2). 2 Co-evolution of parent and offspring traits caused a 0 25 50 75 90 100 125 decreased average cannibalism lag time, compared to the result when only cannibalism delay evolved (Fig. 2a; (b) 16 F1,56 ¼ 97.5, P < 0.0001). The decrease in lag time was significantly different at 25 and 50% RBC only, though * 14 lag time was always lower when co-evolution occurred (Fig. 2a; RBC · co-evolution interaction: F ¼ 57.0, 12 6,56 P < 0.0001). 10 The effect of parent-offspring co-evolution on hatching synchrony depended on the RBC value (Fig. 2b; effect of 8 * co-evolution: F1,64 ¼ 18.9, P < 0.01; RBC · co-evolution 6 interaction: F7,64 ¼ 143.5, P < 0.0001). At 0% RBC,

Hatching asynchrony 4

2 Fig. 2 The effect parent-offspring co-evolution on optimal maternal and offspring phenotypes that influence sibling cannibalism. 0 25 50 75 90 100 110 150 Co-evolution was permitted by allowing both parent and offspring genes to evolve (open squares), or prevented by having each trait (c) evolve alone (filled circles) as described in the text. Of interest is the 8 * change in optimal phenotype as the relative benefit of cannibalism changes (RBC; see the caption for Fig. 1). Asterisks indicate significant * differences among means (P < 0.05) by Tukey post hoc tests. (a) 6 Optimal cannibalism lag time for offspring; longer delays indicate less willingness to cannibalize viable siblings (see text). (b) Hatching synchrony phenotypes are given in Table 1. Low values indicate more 4 * synchronous hatching and, thus, an attempt to prevent cannibalism among offspring. (c) Values for the trophic egg phenotype correspond to the optimal number of trophic eggs produced in a clutch of 16. It

Trophic egg laying Trophic 2 was never optimal to produce more than eight trophic eggs, because offspring could consume one egg at most. The factor ‘co-evolution’ signiﬁcantly affected optimal phenotypes for all three behaviours (P < 0.01; see text). Optimal phenotypes were calculated as described 0 in the caption of Fig. 1. Least-squares means are presented, which 0 25 50 75 90 100 110 125 150 control for variation in optimal phenotypes caused by the RBC and the Relative benefit of cannibalism (RBC) RBC · co-evolution interaction.

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hatching was, on average, less synchronous when co-evolution simulations (F1,72 ¼ 37.1, P < 0.0001); the co-evolution with offspring occurred (Fig. 2b). A likely difference was significant for RBC values of 125 and explanation is that, when cannibalism lag times could 150% (Fig. 2c; RBC · co-evolution interaction: F8,72 ¼ evolve, lag times quickly increased to avoid sibling 46.6, P < 0.0001). The opposite pattern occurred at 75% cannibalism at 0% RBC; hence mothers did not need to RBC; then the trophic egg allele was higher when prevent sibling cannibalism with synchronous hatching. co-evolution occurred. When RBC ¼ 150%, hatching was, on average, more synchronous with co-evolution (Fig. 2b), indicating that Experiment 3: nonevolved infertile eggs mothers did not attempt to facilitate as much sibling cannibalism with co-evolution. When we strengthened the competitive game among More trophic eggs were produced when the trophic siblings by introducing infertile eggs, offspring became egg-laying gene evolved alone, compared to the more willing to risk cannibalizing viable siblings. The average cannibalism lag time decreased significantly (Fig. 3a; F1,80 ¼ 10.2, P ¼ 0.002), compared to results (a) from experiment 2 in which game interactions occurred 16 without infertile eggs. The difference was detectable at 14 10% RBC (Fig. 3a; RBC · infertile eggs interaction: * 12 F9,80 ¼ 4.8, P < 0.0001). At RBC values above 50%, the delay until cannibalism was minimal in the presence and 10 absence of infertile eggs. 8 Mothers produced more synchronously hatching clut- 6 ches when infertile eggs were present (Fig. 3b; F1,80 ¼ 4 6.8, P < 0.05). The difference in synchrony in the Cannibalism lag time presence and absence of infertile eggs was not detectable 2 at any RBC level (Fig. 3b), though the interaction term 0 10 25 50 75 90 100 110 125 150 was significant (RBC · infertile eggs interaction: F9,80 ¼ (b) 3.0, P < 0.01). 12 Unsurprizingly, fewer trophic eggs were produced in the presence of infertile eggs (Fig. 3c; F1,80 ¼ 133.4, 10 P < 0.0001). The difference was detectable at RBC values from 75 to 125% (Fig. 3c; RBC · infertile eggs interac- 8 tion: F9,80 ¼ 5.6, P < 0.0001).

6 Discussion

4 Our results indicate that games among family interactors Hatching asynchrony affect both the extent of selﬁshness expected among 2 siblings and parental attempts to facilitate or limit selﬁsh interactions among offspring. We have elaborated on the 0 10 25 50 75 90 100 110 125 150

(c) 6 Fig. 3 The effect of infertile eggs on optimal maternal and offspring phenotypes related to sibling cannibalism, for a range of values of the relative benefit of cannibalism (RBC; see text). Infertile eggs * * were introduced to strengthen the competitive egg-eating game * 4 * among siblings; clutches had either no infertile eggs (filled circles) or * two per clutch of 16 (open squares). Asterisks indicate a significant difference among means (P < 0.05) by Tukey post hoc tests. (a) In the presence of infertile eggs, optimal cannibalism lag time decreased even at low RBC values – that is, cannibals were more willing to 2 cannibalize potentially viable siblings. (b) Hatching was significantly

Trophic egg laying Trophic more synchronous in the presence of infertile eggs (P < 0.05; see text), though this difference was not detectable at any given level of RBC. (c) The optimal number of trophic eggs (for a clutch of 16 offspring) decreased when infertile eggs were present. Optimal 0 phenotypes were calculated as described in the caption of Fig. 1. 0 10 25 50 75 90 100 110 125 150 Least-squares means are presented, which control for the variation Relative benefit of cannibalism (RBC) in optimal phenotypes caused by factors other than ‘infertile eggs’.

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usual predictions of optimal cannibalism behaviour The effect of co-evolution on hatching synchrony and towards siblings, which are derived for the frequency- trophic egg production – decreasing asynchrony and independent case. Below, we discuss our predicted trophic egg production at RBC values exceeding 100% optimal behaviours in parents and offspring (especially (Fig. 3b, c) – is easily understood. At RBC > 100%, when where these differ from frequency-independent predic- both maternal genes were permitted to evolve, mothers tions) and, where possible, compare our qualitative used a combination of asynchronous hatching and predictions with natural systems. The results of the trophic eggs to facilitate egg eating among offspring. model are directly applicable to species in which offspring More particularly to our next argument, mothers did not interact within a confined physical space (a nursery, sensu use hatching asynchrony alone. It may seem counter- Mock & Forbes, 1995) for some small portion of their intuitive that a mother’s best option is to produce a lives – small because extended interactions likely involve trophic egg (e.g. Dixon, 2000), when instead, she could resource-based competition and, thus, an additional increase hatch asynchrony so that eggs may continue selection pressure favouring siblicide. Our results apply development if they escape cannibalism. In our simula- when clutch size exceeds two, and when there is the tions, it was not, in fact, better to increase hatching possibility of competition among siblings for cannibalism asynchrony than to produce trophic eggs. We suggest opportunities (i.e. at least two offspring are capable of that mothers produce trophic eggs in order to ensure that eating a third); when these conditions do not exist, the egg eating occurs. If hatching asynchrony alone is used, frequency-independent prediction likely applies. Fur- there is some chance that delayed-hatch eggs will hatch thermore, our results may be extended to any selfish acts first. among family members in which the benefit of selfish- The control and experiment 1 simulations – in which ness accrues to one individual only, such that individuals some traits were prevented from evolving – may be may compete to reap that benefit. similar to natural systems in which offspring or parental Previous predictions of the threshold for benefit from traits are constrained. For example, in predatory insects, cannibalizing a sibling (Eickwort, 1973; Crespi, 1992; offspring may experience strong selection for early Dong & Polis, 1992; Pfennig, 1997) considered the predatory ability. Genetic correlations may prevent frequency-independent case. Incorporating game inter- selection from separating the behaviours of attacking actions among siblings – a competition for the resource of prey and cannibalizing siblings soon after emergence. consumable eggs – decreases the predicted benefit Furthermore, mothers may be unable to make hatching threshold (Fig. 1). Sibling games appear to drive the perfectly synchronous, if egg formation and deposition evolution of higher cannibalistic tendency than would are not perfectly precise processes. The presence of otherwise be optimal. constraints gives control of the occurrence of sibling A second evolutionary game – parent-offspring conflict cannibalism to the unconstrained party. Thus, in natural over sibling cannibalism – also affected optimal maternal systems, the observation of sibling cannibalism does not and offspring behaviours. Cannibalism lag time was imply that parents experience a net fitness benefit from reduced in simulations in which parental and offspring cannibalism; they may simply be unable to prevent it. behaviours co-evolved (Fig. 2a), compared to simulations in which maternal traits were constrained (i.e. Empirical predictions mothers could not prevent cannibalism with synchronous hatching, nor facilitate egg eating with asynchronous The results allow several predictions about patterns of hatching and trophic eggs). A possible explanation is that sibling cannibalism in natural systems. First, a key co-evolution intensified the SR game. When maternal prediction from the model is that, when there is genes were permitted to evolve along with cannibalism competition among cannibals for victims, sibling canni- lag time, hatching became synchronous at RBC values balism should occur when the RBC is less than 50%; the less than 50% – perhaps strengthening competition for precise threshold favouring sibling cannibalism should rare cannibalism opportunities. In effect, maternal depend on the strength of competition among cannibals. attempts to limit cannibalism among offspring may In contrast, the frequency independent model (outlined intensify their cannibalistic tendencies. An alternative in the introduction) predicts sibling cannibalism only at explanation is that, with the reduced opportunity for can- RBC > r, the coefficient of relatedness. Testing this nibalism due to synchronous hatching (at RBC < 50%), prediction requires quantitative estimates of the increase selection against sibling-eating individuals may have in survival from eating a sibling, relative to survival weakened. However, this second hypothesis is not probability under normal food conditions without can- supported by the results: in the co-evolution simulations nibalism. Most useful would be systems in which the of experiment 2, at RBC values of 25 and 50%, RBC < relatedness among siblings. However, most cannibalism lag times decreased from the random observations of sibling cannibalism are qualitative (e.g. initialization average of 7.5 time units. This pattern Byrne, 1996; Frechette & Coderre, 2000; Rienks, 2000; indicates strong directional selection, rather than wea- Margalida et al., 2004). We know of six quantitative kened selection and drift. studies of sibling cannibalism (Table 3). Of these, RBC

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Table 3 Quantitative studies of sibling cannibalism. The RBC refers to the increase in survival that cannibals experienced, relative to survival without cannibalism in the food conditions indicated.

Species RBC (%) Comparison Source

Coccinellidae H. axyridis 16 Noncannibals at high aphid (prey) density Osawa (1992) H. axyridis 226 Noncannibals at low aphid (prey) density Osawa (1992) H. axyridis 114 Unfed larvae with access to water Kawai (1978) C. maculata lengi 25 Unfed larvae without water Pienkowski (1965) S. bisellata 37 Unfed larvae without water Ng (1986) Menochilus sexmaculatus 70 Unfed larvae without water Ng (1986) Coleophora inaequalis 84 Unfed larvae without water Ng (1986) Coccinella repanda 135 Unfed larvae without water Ng (1986) Other taxa Subsocial burrower bug Admerus triguttulus 75 Unfed larvae Kudo & Nakahira (2004) Land snails Arianta arbustorum 75 Noncannibals given access to same vegetable diet as cannibals Baur (1990)

values less than 50% were reported for three species. experience strong resource competition, and cannibalism For the ladybird beetle Harmonia axyridis, RBC depended in birds is probably driven by the need to eliminate a strongly on local food conditions (Osawa, 1992); it is not competitor rather than the value of siblings as meals possible to estimate an overall RBC without knowledge (Fitzgerald & Whoriskey, 1992). of how frequently individuals encounter different food In our model, the presence of infertile eggs strength- environments. Ng (1986) reports RBC values of less than ened the competitive game among siblings, further 50% for two other ladybirds, Coleomegilla maculata lengi lowering the RBC threshold for sibling cannibalism (25%) and Spilocaria bisellata (37%; Table 3), in which (Fig. 3a). In the model, cannibal offspring had the option sibling cannibalism is common. Average relatedness in of waiting until viable siblings had hatched before these species is not known; the possibility that offspring consuming infertile eggs; instead, cannibals risked eating are less than full siblings cannot be excluded. However, viable siblings to gain access to infertile eggs first. Thus, a this study measured the benefit of cannibalism relative third prediction is that sibling cannibalism should occur to ‘no food’ conditions, and thus overestimates the RBC more frequently in species that produce infertile eggs, if, experience in natural conditions. Given that offspring as assumed in our model, offspring cannot distinguish within a clutch have relatedness of ‡0.25, cannibal between viable and infertile eggs. This prediction is C. maculata lengi apparently experience an RBC value complicated by the possibility that infertile egg produc- less than relatedness among siblings. Hence, the pattern tion is under maternal control – i.e. that the infertile eggs is consistent with the hypothesis that game interactions are trophic eggs. Trophic eggs are expected only when drive the evolution of increased tendency to cannibalize RBC > 100%, that is, when sibling cannibalism is siblings, but not with the frequency-independent hypo- favoured even without game interactions. Thus, in thesis that offspring should cannibalize full siblings only testing this prediction, it will be important to distinguish if RBC > 50%. Additional studies quantifying RBC infertile eggs produced by constraint from infertile eggs values compared to natural conditions would be of that serve a trophic function. The presence of infertile great interest in light of this prediction. Studies of eggs – common in many taxa – has implications for related taxa in which some species exhibited sibling sibling cannibalism because it strengthens competition cannibalism and others did not (e.g. coccinellids) would among siblings. be especially useful, if noncannibal species could be induced to consume siblings so that the benefit of doing Conclusion so may be measured. A second and related prediction is that sibling canni- Because sibling cannibalism is found in many diverse balism should be more common in species with game taxa, it is important to understand the selective forces interactions among siblings, compared to species in driving its evolution. Previous understanding of sibling which there is no game. Sibling cannibalism should, cannibalism is summarized by Mock & Parker (1997), then, be more common in species that produce clutches p. 6): ‘when a sib is more valuable as food than as a gene of two or more offspring, compared to species in which bearer, it should be consumed’. We may now add to this clutch size is two. The prediction is difficult to test with a condition, ‘it should also be consumed if it will be particular taxonomic group. For example, few insect taxa consumed by another sibling anyway’. Mock & Parker produce clutches of only two eggs. While two-egg (1997) highlighted the potential importance, and deficit clutches are more common in birds, bird nestlings of study, of evolutionary games within family units for

J. EVOL. BIOL. 18 (2005) 1523–1533 ª 2005 EUROPEAN SOCIETY FOR EVOLUTIONARY BIOLOGY 1532 J. C. PERRY AND B. D. ROITBERG

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