Reproductive skew and group size: an N-person staying incentive model

Transactional models of social evolution emphasize that dominantbreeders may donate parcels of reproduction to subordinatesin return for peaceful cooperation. We develop a general transactionalmodel of reproductive partitioning and group size for N-persongroups when (1) expected group output is a concave (decelerating)functiong[N] of the number N of group members, and (2) thesubordinates may receive fractions of total group reproduction("staying incentives") just sufficient to induce them to stayand help the dominant instead of breeding solitarily. We focusespecially on "saturated" groups, that is, groups that havegrown in size just up to the point where subsequent joining by subordinates is no longer beneficial either to them (in parent-offspring groups) or to the dominant (in symmetric-relatedness groups).Decreased expected output for solitary breeding increases thesaturated group size and decreases the staying incentives.Increased relatedness decreases both the saturated group sizeand the staying incentives. However, in saturated groups withsymmetric relatedness, an individual subordinate's staying incentive converges to 1 — g[N^* — 1]/g[N^*]) regardless ofrelatedness, where N^* is the size of a saturated group, providedthat the g[N] function near the saturated group size N^* isapproximately linear. Thus, staying incentives can be insensitiveto relatedness in saturated groups, although the dominant's total fraction of reproduction (total skew) will be more sensitive.The predicted ordering for saturated group size is: Parent-fullsibling offspring = non-relatives > symmetrically relatedrelatives. Strikingly, stable groups of non-relatives can formfor concaveg[N] functions in our model but not in previousmodels of group size lacking skew manipulation by the dominant.Finally, symmetrical relatedness groups should tend to breakup by threatened ejections of subordinates by dominants, whereas parent-offspring groups should tend to breakup via unforceddepartures by subordinates.     

Social and genetic structure of paper wasp cofoundress associations: tests of reproductive skew models

Recent models postulate that the members of a social group assess their ecological and social environments and agree a "social contract" of reproductive partitioning (skew). We tested social contracts theory by using DNA microsatellites to measure skew in 24 cofoundress associations of paper wasps, Polistes bellicosus. In contrast to theoretical predictions, there was little variation in cofoundress relatedness, and relatedness either did not predict skew or was negatively correlated with it; the dominant/subordinate size ratio, assumed to reflect relative fighting ability, did not predict skew; and high skew was associated with decreased aggression by the rank 2 subordinate toward the dominant. High skew was associated with increased group size. A difficulty with measuring skew in real systems is the frequent changes in group composition that commonly occur in social animals. In P. bellicosus, 61% of egg layers and an unknown number of non-egg layers were absent by the time nests were collected. The social contracts models provide an attractive general framework linking genetics, ecology, and behavior, but there have been few direct tests of their predictions. We question assumptions underlying the models and suggest directions for future research.     

Reproductive skew and the threat of eviction: a new perspective

Most recent models of the partitioning of reproduction attempt to explain patterns of skew on the assumption that dominant individuals have complete control over breeding opportunities within the group, but may nevertheless concede a share of direct reproduction to subordinates as an incentive to remain peacefully in the association. Although these models may be applicable to some animal societies, we argue that they fail to provide a comprehensive theory of skew. Instead, we suggest that subordinates may often be able to claim unsanctioned reproduction for themselves, but will be forced to exercise a degree of reproductive restraint lest they incite ejection by the dominant. Reproductive skew, in other words, may reflect the threat of ejection (inducing subordinate restraint) rather than the threat of subordinate departure (inducing reproductive concessions by dominants). We present a simple ESS model of reproductive skew under these circumstances, which demonstrates that a shift in emphasis from reproductive concessions by dominants to reproductive restraint on the part of subordinates, radically alters the predictions of skew models. High group productivity, high relatedness and (when group members are related) strong ecological constraints are all expected to lead to reduced skew (the opposite conclusions to those of previous, concession-based analyses). The reason is that these factors reduce the benefits (or increase the costs) of ejection to the dominant, who therefore does best to tolerate more subordinate reproduction.     

From individual control to majority rule: extending transactional models of reproductive skew in animal societies

Transactional concession models of social evolution explain the reproductive skew within groups by assuming that a dominant individual completely controls the allocation of reproduction to other group members. The models predict when the dominant will benefit from donating parcels of reproduction to other members in return for peaceful cooperation. Using linear programming methods, we present a 'majority-rules' model in which the summed actions of all society members, each with equal power, completely determine the reproductive share of any single member. The majority-rules model predicts that, despite the diffusion of power, a 'virtual dominant' (a dominant lacking special behavioural power) will emerge and that the reproductive skew will be exactly that predicted if the virtual dominant were to control completely the group's reproductive partitioning. The virtual dominant is the individual to which group members have the maximum average genetic relatedness. This result greatly broadens the applicability of transactional models of reproductive skew to social groups of any size, such as large-colony eusocial insects, and explains why queens in such colonies can achieve reproductive domination without any behavioural enforcement. Moreover, the majority-rules model unifies transactional-skew theory with models of worker policing and even generates a new theory for the cooperation among somatic cells in a multicellular organism.     

A Transactional Theory of Within-Group Conflict

Transactional models of social evolution emphasize that dominant members of the society can be favored to donate parcels of reproduction to subordinate members in return for cooperation. I construct a formal theory of intragroup conflict within the framework of transactional models by determining the maximum extent to which colony members can be selfish without destabilizing the group. The difference between the maximum value of the subordinate's fraction of group reproduction that the dominant can tolerate before ejecting the subordinate and the minimum value required by the subordinate to stay and cooperate peacefully in the group defines the "window of selfishness," which in turn predicts the frequency of within-group conflict. The window of selfishness tends to increase with increasing group reproductive output, increasingly harsh ecological constraints on solitary breeding, and, counterintuitively, increasing relatedness between subordinate and dominant. Increasing fighting ability of the subordinate can either widen or narrow the window of selfishness, the latter being most likely when ecological constraints on group living are strong. Although increasing relatedness is predicted to increase the rate of within-group aggression, the mean intensity of an aggressive act should decline, as predicted by the general theory of honest signaling between relatives and the tug-of-war models of within-group selfishness. In the bidding game, in which multiple dominants bid for the services of a subordinate, the window of selfishness is predicted to have zero width. A zero-width window of selfishness and low conflict also are predicted for saturated N-person groups, that is, groups whose total output is a concave function of group size and in which the dominant is not favored to admit additional subordinates. The model's predictions are compared to empirical evidence and to predictions of alternative models of intragroup aggression, including the value-aggression model and the pure tug-of-war model.     

Patterns of reproductive skew in the polygynandrous acorn woodpecker

We compared observed levels of reproductive skew in the cooperatively breeding acorn woodpecker (Melanerpes formicivorus) with those predicted by two alternative transactional models. "Concession" models predict the degree to which parentage is shared assuming that a single dominant is in complete control of reproduction. Alternatively, "restraint" models predict reproductive sharing assuming that the dominant controls only whether subordinates remain in the group but does not control its share of reproduction. Reproductive skew is high among males: on average, the most successful male sires more than three times as many offspring as the next most successful male. Females share parentage equally and have lower constraints on dispersal and lower survival rates compared with males, which is consistent with predictions from the concessions model. Also as predicted by the concessions model, yearly variation in opportunities for dispersal before the breeding season correlates positively with skew. However, in contrast to concessions but consistent with the restraint model, skew decreases with relatedness. Thus, neither model consistently predicts patterns of reproductive skew in this species. We suggest that models of reproductive skew will need to include competitive interactions among potential breeders and mate choice before they will adequately predict patterns of reproductive partitioning in most vertebrate societies.     

Female control of the distribution of paternity in cooperative breeders

Models of reproductive skew have shed light on why animal societies vary in the partitioning of reproduction among group members. However, their application to cooperative vertebrate societies remains controversial. A particular problem is that previous models assume that skew in paternity is determined by interactions among males and males only. This conflicts with observations from many species that indicate that females exert control over the distribution of paternity. Here we address this shortfall in the current theory by developing two models to explore the expected patterns of skew in three member groups in which a female controls the allocation of paternity among two males. The first "staying incentive" model extends previous "transactional" (or "concession") models to examine the conditions where females will be willing to share reproduction among a dominant and a subordinate male to retain the subordinate in the group. The second "work incentive" model explores patterns of skew where females allocate paternity in order to maximize the amount of care their offspring receive. The models make contrasting predictions about the nature of male-female conflict over reproduction and also about the relationships between skew and relatedness, ecological constraints, the relative quality of the subordinate male, and the relative cost of care for the two males. These divergent predictions provide a schema by which the evolutionary causes of variation in skew among males can be evaluated.     

Power Struggles, Dominance Testing, and Reproductive Skew

Models of reproductive skew are concerned with the partitioning of reproduction between dominant and subordinate members of a group. In an interesting extension of these models, Reeve and Ratnieks briefly considered whether it might benefit subordinates to engage in aggressive behavior to test the fighting ability of a dominant. Their analysis suggested that such testing should be more probable in groups that feature high skew and, hence, perhaps among closer relatives (because high relatedness favors high skew). Here we explore in more detail the possibility of dominance testing. Three models that differ in the outcome of fights over dominance are presented: in the first model, the loser of the challenge is killed; in the second model, the loser is evicted from the nest; and, in the third model, the loser becomes (or remains) subordinate. In each case we consider the independent effects of the parameters that determine skew (namely, relatedness, group productivity, and ecological constraints) on the predicted level of dominance testing. We then construct an amalgamated model to examine situations where fights may lead to any one of the three outcomes. Our analysis reveals that, in the majority of cases, higher relatedness will in fact lead to lower levels of aggression. Moreover, dominance testing need not be associated with high skew. Rather, the relationship between skew and dominance testing will depend on which factor (relatedness, group productivity, or level of ecological constraints) is principally responsible for variation in the distribution of reproduction.     

Sociality, mating system and reproductive skew in marmots: evidence and hypotheses

Marmot species exhibit a great diversity of social structure, mating systems and reproductive skew. In particular, among the social species (i.e. all except Marmota monax), the yellow-bellied marmot appears quite different from the others. The yellow-bellied marmot is primarily polygynous with an intermediate level of sociality and low reproductive skew among females. In contrast, all other social marmot species are mainly monogamous, highly social and with marked reproductive skew among females. To understand the evolution of this difference in reproductive skew, I examined four possible explanations identified from reproductive skew theory. From the literature, I then reviewed evidence to investigate if marmot species differ in: (1) the ability of dominants to control the reproduction of subordinates; (2) the degree of relatedness between group members; (3) the benefit for subordinates of remaining in the social group; and (4) the benefit for dominants of retaining subordinates. I found that the optimal skew hypothesis may apply for both sets of species. I suggest that yellow-bellied marmot females may benefit from retaining subordinate females and in return have to concede them reproduction. On the contrary, monogamous marmot species may gain by suppressing the reproduction of subordinate females to maximise the efficiency of social thermoregulation, even at the risk of departure of subordinate females from the family group. Finally, I discuss scenarios for the simultaneous evolution of sociality, monogamy and reproductive skew in marmots.     

Reproduction in foundress associations of the social wasp, Polistes carolina: conventions, competition, and skew

Who reproduces in colonies of social insects is determined bysome combination of direct competition and more peaceful convention.We studied these two alternatives in foundresses of the paperwasp, Polistes carolina, by examining two different contexts:what determines who becomes the dominant reproductive and whatdetermines the amount of reproduction obtained by subordinates.The dominant queen on most nests was the foundress to arrivefirst, rather than the largest foundress, expected to be bestat fighting. This suggests that dominance is initially determinedby convention, although the persistence of some aggressiveconflict throughout the foundress period suggests that thisconvention is not absolute. Attempts to explain the divisionof reproduction using several skew theories were generallyunsuccessful. Skew was not correlated with relatedness, size differences, colony productivity, and challenges by the subordinate.P. carolina showed high constraints against solitary nesting,with a minority of females attempting to nest alone, and nonesucceeding. In this situation, most skew theories predict thatgroup stability will be independent of relatedness, yet nearlyall collected subordinates were full sisters to the queen.Reproductive partitioning in early P. carolina colonies may have more to do with enhancing worker production than with conflictover direct fitness.     

Tug-of-war has no borders: it is the missing model in reproductive skew theory

Cooperative breeding often results in unequal reproduction between dominant and subordinate group members. Transactional skew models attempt to predict how unequal reproduction can be before the groups themselves become unstable. A number of variants of transactional models have been developed, with a key difference being whether reproduction is controlled by one party or contested by all. It is shown here that ESS solutions for all situations of contested control over reproduction are given by the original tug-of-war model (TOW). Several interesting results follow. First, TOW can escalate enough to destabilize some types of groups. Particularly vulnerable are those that have low relatedness and gain little from cooperative breeding relative to solitary reproduction. Second, TOW can drastically reduce group productivity and especially the inclusive fitness of dominant individuals. Third, these results contrast strongly with those from variants of TOW models that include concessions to maintain group stability. Such models are shown to be special cases of the general and simpler TOW framework, and to have assumptions that may be biologically suspect. Finally, the overall analysis suggests that there is no mechanism within existing TOW framework that will prevent a costly struggle for reproductive control. Because social species rarely exhibit the high levels of aggression predicted by TOW models, alternative evolutionary mechanisms are considered that can limit conflict and produce more mutually beneficial outcomes. The further development of alternative models to predict patterns of reproductive skew are highly recommended.     

Reproductive skew in birds: models, problems and prospects

In recent years there has been a resurgence of interest in models to explain the partitioning of direct reproduction ('reproductive skew') among members of one sex within social groups. We review models of skew, identify problems of testing models, and consider how to make progress. One series of models assumes that dominants have complete control of subordinate reproduction, but may allow subordinates some reproduction as a way of enticing them to help or getting them to share the cost of reproduction. Another series of models assume that dominants have limited control of subordinate reproduction. Reproductive skew may also be affected by incest avoidance or control by the opposite sex. Models are largely untested because no study of birds has quantified all relevant parameters, and we see no prospect of this happening soon. A common simplifying approach is to test qualitative predictions about the effect on skew of relatedness among group members. However, these data alone cannot distinguish among models because models do not make unique predictions, partly because skew is also affected by other factors. A major problem in cooperatively-breeding birds is that any effect of relatedness will often be confounded by covariation with relatedness asymmetry and subordinate competitiveness. Progress can be made with the development of theory, controlling confounding variables through the choice of study species or types of social group, and, most importantly, testing assumptions underlying hypotheses.     

Costly young and reproductive skew in animal societies

Many recent models of reproductive skew explain subordinatereproduction as a staying incentive offered by dominants, whocan produce more young with a helper present than without. Here,we present a new, alternative explanation for subordinate reproduction,which applies whenever the fitness cost to a parent of producingyoung is an accelerating function of the number produced (ascommonly assumed in optimal clutch size theory). Under these circumstances,a dominant individual may be selected to offer a share of reproductionto a related subordinate, not as an incentive to stay, but becauseadditional offspring that would be expensive for the dominantto produce are cheap for the subordinate. "Beneficial sharing"of this kind is more likely the more closely related the subordinateis to the dominant, so that the model predicts a negative relationshipbetween skew and relatedness. This result runs directly counterto the positive relationship predicted by previous incentive-basedmodels. We explore the interaction of these contrasting effectsby developing an integrated model that allows for both beneficialsharing and staying incentives. When offspring are cheap to produce,this integrated model predicts that the incentive effect will dominate,and skew will increase with relatedness. When young are costly,in contrast, beneficial sharing will be of greater importance,and skew will decrease with relatedness.     

High reproductive skew in tropical hover wasps.

A plethora of recent models examines how genetic and environmental factors might influence partitioning of reproduction ('skew') in animal societies, but empirical data are sparse. We used three microsatellite loci to estimate skew on 13 nests of the Malaysian hover wasp, Liostenogaster flavolineata. Groups are small in L. flavolineata (1-10 females) and all females are capable of mating and laying eggs. Despite considerable variation between nests in parameters expected to influence skew, skew was uniformly high. On 11 of the 13 nests, all female eggs had been laid by a single dominant female. A second female had laid one to two out of 5-10 eggs respectively on the two remaining nests. A likelihood analysis suggested that on average, 90% of the male eggs had also been laid by the dominant. The slightly lower skew among male eggs might reflect the lower average relatedness of subordinates to male versus female offspring of the dominant. We suggest that high skew in L. flavolineata may result from strong ecological constraints and a relatively high probability that a subordinate will eventually inherit the dominant, egg-laying position.     

Queen–worker ratio affects reproductive skew in a socially polymorphic ant

The partitioning of reproduction among individuals in communally breeding animals varies greatly among species, from the monopolization of reproduction (high reproductive skew) to similar contribution to the offspring in others (low skew). Reproductive skew models explain how relatedness or ecological constraints affect the magnitude of reproductive skew. They typically assume that individuals are capable of flexibly reacting to social and environmental changes. Most models predict a decrease of skew when benefits of staying in the group are reduced. In the ant Leptothorax acervorum, queens in colonies from marginal habitats form dominance hierarchies and only the top‐ranking queen lays eggs (“functional monogyny”). In contrast, queens in colonies from extended coniferous forests throughout the Palaearctic rarely interact aggressively and all lay eggs (“polygyny”). An experimental increase of queen:worker ratios in colonies from low‐skew populations elicits queen–queen aggression similar to that in functionally monogynous populations. Here, we show that this manipulation also results in increased reproductive inequalities among queens. Queens from natural overwintering colonies differed in the number of developing oocytes in their ovaries. These differences were greatly augmented in queens from colonies with increased queen:worker ratios relative to colonies with a low queen:worker ratio. As assumed by models of reproductive skew, L. acervorum colonies thus appear to be capable of flexibly adjusting reproductive skew to social conditions, yet in the opposite way than predicted by most models.     

Reproductive skew, costs, and benefits of cooperative breeding in female wood mice (Apodemus sylvaticus)

Two current models seek to explain reproduction of subordinatesin social groups: incentives given by dominants for peacefullyremaining in the group (reproductive skew model) or incompletecontrol by dominants. These models make different predictionsconcerning genetic relatedness between individuals for thedistribution of reproduction and the stability of cooperativebreeding associations. To test these models and to furtherexplore the relationships between reproductive skew, geneticrelatedness, and investment of each participant, we performedbehavioral observations of female wood mice (Apodemus sylvaticus)raising pups communally. Our results do not support previousmodels. Differences in lifetime reproductive success were significantlygreater within mother—daughter pairs than within pairsof sisters or unrelated females. Subordinate females of eitherbreeding unit did not differ in their direct reproduction.Calculations of inclusive fitness based on our results leadto the following predictions: (1) Communal nests should occuronly when ecological circumstances prevent solitary breeding.(2) Subordinate females gain the highest inclusive fitnessjoining their mothers; they also show the highest nursing investment.(3) Mothers should accept daughters, who have no opportunityfor solitary breeding. (4) Dominant sisters and unrelated femalesshould reject subordinate females because cooperative breedingreduces their reproductive success. However, breeding unitsof dominant sisters and unrelated females nevertheless occurand can be explained by our finding that such females significantlyreduce nursing time, which may help them save energy for futurebreeding cycles. Our data demonstrate that both genetic relatednessand investment skew are important in the complex evolutionof reproductive skew in cooperative breeding.     

Using social parasitism to test reproductive skew models in a primitively eusocial wasp

Remarkable variation exists in the distribution of reproduction (skew) among members of cooperatively breeding groups, both within and between species. Reproductive skew theory has provided an important framework for understanding this variation. In the primitively eusocial Hymenoptera, two models have been routinely tested: concessions models, which assume complete control of reproduction by a dominant individual, and tug-of-war models, which assume on-going competition among group members over reproduction. Current data provide little support for either model, but uncertainty about the ability of individuals to detect genetic relatedness and difficulties in identifying traits conferring competitive ability mean that the relative importance of concessions versus tug-of-war remains unresolved. Here, we suggest that the use of social parasitism to generate meaningful variation in key social variables represents a valuable opportunity to explore the mechanisms underpinning reproductive skew within the social Hymenoptera. We present a direct test of concessions and tug-of-war models in the paper wasp Polistes dominulus by exploiting pronounced changes in relatedness and power structures that occur following replacement of the dominant by a congeneric social parasite. Comparisons of skew in parasitized and unparasitized colonies are consistent with a tug-of-war over reproduction within P. dominulus groups, but provide no evidence for reproductive concessions.     

Transactional skew and assured fitness return models fail to predict patterns of cooperation in wasps

Cooperative breeders often exhibit reproductive skew, where dominant individuals reproduce more than subordinates. Two approaches derived from Hamilton's inclusive fitness model predict when subordinate behavior is favored over living solitarily. The assured fitness return (AFR) model predicts that subordinates help when they are highly likely to gain immediate indirect fitness. Transactional skew models predict dominants and subordinates "agree" on a level of reproductive skew that induces subordinates to join groups. We show the AFR model to be a special case of transactional skew models that assumes no direct reproduction by subordinates. We use data from 11 populations of four wasp species (Polistes, Liostenogaster) as a test of whether transactional frameworks suffice to predict when subordinate behavior should be observed in general and the specific level of skew observed in cooperative groups. The general prediction is supported; in 10 of 11 cases, transactional models correctly predict presence or absence of cooperation. In contrast, the specific prediction is not consistent with the data. Where cooperation occurs, the model accurately predicts highly biased reproductive skew between full sisters. However, the model also predicts that distantly related or unrelated females should cooperate with low skew. This prediction fails: cooperation with high skew is the observed norm. Neither the generalized transactional model nor the special-case AFR model can explain this significant feature of wasp sociobiology. Alternative, nontransactional hypotheses such as parental manipulation and kin recognition errors are discussed.     

A skew model for the evolution of sociality via manipulation: why it is better to be feared than loved

Concession-based reproductive skew models predict that social groups can form via persuasion, whereby dominant individuals forfeit some reproduction to subordinates as an incentive to stay and help. We have developed an alternative skew model based on manipulation, whereby dominant individuals coerce subordinates into staying and helping by imposing costs on their independent reproductive prospects. Stable groups can evolve under a much wider range of genetic and ecological conditions under this manipulation model than under concession models. We describe evidence that various forms of pre-emptive and ongoing manipulation occur in nature and we discuss the implications of the model for the development of a general theory of social evolution.     

The past,present and future of reproductive skew theory and experiments

A major evolutionary question is how reproductive sharing arises in cooperatively breeding species despite the inherent reproductive conflicts in social groups. Reproductive skew theory offers one potential solution: each group member gains or is allotted inclusive fitness equal to or exceeding their expectation from reproducing on their own. Unfortunately, a multitude of skew models with conflicting predictions has led to confusion in both testing and evaluating skew theory. The confusion arises partly because one set of models (the ‘transactional’ type) answer the ultimate evolutionary question of what ranges of reproductive skew can yield fitness‐enhancing solutions for all group members. The second set of models (‘compromise’) give an evolutionarily proximate, game‐theoretic evolutionarily stable state (ESS) solution that determines reproductive shares based on relative competitive abilities. However, several predictions arising from compromise models require a linear payoff to increased competition and do not hold with non‐linear payoffs. Given that for most species it may be very difficult or impossible to determine the true relationship between effort devoted to competition and reproductive share gained, compromise models are much less predictive than previously appreciated. Almost all skew models make one quantitative prediction (e.g. realized skew must fall within ranges predicted by transactional models), and two qualitative predictions (e.g. variation in relatedness or competitive ability across groups affects skew). A thorough review of the data finds that these three predictions are relatively rarely supported. As a general rule, therefore, the evolution of cooperative breeding appears not to be dependent on the ability of group members to monitor relatedness or competitive ability in order to adjust their behaviour dynamically to gain reproductive share. Although reproductive skew theory fails to predict within‐group dynamics consistently, it does better at predicting quantitative differences in skew across populations or species. This suggests that kin selection can play a significant role in the evolution of sociality. To advance our understanding of reproductive skew will require focusing on a broader array of factors, such as the frequency of mistaken identity, delayed fitness payoffs, and selection pressures arising from across‐group competition. We furthermore suggest a novel approach to investigate the sharing of reproduction that focuses on the underlying genetics of skew. A quantitative genetics approach allows the partitioning of variance in reproductive share itself or that of traits closely associated with skew into genetic and non‐genetic sources. Thus, we can determine the heritability of reproductive share and infer whether it actually is the focus of natural selection. We view the ‘animal model’ as the most promising empirical method where the genetics of reproductive share can be directly analyzed in wild populations. In the quest to assess whether skew theory can provide a framework for understanding the evolution of sociality, quantitative genetics will be a central tool in future research.