Are reproductive skew models evolutionarily stable?

Reproductive skew theory has become a popular way to phrase problems and test hypotheses of social evolution. The diversity of reproductive skew models probably stems from the ease of generating new variations. However, I show that the logical basis of skew models, that is, the way in which group formation is modelled, makes use of hidden assumptions that may be problematical as they are unlikely to be fulfilled in all social systems. I illustrate these problems by re-analysing the basic concessive skew model with staying incentives. First, the model assumes that dispersal is an all-or-nothing response: all subordinates disperse as soon as concessions drop below a certain value. This leads to a discontinuous 'cliff-edge' shape of dominant fitness, and it is not clear that selection will balance a population at such an edge. Second, it is assumed that subordinates have perfect knowledge of their benefits if they stay in the group. I examine the effects of relaxing these two assumptions. Relaxing the first one strengthens reproductive skew theory, but relaxing the latter makes evolutionary stability disappear. In cases where subordinates cannot accurately measure benefits provided by the individual dominant with which they live, so that their behaviour instead evolves as a response to population-wide average benefits, the logic of reproductive skew models does not apply. This warns against too indiscriminate an application of reproductive skew theory to problems in social evolution: for example, transactional models of extra-pair paternity assume perfect knowledge of paternity, which is unlikely to hold true in nature. It is recommended that models specify the mechanisms by which individuals can adjust their behaviour to that of others, and pay attention to changes that occur in evolutionary versus behavioural time.     

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.     

Reproductive skew theory unified: The general bordered tug-of-war model

Reproductive skew has been identified as a major dimension along which animal societies vary. Two major kinds of reproductive skew models are transactional models, which explain the distribution of reproduction within animal societies as the result of reproductive payments exchanged among group members with differential leverage, and tug-of-war models, in which the reproductive shares are determined by costly ‘tugs-of-war’. These two models have recently been synthesized to yield the mutual-pay, bordered tug-of-war model. In this paper, we extend the latter, show its evolutionary stability, and demonstrate that the generalized model yields four sub-models, namely the mutual-pay, alpha-pay, beta-pay, and pure tug-of-war. The alpha-pay sub-model turns out to closely resemble the original “concessions” transactional skew model, and the beta-pay sub-model turns out to have properties similar to the “restraint” transactional skew model. Thus, the general model unifies the four major models of reproductive skew and is rich in its predictions, as each sub-model exhibits different qualitative and quantitative relationships between reproductive skew or intra-group conflict and the ecological and genetic factors that determine skew and conflict. The conditions favoring transitions among these sub-models also are precisely predicted by the general model. The general model accommodates data from acorn woodpeckers and primitively eusocial bees potentially can account for many of the highly varied empirical findings on reproductive skew. We suggest further research that focuses on (1) determining which model is suitable for certain species and (2) understanding why and how various social animals resolve their breeding conflict by different conflict resolution mechanisms.     

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.     

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.     

Clutch-size adjustments and skew models: effects on reproductive partitioning and group stability

Reproductive skew theory seeks to integrate social and ecologicalfactors thought to influence the division of reproduction amonggroup-living animals. However, most reproductive skew modelsonly examine interactions between individuals of the same sex.Here, we suggest that females can influence group stabilityand conflict among males by modifying their clutch size andmay do so if they benefit from the presence of subordinate malehelpers or from reduced conflict. We develop 3 models, basedon concessions-based, restraint, and tug-of-war models, in whichfemale clutch size is variable and ask when females will increasetheir clutch size above that which would be optimal in the absenceof male–male conflict. In concessions-based and restraintmodels, females should increase clutch size above their optimaif the benefits of staying for subordinate males are relativelylow. Relatedness between males has no effect on clutch size.When females do increase clutch size, the division of reproductionbetween males is not influenced by relatedness and does notdiffer between restraint and concessions-based models. Bothof these predictions are in sharp contrast to previous models.In tug-of-war models, clutch size is strongly influenced byrelatedness between males, with the largest clutches, but thefewest surviving offspring, produced when males are unrelated.These 3 models demonstrate the importance of considering third-partyinterests in the decisions of group-living organisms.     

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.     

Genetic support for the evolutionary theory of reproductive transactions in social wasps

Recent evolutionary models of reproductive partitioning within animal societies (known as 'optimal skew', 'concessions' or 'transactional' models) predict that a dominant individual will often yield some fraction of the group's reproduction to a subordinate as an incentive to stay in the group and help rear the dominant's offspring. These models quantitatively predict how the magnitude of the subordinate's 'staying incentive' will vary with the genetic relatedness between dominant and subordinate, the overall expected group output and the subordinate's expected output if it breeds solitarily. We report that these predictions accord remarkably well with the observed reproductive partitioning between conesting dominant and subordinate queens in the social paper wasp Polistes fuscatus. In particular, the theory correctly predicts that (i) the dominant's share of reproduction, i.e. the skew, increases as the colony cycle progresses and (ii) the skew is positively associated both with the colony's productivity and with the relatedness between dominant and subordinate. Moreover, aggression between foundresses positively correlated with the skew, as predicted by transactional but not alternative tug-of-war models of societal evolution. Thus, our results provide the strongest (quantitative support yet for a unifying model of social evolution.     

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.     

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.     

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.     

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.     

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.     

Predicting the temporal dynamics of reproductive skew and group membership in communal breeders

Reproductive skew models attempt to predict the fraction ofreproduction contributed by each individual that participatesin a communal brood. One potential limitation of these modelsis that individuals make a single, fixed decision about groupmembership and reproductive allocation at the beginning of thebreeding period. While this is appropriate for animals thatreproduce in a synchronous bout, many cooperative breeders produceoffspring over a prolonged period of time. It is likely thatthese species adjust reproductive allocation and group membershipover time in response to temporal shifts in group productivityand ecological constraints. In this paper we adapt transactionalmodels of reproductive skew to a continuous form, generatingtime-dependent functions of reproductive allocation. We derivea general method for predicting temporal changes in group membershipas well as a general expression for reproductive skew acrossthe regions over which a group is stable. Using a linear approximationfor time-dependent reproduction, we derive new expressions forreproductive skew in cases where the subordinate departs duringthe breeding period. In this case we find that the traditionalmodel always overestimates the subordinate's share of reproductionwhen dominants are in control of both reproductive shares andgroup membership (i.e., concessions models). Conversely, wefind that the traditional model always underestimates the subordinate'sshare of reproduction when subordinates are in control of reproductiveshares (i.e., constraint models). We discuss the implicationsof these new calculations in relation to the traditional skewmodels and more recent empirical tests of reproductive skewin animal societies.     

Reproduction and production in a social context: Group size,reproductive skew and increasing returns

Evolutionary success requires both production (acquisition of food, protection and warmth) and reproduction. We suggest that both may increase disproportionately as group size grows, reflecting ‘increasing returns’ or ‘group augmentation benefits’, raising fitness in groups that cooperate in production and limit reproduction to one or a few high fertility females supported by non-reproductives, with high reproductive skew. In our optimisation theory both Allee effects (when individual fitness increases with group size or density) and reproductive skew arise when increasing returns determine optimal group size and proportion of reproductive females. Depending on which of food or maternal time is more important for reproduction, evolutionary trajectories of lineages may (1) reach a boundary constraint where only one female reproduces in a period (as with African wild dogs) or (2) reach a boundary where all females reproduce during their lifetimes but only during an early life stage (human menopause) or a late life stage (birds with non-dispersing helpers), where stage length optimises the proportion of females that is reproductive at any time or (3) reach the intersection of these boundary constraints where a single reproductive female is fully specialised in reproduction (as with eusocial insects). We end with some testable hypotheses.     

Reproductive skew, concessions and limited control

Models of reproductive skew in cooperative and eusocial societies suggest that dominants allow subordinates to breed to induce them to remain peaceably in the group. However, it is not yet clear how widely the assumptions of these models apply to animal societies, and many of the trends that they predict are consistent with the simpler suggestion that there is a struggle for reproduction between dominants and subordinates, whose outcome depends on the potential costs and benefits of the contest to both parties. Models of reproductive skew that incorporate contests of this kind and empirical studies that can discriminate clearly between reproductive concessions and failures of control are now needed.     

Reproductive Competition Among Males in Multimale Groups of Primates: Modeling the Costs and Effectiveness of Conflict

Multimale groups of primates are characterized by strong reproductive competition among males, generally resulting in an uneven division of male reproductive success (reproductive skew). The observed patterns of conflict and reproductive skew have often been attributed to the so-called tug-of-war model. We show, however, that two important assumptions of this model are not met in male primates. First, the tug-of-war model assumes that reproductive conflict reduces overall group productivity, but in male primates (and most other vertebrates) conflict likely involves mortality rather than fecundity costs. Second, the tug-of-war model does not account for the possibility that male primates can achieve some reproductive success without engagement in open conflict, such as when a single male cannot guard several receptive females at the same time. We therefore develop a dynamic version of the tug-of-war model, in which reproductive competition causes mortality costs, and in which individuals can gain uncontested shares of reproduction dependent on the degree of female receptive overlap. This model differs substantially from the original tug-of-war model, and derives a new and rich set of comparative predictions. For instance, it predicts that the level of conflict among males declines as the queuing success of subordinate males increases (as survival increases), and also, as their uncontested share of reproduction increases, e.g., as female receptive overlap increases. Our model shows how male–male conflict and female receptive overlap collectively determine the level of reproductive skew among male primates, and illustrates that this relationship is more complex than previously thought.     

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.     

Reproductive sharing among queens in the ant Formica fusca

Reproductive sharing among cobreeders, in which reproductiveshares may vary from equal contribution (low reproductive skew)to reproductive dominance by one individual (high reproductiveskew), is a fundamental feature of animal societies. Recenttheoretical work, the reproductive skew models, has focusedon factors affecting the degree to which reproduction is skewedwithin a society. We used the parameters provided by skew modelsas a guideline to study determinants of reproductive sharingin polygyne ants. As a model system we used two-queen laboratorycolonies of the ant Formica fusca in which the reproductiveshares of each queen was assessed from offspring by using allozymesand DNA microsatellites. We tested how the different variablesincluded in reproductive skew models (queen-queen relatedness,potential fighting ability, productivity, and worker relatednessreflected by queen number in the colony of origin) affect reproductivesharing among queens. The results showed that the relatednessamong queens explained 26% of the variation in reproductiveskew. The size difference between queens (reflecting potentialfighting ability), colony productivity, and worker relatednessdid not have an effect on reproductive partitioning among cobreeders.To our knowledge, this is the first study to test for the effectsof various determinants of skew in an experimental setting.     

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.