A general technique for computing evolutionarily stable strategies based on errors in decision-making

Predicting resilience of migratory birds to environmental change

The pace and scale of environmental change represent major challenges to many organisms. Animals that move long distances, such as migratory birds, are especially vulnerable to change since they need chains of intact habitat along their migratory routes. Estimating the resilience of such species to environmental changes assists in targeting conservation efforts. We developed a migration modeling framework to predict past (1960s), present (2010s), and future (2060s) optimal migration strategies across five shorebird species (Scolopacidae) within the East Asian-Australasian Flyway, which has seen major habitat deterioration and loss over the last century, and compared these predictions to empirical tracks from the present. Our model captured the migration strategies of the five species and identified the changes in migrations needed to respond to habitat deterioration and climate change. Notably, the larger species, with single or few major stopover sites, need to establish new migration routes and strategies, while smaller species can buffer habitat loss by redistributing their stopover areas to novel or less-used sites. Comparing model predictions with empirical tracks also indicates that larger species with the stronger need for adaptations continue to migrate closer to the optimal routes of the past, before habitat deterioration accelerated. Our study not only quantifies the vulnerability of species in the face of global change but also explicitly reveals the extent of adaptations required to sustain their migrations. This modeling framework provides a tool for conservation planning that can accommodate the future needs of migratory species.

A critical review of risk-sensitive foraging

Foraging is risk sensitive if choices depend on the variability of returns from the options as well as their mean return. Risk-sensitive foraging is important in behavioural ecology, psychology and neurophysiology. It has been explained both in terms of mechanisms and in terms of evolutionary advantage. We provide a critical review, evaluating both mechanistic and evolutionary accounts. Some derivations of risk sensitivity from mechanistic models based on psychophysics are not convincing because they depend on an inappropriate use of Jensen's inequality. Attempts have been made to link risk sensitivity to the ecology of a species, but again these are not convincing. The field of risk-sensitive foraging has provided a focus for theoretical and empirical work and has yielded important insights, but we lack a simple and empirically defendable general account of it in either mechanistic or evolutionary terms. However, empirical analysis of choice sequences under theoretically motivated experimental designs and environmental settings appears a promising avenue for mapping the scope and relative merits of existing theories. Simply put, the devil is in the sequence.

Kobayashi T. Population dynamics models for various forms of adaptation

Adaptability to changing environments is one of the universal characteristics of living organisms. Because individual modes of adaptation are diverse, a unified understanding of these diverse modes is essential to comprehend adaptation. Adaptations can be categorized from at least two perspectives with respect to information. One is the passivity and activity of adaptation and the other is the type of information transmission. In Darwinian natural selection, organisms are selected among randomly generated traits under which individual organisms are passive in the sense that they do not process any environmental information. On the other hand, organisms can also adapt by sensing their environment and changing their traits. This is an active adaptation in that it makes use of environmental information. In terms of information transfer, adaptation through phenotypic heterogeneity, such as bacterial bet-hedging, is intragenerational in which traits are not passed on to the next generation. In contrast, adaptation through genetic diversity is intergenerational. The theory of population dynamics enables us to unify these various modes of adaptations and their properties can be analyzed qualitatively and quantitatively using techniques from quantitative genetics and information thermodynamics. In addition, such methods can be applied to situations where organisms can learn from past experiences and pass them on from generation to generation. In this work, we introduce the unified theory of biological adaptation based on population dynamics and show its potential applications to evaluate the fitness value of information and to analyze experimental lineage tree data. Finally, we discuss future perspectives for its development. This review article is an extended version of the Japanese article in SEIBUTSU BUTSURI Vol. 57, p. 287-290 (2017).

Predicting the population consequences of acoustic disturbance, with application to an endangered gray whale population

Acoustic disturbance is a growing conservation concern for wildlife populations because it can elicit physiological and behavioral responses that can have cascading impacts on population dynamics. State-dependent behavioral and life history models implemented via Stochastic Dynamic Programming (SDP) provide a natural framework for quantifying biologically meaningful population changes resulting from disturbance by linking environment, physiology, and metrics of fitness. We developed an SDP model using the endangered western gray whale (Eschrichtius robustus) as a case study because they experience acoustic disturbance on their summer foraging grounds. We modeled the behavior and physiological dynamics of pregnant females as they arrived on the feeding grounds and predicted the probability of female and offspring survival, with and without acoustic disturbance and in the presence/absence of high prey availability. Upon arrival in mid-May, pregnant females initially exhibited relatively random behavior before they transitioned to intensive feeding that resulted in continual fat mass gain until departure. This shift in behavior co-occurred with a change in spatial distribution; early in the season, whales were more equally distributed among foraging areas with moderate to high energy availability, whereas by mid-July whales transitioned to predominate use of the location that had the highest energy availability. Exclusion from energy-rich offshore areas led to reproductive failure and in extreme cases, mortality of adult females that had lasting impacts on population dynamics. Simulated disturbances in nearshore foraging areas had little to no impact on female survival or reproductive success at the population level. At the individual level, the impact of disturbance was unequally distributed across females of different lengths, both with respect to the number of times an individual was disturbed and the impact of disturbance on vital rates. Our results highlight the susceptibility of large capital breeders to reductions in prey availability, and indicate that who, where, and when individuals are disturbed are likely to be important considerations when assessing the impacts of acoustic activities. This model provides a framework to inform planned acoustic disturbances and assess the effectiveness of mitigation strategies for large capital breeders.

Sex Allocation Theory for Facultatively Sexual Organisms Inhabiting Seasonal Environments: The Importance of Bet Hedging

Adaptive explanations for dormancy often invoke bet hedging, where reduced mean fitness can be adaptive if it associates with reduced fitness variance. Sex allocation theory typically ignores variance effects and focuses on mean fitness. For many cyclical parthenogens, these themes become linked, as only sexually produced eggs undergo the dormancy needed to survive harsh conditions. We ask how sex allocation and the timing of sex evolve when this constraint exists in the form of a trade-off between asexual reproduction and sexual production of dormant eggs-the former being crucial for within-season success and the latter for survival across seasons. We show that male production can be temporally separated from or co-occur with sex, depending on whether direct (time) or indirect (population density) cues of the season's end are available and whether population growth is density dependent. Sex generally occurs late in the season but is induced earlier in unpredictable environments. When only indirect cues are available, the temporal spread of sex, and with it the production of dormant stages, is even larger and, given sufficient mortality, leads to endogenous population cycles in which frequent sex coincides with high densities. In all scenarios, algorithms maximizing geometric mean fitness have reduced fitness variance compared with a hypothetical non-bet hedger, confirming that the timing of male production and sex in facultative seasonal settings can be bet-hedging traits.

Adaptive and non-adaptive models of depression: A comparison using register data on antidepressant medication during divorce

Divorce is associated with an increased probability of a depressive episode, but the causation of events remains unclear. Adaptive models of depression propose that depression is a social strategy in part, whereas non-adaptive models tend to propose a diathesis-stress mechanism. We compare an adaptive evolutionary model of depression to three alternative non-adaptive models with respect to their ability to explain the temporal pattern of depression around the time of divorce. Register-based data (304,112 individuals drawn from a random sample of 11% of Finnish people) on antidepressant purchases is used as a proxy for depression. This proxy affords an unprecedented temporal resolution (a 3-monthly prevalence estimates over 10 years) without any bias from non-compliance, and it can be linked with underlying episodes via a statistical model. The evolutionary-adaptation model (all time periods with risk of divorce are depressogenic) was the best quantitative description of the data. The non-adaptive stress-relief model (period before divorce is depressogenic and period afterwards is not) provided the second best quantitative description of the data. The peak-stress model (periods before and after divorce can be depressogenic) fit the data less well, and the stress-induction model (period following divorce is depressogenic and the preceding period is not) did not fit the data at all. The evolutionary model was the most detailed mechanistic description of the divorce-depression link among the models, and the best fit in terms of predicted curvature; thus, it offers most rigorous hypotheses for further study. The stress-relief model also fit very well and was the best model in a sensitivity analysis, encouraging development of more mechanistic models for that hypothesis.

Optimal control and cold war dynamics between plant and herbivore

Herbivores eat the leaves that a plant needs for photosynthesis. However, the degree of antagonism between plant and herbivore may depend critically on the timing of their interactions and the intrinsic value of a leaf. We present a model that investigates whether and when the timing of plant defense and herbivore feeding activity can be optimized by evolution so that their interactions can move from antagonistic to neutral. We assume that temporal changes in environmental conditions will affect intrinsic leaf value, measured as potential carbon gain. Using optimal-control theory, we model herbivore evolution, first in response to fixed plant strategies and then under coevolutionary dynamics in which the plant also evolves in response to the herbivore. In the latter case, we solve for the evolutionarily stable strategies of plant defense induction and herbivore hatching rate under different ecological conditions. Our results suggest that the optimal strategies for both plant and herbivore are to avoid direct conflict. As long as the plant has the capability for moderately lethal defense, the herbivore will modify its hatching rate to avoid plant defenses, and the plant will never have to use them. Insights from this model offer a possible solution to the paradox of sublethal defenses and provide a mechanism for stable plant-herbivore interactions without the need for natural enemy control.

The effects of dominance on leadership and energetic gain: a dynamic game between pairs of social foragers

Although social behaviour can bring many benefits to an individual, there are also costs that may be incurred whenever the members of a social group interact. The formation of dominance hierarchies could offer a means of reducing some of the costs of social interaction, but individuals within the hierarchy may end up paying differing costs dependent upon their position within the hierarchy. These differing interaction costs may therefore influence the behaviour of the group, as subordinate individuals may experience very different benefits and costs to dominants when the group is conducting a given behaviour. Here, a state-dependent dynamic game is described which considers a pair of social foragers where there is a set dominance relationship within the pair. The model considers the case where the subordinate member of the pair pays an interference cost when it and the dominant individual conduct specific pairs of behaviours together. The model demonstrates that if the subordinate individual pays these energetic costs when it interacts with the dominant individual, this has effects upon the behaviour of both subordinate and the dominant individuals. Including interaction costs increases the amount of foraging behaviour both individuals conduct, with the behaviour of the pair being driven by the subordinate individual. The subordinate will tend to be the lighter individual for longer periods of time when interaction costs are imposed. This supports earlier suggestions that lighter individuals should act as the decision-maker within the pair, giving leadership-like behaviours that are based upon energetic state. Pre-existing properties of individuals such as their dominance will be less important for determining which individual makes the decisions for the pair. This suggests that, even with strict behavioural hierarchies, identifying which individual is the dominant one is not sufficient for identifying which one is the leader.

A quantitative test of Hamilton's rule for the evolution of altruism

The evolution of altruism is a fundamental and enduring puzzle in biology. In a seminal paper Hamilton showed that altruism can be selected for when rb - c > 0, where c is the fitness cost to the altruist, b is the fitness benefit to the beneficiary, and r is their genetic relatedness. While many studies have provided qualitative support for Hamilton's rule, quantitative tests have not yet been possible due to the difficulty of quantifying the costs and benefits of helping acts. Here we use a simulated system of foraging robots to experimentally manipulate the costs and benefits of helping and determine the conditions under which altruism evolves. By conducting experimental evolution over hundreds of generations of selection in populations with different c/b ratios, we show that Hamilton's rule always accurately predicts the minimum relatedness necessary for altruism to evolve. This high accuracy is remarkable given the presence of pleiotropic and epistatic effects as well as mutations with strong effects on behavior and fitness (effects not directly taken into account in Hamilton's original 1964 rule). In addition to providing the first quantitative test of Hamilton's rule in a system with a complex mapping between genotype and phenotype, these experiments demonstrate the wide applicability of kin selection theory.

Cooperation among non-relatives evolves by state-dependent generalized reciprocity

For decades, attempts to understand cooperation between non-kin have generated substantial theoretical and empirical interest in the evolutionary mechanisms of reciprocal altruism. There is growing evidence that the cognitive limitations of animals can hinder direct and indirect reciprocity because the necessary mental capacity is costly. Here, we show that cooperation can evolve by generalized reciprocity (help anyone, if helped by someone) even in large groups, if individuals base their decision to cooperate on a state variable updated by the outcome of the last interaction with an anonymous partner. We demonstrate that this alternative mechanism emerges through small evolutionary steps under a wide range of conditions. Since this state-based generalized reciprocity works without advanced cognitive abilities it may help to understand the evolution of complex social behaviour in a wide range of organisms.

Make love not war: when should less competitive males choose low-quality but defendable females?

Male choosiness for mates is an underexplored mechanism of sexual selection. A few theoretical studies suggest that males may exhibit--but only under rare circumstances--a reversed male mate choice (RMMC; i.e., highly competitive males focus on the most fecund females, while the low-quality males exclusively pair with less fecund mates to avoid being outcompeted by stronger rivals). Here we propose a new model to explore RMMC by relaxing some of the restrictive assumptions of the previous models and by considering an extended range of factors known to alter the strength of sexual selection (males' investment in reproduction, difference of quality between females, operational sex ratio). Unexpectedly, we found that males exhibited a reversed mate choice under a wide range of circumstances. RMMC mostly occurs when the female encounter rate is high and males devote much of their time to breeding. This condition-dependent strategy occurs even if there is no risk of injury during the male-male contest or when the difference in quality between females is small. RMMC should thus be a widespread yet underestimated component of sexual selection and should largely contribute to the assortative pairing patterns observed in numerous taxa.

Learning your own strength: winner and loser effects should change with age and experience

Winner and loser effects, in which the outcome of an aggressive encounter influences the tendency to escalate future conflicts, have been documented in many taxa, but we have limited understanding of why they have evolved. One possibility is that individuals use previous victories and defeats to assess their fighting ability relative to others. We explored this idea by modelling a population of strong and weak individuals that do not know their own strength, but keep track of how many fights they have won. Under these conditions, adaptive behaviour generates clear winner and loser effects: individuals who win fights should escalate subsequent conflicts, whereas those who lose should retreat from aggressive opponents. But these effects depend strongly on age and experience. Young, naive individuals should show highly aggressive behaviour and pronounced loser effects. For these inexperienced individuals, fighting is especially profitable because it yields valuable information about their strength. Aggression should then decline as an individual ages and gains experience, with those who lose fights becoming more submissive. Older individuals, who have a better idea of their own strength, should be more strongly influenced by victories than losses. In conclusion, we predict that both aggressiveness and the relative magnitude of winner and loser effects should change with age, owing to changes in how individuals perceive their own strength.

Optimal annual routines: new tools for conservation biology?

Many applied problems in ecology and conservation require prediction, and population models are important tools for that purpose. Formerly, the majority of predictive population models were based on matrix models. As the limitations of classical matrix models have become clearer, the use of individual-based models has increased. These models use behavioral rules imposed at the level of the individual to establish the emergent consequences of those rules at the population level. Individual behaviors in such models use an array of different rule types, from empirically derived probabilities to long-term fitness considerations. There has been surprisingly little discussion of the strengths and weaknesses of these different rule types. Here, we consider different strategies for modeling individual behaviors, together with some problems associated with individual-based models. We propose a novel approach based on modeling optimal annual routines. Annual routines allow individual behaviors to be predicted over a whole annual cycle within the context of long-term fitness considerations. Temporal trade-offs between different behaviors are automatically included in annual routine models, overcoming some of the primary limitations of other individual-based models. Furthermore, as well as population predictions, individual behaviors and indices of condition are emergent features of annual routine models. We show that these can be more sensitive to environmental change than population size, offering alternative, repeatable metrics for monitoring population status. Annual routine models provide no panacea for the problems of data limitations in predictive population modeling. However, as a result of their ability to deal with life-history trade-offs, as well as their potential for relatively rapid and accurate validation and parameterization, we suggest that annual routine models have strong potential for predictive population modeling in applied conservation settings.

The consequences of climate-driven stop-over sites changes on migration schedules and fitness of Arctic geese

1. How climatic changes affect migratory birds remains difficult to predict because birds use multiple sites in a highly interdependent manner. A better understanding of how conditions along the flyway affect migration and ultimately fitness is of paramount interest. 2. Therefore, we developed a stochastic dynamic model to generate spatially and temporally explicit predictions of stop-over site use. For each site, we varied energy expenditure, onset of spring, intake rate and day-to-day stochasticity independently. We parameterized the model for the migration of pink-footed goose Anser brachyrhynchus from its wintering grounds in Western Europe to its breeding grounds on Arctic Svalbard. 3. Model results suggested that the birds follow a risk-averse strategy by avoiding sites with comparatively high energy expenditure or stochasticity levels in favour of sites with highly predictable food supply and low expenditure. Furthermore, the onset of spring on the stop-over sites had the most pronounced effect on staging times while intake rates had surprisingly little effect. 4. Subsequently, using empirical data, we tested whether observed changes in the onset of spring along the flyway explain the observed changes in migration schedules of pink-footed geese from 1990 to 2004. Model predictions generally agreed well with empirically observed migration patterns, with geese leaving the wintering grounds earlier while considerably extending their staging times in Norway.

Optimal annual routines: behaviour in the context of physiology and ecology

Organisms in a seasonal environment often schedule activities in a regular way over the year. If we assume that such annual routines have been shaped by natural selection then life-history theory should provide a basis for explaining them. We argue that many life-history trade-offs are mediated by underlying physiological variables that act on various time scales. The dynamics of these variables often preclude considering one period of the year in isolation. In order to capture the essence of annual routines, and many life-history traits, a detailed model of changes in physiological state over the annual cycle is required. We outline a modelling approach based on suitable physiological and ecological state variables that can capture this underlying biology, and describe how models based on this approach can be used to generate a range of insights and predictions.

Sequential decision-making in a variable environment: Modeling elk movement in Yellowstone National Park as a dynamic game

We develop a suite of models with varying complexity to predict elk movement behavior during the winter on the Northern Range of Yellowstone National Park (YNP). The models range from a simple representation of optimal patch choice to a dynamic game, and we show how the underlying theory in each is related by the presence or absence of state- and frequency-dependence. We compare predictions from each of the models for three variables that are of basic and applied interest: elk survival, aggregation, and use of habitat outside YNP. Our results suggest that despite low overall forage depletion in the winter, frequency-dependence is crucial to the predictions for elk movement and distribution. Furthermore, frequency-dependence interacts with mass-dependence in the predicted outcome of elk decision-making. We use these results to show how models that treat single movement decisions in isolation from the seasonal sequence of decisions are insufficient to capture landscape scale behavior.

Can non-directional male mating preferences facilitate honest female ornamentation?

Recent studies have demonstrated male mate choice for female ornaments in species without sex-role reversal. Despite these empirical findings, little is known about the adaptive dynamics of female signalling, in particular the evolution of male mating preferences. The evolution of traits that signal mate quality is more complex in females than in males because females usually provide the bulk of resources for the developing offspring. Here, we investigate the evolution of male mating preferences using a mathematical model which: (i) specifically accounts for the fact that females must trade-off resources invested in ornaments with reproduction; and (ii) allows male mating preferences to evolve a non-directional shape. The optimal adaptive strategy for males is to develop stabilizing mating preferences for female display traits to avoid females that either invests too many or too few resources in ornamentation. However, the evolutionary stability of this prediction is dependent upon the level of error made by females when allocating resources to either signal or fecundity.

Statistical measures for defining an individual's degree of independence within state-dependent dynamic games

Background

For organisms living or interacting in groups, the decision-making processes of an individual may be based upon aspects of both its own state and the states of other organisms around it. Much research has sought to determine how group decisions are made, and whether some individuals are more likely to influence these decisions than others. State-dependent modelling techniques are a powerful tool for exploring group decision-making processes, but analyses conducted so far have lacked methods for identifying how dependent an individual's actions are on the rest of the group.

Results

Here, we introduce and evaluate two easy-to-calculate statistics that quantify how dependent an individual's actions are upon the state of a co-player in a two-player state-dependent dynamic game. We discuss the merits of these statistics, and situations in which they would be useful.

Conclusion

Our statistical measures provide a means of quantifying how independent an individual's actions are. They also allow researchers to quantify the output of state-dependent dynamic games, and quantitatively assess the predictions of these models.

When should signals of submission be given?-A game theory model

During contests, losing animals often show signals communicating submission. From an evolutionary viewpoint, however, it is not so obvious why the losing individual gives such a signal instead of running away and why the winning individual accepts the signal instead of inflicting more severe damage. We investigated factors influencing the evolution of signals of submission using a numerical ESS model. The present analysis reveals that there is much space for the evolution of signals of submission, even when the winner of an escalated contest gets some extra benefit. In most cases, signals of submission are given by animals which are slightly or moderately weaker than the opponent. Signals of submission are expected to occur frequently (1) when the value of contested resource does not differ greatly from the cost of injury, (2) when the extra benefit of winning an escalated contest is small, (3) when the opportunity for safe retreat by the losing animal is small, and (4) when the estimation of the difference in the resource holding potential (RHP) between the combatants is accurate but not perfect.

Time-dependent animal conflicts: 1. The symmetric case

Animal conflicts are often characterized by time-dependent strategy sets. This paper considers the following type of animal conflicts: a member of a group is at risk and needs the assistance of another member to be saved. As long as assistance is not provided, the individual which is at risk has a positive, time-dependent rate of dying. Each of the other group members is a potential helper. Assisting this individual accrues a cost, but losing him decreases the inclusive fitness of each group member. A potential helper's interval between the moment an individual finds itself at risk and the moment it assists is a random variable, hence its strategy is to choose the probability distribution for this random variable. Assuming that each of the potential helpers knows the others' strategies, we show that the ability to observe their realizations influences the evolutionarily stable strategies (ESS) of the game. According to our results, where the realizations can be observed ESS always exist: immediate assistance, no assistance and delayed assistance. Where the realizations cannot be observed ESS do not always exist, immediate assistance and no assistance are possible ESS, while delayed assistance cannot be an ESS. We apply our model to the n brothers' problem and to the parental investment conflict.

Time-dependent animal conflicts: 2. The asymmetric case

This paper presents an asymmetric game-theoretical model to the following type of animal conflicts: a member of a group is at risk and needs the help of another member to be saved. As long as assistance is not provided, this individual has a positive, time-dependent rate of dying. Assisting the individual which is at risk accrues a cost, but losing it decreases each member's inclusive fitness. A potential helper's interval between the moment a group member gets into trouble and the moment it assists is a random variable, hence its strategy is to choose the distribution of this random variable. In the asymmetric conflict all the potential helpers have identical strategy sets, but each plays a different role. For example, male or female and young or old. We consider both payoff-irrelevant asymmetry and payoff-relevant asymmetry and characterize each role's stable replies. The evolutionarily stable strategies (ESS) are computed, and the model is applied to the n brothers' problem. According to our results immediate assistance and no assistance are possible ESS both under payoff-relevant asymmetry and under payoff-relevant asymmetry.

Dispersal, Eviction, and Conflict in Meerkats (Suricata suricatta): An Evolutionarily Stable Strategy Model

Decisions regarding immigration and emigration are crucial to understanding group dynamics in social animals, but dispersal is rarely treated in models of optimal behavior. We developed a model of evolutionarily stable dispersal and eviction strategies for a cooperative mammal, the meerkat Suricata suricatta. Using rank and group size as state variables, we determined state-specific probabilities that subordinate females would disperse and contrasted these with probabilities of eviction by the dominant female, based on the long-term fitness consequences of these behaviors but incorporating the potential for error. We examined whether long-term fitness considerations explain group size regulation in meerkats; whether long-term fitness considerations can lead to conflict between dominant and subordinate female group members; and under what circumstances those conflicts were likely to lead to stability, dispersal, or eviction. Our results indicated that long-term fitness considerations can explain group size regulation in meerkats. Group size distributions expected from predicted dispersal and eviction strategies matched empirical distributions most closely when emigrant survival was approximately that determined from the field study. Long-term fitness considerations may lead to conflicts between dominant and subordinate female meerkats, and eviction is the most likely result of these conflicts. Our model is computationally intensive but provides a general framework for incorporating future changes in the size of multimember cooperative breeding groups.

Cooperation and Punishment, Especially in Humans

Explaining altruistic cooperation is one of the greatest challenges faced by sociologists, economists, and evolutionary biologists. The problem is determining why an individual would carry out a costly behavior that benefits another. Possible solutions to this problem include kinship, repeated interactions, and policing. Another solution that has recently received much attention is the threat of punishment. However, punishing behavior is often costly for the punisher, and so it is not immediately clear how costly punishment could evolve. We use a direct (neighbor-modulated) fitness approach to analyze when punishment is favored. This methodology reveals that, contrary to previous suggestions, relatedness between interacting individuals is not crucial to explaining cooperation through punishment. In fact, increasing relatedness directly disfavors punishing behavior. Instead, the crucial factor is a positive correlation between the punishment strategy of an individual and the cooperation it receives. This could arise in several ways, such as when facultative adjustment of behavior leads individuals to cooperate more when interacting with individuals who are more likely to punish. More generally, our results provide a clear example of how the fundamental factor driving the evolution of social traits is a correlation between social partners and how this can arise for reasons other than genealogical kinship.

Can too strong female choice deteriorate male ornamentation?

Competition for limited resources can have fundamental implications for population dynamics. However, the effects of resource depletion have rarely been discussed in the context of sexual selection, even though mate choice typically favours males who outperform others in securing access to some limited resource. Here, we develop a model to investigate the question of resource competition as a form of male-male competition in the context of male sexual displays. We phrase our model in terms of male bowerbirds either searching for or stealing resources (ornamental objects) valued by females, and compare the model findings with published studies of time allocation to various activities in different species of bowerbirds. The basic idea of the model, however, extends to cases where the resource is used less directly for the development of sexual ornamentation, such as males excluding others' access to food. We show that if males compete for resources used in sexual displays, intense female preference for high-quality displays can lead to poorer prospects for efficient choice by females. This is because males benefit from excluding others' access to resources used in displays, damaging the overall efficiency of resource use in the population, and the accuracy with which females can judge male ability to gain such resources. The evolution of female choice may therefore have a self-limiting nature when it poses a selection pressure on male resource acquisition.

How Predation Risk Affects the Temporal Dynamics of Avian Leks: Greater Sage Grouse versus Golden Eagles

Leks often attract predators as well as mates, yet most evolutionary models have assumed that sexual selection, not predation, drives lekking behavior. We explored the influence of predation on lek dynamics using a stochastic dynamic game model based on the lek-breeding greater sage grouse (Centrocercus urophasianus) and its principal avian predator, the golden eagle (Aquila chrysaetos). The model predicts time-dependent male lek attendance as a function of factors affecting both mating success (female arrival rate, male numbers, and social status) and predation risk (eagle arrival rate and group size). Dominant males are predicted to arrive sooner and leave later than subordinates, especially if mating skew is high, predation risk is low, or the relationship between lek size and female arrival rate is weak. Both high mean levels of predation risk and small lek size should reduce lek attendance, but the relative tendency of predators to attack large versus small leks has little influence on predicted lekking behavior. Field observations confirmed the predicted effects of female arrival rate, lek size, male dominance, and weather-dependent predator arrival rates on lek departure times. Predicted effects of female arrival rates and male dominance on seasonal lek attendance were also supported. Our model provides an empirically supported adaptive explanation for short-term lek dynamics. It also suggests alternative interpretations for phenomena previously invoked to support the hotshot and skew models of lek formation.

Spontaneous emergence of leaders and followers in foraging pairs

Animals that forage socially often stand to gain from coordination of their behaviour. Yet it is not known how group members reach a consensus on the timing of foraging bouts. Here we demonstrate a simple process by which this may occur. We develop a state-dependent, dynamic game model of foraging by a pair of animals, in which each individual chooses between resting or foraging during a series of consecutive periods, so as to maximize its own individual chances of survival. We find that, if there is an advantage to foraging together, the equilibrium behaviour of both individuals becomes highly synchronized. As a result of this synchronization, differences in the energetic reserves of the two players spontaneously develop, leading them to adopt different behavioural roles. The individual with lower reserves emerges as the 'pace-maker' who determines when the pair should forage, providing a straightforward resolution to the problem of group coordination. Moreover, the strategy that gives rise to this behaviour can be implemented by a simple 'rule of thumb' that requires no detailed knowledge of the state of other individuals.

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.

Why is mutual mate choice not the norm? Operational sex ratios, sex roles and the evolution of sexually dimorphic and monomorphic signalling

Biases in the operational sex ratio (OSR) are seen as the fundamental reason behind differential competition for mates in the two sexes, and as a strong determinant behind differences in choosiness. This view has been challenged by Kokko and Monaghan, who argue that sex-specific parental investment, mortalities, mate-encounter rates and quality variation determine the mating system in a way that is not reducible to the OSR. We develop a game-theoretic model of choosiness, signalling and parental care, to examine (i) whether the results of Kokko and Monaghan remain robust when its simplifying assumptions are relaxed, (ii) how parental care coevolves with mating strategies and the OSR and (iii) why mutual mate choice is observed relatively rarely even when both sexes vary in quality. We find qualitative agreement with the simpler approach: parental investment is the primary determinant of sex roles instead of the OSR, and factors promoting choosiness are high species-specific mate-encounter rate, high sex-specific mate-encounter rate, high cost of breeding (parental investment), low cost of mate searching and highly variable quality of the opposite sex. The coevolution of parental care and mating strategies hinders mutual mate choice if one parent can compensate for reduced care by the other, but promotes it if offspring survival depends greatly on biparental care. We argue that the relative rarity of mutual mate choice is not due to biases in the OSR. Instead, we describe processes by which sexual strategies tend to diverge. This divergence is prevented, and mutual mate choice maintained, if synergistic benefits of biparental care render parental investment both high and not too different in the two sexes.

A dynamic game-theoretic model of parental care

We present a model in which members of a mated pair decide whether to care for their offspring or desert them. There is a breeding season of finite length during which it is possible to produce and raise several batches of offspring. On deserting its offspring, an individual can search for a new mate. The probability of finding a mate depends on the number of individuals of each sex that are searching, which in turn depends upon the previous care and desertion decisions of all population members. We find the evolutionarily stable pattern of care over the breeding season. The feedback between behaviour and mating opportunity can result in a pattern of stable oscillations between different forms of care over the breeding season. Oscillations can also arise because the best thing for an individual to do at a particular time in the season depends on future behaviour of all population members. In the baseline model, a pair splits up after a breeding attempt, even if they both care for the offspring. In a version of the model in which a pair stays together if they both care, the feedback between behaviour and mating opportunity can lead to more than one evolutionarily stable form of care.

Daily Patterns of Optimal Producer and Scrounger Use under Predation Hazard: A State-Dependent Dynamic Game Analysis

Feeding in groups often gives rise to joining: feeding from other's discoveries. The joining decision has been modeled as a producer-scrounger game where the producer strategy consists of searching for one's food and the scrounger strategy consists of searching for food discovered by others. Previous models revealed that the evolutionarily stable proportion of scrounging mostly depends on the fraction of each food patch available only to its producer. These early models are static and state independent and are therefore unable to explore whether the time of day, the animal's state, and the degree of predation hazard influence an individual's decision of whether to use the producer or scrounger strategy. To investigate these issues, we developed a state-dependent dynamic producer-scrounger game model. The model predicts that, early in the day, low reserves promote a preference for the scrounger strategy, while the same condition late in the day favors the use of the producer strategy. Under rich and clumped food, the availability of scrounging can improve the daily survival of any average group member. The model suggests only weak effects of predation hazard on the use of scrounging. Future developments should consider the effects of dominance asymmetries and allowing foragers a choice between foraging alone or in a group harboring an evolutionarily stable frequency of scrounger.

Seasonal Sex Ratio Trend in the European Kestrel: An Evolutionarily Stable Strategy Analysis

We present an evolutionarily stable strategy (ESS) model to analyze selection on seasonal variation in the brood sex ratio, as observed in several species of raptorial birds. The model is specifically tailored to the life history of the European kestrel, and it reflects the maturation time hypothesis, the idea that a seasonal sex ratio trend has evolved because of sex differences in the dependence of age of first breeding on date of birth. First we show how to derive a fitness function in the context of a seasonal environment. Model parameters are estimated from field data in order to derive quantitative predictions. Since little is known about constraints on sex ratio control in birds, we analyze three scenarios, each corresponding to a different strategy set. We consider a model without constraints on sex ratio control, a model where the sex ratio trend is constrained to be linear, and a mechanistic model incorporating a plausible mechanism of sex ratio control in birds. One of the models yields an ESS sex ratio trend that closely resembles the trend observed in the field. However, the predictions are very sensitive to the choice of strategy set. Moreover, the selective forces generated by sex differences in maturation are rather weak. In fact, the mechanistic model shows that seemingly negligible costs of sex ratio control may be sufficient to overcome the adaptive value of adjusting the sex ratio.