Game Theory in Biology: Moving beyond Functional Accounts.

AbstractThe idea of applying game theory to problems in biology was given a formal basis nearly 50 years ago. Since then, the theory has advanced, and there have been numerous applications of it to a diversity of empirical systems. Most of this work takes a straightforward functional approach, finding a behavioral strategy that is evolutionarily stable in a well-specified specific situation. Relatively little attention has been devoted to the role of phylogeny, the role of learning during development, and the limitations imposed by the psychological and physiological mechanisms that bring about behavior in a complex world. Here I argue that a focus on these elements can improve the link between the theory and empirical systems and hence help us to understand how natural selection has shaped observed behavior.

Social interaction can select for reduced ability.

Animals, including humans, differ in a wide range of physical and cognitive abilities ranging from measures of running speed and physical strength to learning ability and intelligence. We consider the evolution of ability when individuals interact pairwise over their contribution to a common good. In this interaction, the contribution of each is assumed to be the best given their own ability and the contribution of their partner. Since there is a tendency for individuals to partially compensate for a low contribution by their partner, low-ability individuals can do well. As a consequence, for benefit and cost structures for which individuals have a strong response to partner's contribution, there can be selection for reduced ability. Furthermore, there can be disruptive selection on ability, leading to a bimodal distribution of ability under some modes of inheritance.

Behavioural specialization and learning in social networks.

Interactions in social groups can promote behavioural specialization. One way this can happen is when individuals engage in activities with two behavioural options and learn which option to choose. We analyse interactions in groups where individuals learn from playing games with two actions and negatively frequency-dependent payoffs, such as producer-scrounger, caller-satellite, or hawk-dove games. Group members are placed in social networks, characterized by the group size and the number of neighbours to interact with, ranging from just a few neighbours to interactions between all group members. The networks we analyse include ring lattices and the much-studied small-world networks. By implementing two basic reinforcement-learning approaches, action-value learning and actor-critic learning, in different games, we find that individuals often show behavioural specialization. Specialization develops more rapidly when there are few neighbours in a network and when learning rates are high. There can be learned specialization also with many neighbours, but we show that, for action-value learning, behavioural consistency over time is higher with a smaller number of neighbours. We conclude that frequency-dependent competition for resources is a main driver of specialization. We discuss our theoretical results in relation to experimental and field observations of behavioural specialization in social situations.

An evolutionary perspective on stress responses, damage and repair.

Variation in stress responses has been investigated in relation to environmental factors, species ecology, life history and fitness. Moreover, mechanistic studies have unravelled molecular mechanisms of how acute and chronic stress responses cause physiological impacts ('damage'), and how this damage can be repaired. However, it is not yet understood how the fitness effects of damage and repair influence stress response evolution. Here we study the evolution of hormone levels as a function of stressor occurrence, damage and the efficiency of repair. We hypothesise that the evolution of stress responses depends on the fitness consequences of damage and the ability to repair that damage. To obtain some general insights, we model a simplified scenario in which an organism repeatedly encounters a stressor with a certain frequency and predictability (temporal autocorrelation). The organism can defend itself by mounting a stress response (elevated hormone level), but this causes damage that takes time to repair. We identify optimal strategies in this scenario and then investigate how those strategies respond to acute and chronic exposures to the stressor. We find that for higher repair rates, baseline and peak hormone levels are higher. This typically means that the organism experiences higher levels of damage, which it can afford because that damage is repaired more quickly, but for very high repair rates the damage does not build up. With increasing predictability of the stressor, stress responses are sustained for longer, because the animal expects the stressor to persist, and thus damage builds up. This can result in very high (and potentially fatal) levels of damage when organisms are exposed to chronic stressors to which they are not evolutionarily adapted. Overall, our results highlight that at least three factors need to be considered jointly to advance our understanding of how stress physiology has evolved: (i) temporal dynamics of stressor occurrence; (ii) relative mortality risk imposed by the stressor itself versus damage caused by the stress response; and (iii) the efficiency of repair mechanisms.

Behavioural flexibility and reputation formation.

Limited flexibility in behaviour gives rise to behavioural consistency, so that past behaviour is partially predictive of current behaviour. The consequences of limits to flexibility are investigated in a population in which pairs of individuals play a game of trust. The game can either be observed by others or not. Reputation is based on trustworthiness when observed and acts as a signal of behaviour in future interactions with others. Individuals use the reputation of partner in deciding whether to trust them, both when observed by others and when not observed. We explore the effects of costs of exhibiting a difference in behaviour between when observed and when not observed (i.e. a cost of flexibility). When costs are low, individuals do not attempt to signal that they will later be trustworthy: their signal should not be believed since it will always pay them to be untrustworthy if trusted. When costs are high, their local optimal behaviour automatically acts as an honest signal. At intermediate costs, individuals are very trustworthy when observed in order to convince others of their trustworthiness when unobserved. It is hypothesized that this type of strong signalling might occur in other settings.

Environmental variability, reliability of information and the timing of migration.

The timing of migration and migratory steps is highly relevant for fitness. Because environmental conditions vary between years, the optimal time for migration varies accordingly. Therefore, migratory animals could clearly benefit from acquiring information as to when it is the best time to migrate in a specific year. Thus, environmental predictability and variability are fundamental characteristics of migration systems but their relationship and consequence for migratory progression has remained unexplored. We develop a simple dynamic model to identify the optimal migration behaviour in environments that differ in predictability, variability and the number of intermediate stop-over sites. Our results indicate that higher predictability along migration routes enables organisms to better time migration when phenology deviates from its long-term average and thus, increases fitness. Information is particularly valuable in highly variable environments and in the final migration-step, i.e. before the destination. Furthermore, we show that a general strategy for obtaining information in relatively uninformative but variable environments is using intermediate stop-over sites that enable migrants to better predict conditions ahead. Our study contributes to a better understanding of the relationship between animal movement and environmental predictability-an important, yet underappreciated factor that strongly influences migratory progression.

Ecological Genetic Conflict: Genetic Architecture Can Shift the Balance between Local Adaptation and Plasticity.

Genetic polymorphism can contribute to local adaptation in heterogeneous habitats, for instance, as a single locus with alleles adapted to different habitats. Phenotypic plasticity can also contribute to trait variation across habitats, through developmental responses to habitat-specific cues. We show that the genetic architecture of genetically polymorphic and plasticity loci may influence the balance between local adaptation and phenotypic plasticity. These effects of genetic architecture are instances of ecological genetic conflict. A reduced effective migration rate for genes tightly linked to a genetic polymorphism provides an explanation for the effects, and they can occur both for a single trait and for a syndrome of coadapted traits. Using individual-based simulations and numerical analysis, we investigate how among-habitat genetic polymorphism and phenotypic plasticity depend on genetic architecture. We also study the evolution of genetic architecture itself, in the form of rates of recombination between genetically polymorphic loci and plasticity loci. Our main result is that for plasticity genes that are unlinked to loci with between-habitat genetic polymorphism, the slope of a reaction norm is steeper in comparison with the slope favored by plasticity genes that are tightly linked to genes for local adaptation.

Trust your gut: using physiological states as a source of information is almost as effective as optimal Bayesian learning.

Approaches to understanding adaptive behaviour often assume that animals have perfect information about environmental conditions or are capable of sophisticated learning. If such learning abilities are costly, however, natural selection will favour simpler mechanisms for controlling behaviour when faced with uncertain conditions. Here, we show that, in a foraging context, a strategy based only on current energy reserves often performs almost as well as a Bayesian learning strategy that integrates all previous experiences to form an optimal estimate of environmental conditions. We find that Bayesian learning gives a strong advantage only if fluctuations in the food supply are very strong and reasonably frequent. The performance of both the Bayesian and the reserve-based strategy are more robust to inaccurate knowledge of the temporal pattern of environmental conditions than a strategy that has perfect knowledge about current conditions. Studies assuming Bayesian learning are often accused of being unrealistic; our results suggest that animals can achieve a similar level of performance to Bayesians using much simpler mechanisms based on their physiological state. More broadly, our work suggests that the ability to use internal states as a source of information about recent environmental conditions will have weakened selection for sophisticated learning and decision-making systems.

Optimal gut size of small birds and its dependence on environmental and physiological parameters.

Most optimal foraging models assume that the foraging behaviour of small birds depends on a single state variable, their energy reserves in the form of stored fat. Here, we include a second state variable-the contents of the bird's gut-to investigate how a bird should optimise its gut size to minimise its long-term mortality, depending on the availability of food, the size of meal and the bird's digestive constraints. Our results show that (1) the current level of fat is never less important than gut contents in determining the bird's survival; (2) there exists a unique optimal gut size, which is determined by a trade-off between the energetic gains and costs of maintaining a large digestive system; (3) the optimal gut size increases as the bird's digestive cycle becomes slower, allowing the bird to store undigested food; (4) the critical environmental factor for determining the optimal gut size is the mass of food found in a successful foraging effort ("meal size"). We find that when the environment is harsh, it is optimal for the bird to maintain a gut that is larger than the size of a meal. However, the optimal size of the gut in rich environments exactly matches the meal size (i.e. the mass of food that the optimal gut can carry is exactly the mass of food that can be obtained in a successful foraging attempt).

Echoes of Early Life: Recent Insights From Mathematical Modeling.

In the last decades, developmental origins of health and disease (DOHaD) has emerged as a central framework for studying early-life effects, that is, the impact of fetal and early postnatal experience on adult functioning. Apace with empirical progress, theoreticians have built mathematical models that provide novel insights for DOHaD. This article focuses on three of these insights, which show the power of environmental noise (i.e., imperfect indicators of current and future conditions) in shaping development. Such noise can produce: (a) detrimental outcomes even in ontogenetically stable environments, (b) individual differences in sensitive periods, and (c) early-life effects tailored to predicted future somatic states. We argue that these insights extend DOHaD and offer new research directions.

The erroneous signals of detection theory.

Signal detection theory has influenced the behavioural sciences for over 50 years. The theory provides a simple equation that indicates numerous 'intuitive' results; e.g. prey should be more prone to take evasive action (in response to an ambiguous cue) if predators are more common. Here, we use analytical and computational models to show that, in numerous biological scenarios, the standard results of signal detection theory do not apply; more predators can result in prey being less responsive to such cues. The standard results need not apply when the probability of danger pertains not just to the present, but also to future decisions. We identify how responses to risk should depend on background mortality and autocorrelation, and that predictions in relation to animal welfare can also be reversed from the standard theory.

Genes as Cues of Relatedness and Social Evolution in Heterogeneous Environments.

There are many situations where relatives interact while at the same time there is genetic polymorphism in traits influencing survival and reproduction. Examples include cheater-cooperator polymorphism and polymorphic microbial pathogens. Environmental heterogeneity, favoring different traits in nearby habitats, with dispersal between them, is one general reason to expect polymorphism. Currently, there is no formal framework of social evolution that encompasses genetic polymorphism. We develop such a framework, thus integrating theories of social evolution into the evolutionary ecology of heterogeneous environments. We allow for adaptively maintained genetic polymorphism by applying the concept of genetic cues. We analyze a model of social evolution in a two-habitat situation with limited dispersal between habitats, in which the average relatedness at the time of helping and other benefits of helping can differ between habitats. An important result from the analysis is that alleles at a polymorphic locus play the role of genetic cues, in the sense that the presence of a cue allele contains statistical information for an organism about its current environment, including information about relatedness. We show that epistatic modifiers of the cue polymorphism can evolve to make optimal use of the information in the genetic cue, in analogy with a Bayesian decision maker. Another important result is that the genetic linkage between a cue locus and modifier loci influences the evolutionary interest of modifiers, with tighter linkage leading to greater divergence between social traits induced by different cue alleles, and this can be understood in terms of genetic conflict.

Towards a behavioural ecology of obesity.

Addressing the obesity epidemic depends on a holistic understanding of the reasons that people become and maintain excessive fat. Theories about the causes of obesity usually focus proximately or evoke evolutionary mismatches, with minimal clinical value. There is potential for substantial progress by adapting strategic body mass regulation models from evolutionary ecology to human obesity by assessing the role of information.

Detection vs. selection: integration of genetic, epigenetic and environmental cues in fluctuating environments.

There are many inputs during development that influence an organism's fit to current or upcoming environments. These include genetic effects, transgenerational epigenetic influences, environmental cues and developmental noise, which are rarely investigated in the same formal framework. We study an analytically tractable evolutionary model, in which cues are integrated to determine mature phenotypes in fluctuating environments. Environmental cues received during development and by the mother as an adult act as detection-based (individually observed) cues. The mother's phenotype and a quantitative genetic effect act as selection-based cues (they correlate with environmental states after selection). We specify when such cues are complementary and tend to be used together, and when using the most informative cue will predominate. Thus, we extend recent analyses of the evolutionary implications of subsets of these effects by providing a general diagnosis of the conditions under which detection and selection-based influences on development are likely to evolve and coexist.

Fatness and fitness: exposing the logic of evolutionary explanations for obesity.

To explore the logic of evolutionary explanations of obesity we modelled food consumption in an animal that minimizes mortality (starvation plus predation) by switching between activities that differ in energy gain and predation. We show that if switching does not incur extra predation risk, the animal should have a single threshold level of reserves above which it performs the safe activity and below which it performs the dangerous activity. The value of the threshold is determined by the environmental conditions, implying that animals should have variable 'set points'. Selection pressure to prevent energy stores exceeding the optimal level is usually weak, suggesting that immediate rewards might easily overcome the controls against becoming overweight. The risk of starvation can have a strong influence on the strategy even when starvation is extremely uncommon, so the incidence of mortality during famine in human history may be unimportant for explanations for obesity. If there is an extra risk of switching between activities, the animal should have two distinct thresholds: one to initiate weight gain and one to initiate weight loss. Contrary to the dual intervention point model, these thresholds will be inter-dependent, such that altering the predation risk alters the location of both thresholds; a result that undermines the evolutionary basis of the drifty genes hypothesis. Our work implies that understanding the causes of obesity can benefit from a better understanding of how evolution shapes the mechanisms that control body weight.

The evolution of transgenerational integration of information in heterogeneous environments.

An organism's phenotype can be influenced by maternal cues and directly perceived environmental cues, as well as by its genotype at polymorphic loci, which can be interpreted as a genetic cue. In fluctuating environments, natural selection favors organisms that efficiently integrate different sources of information about the likely success of phenotypic alternatives. In such situations, it can be beneficial to pass on maternal cues that offspring can respond to. A maternal cue could be based on environmental cues directly perceived by the mother but also partly on cues that were passed on by the grandmother. We have used a mathematical model to investigate how the passing of maternal cues and the integration of different sources of information evolve in response to qualitatively different kinds of temporal and spatial environmental fluctuations. The model shows that the passing of maternal cues and the transgenerational integration of sources of information readily evolve. Factors such as the degree of temporal autocorrelation, the predictive accuracy of different environmental cues, and the level of gene flow strongly influence the expression of adaptive maternal cues and the relative weights given to different sources of information. We outline the main features of the relation between the characteristics of environmental fluctuations and the adaptive systems of phenotype determination and compare these predictions with empirical studies on cue integration.

Sexual conflict over parental care promotes the evolution of sex differences in care and the ability to care.

Strong asymmetries in parental care, with one sex providing more care than the other, are widespread across the animal kingdom. At present, two factors are thought to ultimately cause sex differences in care: certainty of parentage and sexual selection. By contrast, we here show that the coevolution of care and the ability to care can result in strong asymmetries in both the ability to care and the level of care, even in the absence of these factors. While the coevolution of care and the ability to care does not predict which sex evolves to care more than the other, once other factors give rise to even the slightest differences in the cost and benefits of care between the sexes (e.g. differences in certainty in parentage), a clear directionality emerges; the sex with the lower cost or higher benefit of care evolves both to be more able to care and to provide much higher levels of care than the other sex. Our findings suggest that the coevolution of levels of care and the ability to care may be a key factor underlying the evolution of sex differences in care.

Capital and income breeding: the role of food supply.

An aspect of life history that has seen increasing attention in recent years is that of strategies for financing the costs of offspring production. These strategies are often described by a continuum ranging from capital breeding, in which costs are met purely from endogenous reserves, to income breeding, in which costs are met purely from concurrent intake. A variety of factors that might drive strategies toward a given point on the capital-income continuum has been reviewed, and assessed using analytical models. However, aspects of food supply, including seasonality and unpredictability, have often been cited as important drivers of capital and income breeding, but are difficult to assess using analytical models. Consequently, we used dynamic programming to assess the role of the food supply in shaping offspring provisioning strategies. Our model is parameterized for a pinniped (one taxon remarkable for the range of offspring-provisioning strategies that it illustrates). We show that increased food availability, increased seasonality, and, to a lesser extent, increased unpredictability can all favor the emergence of capital breeding. In terms of the conversion of energy into offspring growth, the shorter periods of care associated with capital breeding are considerably more energetically efficient than income breeding, because shorter periods of care are associated with a higher ratio of energy put into offspring growth to energy spent on parent and offspring maintenance metabolism. Moreover, no clear costs are currently associated with capital accumulation in pinnipeds. This contrasts with general assumptions about endotherms, which suggest that income breeding will usually be preferred. Our model emphasizes the role of seasonally high abundances of food in enabling mothers to pursue an energetically efficient capital-breeding strategy. We discuss the importance of offspring development for dictating strategies for financing offspring production.

The starvation-predation trade-off shapes the strategic use of protein for energy during fasting.

The primary function of lipid storage by animals is as an energy source for surviving periods without food. However, muscle and organ protein can be metabolised for energy, and empirical studies have shown that the onset of protein metabolism begins before the exhaustion of lipid reserves. Since protein tissues are important for reasons other than resisting starvation, the adaptive basis for this early onset is unclear. Here, we report the results of a model of the optimal proportion of energy to obtain from protein catabolism during a period without food of unpredictable duration. We assume either that the animal aims only to maximise the duration of survival or that it also has to take account of its future reproductive success given its state when the food supply recommences. In the latter case we find impressive quantitative agreement with observations on lean and obese penguins and rats. Analysis shows that this agreement breaks down if predation risk is insignificant, protein in the form of muscle is ineffective against predation, or there is no benefit to conserving lipid (e.g. for reproduction). This result implies that animals have not evolved to maximise their starvation resistance because doing so would leave them vulnerable when an interruption ends. Our model allows us to make several specific predictions concerning the relationship between the ecological pressures on animals and their starvation survival strategies.

Foraging currencies, metabolism and behavioural routines.

A fundamental issue in foraging theory is whether it is possible to find a simple currency that characterizes foraging behaviour. If such a currency exists, then it is tempting to argue that the selective forces that have shaped the evolution of foraging behaviour have been understood. We review previous work on currencies for the foraging behaviour of an animal that maximizes total energy gained. In many circumstances, it is optimal to maximize a suitably modified form of efficiency. We show how energy gain, predation and damage can be combined in a single currency based on reproductive value. We draw attention to the idea that hard work may have an adverse effect on an animal's condition. We develop a model of optimal foraging over a day when a forager's state consists of its energy reserves and its condition. Optimal foraging behaviour in our model depends on energy reserves, condition and time of day. The pattern of optimal behaviour depends strongly on assumptions about the probability that the forager is killed by a predator. If condition is important, no simple currency characterizes foraging behaviour, but behaviour can be understood in terms of the maximization of reproductive value. It may be optimal to adopt a foraging option that results in a rate of energy expenditure that is less than the rate associated with maximizing efficiency.