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Animals that hunt for food underwater and return to the surface for air (‘divers’) are limited by their ability to store oxygen. The aerobic dive limit (ADL) is the dive duration at which all the possible oxygen stores have been used. It has been claimed that models of optimal diving predict that divers will be close to this limit and that the data do not match this prediction. I characterize closeness to the ADL by the fraction ψ of the maximum amount of stored oxygen that is used during a dive. At the ADL this fraction is 1. I show that an optimal diver does not necessarily have a ψ close to 1 and point out that the key feature predicted by the model is that the diver should have no oxygen stores left when it returns to the surface. The data cited against optimal diving do not address this issue.

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.

Models of optimal group size need to identify the currency that correctly captures the fitness consequences of foraging. Although daily intake or daily net energy gain per animal are widely used as currencies, they are not ideal. They predict that all available time should be spent hunting and do not reflect performance during a hunt. We argue that the net rate while hunting is a better currency. Using an example based on the African wild dog, we illustrate the difference between maximizing daily net energy and net rate. Using the same example, we show that if foraging is limited by constraints on energy expenditure, then the optimal group size can be different from the size that maximizes the net rate while hunting. The direction of the effect depends on whether costs increase or decrease with group size. Furthermore, the proportion of time spent resting can be predicted. We suggest two novel approaches for future models: to consider the optimal hunting group size given a fixed group size and to investigate how the presence of dependent young may affect foraging behavior. We hope this will lead to meaningful conclusions on the role cooperative hunting has played in the evolution of sociality in social carnivores.

Neo-Darwinism characterises biological adaptation as a one-sided process, in which organisms adapt to their environment but not vice versa. This asymmetric relationship – here called Williams’ asymmetry – is called into question by Niche Construction Theory, which emphasises that organisms and their environments often mutually affect each other. Here we clarify that Williams’ asymmetry is specifically concerned with (quasi-) directed modifications towards phenotypes that increase individual fitness. This directedness – which drives the adaptive fit between organism and environment – entails far more than the mere presence of cause-effect relationships. We argue that difficulties with invoking fitness as the guiding principle of adaptive evolution are resolved with an appropriate definition of fitness and that objections against Williams’ asymmetry reflect confusions about the nature of biological adaptation. peerReviewed

The inverse optimality approach can allow us to learn about an animal's environment by assuming their behaviour is optimal. This approach has been applied to animals diving underwater for food to produce the index of patch quality (IPQ), which aims to provide a proxy for prey abundance or quality in a foraging patch based on the animal's diving behaviour. The IPQ has been used in several empirical studies but has never been evaluated theoretically. Here, we discuss the strengths and weaknesses of the IPQ approach from a theoretical angle and review the empirical evidence supporting its use. We highlight several potential issues, in particular with the gain function—the function describing the energetic gain of an animal during a dive—used to calculate the IPQ. We investigate an alternative gain function which is appropriate in some cases, provide a new model based on this function, and discuss differences between the IPQ model and ours. We also find that there is little supporting empirical evidence justifying the general use of the IPQ and suggest future empirical validation methods which could help strengthen the case for the IPQ. Our findings have implications for the field of diving ecology and habitat assessment.

Matching describes how behaviour is related to rewards. The matching law holds when the ratio of an individual's behaviours equals the ratio of the rewards obtained. From its origins in the study of pigeons working for food in the laboratory, the law has been applied to a range of species, both in the laboratory and outside it (e.g., human sporting decisions). Probability matching occurs when the probability of a behaviour equals the probability of being rewarded. Input matching predicts the distribution of individuals across habitats. We evaluate the rationality of the matching law and probability matching, expose the logic of matching in real-world cases, review how recent neuroscience findings relate to matching, and suggest future research directions.

Tversky and Kahneman introduced the term framing for the finding that people give different answers to the same question depending on the way it is posed. One form of framing involves presenting the same outcome as either a gain or a loss. An experiment on starlings by Marsh and Kacelnik suggests that this form of framing occurs in non-humans. We argue that the experimental result demonstrates framing in the general sense of context dependence but does not provide compelling evidence of framing in terms of gains and losses. A version of scalar utility theory which is extended to include the possibility of memory errors accounts for the data and suggests future lines of research.

In the theory outlined in the target article, an animal forages continuously, making sequential decisions in a world where the amount of food and its uncertainty are fixed, but delays are variable. These assumptions contrast with the risk-sensitive foraging theory and create a problem for comparing the predictions of this model with many laboratory experiments that do not make these assumptions.

We focus on learning during development in a group of individuals that play a competitive game with each other. The game has two actions and there is negative frequency dependence. We define the distribution of actions by group members to be an equilibrium configuration if no individual can improve its payoff by unilaterally changing its action. We show that at this equilibrium, one action is preferred in the sense that those taking the preferred action have a higher payoff than those taking the other, more prosocial, action. We explore the consequences of a simple ‘unbiased’ reinforcement learning rule during development, showing that groups reach an approximate equilibrium distribution, so that some achieve a higher payoff than others. Because there is learning, an individual’s behaviour can influence the future behaviour of others. We show that, as a consequence, there is the potential for an individual to exploit others by influencing them to be the ones to take the non-preferred action. Using an evolutionary simulation, we show that population members can avoid being exploited by over-valuing rewards obtained from the preferred option during learning, an example of a bias that is ‘rational’.

We consider a behavioural model of an animal choosing between two activities, based on positive feedback, and examine the effect of introducing cross inhibition between the motivations for the two activities. While cross-inhibition has previously been included in models of decision making, the question of what benefit it may provide to an animal’s activity selection behaviour has not previously been studied. In neuroscience and in collective behaviour cross-inhibition, and other equivalent means of coupling evidence-accumulating pathways, have been shown to approximate statistically-optimal decision-making and to adaptively break deadlock, thereby improving decision performance. Switching between activities is an ongoing decision process yet here we also find that cross-inhibition robustly improves its efficiency, by reducing the frequency of costly switches between behaviours.

Social animals that bring resources to a central place have commonly been used to test the predictions of optimal foraging models. Such animals are amenable to test because they do not themselves reproduce, and so we might expect them to be selected to maximise some measure of input of food to the colony. Several currencies have been proposed to predict behaviour, such as net rate, efficiency, and the ratio of the mortality rate to energy gain rate. Observations on social animals, especially bees, show mixed support for each currency. Here, we examine how these currencies can be united by considering the expected lifetime input of energy to the colony in a representative study of patch residence time. This currency explains partial loads because it leads to the prediction that the energy that a forager delivers to the colony over its lifetime is maximised by returning to the colony after a critical amount has been collected, even if energy is gained at a constant rate. We show that the extent to which foraging carries a greater mortality risk than travelling controls whether this currency makes similar predictions to net rate or to efficiency. We assess the evidence that bee behaviour actually maximises this currency and argue that mortality risk at resource sites is likely to be a critical determinant of foraging strategies in central-place foragers.

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).

When given a choice between options with uncertain outcomes, people tend to be loss averse and risk averse regarding potential gains and risk prone regarding potential losses. These features of human decision making are captured by prospect theory (PT)—a hugely influential descriptive model of choice, but one which lacks any unifying principle that might explain why such preferences exist. Recently there have been several attempts to connect PT with risk-sensitive foraging theory (RSFT), a normative framework developed by evolutionary biologists to explain how animals should choose optimally when faced with uncertain foraging options. Although this seems a promising direction, here we show that current approaches are overly simplistic, and, despite their claims, they leave key features of PT unaccounted for. A common problem is the failure to appreciate the central concept of reproductive value in RSFT, which depends on the decision maker's current state and the particular situation it faces. Reproductive value provides a common currency in which decisions can be compared in a logical way. In contrast, existing models provide no rational justification for the reference state in PT. Evolutionary approaches to understanding PT preferences must confront this basic problem.

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.

Behavioral ecologists often assume that natural selection will produce organisms that make optimal decisions. In the context of information processing, this means that the behavior of animals will be consistent with models from fields such as signal detection theory and Bayesian decision theory. We discuss work that applies such models to animal behavior and use the case of Bayesian updating to make the distinction between a description of behavior at the level of optimal decisions and a mechanistic account of how decisions are made. The idea of ecological rationality is that natural selection shapes an animal's decision mechanisms to suit its environment. As a result, decision-making mechanisms may not perform well outside the context in which they evolved. Although the assumption of ecological rationality is plausible, we argue that the exact nature of the relationship between ecology and cognitive mechanism may not be obvious.

Discounting refers to the way in which the value of an outcome depends on the delay until it is obtained. If an organism’s discount function is known, then its rate of discounting at any delay can be found. If the function is not known, the normalised area under an estimate of the discount function has been used as a measure that summarises the strength of discounting over a range of delays. We propose a new measure of the strength of discounting: the overall discount rate W, which is the drop in value from the start to the end of the value curve divided by the area under this curve. We show that our measure has various advantages over the normalised area, namely it can be linked to the instantaneous rate of discounting and it respects the special nature of exponential discounting. It does not give a unique value to each curve, but we prove that this is incompatible with the requirement that similar discount functions be assigned similar values, and so this is not a defect of the measure.

In his paper ‘Parental investment: a prospective analysis’, Maynard Smith (1977, Animal Behaviour, 25, 1–9) introduced a game-theoretic approach to understanding the evolution of parental behaviour and addressed the broad issue of which sex should provide care for the young. This paper was important in that it introduced the use of game theory to the analysis of parental care. It also stimulated empirical work on care. We identify progress that has been made since the publication of the paper. In particular, although Model 2 of Maynard Smith (1977) has been used in several textbooks to explain the evolution of care, subsequent work has shown that this model is not built on a consistent view of how parental care influences future reproductive success through its effect on the sex ratio. Several models incorporate a consistent account in which opportunities to remate after desertion emerge from the analysis, rather than being specified in advance. More generally, it is not possible to consider parental care in isolation from factors such as paternity, mating preferences and mate choice behaviour. We identify various theoretical and empirical issues in the area of parental care research that we believe deserve further study if our understanding of care decisions is to advance. Taken together, the landmark paper of Maynard Smith (1977) stimulated new theoretical and empirical studies in parental care research and led to new insights into the behavioural interactions between males and females.

Moods can be regarded as fluctuating dispositions to make positive and negative evaluations. Developing an evolutionary approach to mood as an adaptive process, we consider the structure and function of such states in guiding behavioural decisions regarding the acquisition of resources and the avoidance of harm in different circumstances. We use a drift diffusion model of decision making to consider the information required by individuals to optimise decisions between two alternatives, such as whether to approach or withdraw from a stimulus that may be life enhancing or life threatening. We show that two dimensions of variation (expectation and preparedness) are sufficient for such optimal decisions to be made. These two dispositional dimensions enable individuals to maximize the overall benefits of behavioural decisions by modulating both the choice made (e.g., approach/withdraw) and decision speed. Such a structure is compatible with circumplex models of subjectively experienced mood and core affect, and provides testable hypotheses concerning the relationships that occur between valence and arousal components of mood in differing ecological niches. The paper is therefore a useful step toward being able to predict moods (and the effect of moods) using an optimality approach.

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.

Scalar Utility Theory (SUT) is a model used to predict animal and human choice behaviour in the context of reward amount, delay to reward, and variability in these quantities (risk preferences). This article reviews and extends SUT, deriving novel predictions. We show that, contrary to what has been implied in the literature, (1) SUT can predict both risk averse and risk prone behaviour for both reward amounts and delays to reward depending on experimental parameters, (2) SUT implies violations of several concepts of rational behaviour (e.g. it violates strong stochastic transitivity and its equivalents, and leads to probability matching) and (3) SUT can predict, but does not always predict, a linear relationship between risk sensitivity in choices and coefficient of variation in the decision-making experiment. SUT derives from Scalar Expectancy Theory which models uncertainty in behavioural timing using a normal distribution. We show that the above conclusions also hold for other distributions, such as the inverse Gaussian distribution derived from drift-diffusion models. A straightforward way to test the key assumptions of SUT is suggested and possible extensions, future prospects and mechanistic underpinnings are discussed.

We review the possible effects of placebos from an evolutionary perspective. Although the term ‘placebo effect’ has become synonymous with a good outcome, it is more useful to recognise that a placebo (i.e. a ‘dummy treatment’) may produce positive, neutral or negative outcomes. From this basis, we identify situations where evolutionary theory predicts that placebos should have positive or negative effects on patients, and how this will depend on numerous factors, such as age and health status. The evolutionary perspective highlights the many trade-offs involved in how the immune system can be affected by placebos, and the potential danger of confusing symptoms with an underlying ailment when considering effects.

Animals live in complex environments in which predation risk and food availability change over time. To deal with this variability and maximize their survival, animals should take into account how long current conditions may persist and the possible future conditions they may encounter. This should affect their foraging activity, and with it their vulnerability to predation across periods of good and bad conditions. Here we develop a comprehensive theory of optimal risk allocation that allows for environmental persistence and for fluctuations in food availability as well as predation risk. We show that it is the duration of good and bad periods, independent of each other, rather than the overall proportion of time exposed to each that is the most important factor affecting behavior. Risk allocation is most pronounced when conditions change frequently, and optimal foraging activity can either increase or decrease with increasing exposure to bad conditions. When food availability fluctuates rapidly, animals should forage more when food is abundant, whereas when food availability fluctuates slowly, they should forage more when food is scarce. We also show that survival can increase as variability in predation risk increases. Our work reveals that environmental persistence should profoundly influence behavior. Empirical studies of risk allocation should therefore carefully control the duration of both good and bad periods and consider manipulating food availability as well as predation risk.

A fundamental question relating to animal behaviour is how animals learn; in particular, how they come to associate stimuli with rewards. Numerous empirical findings can be explained by assuming that animals use some mechanism similar to the Rescorla-Wagner learning rule, which is a relatively simple and highly general method of updating the associative strength between different stimuli. However, the Rescorla-Wagner rule is often not optimal, which raises the question of why a rule with such properties should have evolved. We consider the evolution of learning rules in a simple environment where there exists an optimal rule of similar complexity to the Rescorla-Wagner rule. We show that because the Rescorla-Wagner rule is less sensitive to changes in its parameters than the optimal rule, there is a wider range of parameter values over which the rule structure is initially viable. Consequently, the Rescorla-Wagner rule can be favoured by natural selection, ahead of other rules which are more accurate.

The storage of lipids to buffer energy shortage may incur such costs as increased vulnerability to predation, and animals may be more muscular in order to reduce such costs. If muscle and lipid mass interact to determine survival, then both the muscularity and the adiposity of animals will be affected by factors such as predator density and food availability. Here we explore how adiposity and muscularity may depend on such factors. We confirm the expectation that adiposity should decrease with the risk of predation and increase with the frequency of interruptions to the food supply. More surprisingly, the predicted relationships between skeletal size, muscularity, and adiposity qualitatively depended on various factors: for example, adiposity should increase with foraging costs only for small animals and should decrease with total body mass if competition for food is intense. Furthermore, if the locomotive costs of carrying lipids are low, then adiposity should increase with body mass, whereas if ...

We investigate the optimal behaviour of an organism that is unable to obtain a reliable estimate of its mortality risk. In this case, natural selection will shape behaviour to be approximately optimal given the probability distribution of mortality risks in possible environments that the organism and its ancestors encountered. The mean of this distribution is the average mortality risk experienced by a randomly selected member of the species. We show that if an organism does not know the exact mortality risk, it should act as if the risk is less than the mean risk. This can be viewed as being optimistic. We argue that this effect is likely to be general.

Laboratory studies on a range of animals have identified a bias that seems to violate basic principles of rational behavior: a preference is shown for feeding options that previously provided food when reserves were low, even though another option had been found to give the same reward with less delay. The bias presents a challenge to normative models of decision making (which only take account of expected rewards and the state of the animal at the decision time). To understand the behavior, we take a broad ecological perspective and consider how valuation mechanisms evolve when the best action depends upon the environment being faced. We show that in a changing and uncertain environment, state-dependent valuation can be favored by natural selection: Individuals should allow their hunger to affect learning for future decisions. The valuation mechanism that typically evolves produces the kind of behavior seen in standard laboratory tests. By providing an insight into why learning should be affected by the state of an individual, we provide a basis for understanding psychological principles in terms of an animal's ecology.

Quantifying the effect of disturbance is a central issue in conservation. Using time and energy budgets, we obtain a range of ways to assess the importance of disturbance. One measure is the time that must be spent foraging in order to balance the energy budget. From this we derive critical levels of wastage (rate of disturbance multiplied by duration of disturbance) at which the animal runs out of time or reaches a limit on energy expenditure. In the case of the time constraint, the critical wastage is the net rate of energetic gain while foraging divided by the rate of energetic expenditure during a disturbance. The associated critical rate of disturbance is the net rate of energetic gain while foraging divided by the energy spent during a disturbance. The model is illustrated using data from the African wild dog, which suffers disturbance from lions and kleptoparasitism from hyenas. Findings suggest that disturbance imposes significant costs on wild dog time and energy budgets. We show how alternative environments can be evaluated in terms of their effective rate of gain, which is the net rate of gain from foraging minus the rate of energy expenditure as a result of disturbance.

Foraging theory has typically been concerned with the acquisition of a single resource even though organisms from mammals to protozoa are capable of balancing their requirements for multiple resources. Existing theory concerning multiple nutrients from multiple foods does not predict the sequence of food selection. We constructed an optimisation model of the simplest case of two foods containing differing amounts of two nutrients. We begin with the well-supported assumption that reproductive value declines with the distance from target nutrient intake. We show that nutrient space divides into two distinct areas where the animal should exclusively consume one food or the other. The organism thus initially concentrates on one food type until the border between the areas is reached and then moves as closely as possible along the border to approach the target. This strategy is commonly observed in a range of organisms, suggesting that the assumed fitness function is common.

Organisms living in periodically varying environments adjust their life history events to the changes in food availability. When these changes are not entirely predictable animals face a trade-off between maintaining physiological preparedness (which can be costly) and being unprepared (which decreases the chances of successful reproduction). To investigate this problem, we developed an optimal annual routine model of gonad regulation in birds. Most birds regress their reproductive organs during non-breeding periods, but to start breeding again they need to have functional gonads. Maintaining the gonads in this state is costly, but because it takes time to achieve this state, if gonads are not functional the bird may miss a possible breeding opportunity. We explore the resolution of this trade-off in environments where favorable periods can occur at any time of the year and variability in the length of good and bad periods can be altered. Consistent with empirical studies of reproductive behavior in unpredictable environments, we find that birds maintain the gonads partially activated during unfavorable conditions in many cases. However, gonad regulation may differ strikingly depending on the consistency of the good and bad periods. Furthermore, seasonal changes in food availability lead to the entrainment of reproduction and the segregation of the breeding and non-breeding season, even if the magnitude of seasonality is small compared to the degree of environmental fluctuations. These results indicate that several aspects of the environment need to be taken into account to understand reproductive behavior in unpredictable environments. Given that the trade-off between the costs and benefits of maintaining physiological preparedness is not limited to birds, our results have implications for understanding behavioral flexibility in other organisms as well.

Many birds and mammals forage under water and have to return to the surface to breathe. Models of optimal diving attempt to explain the behaviour of such animals in terms of selection for successful foraging given the constraints imposed by physiology. Several recent papers have questioned the accuracy of both the assumptions and the predictions of these models. Here, I provide a critical review of these papers, arguing that they misrepresent both the models and the data. As a result, they focus on inappropriate tests. I use the debate to suggest various new models and to explore the general relationship between theory and data in behavioural ecology. In particular, I consider the merits of qualitative and quantitative predictions.

The year 2009 marked both the bicentenary of Charles Darwin’s birth, and the passage of 150 years since the publication of his revolutionary book, commonly referred to as The Origin of Species (Darwin 1859). As part of the national celebrations that took place in the UK, a meeting on ‘Mathematical Models in Ecology and Evolution’ was held in Bristol on September 10 and 11, with a special focus on the mathematical modelling and application of Darwin’s key theories. This special issue collects together selected papers presented at the meeting, including contributions by the four invited keynote speakers, Rob Boyd, A. W. F. Edwards, Hanna Kokko and Franjo Weissing, as well as papers received after the event. The topics of these papers span the modelling of a very wide range of Darwin’s ideas, particularly evolution through natural selection, the origin of species, sexual selection, altruism and cooperation, and pangenesis, as well as applications of Darwinian thinking to the behaviour of animals, humans, and even human societies. It is hoped that this collection of papers will provide a useful snapshot of the state-of-the-art in Darwinian theory after the last one and a half centuries, and help to identify potential directions for research over the next.

The Darwinian approach to behavior generates models that are widely used by anthropologists and archeologists. In this paper, I concentrate on a particular group of models based on cases in which a forager (or group of foragers) brings resources to a location known as a central place. I examine two topics in detail: (1) the economics of transporting a load to the central place, and (2) the extent to which items should be processed before they are brought back to the central place. In addition to presenting new results and bringing out common themes in archeology and behavioral ecology, I discuss problems with some of the models that have been used in archeology and offer suggestions for further work.

We propose operational definitions of reproductive optimism and pessimism; optimism involves behaving in a way that gives too much weight (in terms of producing surviving offspring) to positive events, pessimism gives too much weight to negative events. Natural selection maximizes the long-term growth of a lineage rather than short-term measures such as numbers of offspring. Consequently, optimism or pessimism can be favoured by natural selection, even though such biases appear irrational from a short-term perspective. We investigate the evolution of optimism in a metapopulation. The circumstances of a patch change over time, independently of other patches. With sufficient dispersal between patches, stochasticity affects members of a lineage largely independently and optimism is favoured. With little dispersal, the temporal fluctuations of a patch affect many members similarly; pessimism is then favoured. Our results establish that the spatial and temporal structure of the environment is crucial in determining the direction of evolved biases.

The extant auks show three strategies of chick rearing – precocial (chicks leave the nest site when a few days old), intermediate (young raised to a mass of around 20% of adult mass) and semi-precocial (young raised to a mass of around 65% of adult mass). It is not known which strategy the extinct Great Auk used. In this paper, we investigate this issue by a novel combination of a time and energy budget model and phylogenetic comparison. The first approach indicates that for reasonable estimates of the equation parameters, the Great Auk could have followed an intermediate strategy. For a limited range of parameters, the Great Auk could have followed the semi-precocial strategy. Phylogenetic comparison shows that it is unlikely that the Great Auk followed a precocial strategy. The results suggest that the Great Auk followed an intermediate strategy as does its presumed closest extant relative the Razorbill.

Behavioural ecology often makes the assumption that animals can respond flexibly by adopting the optimal behaviour for each circumstance. However, as ethologists have long known, behaviour is determined by mechanisms that are not optimal in every circumstance. As we discuss here, we believe that it is necessary to integrate these separate traditions by considering the evolution of mechanisms, an approach referred to as 'Evo-mecho'. This integration is timely because there is a growing awareness of the importance of environmental complexity in shaping behaviour; there are established and effective computational procedures for simulating evolution and there is rapidly increasing knowledge of the neuronal basis of decision-making. Although behavioural ecologists have built complex models of optimal behaviour in simple environments, we argue that they need to focus on simple mechanisms that perform well in complex environments.

Gould and Lewontin use San Marco, Venice, to criticise the adaptationist program in biology. Following their lead, the architectural term “spandrel” is now widely used in biology to denote a feature that is a necessary byproduct of other aspects of the organism. I review the debate over San Marco and argue that the spandrels are not necessary in the sense originally used by Gould and Lewontin. I conclude that almost all the claims that Gould makes about San Marco are wrong and that it is reasonable to view the architectural spandrel as an adaptation. The spandrels example has not provided a good illustration of why adaptive explanations should be avoided. In fact, it can be used as an example of how adaptive explanations can be dismissed even when there is evidence in their favour. I also discuss the use of the concept of a spandrel in biology.

We analyse a model of mate choice when males differ in reproductive quality and provide care for their offspring. Females choose males on the basis of the success they will obtain from breeding with them and a male chooses his care time on the basis of his quality so as to maximise his long-term rate of reproductive success. We use this model to establish whether high-quality males should devote a longer period of care to their broods than low-quality males and whether females obtain greater reproductive success from mating with higher quality males. We give sufficient conditions for optimal care times to decrease with increasing male quality. When care times decrease, this does not necessarily mean that high-quality males are less valuable to the female because quality may more than compensate for the lack of care. We give a necessary and sufficient condition for high-quality males to be less valuable mates, and hence for females to prefer low-quality males. Females can prefer low-quality males if offspring produced and cared for by high-quality males do well even if care is short, and do not significantly benefit from additional care, while offspring produced and cared for by low-quality males do well only if they receive a long period of care.

Interest in the evolution and maintenance of personality is burgeoning. Individuals of diverse animal species differ in their aggressiveness, fearfulness, sociability and activity. Strong trade-offs, mutation–selection balance, spatio-temporal fluctuations in selection, frequency dependence and good-genes mate choice are invoked to explain heritable personality variation, yet for continuous behavioural traits, it remains unclear which selective force is likely to maintain distinct polymorphisms. Using a model of trust and cooperation, we show how allowing individuals to monitor each other's cooperative tendencies, at a cost, can select for heritable polymorphisms in trustworthiness. This variation, in turn, favours costly ‘social awareness’ in some individuals. Feedback of this sort can explain the individual differences in trust and trustworthiness so often documented by economists in experimental public goods games across a range of cultures. Our work adds to growing evidence that evolutionary game theorists can no longer afford to ignore the importance of real world inter-individual variation in their models.

Tropical birds lay smaller clutches than birds breeding in temperate regions and care for their young for longer. We develop a model in which birds choose when and how often to breed and their clutch size, depending on their foraging ability and the food availability. The food supply is density dependent. Seasonal environments necessarily have a high food peak in summer; in winter, food levels drop below those characteristic of constant environments. A bird that cannot balance its energy needs during a week dies of starvation. If adult predation is negligible, birds in low seasonal environments are constrained by low food during breeding seasons, whereas birds in high seasonal environments die during the winter. Low food seasonality selects for small clutch sizes, long parental care times, greater age at first breeding, and high juvenile survival. The inclusion of adult predation has no major effect on any life-history variables. However, increased nest predation reduces clutch size. The same trends with seasonality are also found in a version of the model that includes a condition variable. Our results show that seasonal changes in food supply are sufficient to explain the observed trends in clutch size, care times, and age at first breeding.

The classical viewpoint in sperm competition theory, which holds that males evolve sperm allocation strategies in response to a given degree of sperm competition, has recently been challenged by an alternative viewpoint, which holds that the degree of sperm competition is itself a consequence of these same strategies. Here, we present a game theory model that unites these alternative views as the endpoints of a continuum. Based on the recognition that female control over mating may limit the extent to which male strategies affect the degree of sperm competition, we investigate sperm allocation strategies in a setting where females can resist excessive matings more or less successfully. We discuss how conflicting predictions made by previous theory relate to implicit assumptions about female resistance behavior. Moreover, we show that female resistance, while being highly relevant to the predicted relationship between ejaculate size and the degree of sperm competition, has little effect on the predicted positive correlation between relative testis size and the degree of sperm competition. This result strengthens one of the central predictions of sperm competition theory and is in accordance with empirical findings from a wide range of taxa.

Ideal free distributions characterise how a group of animals should be distributed between sources of food. In a simple case, the ratio of the number of animals matches the ratio of input rates, a result known as input matching. The matching law characterises how an animal should allocate responses to sources of food. If matching holds then the ratio of behaviour allocated to the sources matches the ratio of rewards obtained. Several authors have drawn attention to the analogy between input matching and the matching law. I present a critical review of this topic, and go on to investigate the claim that the distribution of animals should be analyzed in the same way that the generalized matching law is analyzed. This involves assuming that the relationship between the ratio of animals and the ratio of resources obeys a power law with two parameters, one corresponding to bias and the other to sensitivity. On this view, a plot of the log of the ratio of animals against the log of the ratio of input rates will be a straight line and its intercept and slope will provide estimates of bias and sensitivity. I show that this approach can give a good fit even when the underlying model does not result in a power law. A consequence is that the parameters estimated cannot be interpreted as bias and sensitivity. I conclude that there are no compelling reasons for analyzing the distribution of animals using log-log plots, and the method has the disadvantage of encouraging the mistaken view that deviations from input matching follow a power law.

The authors acknowledge the Natural Environment Research Council for support with this work (grant NER/A/S/2003/00616). Simple scaling arguments suggest that, among air-breathing divers, dive duration should scale approximately with mass to the one-third power. Recent phylogenetic analyses appear to confirm this. The same analyses showed that duration of time spent at the surface between dives has scaling very similar to that of dive duration, with the result that the ratio of dive duration to surface pause duration is approximately mass invariant. This finding runs counter to other arguments found in the diving literature that suggest that surface pause duration should scale more positively with mass, leading to a negative scaling of the dive-pause ratio. We use a published model of optimal time allocation in the dive cycle to show that optimal decisions can predict approximate mass invariance in the dive-pause ratio, especially if metabolism scales approximately with mass to the two-thirds power (as indicated by some recent analyses) and oxygen uptake is assumed to have evolved to supply the body tissues at the required rate. However, emergent scaling rules are sensitive to input parameters, especially to the relationship between the scaling of metabolism and oxygen uptake rate at the surface. Our results illustrate the utility of an optimality approach for developing predictions and identifying key areas for empirical research on the allometry of diving behavior. Publisher PDF

Sexual selection theory predicts that males should attempt to mate with several females, unless the benefits of male promiscuity are trumped by alternative benefits associated with male monogamy (monogyny). Here we use a game theory model to address the adaptive value of a monogynous strategy, which has the sole benefit of enhancing a male's paternity share in the context of competition with other males. We consider two ways in which monogynists might enhance their paternity: by outcompeting rival ejaculates in sperm competition, and by reducing the probability that a female remates with rival males. The model is based on the biology of some particularly well-studied spider species, in which males are morphologically restricted to mate with either one or at most two females in their lifetime. Our results suggest that, regardless of the mechanism of paternity enhancement involved, a male-biased sex ratio is generally required for the evolution and maintenance of monogyny. Moreover, we show that there is a large region of parameter space where monogyny and bigyny can coexist as alternative mating strategies under negative frequency dependent selection. There is also a narrow range of conditions where either monogyny or bigyny can be evolutionarily stable. Our results are in qualitative agreement with empirical findings in spiders.

If natural selection favours selfish behaviour, how is it that cooperation is so common in many species, including humans? Working with evolutionary simulations, McNamara et al. propose a novel evolutionary mechanism based on a positive coevolutionary feedback between cooperativeness and choosiness. If individuals vary in their degree of cooperativeness, and if they can decide whether or not to continue interacting with each other on the basis of their respective levels of cooperativeness, then cooperation can gradually evolve from an uncooperative state. On this model, individual behavioural differences are the key to the evolution of cooperation. It is shown that if individuals vary in their degree of cooperativeness, and if they can decide whether or not to continue interacting with each other on the basis of their respective levels of cooperativeness, then cooperation can gradually evolve from an uncooperative state. These results highlight the importance of individual behavioural differences in fostering the evolution of cooperation. Explaining the rise and maintenance of cooperation is central to our understanding of biological systems1,2 and human societies3,4. When an individual’s cooperativeness is used by other individuals as a choice criterion, there can be competition to be more generous than others, a situation called competitive altruism5. The evolution of cooperation between non-relatives can then be driven by a positive feedback between increasing levels of cooperativeness and choosiness6. Here we use evolutionary simulations to show that, in a situation where individuals have the opportunity to engage in repeated pairwise interactions, the equilibrium degree of cooperativeness depends critically on the amount of behavioural variation that is being maintained in the population by processes such as mutation. Because our model does not invoke complex mechanisms such as negotiation behaviour, it can be applied to a wide range of species. The results suggest an important role of lifespan in the evolution of cooperation.

Empirical evidence for changed timing of migration in birds is emerging from both American and Euro-African migration systems. These changes are usually interpreted as a consequence of changes in climate. Responses in timing of migration and breeding may differ among species, and the adaptive significance is not well understood. There is a lack of theoretical understanding about time-shifts in life-history events due to climatic changes. In the present paper, we use 2 separate modelling approaches to investigate the effects of climate change on migration. We first use a simple model of flight speed and foraging to explore which factors may influence migration speed and stopover itinerary. Our second approach derives predictions based on an annual routine model, where behavioural strategies regarding timing of migration, breeding, moult and number of breeding attempts are modelled in an environment comprising 4 locations (breeding and wintering sites and 2 stopover sites). This approach takes account of interrelationships between behaviours and seasons as a step towards realistic modelling of migratory connectivity. Departure from the wintering site is advanced in relation to the advancement of spring if the moult is in summer, but not so for species with a winter moult, while arrival at the breeding site is advanced for both moult scenarios. Timing of breeding and number of successful broods were also affected by spring advancement, while start of moult is relatively unaffected by climate change. These optimal solutions under the modelled set of parameters are discussed with respect to current knowledge of the mechanisms underlying seasonal timing in birds.

In order to avoid both starvation and disease, animals must allocate resources between energy reserves and immune defence. We investigate the optimal allocation. We find that animals with low reserves choose to allocate less to defence than animals with higher reserves because when reserves are low it is more important to increase reserves to reduce the risk of starvation in the future. In general, investment in immune defence increases monotonically with energy reserves. An exception is when the animal can reduce its probability of death from disease by reducing its foraging rate. In this case, allocation to immune defence can peak at intermediate reserves. When food changes over time, the optimal response depends on the frequency of changes. If the environment is relatively stable, animals forage most intensively when the food is scarce and invest more in immune defence when the food is abundant than when it is scarce. If the environment changes quickly, animals forage at low intensity when the food is scarce, but at high intensity when the food is abundant. As the rate of environmental change increases, immune defence becomes less dependent on food availability. We show that the strength of selection on reserve-dependent immune defence depends on how foraging intensity and immune defence determine the probability of death from disease.

An interpretation of the conflict between male and female parents during the process of caring for their common offspring by means of Game Theory was given in Houston and Davies. [A.I. Houston, N.B. Davies, The evolution of cooperation and life history in the dunnock Prunella modularis, in: R.M. Sibly, R.H. Smith (Eds.), Behavioral Ecology, Blackwell Scientific Publications, 1985, pp. 471–487]. Mathematically, this model represents a static game with continuous strategy sets. Recently, this model was reconsidered in a dynamic discrete time framework which also included state dependencies [J.M. McNamara et al., A dynamic game-theoretic model of parental care, J. Theor. Biol. 205 (2000) 605–623]. In this article, we give an interpretation of the parental care conflict in continuous time by means of a differential game with state dependent strategies.

Many animals possess camouflage markings that reduce the risk of detection by visually hunting predators. A key aspect of camouflage involves mimicking the background against which the animal is viewed. However, most animals experience a wide variety of backgrounds and cannot change their external appearance to match each selectively. We investigate whether such animals should adopt camouflage specialized with respect to one background or adopt a compromise between the attributes of multiple backgrounds. We do this using a model consisting of predators that hunt prey in patches of 2 different types, where prey adopt the camouflage that minimizes individual risk of predation. We show that the optimal strategy of the prey is affected by a number of factors, including the relative frequencies of the patch types, the travel time of predators between patches, the mean prey number in each patch type, and the trade-off function between the levels of crypsis in the patch types. We find evidence that both specialist and compromise strategies of prey camouflage are favored under different model parameters, indicating that optimal concealment may not be as straightforward as previously thought. Copyright 2007, Oxford University Press.