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.

A general framework for modelling trade-offs in adaptive behaviour

An animal's behaviour can influence many variables, such as its energy reserves, its risk of injury or mortality, and its rate of reproduction. To identify the optimal action in a given situation, these various effects can be compared in the common currency of reproductive value. While this idea has been widely used to study trade-offs between pairs of variables, e.g. between energy gain versus survival, here we present a unified framework that makes explicit how these various trade-offs fit together. This unification covers a wide range of biological phenomena, highlighting similarities in their logical structure and helping to identify knowledge gaps. To fill one such gap, we present a new model of foraging under the risk of predation and damage accumulation. We conclude by discussing the use and limitations of state-dependent optimisation theory in predicting biological observations.

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.

Biological adaptation in light of the Lewontin-Williams (a)symmetry

Neo-Darwinism characterizes 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 emphasizes that organisms and their environments often mutually affect each other. Here, we clarify that Williams' asymmetry is specifically concerned with (quasi)-directed modifications toward 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.

A critical evaluation of the index of patch quality

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.

How to Model Optimal Group Size in Social Carnivores

AbstractModels 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.

Matching Behaviours and Rewards

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.

Learning, exploitation and bias in games

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'.

The overall discount rate

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.

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).

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.

Risk attitudes in a changing environment: An evolutionary model of the fourfold pattern of risk preferences

A striking feature of human decision making is the fourfold pattern of risk attitudes, involving risk-averse behavior in situations of unlikely losses and likely gains, but risk-seeking behavior in response to likely losses and unlikely gains. Current theories to explain this pattern assume particular psychological processes to reproduce empirical observations, but do not address whether it is adaptive for the decision maker to respond to risk in this way. Here, drawing on insights from behavioral ecology, we build an evolutionary model of risk-sensitive behavior, to investigate whether particular types of environmental conditions could favor a fourfold pattern of risk attitudes. We consider an individual foraging in a changing environment, where energy is needed to prevent starvation and build up reserves for reproduction. The outcome, in terms of reproductive value (a rigorous measure of evolutionary success), of a one-off choice between a risky and a safe gain, or between a risky and a safe loss, determines the risk-sensitive behavior we should expect to see in this environment. Our results show that the fourfold pattern of risk attitudes may be adaptive in an environment in which conditions vary stochastically but are autocorrelated in time. In such an environment the current options provide information about the likely environmental conditions in the future, which affect the optimal pattern of risk sensitivity. Our model predicts that risk preferences should be both path dependent and affected by the decision maker's current state.

Scalar utility theory and proportional processing: What does it actually imply?

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.

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.

Costs of Foraging Predispose Animals to Obesity-Related Mortality when Food Is Constantly Abundant

Obesity is an important medical problem affecting humans and animals in the developed world, but the evolutionary origins of the behaviours that cause obesity are poorly understood. The potential role of occasional gluts of food in determining fat-storage strategies for avoiding mortality have been overlooked, even though animals experienced such conditions in the recent evolutionary past and may follow the same strategies in the modern environment. Humans, domestic, and captive animals in the developed world are exposed to a surplus of calorie-rich food, conditions characterised as ‘constant-glut’. Here, we use a mathematical model to demonstrate that obesity-related mortality from poor health in a constant-glut environment should equal the average mortality rate in the ‘pre-modern’ environment when predation risk was more closely linked with foraging. It should therefore not be surprising that animals exposed to abundant food often over-eat to the point of ill-health. Our work suggests that individuals tend to defend a given excessive level of reserves because this level was adaptive when gluts were short-lived. The model predicts that mortality rate in constant-glut conditions can increase as the assumed health cost of being overweight decreases, meaning that any adaptation that reduced such health costs would have counter-intuitively led to an increase in mortality in the modern environment. Taken together, these results imply that efforts to reduce the incidence of obesity that are focussed on altering individual behaviour are likely to be ineffective because modern, constant-glut conditions trigger previously adaptive behavioural responses.

Adaptive learning can result in a failure to profit from good conditions: implications for understanding depression

BACKGROUND AND OBJECTIVES

Depression is a major medical problem diagnosed in an increasing proportion of people and for which commonly prescribed psychoactive drugs are frequently ineffective. Development of treatment options may be facilitated by an evolutionary perspective; several adaptive reasons for proneness to depression have been proposed. A common feature of many explanations is that depressive behaviour is a way to avoid costly effort where benefits are small and/or unlikely. However, this viewpoint fails to explain why low mood persists when the situation improves. We investigate whether a behavioural rule that is adapted to a stochastically changing world can cause inactivity which appears similar to the effect of depression, in that it persists after the situation has improved.

METHODOLOGY

We develop an adaptive learning model in which an individual has repeated choices of whether to invest costly effort that may result in a net benefit. Investing effort also provides information about the current conditions and rates of change of the conditions.

RESULTS

An individual following the optimal behavioural strategy may sometimes remain inactive when conditions are favourable (i.e. when it would be better to invest effort) when it is poorly informed about the current environmental state. Initially benign conditions can predispose an individual to inactivity after a relatively brief period of negative experiences.

CONCLUSIONS AND IMPLICATIONS

Our approach suggests that the antecedent factors causing depressed behaviour could go much further back in an individual s history than is currently appreciated. The insights from our approach have implications for the ongoing debate about best treatment options for patients with depressive symptoms.

Cross inhibition improves activity selection when switching incurs time costs

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.

Evolution of a flexible rule for foraging that copes with environmental variation

Models of adaptive behaviour typically assume that animals behave as though they have highly complex, detailed strategies for making decisions. In reality, selection favours the optimal balance between the costs and benefits of complexity. Here we investigate this trade-off for an animal that has to decide whether or not to forage for food – and so how much energy reserves to store – depending on the food availability in its environment. We evolve a decision rule that controls the target reserve level for different ranges of food availability, but where increasing complexity is costly in that metabolic rate increases with the sensitivity of the rule. The evolved rule tends to be much less complex than the optimal strategy but performs almost as well, while being less costly to implement. It achieves this by being highly sensitive to changing food availability at low food abundance – where it provides a close fit to the optimal strategy – but insensitive when food is plentiful. When food availability is high, the target reserve level that evolves is much higher than under the optimal strategy, which has implications for our understanding of obesity. Our work highlights the important principle of generalisability of simple decision-making mechanisms, which enables animals to respond reasonably well to conditions not directly experienced by themselves or their ancestors.

A dynamic framework for the study of optimal birth intervals reveals the importance of sibling competition and mortality risks

Human reproductive patterns have been well studied, but the mechanisms by which physiology, ecology and existing kin interact to affect the life history need quantification. Here, we create a model to investigate how age-specific interbirth intervals adapt to environmental and intrinsic mortality, and how birth patterns can be shaped by competition and help between siblings. The model provides a flexible framework for studying the processes underlying human reproductive scheduling. We developed a state-based optimality model to determine age-dependent and family-dependent sets of reproductive strategies, including the state of the mother and her offspring. We parameterized the model with realistic mortality curves derived from five human populations. Overall, optimal birth intervals increase until the age of 30 after which they remain relatively constant until the end of the reproductive lifespan. Offspring helping each other does not have much effect on birth intervals. Increasing infant and senescent mortality in different populations decreases interbirth intervals. We show that sibling competition and infant mortality interact to lengthen interbirth intervals. In lower-mortality populations, intense sibling competition pushes births further apart. Varying the adult risk of mortality alone has no effect on birth intervals between populations; competition between offspring drives the differences in birth intervals only when infant mortality is low. These results are relevant to understanding the demographic transition, because our model predicts that sibling competition becomes an important determinant of optimal interbirth intervals only when mortality is low, as in post-transition societies. We do not predict that these effects alone can select for menopause.

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.

Natural selection can favour 'irrational' behaviour

Understanding decisions is the fundamental aim of the behavioural sciences. The theory of rational choice is based on axiomatic principles such as transitivity and independence of irrelevant alternatives (IIA). Empirical studies have demonstrated that the behaviour of humans and other animals often seems irrational; there can be a lack of transitivity in choice and seemingly irrelevant alternatives can alter decisions. These violations of transitivity and IIA undermine rational choice theory. However, we show that an individual that is maximizing its rate of food gain can exhibit failure of transitivity and IIA. We show that such violations can be caused because a current option may disappear in the near future or a better option may reappear soon. Current food options can be indicative of food availability in the near future, and this key feature can result in apparently irrational behaviour.

On the evolution and optimality of mood States

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.

An adaptive response to uncertainty generates positive and negative contrast effects

Successive contrast effects, in which behavior is dependent on whether conditions are currently better or worse than they were before, are a striking illustration of the fact that animals evaluate the world in relative terms. Existing explanations for these effects are based on descriptive models of psychological and physiological processes, but little attention has been paid to the factors promoting their evolution. Using a simple and general optimality model, we show that contrast effects can result from an adaptive response to uncertainty in a changing, unpredictable world. A wide range of patterns of environmental change will select for sensitivity to past conditions, generating positive and negative contrast effects. Our analysis reveals the importance of incorporating uncertainty and environmental stochasticity into models of adaptive behavior.

Comparing pleasure and pain: the fundamental mathematical equivalence of reward gain and shock reduction under variable interval schedules

The relationship between positive and negative reinforcement and the symmetry of Thorndike's law of effect are unresolved issues in operant psychology. Here we show that, for a given pattern of responding on variable interval (VI) schedules with the same programmed rate of food rewards (positive reinforcement VI) or electric shocks (negative reinforcement VI), there is a fundamental mathematical equivalence between reward gain and shock reduction. We also provide the first normative account of how animals should respond on a negative VI schedule, showing that it is better to space responses evenly than to respond with a variable interresponse time (IRT). Published data from rats, however, indicate that these animals respond irregularly, often with a burst of activity immediately following a shock. While this is irrational in the experimental setting, it may represent an appropriate response to the heterogeneity of stimuli commonly encountered in natural environments. We discuss the broader implications of our analysis for understanding how animals evaluate appetitive and aversive stimuli.

Does natural selection favour the Rescorla-Wagner rule?

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.

It is optimal to be optimistic about survival

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.

The starvation-predation trade-off predicts trends in body size, muscularity, and adiposity between and within Taxa

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 such costs are high, then adiposity should decrease with body mass. These predictions are supported by observations of variation between and within species. Our approach demonstrates that broad patterns of body composition can be understood in terms of the fundamental ecological trade-off between starvation and predation.

Is optimism optimal? Functional causes of apparent behavioural biases

We review the use of the terms 'optimism' and 'pessimism' to characterize particular types of behaviour in non-human animals. Animals can certainly behave as though they are optimistic or pessimistic with respect to specific motivations, as documented by an extensive range of examples in the literature. However, in surveying such examples we find that these terms are often poorly defined and are liable to lead to confusion. Furthermore, when considering behaviour within the framework of optimal decision theory using appropriate currencies, it is often misleading to describe animals as optimistic or pessimistic. There are two common misunderstandings. First, some apparent cases of biased behaviour result from misidentifying the currencies and pay-offs the animals should be maximising. Second, actions that do not maximise short-term pay-offs have sometimes been described as optimistic or pessimistic when in fact they are optimal in the long term; we show how such situations can be understood from the perspective of bandit models. Rather than describing suboptimal, unrealistic behaviour, the terms optimism and pessimism are better restricted to informal usage. Our review highlights the importance of choosing the relevant currency when attempting to predict the action of natural selection.

The ecological rationality of state-dependent valuation

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.

Decision-making under uncertainty: biases and Bayesians

Animals (including humans) often face circumstances in which the best choice of action is not certain. Environmental cues may be ambiguous, and choices may be risky. This paper reviews the theoretical side of decision-making under uncertainty, particularly with regard to unknown risk (ambiguity). We use simple models to show that, irrespective of pay-offs, whether it is optimal to bias probability estimates depends upon how those estimates have been generated. In particular, if estimates have been calculated in a Bayesian framework with a sensible prior, it is best to use unbiased estimates. We review the extent of evidence for and against viewing animals (including humans) as Bayesian decision-makers. We pay particular attention to the Ellsberg Paradox, a classic result from experimental economics, in which human subjects appear to deviate from optimal decision-making by demonstrating an apparent aversion to ambiguity in a choice between two options with equal expected rewards. The paradox initially seems to be an example where decision-making estimates are biased relative to the Bayesian optimum. We discuss the extent to which the Bayesian paradigm might be applied to the evolution of decision-makers and how the Ellsberg Paradox may, with a deeper understanding, be resolved.

Evolutionary models of metabolism, behaviour and personality

I explore the relationship between metabolism and personality by establishing how selection acts on metabolic rate and risk-taking in the context of a trade-off between energy and predation. Using a simple time budget model, I show that a high resting metabolic rate is not necessarily associated with a high daily energy expenditure. The metabolic rate that minimizes the time spent foraging does not maximize the net gain rate while foraging, and it is not always advantageous for animals to have a higher metabolic rate when food availability is high. A model based on minimizing the ratio of mortality rate to net gain rate is used to determine how a willingness to take risks should be correlated with metabolic rate. My results establish that it is not always advantageous for animals to take greater risks when metabolic rate is high. When foraging intensity and metabolic rate coevolve, I show that in a particular case different combinations of foraging intensity and metabolic rate can have equal fitness.

What currency do bumble bees maximize?

In modelling bumble bee foraging, net rate of energetic intake has been suggested as the appropriate currency. The foraging behaviour of honey bees is better predicted by using efficiency, the ratio of energetic gain to expenditure, as the currency. We re-analyse several studies of bumble bee foraging and show that efficiency is as good a currency as net rate in terms of predicting behaviour. We suggest that future studies of the foraging of bumble bees should be designed to distinguish between net rate and efficiency maximizing behaviour in an attempt to discover which is the more appropriate currency.