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.

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.

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.

Gains v. losses, or context dependence generated by confusion?

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.

Mechanistic models must link the field and the lab.

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.

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).

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.

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.

Capital and income breeding: the role of food supply.

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

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

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

Foraging currencies, metabolism and behavioural routines.

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

The coevolution of choosiness and cooperation.

Explaining the rise and maintenance of cooperation is central to our understanding of biological systems and human societies. 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 altruism. The evolution of cooperation between non-relatives can then be driven by a positive feedback between increasing levels of cooperativeness and choosiness. 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.

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.

Is quantum probability rational?

We concentrate on two aspects of the article by Pothos & Busemeyer (P&B): the relationship between classical and quantum probability and quantum probability as a basis for rational decisions. We argue that the mathematical relationship between classical and quantum probability is not quite what the authors claim. Furthermore, it might be premature to regard quantum probability as the best practical rational scheme for decision making.

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.

Generalized optimal risk allocation: foraging and antipredator behavior in a fluctuating environment.

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.

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.