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.

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.

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.

How did the Great Auk raise its young?

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.

Seasonal dispersal of pests: one surge or two?

Many agricultural pest species occur in seasonal metapopulations with a period of asexual reproduction. We use evolutionary theory to predict timing of dispersal for such species, and identify four sequential phases: no dispersal, dispersal from initially occupied patches, dispersal from later colonized patches, and no dispersal. The third type of phase occurs only when reproductive rates are relatively high; we speculate that this could explain why among aphids there can be either one or two waves of dispersal during a season, depending on the species. Our model also explains other features of aphid biology, including a summer crash in colony size, and a decline in the number of colonies towards the end of each reproductive season. The presence of an additional surge of dispersal becomes more likely as season length increases, and does not require further evolution. This could have profound implications for pest management during future climatic warming.

A dynamic model of hypothermia as an adaptive response by small birds to winter conditions.

We present a dynamic programming model which is used to investigate hypothermia as an adaptive response by small passerine birds in winter. The model predicts that there is a threshold function of reserves during the night, below which it is optimal to enter hypothermia, and above which it is optimal to rest. This threshold function decreases during the night, with a particularly sharp drop at the end of the night, representing the time and energy costs associated with returning to normal body temperature. The results of the model emphasise the trade-off between energy and predation, not just between foraging options, but also between foraging during the day and entering hypothermia at night. The value of being able to use hypothermia represents not just energy savings, but also reduced predation risk due to changes in the optimal foraging strategy. Conditions which give a high value of hypothermia are short photoperiod, variable food supply, low temperatures, poor and scarce food supplies.

A theoretical investigation into the direct and indirect effects of state on the risk of predation.

As well as there being a direct physical effect of the state (for example fat reserves, or size) of an animal on the risk of being caught by a predator, state also has an effect on predation risk indirectly through changes in behaviour. We present a mathematical model which looks at these two components of the effect of state on predation risk. We focus on two different models, (i) where the animal must achieve a fixed state and its fitness depends on the time at which this state is reached and (ii) where the animal must survive until a fixed time and its fitness depends on its final state. We investigate conditions under which the indirect effect of increased state is to increase or decrease predation risk, and give some numerical illustrations. Under certain conditions in the fixed-state model, the indirect effect of state is to increase predation risk, whereas under certain conditions in the fixed-time model the indirect effect of state is to decrease predation risk. We discuss the implications of our results for empirical investigations into the effect of state on predation risk.

A dynamic game-theoretic model of parental care.

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

Prey processing in central place foragers.

The importance of prey processing as an integral part of foraging behaviour has long been acknowledged, but little theoretical consideration has been given to the optimization of the processing behaviour itself. Processing renders food down to ingestible, palatable portions, and also removes non-essential mass thus reducing transport costs. Here, several models of processing are developed for a central place forager. When the forager has to make a simple choice between processing the prey and not, a critical distance from the central place can be calculated, beyond which it is optimal to process prey. If the forager also decides on how much of the prey to remove, the optimal amount to be removed can also be calculated. Imposing a ceiling on overall metabolic expenditure is shown to reduce the distances at which processing becomes the optimal strategy. The models are tested using parameters derived for a provisioning merlin, Falco columbarius, and alternative explanations as to why observed behaviours should differ from the optimal behaviour predicted are discussed.

The strength of selection in the context of migration speed.

I use a model of avian migration based on maximization of overall migration speed to compare the strength of selection acting on foraging performance and flight speed. Let the optimal foraging behaviour be u* and the optimal flight speed be v*. It is shown that at this optimum, the ratio of the strength of selection on foraging to the strength of selection on flight speed is theta = -(u*2Pgamma"/v*2gammaP"), where gamma is the rate of energy expenditure during flight and P is the rate at which energy is gained during foraging. The dimensionless ratio P/gamma is the ratio of time spent building up fuel to time spent flying which A. Hedenström and T. Alerstam showed was much greater than unity. Although theta depends on this ratio, it also depends on the curvatures of the functions, as represented by gamma" and P". I use this simple example to make some general points about the strength of selection.

Incorporating rules for responding into evolutionary games.

Evolutionary game theory is concerned with the evolutionarily stable outcomes of the process of natural selection. The theory is especially relevant when the fitness of an organism depends on the behaviour of other members of its population. Here we focus on the interaction between two organisms that have a conflict of interest. The standard approach to such two-player games is to assume that each player chooses a single action and that the evolutionarily stable action of each player is the best given the action of its opponent. We argue that, instead, most two-player games should be modelled as involving a series of interactions in which opponents negotiate the final outcome. Thus we should be concerned with evolutionarily stable negotiation rules rather than evolutionarily stable actions. The evolutionarily stable negotiation rule of each player is the best rule given the rule of its opponent. As we show, the action chosen as a result of the negotiation is not the best action given the action of the opponent. This conclusion necessitates a fundamental change in the way that evolutionary games are modelled.

Currencies for foraging based on energetic gain.

We carry out a theoretical investigation of the behavior of a foraging animal that maximizes either the net amount of energy obtained (self-feeding) or the amount of energy delivered to another animal such as its young or to a store (provisioning). Using an novel graphical approach, we derive general results concerning the effects of constraints on the amount of energy the animal can spend or acquire. In the context of an animal that is provisioning, that is, both feeding itself and delivering energy to a given location, we establish a general relationship between the best foraging option when feeding itself and the best option to use when delivering energy. Our results extend and unify previous results in this area.

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

Realistic models of contests between animals will often involve a series of state-dependent decisions by the contestants. Computation of evolutionarily stable strategies for such state-dependent dynamic games are usually based on damped iterations of the best response map. Typically this map is discontinuous so that iterations may not converge and even if they do converge it may not be clear if the limiting strategy is a Nash equilibrium. We present a general computational technique based on errors in decision making that removes these computational difficulties. We show that the computational technique works for a simple example (the Hawk-Dove game) where an analytic solution is known, and prove general results about the technique for more complex games. It is also argued that there is biological justification for inclusion of the types of errors we have introduced.

State-dependent life histories.

Life-history theory is concerned with strategic decisions over an organism's lifetime. Evidence is accumulating about the way in which these decisions depend on the organism's physiological state and other components such as external circumstances. Phenotypic plasticity may be interpreted as an organism's response to its state. The quality of offspring may depend on the state and behaviour of the mother. Recent theoretical advances allow these and other state-dependent effects to be modelled within the same framework.

State-dependent life history evolution in Soay sheep: dynamic modelling of reproductive scheduling.

Adaptive decisions concerning the scheduling of reproduction in an animal's lifetime, including age at maturity and clutch or litter size, should depend on an animal's body condition or state. In this state-dependent case, we are concerned with the optimization of sequences of actions and so dynamic optimization techniques are appropriate. Here we show how stochastic dynamic programming can be used to study the reproductive strategies and population dynamics of natural populations, assuming optimal decisions. As examples we describe models based upon field data from an island population of Soay sheep on St. Kilda. This population shows persistent instability, with cycles culminating in high mortality every three or four years. We explore different assumptions about the extent to which Soay ewes use information about the population cycle in making adaptive decisions. We compare the observed distributions of strategies and population dynamics with model predictions; the results indicate that Soay ewes make optimal reproductive decisions given that they have no information about the population cycle. This study represents the first use of a dynamic optimization life history model of realistic complexity in the study of a field population. The techniques we use are potentially applicable to many other populations, and we discuss their extension to other species and other life history questions.

Beyond the prisoner's dilemma: Toward models to discriminate among mechanisms of cooperation in nature.

The iterated prisoner's dilemma game, or IPD, has now established itself as the orthodox paradigm for theoretical investigations of the evolution of cooperation; but its scope is restricted to reciprocity, which is only one of three categories of cooperation among unrelated individuals. Even within that category, a cooperative encounter has in general three phases, and the IPD has nothing to say about two of them. To distinguish among mechanisms of cooperation in nature, future theoretical work on the evolution of cooperation must distance itself from economics and develop games as a refinement of ethology's comparative approach.

Risk-sensitive foraging theory and operant psychology.

Hastjarjo, Silberberg, and Hursh (1990) have presented data on the foraging behavior of rats and discussed it in terms of risk-sensitive foraging theory. Because risk-sensitive foraging theory is comprised of several different models, it does not lead to general predictions about when an organism should prefer a foraging option with high variance to a foraging option with low variance. Any comparison of data with the predictions of the theory must be based on an appropriate model. I draw attention to various experiments that are potentially relevant to the results reported by Hastjarjo et al. and show how the time period over which the organism must survive can influence a model's predictions about risk sensitivity.