We present a general framework for analyzing the contribution to reproductive success of a behavioural action. An action may make a direct contribution to reproductive success, but even in the absence of a direct contribution it may make an indirect contribution by changing the animal's state. We consider actions over a period of time, and define a reward function that characterizes the relationship between the animal's state at the end of the period and its future reproductive success. Working back from (...) the end of the period using dynamic programming, the optimal action as a function of state and time can be found. The procedure also yields a measure of the cost, in terms of future reproductive success, of a suboptimal action. These costs provide us with a common currency for comparing activities such as eating and drinking, or eating and hiding from predators. The costs also give an indication of the robustness of the conclusions that can be drawn from a model. We review how our framework can be used to analyze optimal foraging decisions in a stochastic environment. We also discuss the modelling of optimal daily routines and provide an illustration based on singing to attract a mate. We use the model to investigate the features that can produce a dawn song burst in birds. State is defined very broadly so that it includes the information an animal has about its environment. Thus, exploration and learning can be included within the framework. (shrink)

A general framework for analysing the effects of variability and the effects of interruptions on foraging is presented. The animal is characterised by its level of energetic reserves, x. We consider behaviour over a period of time [0,T]. A terminal reward function R(x) determines the expected future reproductive success of an animal with reserves x at time T. For any state x at a time in the period, we give the animal a choice between various options and then constrain it (...) to follow a background strategy. The best option is the one that maximizes expected future reproductive success. Using this framework, we show that sensitivity to variability in amount of energy gained is logically distinct from sensitivity to variability in the time at which food is obtained. We also show that incorporating interruptions results in both a preference for variability in time and a preference for a reward followed by a delay as opposed to the same delay before the reward. (shrink)

It is shown that in a range of models, the probability that a forager dies from starvation is, to a good approximation, an exponential function of energy reserves. Using a time and energy budget for a 19g passerine, we explore the consequences, in terms of starvation and predation, of various levels of energy reserves. It is shown that there exists an optimal level L of reserves at which total mortality (starvation plus predation) is minimized. L increases when the environment deteriorates (...) as a result of a decrease in either temperature or mean gross gain or an increase in the mean search time. The effect of combined deteriorations is greater than the sum of their individual effects. At L, the probability of predation is much higher than the probability of starvation. A simple analytic model suggests that this result will be fairly general, but also indicates conditions under which the result might not hold. (shrink)

Rolls discusses various adaptive explanations of physiological processes and the emotions. We give a critical analysis of some of these from the perspective of behavioural ecology. While agreeing with the approach adopted by Rolls, we identify topics that could have been better presented by making use of the existing literature.

John Maynard Smith was the founder of evolutionary game theory. He has also been the major influence on the direction of this field, which now pervades behavioural ecology and evolutionary biology. In its original formulation the theory had three components: a set of strategies, a payoff structure, and a concept of evolutionary stability. These three key components are still the basis of the theory, but what is assumed about each component is often different to the original assumptions. We review modern (...) approaches to these components. We emphasis that if a game is considered in isolation, and arbitrary payoffs are assumed, then the payoffs may not be consistent with other components of the system which are not modelled. Modelling the whole system, including not only the focal game, but also the future behaviour of the players and the behaviour of other population members, allows a consistent model to be constructed. We illustrate this in the case of two models of parental care, showing how linking a focal game to other aspects of the system alters what is predicted. (shrink)

Matrix population models provide a natural tool to analyse state-dependent life-history strategies. Reproductive value and the intrinsic rate of natural increase under a strategy, and the optimal life-history strategy can all be easily characterised using projection matrices. The resultant formulae, however, are not directly comparable with the corresponding formulae for age structured populations such as Lotka's equations and Fisher's formula for reproductive value. This is because formulae involving projection matrices lose track of what happens to an individual over its lifetime (...) and are only concerned with expected numbers of descendants one time step in the future. In contrast the usual age-dependent formulae explicitly followed a single individual through from birth to death.In this paper I show how the state-dependent formulae can be rewritten to be directly comparable with the standard age-structured formulae. Although the formulae are intuitively obvious the decomposition into current and future reproductive success differs from that previously given and is, I suggest, a more natural definition. The derivation of appropriate equations for optimal life-histories relies on results from dynamic programming theory; and is much more general and easier than previous derivations. (shrink)