Alasdair I. Houston

Honeybees maximize efficiency by not filling their crop

SummaryHoneybees often abandon non-depleting food sources with a partially filled crop. This behaviour does not maximise the net rate of energy extraction from the food sources, and thus contradicts predictions of some common models for central place foragers. We show that including the metabolic costs of transport of nectar leads to models that predict partial crop-loading. Furthermore, the observed crop loads of honeybees are less consistent with those predicted by maximization of delivery rate to the hive (net energetic gain/ unit time), than with those predicted by maximization of energetic efficiency (net energetic gain/unit energy expenditure). We argue that maximization of energetic efficiency may be an adaptation to a limited flight-cost budget. This constraint is to be expected because a workers condition seems to deteriorate as a function of the amount of flight performed.

The application of statistical decision theory to animal behaviour

Abstract Statistical decision theory is discussed as a general framework for analysing how animals should learn. Attention is focused on optimal foraging behaviour in stochastic environments. We emphasise the distinction between the mathematical procedure that can be used to find optimal solutions and the mechanism an animal might use to implement such solutions. The mechanisms might be specific to a restricted class of problems and produce suboptimal behaviour when faced with problems outside this class. We illustrate this point by an example based on what is known in the literature on animal learning as the partial reinforcement effect.

A framework for the functional analysis of behaviour

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 animals state. We consider actions over a period of time, and define a reward function that characterizes the relationship between the animals 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.

Evolutionarily stable levels of vigilance as a function of group size

An animals level of vigilance is usually interpreted as a trade-off between gaining food and reducing the danger of predation. In the context of a group of animals, vigilance has been analysed using the evolutionarily stable strategy (ESS) concept. In this paper a general ESS model of vigilance as a function of group size is developed. The model is based on an explicit foraging process that may be terminated prematurely by events such as bad weather that are outside the animals control. It can be used to investigate the effect of both environmental parameter, such as the rate of attack by predators and the rate of food intake, and the animals internal state on evolutionarily stable levels of vigilance. The biological assumptions underlying other models of vigilance are explored, demonstrating why some factors influence the level of vigilance in some models but not in others. Pulliam et al. (J. theor. Biol., 1982, 95, 89–103) presented data on vigilance as a function of group size that they found hard to explain in terms of an ESS model. This paper introduces various modifications to their model and shows that a reasonable fit to the data can be obtained.

Optimal foraging and learning

Optimal foraging thoery usually assumes that certain key environmental parameters are known to a foraging animal, and predicts the animals behaviour under this assumption. However, an animal entering a new environment has incomplete knowledge of these parameters. If the predictions of optimal foraging theory are to hold the animal must use a behavioural rule which both learns the parameters and optimally exploits what it has learnt. In most circumstances it is not obvious that there exists any simple rule which has both these properties. We consider an environment composed of well-defined patches of food, with each patch giving a smooth decelerating flow of food ( Charnov, 1976 ). We present a simple rule which (asymptotically) learns about and optimally exploits this environment. We also show the rule can be modified to cope with a changing environment. We discuss what is meant by optimal behaviour in an unknown and possibly changing environment, using the simple rule we have presented for illustrative purposes.

Phenotypic plasticity as a state-dependent life-history decision

SummaryA genotype is said to show phenotypic plasticity if it can produce a range of environmentally dependent phenotypes. Plasticity may or may not be adaptive. We consider plasticity as a genetically determined trait and thus find the optimal response of an animal to its environment. Various aspects of this optimal response are illustrated with examples based on reproductive effort. We investigate the selection pressure for plastic as opposed to fixed strategies. An example with spatial heterogeneity is used to compare our approach with that of Stearns and Koella (1986).

OPTIMAL DAILY ROUTINES OF SINGING AND FORAGING IN A BIRD SINGING TO ATTRACT A MATE

SummaryIn this paper we develop a dynamic programming model to explore the optimal organization of daily routines of singing and foraging in a small bird. While singing the bird may attract a mate but uses up energy. Most of the patterns of daily variation in singing generated have basic features very characteristic of typical passerine song output. The predictions are remarkably robust to changes in a wide range of parameters, showing which parameters are important. A peak of singing at dawn can result from variability in overnight energy expenditure in the absence of any circadian patterns in the environment.

Singing to attract a mate: a stochastic dynamic game

We discuss the difficulties that arise in finding evolutionarily stable policies for stochastic dynamic games. Using a simplifying assumption we present an interative technique for solving such problems. We illustrate the technique in the context of a bird that sings to attract a mate. Starting from a dynamic problem in which the probability of attracting does not depend on the behaviour of other birds, we introduce interactions between birds and find the evolutionarily stable policy.

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

The iterated prisoners 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 ethologys comparative approach.

Genetic algorithms and evolution.

The genetic algorithm (GA) as developed by Holland (1975, Adaptation in Natural and Artificial Systems. Ann Arbor: University of Michigan Press) is an optimization technique based on natural selection. We use a modified version of this technique to investigate which aspects of natural selection make it an efficient search procedure. Our main modification to Hollands GA is the subdividing of the population into semi-isolated demes. We consider two examples. One is a fitness landscape with many local optima. The other is a model of singing in birds that has been previously analysed using dynamic programming. Both examples have epistatic interactions. In the first example we show that the GA can find the global optimum and that its success is improved by subdividing the population. In the second example we show that GAs can evolve to the optimal policy found by dynamic programming.