Ways to test stochastic dynamic programming models empirically.

Stochastic dynamic programming (SDP) models are widely used to predict optimal behavioural and life history strategies. We discuss a diversity of ways to test SDP models empirically, taking as our main illustration a model of the daily singing routine of birds. One approach to verification is to quantify model parameters, but most SDP models are schematic. Because predictions are therefore qualitative, testing several predictions is desirable. How state determines behaviour (the policy) is a central prediction that should be examined directly if both state and behaviour are measurable. Complementary predictions concern how behaviour and state change through time, but information is discarded by considering behaviour rather than state, by looking only at average state rather than its distribution, and by not following individuals. We identify the various circumstances in which an individual's state/behaviour at one time is correlated with its state/behaviour at a later time. When there are several state variables the relationships between them may be informative. Often model parameters represent environmental conditions that can also be viewed as state variables. Experimental manipulation of the environment has several advantages as a test, but a problem is uncertainty over how much the organism's policy will adjust. As an example we allow birds to use different assumptions about how well past weather predicts future weather. We advocate mirroring planned empirical investigations on the computer to investigate which manipulations and predictions will best test a model. Copyright 2000 The Association for the Study of Animal Behaviour.

Multiple patterns of parental care.

Many animals show multiple patterns of parental care, where more than one of the four basic patterns (biparental care, uniparental care by males or females, or no care) is present within a single population during a single breeding season. We consider three reasons for the existence of multiple patterns of parental care: (1) mixed-strategy behaviours; (2) time-dependent behaviour with parents changing their care decision during the breeding season; and (3) quality differences between individuals leading to different care decisions being made depending on the qualities of both parents. The basic framework we use to investigate these is a two-stage game-theoretical model, and we highlight the importance of including feedback between the parental care decisions made by population members and the probability that a deserting individual will find a new mate. Including this feedback may introduce a nonlinear dependence of the fitness payoffs on the frequencies with which the pure strategies ('care' and 'desert') are played by each of the sexes. This can have important consequences for the existence of evolutionarily stable strategies (ESSs). For example, mixed-strategy ESSs may exist (an outcome forbidden if the feedback is not included) and, in one model, the feedback also prevents uniparental care by either sex from being evolutionarily stable. We also point out that decisions made by animals without dependent offspring can have important consequences for observed parental care behaviour. Copyright 1999 The Association for the Study of Animal Behaviour.

Interruptions to foraging and learning in a changing environment.

Many resources are both stochastic and variable in their average profitability. Animals have to sample them to track their current states, but whether it is economic to attempt this depends on many factors. Furthermore, there are many interruptions and distractions from foraging (e.g. escape from predators, bad weather, displacement by competitors) which interfere with the acquisition of information. We present a dynamic model of foraging in a stochastic and varying environment, under the constant threat of interruption, to investigate this very general problem. A forager faces two foraging options, one of which provides a known and constant reward, the other providing a reward that is not only stochastic, but whose mean payoff varies in time. The forager has to learn which option has the highest current payoff by sampling. However, interruptions to foraging can occur at any time, the timing and duration of which are beyond the animal's control. When there is a small probability of foraging being interrupted, the forager should forage extensively on the unknown option, but as the probability of interruptions is increased, there is a sudden transition to foraging only on the known option. This occurs because interruptions affect both the level of information required to make exploitation of the unknown option profitable, and the ability to acquire and maintain that information. At what probability of being interrupted this threshold emerges is affected by the value of learning about the unknown option and the duration of interruptions. We discuss the generality of our results with reference to the pervasive problem of updating information in the face of different types of interruption. Copyright 1999 The Association for the Study of Animal Behaviour.