## Adaptive decisionmaking and population dynamics

In the last chapter we discussed a foraging model known as the marginal value theorem (Charnov 1976). The model considers a patchy environment with patches differing in productivity and is asked how a single organism should behave in response to them. We assumed that the final phenotypic state of the organism would be that which maximized fitness, according to the optimization principle.We will now consider a whole population of individuals inhabiting the environment, and assume that the food supply in a patch replenishes so that organisms can inhabit them full-time. How will the individuals distribute themselves between patches that vary in productivity?

This problem was first considered by Fretwell and Lucas (1970). Imagine the first organism to arrive in the habitat. It should, following the optimization principle, settle in the most productive patch, where its food intake will be highest. By foraging, however, the first organism reduces the productivity of the patch for subsequent foragers through competition (Figure 8.1). The second individual to arrive in the habitat therefore faces a slightly different decision because the productivity of the best patch will now appear lower and hence closer to that of the other patches. If it is still higher than all the others, however, the second organism should still settle there. Individuals continue to occupy the most productive patch until its apparent productivity to the subsequent individual equals that of the second most productive patch. At that stage subsequent organisms to arrive should alternately choose the first and then the second patch as one is depleted below the level of the other in turn. If all individuals are equal competitors and they know

Fig. 8.1 The ideal free distribution. The two curves represent food rewards per individual in a rich and poor habitat as the habitat fills up with competitors. The first set of individuals enters the rich habitat, continuing until such time as the individual rewards are the same as in the poor habitat (horizontal line). Thereafter, individuals fill up both habitats such that rewards are the same in both. After Fretwell and Lucas (1970), with permission from Springer Science and Business Media.

Fig. 8.1 The ideal free distribution. The two curves represent food rewards per individual in a rich and poor habitat as the habitat fills up with competitors. The first set of individuals enters the rich habitat, continuing until such time as the individual rewards are the same as in the poor habitat (horizontal line). Thereafter, individuals fill up both habitats such that rewards are the same in both. After Fretwell and Lucas (1970), with permission from Springer Science and Business Media.

both the productivities of the different patches and the distribution of competitors among them, the end distribution, one in which no individual can do better by moving to another patch, is called the ideal free distribution. This is an evolutionary stable strategy, the concept that applies to maximization situations when the fitness of a given strategy depends on the strategies adopted by other individuals in the population (Chapter 6). At the ESS (the ideal free distribution here), the number of individuals per patch is proportional to their productivity, with more individuals in the best patches.

The ideal free distribution model allows us to predict the distribution of organisms among patches and also their fitness in those habitats. The implicit assumptions, that individuals have perfect knowledge of the habitat, of the distribution of conspecifics, and that they can move freely among habitats, are obviously inappropriate for less mobile organisms, but for some, such as migratory birds, they might be fair approximations. The ESS models of habitat selection like the ideal free distribution can then allow us to predict the productivity of individuals in a population in response to changes in density. These 'density-fitness functions' can then be used to predict how the population will respond to changes in the environment, such as removal of some of the available habitat or a decrease in its quality.

Imagine then a migratory bird population that breeds at one location in summer and then spends the winter in another site where it only feeds. Suppose one summer some of the winter-feeding habitat for the species is removed by a new housing development. What will happen to the population? The modelling logic is roughly this (Goss-Custard and Sutherland 1997): the population migrating to the feeding ground for the winter must be packed into a smaller area of habitat. An ESS model such as the ideal free distribution is used to predict the relationship between bird density and per capita food intake rate in the new smaller habitat. By making some appropriate assumptions relating food intake to winter mortality, we can describe the relationship between density and mortality for the new smaller habitat. An ESS model can also be used to describe the way that bird breeding-habitat fills up and responds to density, and using some appropriate assumptions, how birth rate relates to density. The equilibrium density of the population will be when the birth rate exactly balances the death rate (Figure 8.2). It is now simple to predict the new equilibrium population size if we know how much habitat has been lost, hence, how much the mortality-density function has been shifted.

Sutherland (1996) has done this for the European oystercatcher (Figure 8.3), a wading bird that winters on western European coasts and breeds throughout

Density

Fig. 8.2 How to find the equilibrium population density from the per capita mortality and fecundity curves.

Density

Fig. 8.2 How to find the equilibrium population density from the per capita mortality and fecundity curves.

Fig. 8.3 An oystercatcher, Haematopus ostralagus, foraging. Photo courtesy of Stephane Moniotte.

the north of the continent. He used ESS models to predict the winter mortality-density function, using data from birds wintering on the Exe estuary in Britain, which harbours around 2,000 birds. From long-term studies of these birds, we know that at high density there is more interference between foraging birds as well as greater food depletion, all of which increases winter mortality. For the slope of the birth rate-density function he used data on a breeding population from the Dutch island of Schriermonnikoog.When density is low on the island, birds can all occupy productive territories by the sea, and the birth rate is high. When density is high, birds are either forced to occupy lower quality territories away from the sea, from which they have to commute to the coast to find food, or they do not breed at all but wait at the coast in the hope of occupying a coastal territory if one becomes vacant. As a result, the per capita birth rate is reduced. Consequently, Sutherland was able to predict that if wintering habitat on the Exe estuary were reduced by 1%, the population of oystercatchers would be reduced by 0.69%. The reduction in population size is therefore subproportional to the loss of wintering habitat.

How accurate might the predictions of such 'behavioural-based models' be? In general, we expect them to be better than the major alternative, so-called 'demographic models' which make predictions through direct measurements of the density-mortality and density-birth rate relationships. There are two problems with the demographic approach; one practical and one theoretical. The practical problem is that obtaining accurate data on these relationships can be very difficult. In contrast, studying the behaviour of individuals is much more practical. The theoretical problem is that the new environment, whose effects we want to predict, is very likely to change the density-fitness relationships. For example, reducing the amount of winter feeding-habitat is likely to increase the mortality rate for a given density. The overall behavioural strategy that underlies these changes, however, is likely to remain fixed, therefore by studying behaviour we are studying the mechanistic basis for any change and can detect them.

There is also now some empirical evidence emerging for such advantages of the 'behaviour-based' approach. Stillman et al. (2000) have constructed a very detailed behavioural-based model to predict the population responses of oystercatchers on the Exe estuary. The model was constructed using behavioural observations in the late 1970s, when the population was relatively low. Since then there has been an increase in the wintering oystercatcher population. As a result mortality on the estuary has also risen, and the behavioural-based model was able to predict the level of increased mortality relatively well. In contrast, the density-mortality relationship in the late 1970s was a poor predictor of the relationship later on.

We therefore have grounds for optimism in the value of population models based on adaptive behaviour. They have now been applied to a range of bird and some mammal populations, aimed at predicting effects of environment change, such as human disturbance, habitat loss, habitat exploitation, sea level rise, and changing agricultural practice (see Sutherland and Norris 2002). Thus, using adaptive models to predict how organisms will change their behaviour in response to changes in their environment can help us to predict the consequences of those changes for the population biology. This assumes that all the evolution has happened in the past leaving the organism with a plastic adaptive response to the environment. Another possibility exists however, that organisms will evolve to changing circumstances on timescales that are relevant to population ecologists.

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