## Ideal Free Distribution and Despotic Distribution

If there are two habitats of different qualities, the theory of free distribution of individuals between these habitats predicts that the number of individuals should be proportional to the quality of the habitat, but the average fitness of individuals should be identical in these two habitats (Figure 3). This theory, developed by Stephen D. Fretwell, is based on the assumptions that (1) the cost of changing the habitat is insignificant and (2) there is no kind of monopolization of resources in the habitat, against the encroachment of others. Theory of the free distribution does not specify individual differences in resource intakes and consequently in individual fitness, since it is concerned with the average values of these parameters. However, experimental studies of free distribution, with controlled amount of food supplied in two different places, show that animals distribute themselves proportionally to the amount of food supplied but there are large differences in individual food intakes.

The theory of free distribution shows how animals maximize their fitness by the simplest behavior: choose a

Fitness

nw nb Number of individuals

Isodar

### Nw nw nb Number of individuals

Figure 3 Graphic representation of the ideal free distribution. Left diagram: average fitness of individuals in a better (upper right line - B) and a worse (lower left line - W) habitat, as the function of number of individuals in these habitats. At the start, the individuals choose the better habitat but with their number NB increasing, competition leads to deterioration of their average fitness Fb, up to the point in which it is the same as in the worse habitat. The model of free distribution (left diagram) assumes that there are not any costs of changing the habitat and any obstacles to move between these two habitats. If so, then the individuals move where their fitness is the highest and their average fitness in both habitats is equal to each other (FB = FW), but the number of individuals is lower in the worse habitat (NB >NW). Right diagram: thick line on this diagram, with coordinates given by number of individuals in the better NB and worse NW habitats is isodar - a line connecting numbers NB and NW at which the fitness in both habitats is identical. Isodars can be empirically determined by finding out how, with increasing number of individuals, they distribute themselves between two habitats. From the shape of the isodars one may infer not only qualities and interrelations between different habitats but also competitive behavior of animals occupying these habitats.

Fitness

Fitness

Number of individuals

Isodar

Number of individuals

Figure 4 Graphic representation of the despotic distribution. Left diagram: average fitness of individuals in a better (upper right line - B) and a worse (lower left line - W) habitat, as the function of number of individuals in these habitats. At the start, the individuals choose the better habitat but at certain density, some individuals are able to monopolize the better habitat, so that their average fitness FB does not fall. With increasing number of individuals, they are forced to move into the worse habitat in which their fitness FW is lower. The departure from the model of free distribution toward despotic distribution may be for different reasons. The fitness is higher in the better habitat (FB >FW), but the number of individuals may be either higher or lower. Right diagram: thick line on this diagram, with coordinates given by number of individuals in the better NB and worse NW habitats, is an isodar (for further explanation see the legend to Figure 3), for the case of despotic distribution with the monopolization of resources in the better habitat by a limited number of individuals.

habitat with more resources and less competitors. Any kind of departure from the ideal free distribution suggests some behavioral interactions preventing such a distribution - for example, the monopolization of the resources of high qualities by some individuals, which results in the despotic distribution (Figure 4). If the movement between different habitats and the assessment of their qualities is costly or ifthe investments ofsome individuals in a habitat prevent them from moving to another one, a departure from the free distribution occurs. An empirical example of despotic distribution is not only higher density but also higher reproductive output of great tits in more favorable deciduous forests than in poorer coniferous forests. The reason of such distribution is due to territoriality.

From the theory of ideal free habitat selection Douglas W. Morris has developed the concept of isodars. Isodar is a line connecting the points of identical fitness in two different habitats, in the plane in which coordinates are numbers of individuals in these habitats. Examples of isodars for the models of ideal free distribution and despotic distribution are in Figures 3 and 4, respectively. If one does not know the fitness as a function of density for different habitats, one may still learn how increasing density of individuals change in these habitats and from these data determine the shape of the isodar. This shape allows us to see what the differences between the habitats are and how the competitive behavior of an animal population occupying these habitats looks like. The isodars can also be considered as trajectories along which number of individuals in two habitats increases.

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