## Evolution of Prey Predator Systems

To describe the strategies of prey and predators, we consider a in eqn [2] as a function of C and E, where C is the vulnerability of the prey to the predator (opposite of the antipredator effort) and E is the average capture effort of the predator. Because of the assumptions of tradeoffs between antipredator effort and growth rate for the prey, and between predation rate and death rate for the predator, we also assume r as a function of C, and d as a function of E in eqn [2]. In addition, C and E may be evolutionary variables that increase their own fitness. Two types of dynamic models can be used to describe temporal changes in trait values by adaptive evolution: (1) a quantitative genetic model; and (2) adaptive dynamics. Quantitative genetic models describe intergenerational changes in the population mean trait value in proportion to the selection differential of its fitness, with respect to an individual trait value. In adaptive dynamics, populations consist of asexual clones with mutations. Here we use a quantitative genetic model as explained below.

Several models have investigated the effects of evolutionary change in either prey or predator species on prey-predator systems, although only some authors

Table 1 Preference indices for a predator's choice of prey

Case

Abundance of prey in the habitat

Abundance of prey consumed by a predator

IvIev's index I,

Chesson's index a,

10 1o

91 1

have considered coevolution of prey and predators. First, we introduce the effects of predator evolution on prey-predator dynamics.

The evolution of the predator's capture rate is modeled by:

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