Modeling Predator–Prey Dynamics
255
In this review I touch only briefly on more complex models involving multiple species, but of course, seldom is a two-species interaction sufficient to capture the complexity of biological interactions that occur in ecosystems.
NONINTERACTIVE MODELS
Predator–prey models are by definition based on a predator having a negative
effect on a prey population while the predator benefits from consuming the
prey. Yet to simplify the system, many ecologists choose to ignore the interaction by assessing only the dynamics of a single species. This can take at least
four forms: single-species models of predators or prey, demographic trajectories of prey anticipating the consequences of predator-imposed mortality,
attempts to assess whether predator-imposed mortality on prey is compensatory or additive, and habitat capability models. Each of these approaches circumvents the issue of predator–prey interactions; consequently, noninteractive models are less likely to capture the dynamic behaviors of a predator–prey
system. However, these approaches pervade the wildlife ecology literature and
deserve to be placed into context.
Single-species models
We can model the effect of a predator population on a prey population with a
single equation for the prey. For example, consider a population of prey governed by the differential equation
dV/dt = r × V (1 – V /K ) – P × F (V )
(8.1)
where V ϵ V (t) is the victim or prey population size at time t, r is the potential per capita growth rate for the prey, K is the prey carrying capacity (i.e.,
where dV /dt = 0 in the absence of predators), P is the number of predators,
and the function F (·) is the functional response characterizing the number of
prey killed per predator (figure 8.1). This simple single-species model is useful
because it can be used to illustrate the consequences of variation in the functional response and how multiple equilibria can emerge when F (·) is logistic
in shape (see Yodzis 1989:16–17). But we must assume that the number of
predators is constant and there is no opportunity to anticipate the dynamics of
the predator population without another equation for dP/dt.
255
In this review I touch only briefly on more complex models involving multiple species, but of course, seldom is a two-species interaction sufficient to capture the complexity of biological interactions that occur in ecosystems.
NONINTERACTIVE MODELS
Predator–prey models are by definition based on a predator having a negative
effect on a prey population while the predator benefits from consuming the
prey. Yet to simplify the system, many ecologists choose to ignore the interaction by assessing only the dynamics of a single species. This can take at least
four forms: single-species models of predators or prey, demographic trajectories of prey anticipating the consequences of predator-imposed mortality,
attempts to assess whether predator-imposed mortality on prey is compensatory or additive, and habitat capability models. Each of these approaches circumvents the issue of predator–prey interactions; consequently, noninteractive models are less likely to capture the dynamic behaviors of a predator–prey
system. However, these approaches pervade the wildlife ecology literature and
deserve to be placed into context.
Single-species models
We can model the effect of a predator population on a prey population with a
single equation for the prey. For example, consider a population of prey governed by the differential equation
dV/dt = r × V (1 – V /K ) – P × F (V )
(8.1)
where V ϵ V (t) is the victim or prey population size at time t, r is the potential per capita growth rate for the prey, K is the prey carrying capacity (i.e.,
where dV /dt = 0 in the absence of predators), P is the number of predators,
and the function F (·) is the functional response characterizing the number of
prey killed per predator (figure 8.1). This simple single-species model is useful
because it can be used to illustrate the consequences of variation in the functional response and how multiple equilibria can emerge when F (·) is logistic
in shape (see Yodzis 1989:16–17). But we must assume that the number of
predators is constant and there is no opportunity to anticipate the dynamics of
the predator population without another equation for dP/dt.