Dynamics: Generalist Predators

Generalists predators feed on many different prey species, often have life cycles that are quite different from any particular prey species, and do not usually have searching behaviors that are finely tuned to the habitats of specific prey. In this section we study the dynamics of consumers with nonspecific feeding habits using the logistic individual survival model.

Consider the general logistic R-function for any member of a food chain

remembering that

R_i = the realized per-capita rate of population change for a given physical environment with given density of species X_i, resources X_i-1, and predators X_i+1.

a_i = the maximum per-capita rate of population change in a given environment when population density is very small, food and space are unlimited and predators are absent.

b_i = the coefficient of intra-specific competition for fixed resources, usually some kind of spatial resource.

c_i = the coefficient of intra-specific competition for depletable resources, usually food from the lower trophic level.

d_i = the per-capita demand of predators for food, with respect to the species we are considering.

w_i = the relative abundance of other sources of food for the species we are considering, in units relative to species X_i-1.

w_i+1 = the relative abundance of other sources of food for the predators, in units relative to species X_i.

In a generalized food chain, the abundance of alternative food will be greater than zero, and the R-function for an herbivore (H) with the density of plants (P) constant, is

remembering that b_hcontains the three constants, old b_h, c_h, and P. The R-function for the carnivore (C) has a similar configuration

The zero growth isoclines for prey and predator are

prey isocline

predator isocline

The isoclines are shown below. Notice that the isocline structure is similar to that for a specialized predator with the exception that both prey and predator isoclines intercept the predator axis at a positive density, which is related to the abundance of alternative prey (i.e., the magnitude of parameter w_c determines the value of the intercept).

Figure. (Left) Herbivore (H) and carnivore (C) phase space showing zero-growth isoclines for the logistic individual survival model (prey isocline = blue line, predator isocline = red line), and (Right) the time series plot of the herbivore (blue) and carnivore (red) populations showing a damped-stable cyclic approach to equilibrium.

Generalists not Dynamically Coupled to Prey Density

The reproductive response of many generalist predators is not associated with the density of any specific prey population. For instance, predator densities may be limited by territories or other spatial constraints or they may have a shorter life cycle than their hosts and therefore depend on several host species to complete their life cycles. Under these conditions the parameter c_c will be zero and the last term in the predator R-function will vanish so that

The predator isoclines is now given by

where K_c is the equilibrium density or carrying capacity of the predator population as determined by intra-specific competition for fixed resources amongst predators. The isocline structure of the interacting system is shown below. Notice that there are 2 equilibrium points, an unstable low-density threshold and a stable high-density equilibrium, and that the prey population will be driven to extinction should it get below the unstable threshold.

Figure. (Left) Herbivore (H) and carnivore (C) phase space showing zero-growth isoclines for the logistic food survivorship model (prey isocline = solid line, predator isocline = broken line) with parameters a_h = 1, b_h = 0.003, a_c = 0.5, b_c = 0.025, c_c = 6, d_c = 4, w_c = 50.

(Right) the time series plot of the herbivore (blue) and carnivore (red) populations showing damped approach to equilibrium.

Prey Switching and Aggregation

Generalist predators frequently switch from one host species to another depending on their relative abundance. As discussed earlier, this kind of behavior can give rise to sigmoid functional responses. In effects the switching from less abundant to the more abundant prey species provides a kind of refuge for the prey because the predators basically ignore them when they are very sparse. Predator aggregations in response to prey density can have a similar effect when predators fail to aggregate on sparse prey populations. As a result of this switching and aggregation, predator-caused prey mortality will approach zero when the prey population attains a very low density, say H_c. Under these conditions the prey R-function can be described by

and the equilibrium isocline by

The isocline structure for this system with an uncoupled predator population is shown below. Notice that this system has 3 equilibrium points, a stable low-density equilibrium, an unstable threshold, and a stable high-density equilibrium. In this system the prey population can be stabilized at either a very sparse density or a very high density, and can switch from one to the other following environmental disturbances (= multiple stable states).

(Right) Time series plot of the herbivore (blue) and carnivore (red) populations showing damped approach to the high-density equilibrium when starting with 50 prey and 5 predators.

(Bottom) Time series plot of the herbivore (blue) and carnivore (red) populations showing the approach to the low-density equilibrium when starting with 30 prey and 15 predators.