Geoscience Reference
In-Depth Information
In this review I touch only briefly on more complex models involving multi-
ple species, but of course, seldom is a two-species interaction sufficient to cap-
ture 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 interac-
tion by assessing only the dynamics of a single species. This can take at least
four forms: single-species models of predators or prey, demographic trajecto-
ries of prey anticipating the consequences of predator-imposed mortality,
attempts to assess whether predator-imposed mortality on prey is compensa-
tory or additive, and habitat capability models. Each of these approaches cir-
cumvents the issue of predator-prey interactions; consequently, noninterac-
tive 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 gov-
erned by the differential equation
´
´
dV
/
dt
=
r
V
(1 -
V
/
K
) -
P
F
(
V
)
(8.1)
;
where
V
V
(
t
) is the victim or prey population size at time
t
,
r
is the poten-
tial 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 func-
tional 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
.
