untitled

where Brepresents the density of the endemic prey species, Rrepresents the density

of the exotic prey species, and Crepresents the density of the predator that both

prey have in common. You should note the similarity in structure to other con-

sumer–resource models that we discussed in Chapter 12. Both prey species have logis-

tic patterns of growth in the absence of predation, with maximum rate of increase

dictated by rmaxand carrying capacity dictated by K. The predator is assumed to have

a Type I (linear) functional response to changes in prey density, with an attack rate

of μon each prey type. The predator is assumed to have a fixed preference for the

endemic species, the magnitude of which is proportional to α(defined as the fre-

quency of captures of preferred endemic prey to less preferred exotic prey when both

are equally abundant). Nonetheless, the actual fraction of each prey in the predator’s

diet changes proportionately with shifts in their relative abundance, according to the

ratio αB/(R +αB). The presumption used in the model is that exotic prey individuals

are much less easy to catch than endemic prey (αis much greater than 1). Any prey

individuals that are successfully attacked are converted into new predators with an

efficiency of λ, but predators also have a constant per capita rate of mortality ν.

Depending on the magnitude of the key parameters, these equations can lead to

several different outcomes of conservation interest: (i) extinction of endemic prey,

but perpetuation of exotics and predators; (ii) extinction of exotics, but perpetu-

ation of endemic prey and predators; (iii) extinction of predators, but perpetuation of

both prey; and (iv) coexistence of all three species. A common outcome is depicted

in Fig. 17.8: introduction of the exotic leads to high predator density, collapse of

endemic prey to dangerously low levels at which demographic or environmental stochas-

ticity threaten extinction, and substantial numbers of exotics. This scenario tends to

play out when the exotic species has much higher carrying capacity and intrinsic

growth rate than the endemic species (both of which are often true of introduced

pest species like rabbits) and the predator tends to have a stronger probability of

encountering endemic prey than exotic prey (which is also often true when the endemic

has little or no prior experience with predation).

A superb example of this kind of process is seen on the Channel Islands off the

coast of California. Several islands have had accidental translocations of an exotic

herbivore, the feral pig (Sus scrofa). In response to exploding pig populations,

CONSERVATION IN THEORY 307

10 000

1000

100

10

1

0.1

01020304050

Year, t

Population density

Predators

Endemic prey

Exotic prey

Fig. 17.8Simulation of
hyperpredation, leading
to collapse of an
endemic prey species
when an exotic
alternative prey species
is translocated into the
system. The following
parameter values were
used: α=3, rmaxB=0.1,
rmaxR=2.0, KB=1000,
KR=5000, μB=0.1,
μR=0.1, λB=0.01,
λR=0.01, and ν=0.5.
(After Courchamp
et al. 2000b.)