untitled

among territory-holders might escalate with increasing marten abundance. Such a mix

of direct density dependence (interference competition, see Chapter 8) and indirect

density dependence through variation in food supplies (scramble competition) has

strong stabilizing properties (Fryxell et al. 1999).

As we discuss in Chapter 15, Akaike’s information criterion is a useful means of

evaluating alternative models of population growth. The model with both density and

prey dependence fits the estimates of rsubstantially better (AICc=−20.5) than either

a density-dependent model (AICc=−11.3) or a prey-dependent model (AICc=−14.9),

so we shall use this as our best deterministic model forecasting the next population:

f(N, Z) =Nexp(a+bN+cZ)

where the intrinsic growth base rate (a=0.57) is diminished by the density-

dependent coefficient (b =−0.0005) multiplied by marten abundance (N), but

augmented by the prey-dependent coefficient (c=0.0016) multiplied by prey abun-

dance (Z). This relationship (Fig. 19.4) predicts that the net recruitment should be

a dome-shaped function of marten abundance, with the height of the dome dictated

by prey abundance in a given year.

Of course, there is still some additional unexplained variation in r(in this case,

with a standard deviation of approximately 0.10) that is due to variability in environ-

mental conditions, such as weather, represented by the variable (ε), added to the other

predictor variables in a model forecasting stochastic population growth:

g(N, Z, ε) =Nexp(a+bN+cZ+ε)

We are now in a suitable position to model different harvesting strategies that could

be applied to this population. We start with a constant quota system, with annual

quotas set at the expected MSY (423 martens per year, based on average prey abun-

dance and ε=0). Year-to-year variation in marten abundance can be modeled by the

following set of equations:

WILDLIFE HARVESTING 339

1000

800

600

400

200

0

0 500 1000 1500 2000

Marten abundance

Net recruitment

Average recruitment

Best year

Poorest year

Fig. 19.4Marten net
recruitment in the
Bracebridge District of
Ontario in relation to
marten abundance
(Fryxell et al. 2001).
Three curves are shown,
corresponding to average
prey abundance over the
45 years of monitoring
(Fryxell et al. 1999), as
well as the highest and
lowest levels of prey
abundance on record. Net
recruitment in any given
year is expected to fall in
the area bracketed by the
broken lines. (After Haydon
and Fryxell 2004.)