Bird Ecology and Conservation A Handbook of Techniques

Once the equilibrium population size (for a particular fixed harvest rate) is
reached, the annual harvest is also constant and is given by

(13.3)

which is parabolic with respect to h(Figure 13.1b).
It is important to note that anyfixed value of harvest rate less than rmaxwill
produce an equilibrium population size and annual harvest that are both greater
than zero. In this sense, any harvest rate less than rmaxis sustainable. We can find
the maximum sustainable harvest rate by differentiating equation 13.3 with
respect to h, setting the result equal to zero, and solving for h(Runge and
Johnson 2002). For the logistic growth model, the maximum sustainable harvest
rate is h
rmax/2, which produces an equilibrium population size N
K/2,
and an annual harvest of H*
rmaxK/4 (Caughley 1977).

13.2.2 Incorporating uncertainty: potential biological removal

For application to real populations, the preceding discussion forms the basis for
sustainable harvest, but uncertainties complicate its implementation. First, real
population dynamics are more complex than implied by equation 13.1, because
of differences in life-history parameters by age, sex, reproductive status, etc.
Second, the nature of density-dependence may be different from that expressed by
equation 13.1. Third, most wild populations exhibit considerable stochasticity,
due to random fluctuations in environmental driving factors. Fourth, sampling
bias and error in measuring Ntand estimating rmaxandKintroduce uncertainty
into the calculation of sustainable harvest levels. Finally, managers typically can-
not control exploitation with much precision. This last point can be particularly
important depending on whether total harvest or harvest rate is the management
variable being controlled. When harvest ratecan be managed to achieve a maxi-
mum sustained yield (by setting h
h), that equilibrium point is quite stable.
But in many cases, it is easier to manage the total harvest (H), perhaps through
a quota system. The maximum equilibrium point achieved by setting H
H
is dangerously unstable. If the harvest by chance is above H, or if the population
size by chance drifts below N, continued extraction of the maximum sustained
yield (H*) will lead to extinction.
In a precisely managed system, with frequent and timely monitoring data, and
the ability to adjust harvest or harvest rates on a regular basis in response to current
conditions, these uncertainties can be accommodated. But how can a conserva-
tion biologist make an assessment in cases where the uncertainties are great?
This question has been carefully considered by biologists worried about the

Heq(h)
hNeq

rmaxKhKh^2

rmax ,

Theoretical basis for sustainable exploitation| 307