untitled

sustained yield is appropriate; more where year-to-year variation in weather is above

average.

If a constant proportion of animals is taken each year from a previously unharvested

population, the population will decline and stabilize, depending on the rate of

harvesting, at any level between unharvested density and the threshold of extinction

(Fig. 19.7). So long as the harvest rate (h) does not exceed the maximum intrinsic

rate of population growth (rmax), harvesting a fixed proportion of the population should

settle the population upon a stable population density, generating a sustained yield,

even in the presence of stochastic variation in environmental conditions. Provided

a wildlife or fisheries manager had perfect information on abundance in any given

year before the harvest, a proportionate strategy would be guaranteed to allow sus-

tainable harvests forever. The trouble is, wildlife or fisheries managers rarely have

up-to-date information on current abundance, and they must set harvest levels

(through licensing or allocation of quotas) long before annual recruitment is known.

Indeed, the most common situation is that managers know little more about the

population than the information gained from the harvest success during the pre-

vious year. Such information would permit, at best, a forecast of the current recruit-

ment, based on an index of population abundance at the end of the previous

harvest. In other words, population managers must guess the current level of

abundance in setting an annual quota whose magnitude is intended to be a constant

fraction of the population. The uncertainty thus introduced considerably increases

the risk of unintentional overharvesting.

As an example of applying a fixed proportion harvest strategy with uncertainty in

current population levels, let us consider once again stochastic population growth

by martens. As before, we presume that marten population growth tracks changes in

abundance of their prey, as well as being influenced by weather conditions or other

stochastic environmental features. We presume that the wildlife manager has know-

ledge of past population abundance, based on the previous year’s harvest, which when

combined with an assessment of prey abundance allows a forecast of the current

WILDLIFE HARVESTING 341

40

30

20

10

0

–10

0 20 40 60 80 100 120

N

Net recruitment or harvestNet recruitmentHarvest

Stable equilibrium

Fig. 19.7Net
recruitment in the
absence of harvest in
relation to population
density, plotted relative
to a constant
proportionate harvest.
The intersection of the
net recruitment curve
and the harvest line
identifies the stable
equilibrium, at which
offtake equals the
growth increment to the
population.

19.3 Fixed proportion harvesting strategy

19.3.1Fixed

proportion harvesting

of martens in a

stochastic

environment