untitled

For a population conforming to the relationship between sustained yield and popula-

tion size or density given in Fig. 19.1, a sustained yield of a given size may be taken

from either of two densities, at the points at which the horizontal harvest line inter-

sects the hump-shaped net recruitment curve. They comprise what is known as a

sustained-yield pair. The member of the pair taken from the lower density is to be

avoided because its harvesting requires more effort than is required to harvest the

same yield from the higher density. Even more importantly, any reduction of popula-

tion density below the level of the sustained-yield pair would inevitably lead to over-

harvesting relative to growth capacity of the population. When a constant number

of animals is taken each year from a previously unharvested population, provided

that there is no stochastic variation in weather or other factors that influence net

recruitment, the population will decline and stabilize at the upper density for which

that harvest is a sustained yield. Should that number exceed the maximum sustained

yield, the population would inevitably decline to extinction.

The harvest that intersects the peak of the hump-shaped net recruitment curve is

known as the maximum sustained yield (MSY). Harvesting a population at the MSY

should never be contemplated. It imparts instability to the population’s dynamics.

The MSY can be taken only from the unique MSY density. If the population density

has, for environmental reasons (such as drought or crusted snow), dropped below

that value then the MSY represents an overharvest and the population’s density is

reduced further. Continued harvesting of the MSY will make the problem worse and

even lead to extinction. This can be visualized more readily by considering a con-

crete example.

The American marten (Martes americana) is a forest carnivore species in the family

Mustelidae (the weasel group) and is an important economic resource for many com-

mercial trappers. It has a widespread distribution across the more northerly reaches

of the USA and most of Canada. The marten lives in large tracts of coniferous and

mixed forests, feeding on a wide variety of small mammals and berries, augmented

occasionally by birds’ eggs, insects, and other assorted invertebrate prey. Adult

WILDLIFE HARVESTING 337

19.2.2The two levels
of sustained yield in
constant quota
systems

19.2.3The maximum
sustained yield

19.2.4Harvesting in
a stochastic
environment:
trapping of martens
in Ontario

40

30

20

10

0

–10 0 20 40 60 80 100 120

N

Net recruitment or harvest

Net recruitment

Harvest

Unstable equilibrium

Stable equilibrium

Fig. 19.1Net recruitment
in the absence of harvest in
relation to population
density, plotted relative to
an arbitrary constant level
of harvest. At a given
harvest quota, there are
stable (circle) and unstable
(×) equilibria. At
population densities above
×, the population would
tend to converge on the
stable equilibrium.
Perturbation of the
population below ×, on the
other hand, would lead to
eventual extinction.