untitled

population size to which we apply an adjustable quota approximating a fixed pro-

portion of the population. To enable direct comparison with the earlier fixed quota

model, we choose a harvest proportion (h=36%) whose yield under equilibrium

conditions would be identical to the MSY (423 martens per year). Incidentally, this

is quite close to the 34% harvest applied to the real marten population during 1973–91

(Fryxell et al. 2001). Population managers used the proportion of juvenile animals

in the previous year’s harvest as an index of growth potential for the population, based

on the assumption (correct in this case) that reproductive success is inversely related

to population abundance. Hence, monitoring age structure allowed them to maintain

approximately constant harvest intensity, despite large swings in marten abundance

over time. The equation of population change is calculated in the following manner:

We have once again set a condition to ensure that the population never declines below

zero. The simulation results (Figs 19.8 and 19.9) demonstrate that a fixed propor-

tion harvest strategy is much more sustainable than a fixed quota strategy, at least

in this case.

Note that harvests vary over time to a greater extent using a fixed proportion har-

vest strategy (Fig. 19.9) than they did under the fixed quota system (Fig. 19.6). This

difference in variation arises because harvests are adjusted to absorb the impact

of stochastic environmental variation, so quotas drop in years of poor per capita

recruitment whereas harvest goes up in years of above-average per capita recruitment.

This variation in harvest provides a stabilizing influence to fixed proportion harvest

systems. However, a proportionate harvest strategy can still produce overharvesting

when there are several years with unusually low recruitment, because managers do

not know with certainty how many individuals have been recruited to the population.

In the not-so-distant past, fixed quota systems tended to be the norm in harvested

fish and wildlife populations. Proportionate harvesting policies have become pre-

dominant in more recent years, mainly because of the improvement in resource con-

servation (Rosenberg et al. 1993).

N

gN Z hfN Z

gN Z hfN Z

t

ttt tt

ttt tt

+ =

≤

−

1

0

( , , ) ( , )

(, , ) (, )

if

otherwise

ε

ε

342 Chapter 19

1000

800

600

400

200

0

0 5 10 15

Year

Predicted marten abundance

Fig. 19.8Predicted
variation in marten
abundance under a fixed
proportion harvest
policy, with annual
marten harvests set at
the proportion (h=
0.36) approximating the
maximum sustainable
yield (H=423 martens
per year), starting from
a population size of 400
animals in 1973.