Harvest management - Ecological Applications: Toward a Sustainable World - page 189

Recruitment rate
Harvesting rate

H H
H M

H H
H M

H L

H L

N M K

Population size ( N )

Fig. 7.2 Fixed quota harvesting. The fi gure shows a single recruitment curve and three fi xed
quota harvesting curves: high quota ( H H ), medium quota ( H M ) and low quota ( H L ). Arrows in
the fi gure refer to changes to be expected in abundance under the infl uence of the harvesting
rate to which the arrows are closest. Black circles are equilibruim points. At H H the only
'equilibrium' is when the population is driven to extinction. At H L there is a stable equilib-
rium at a relatively high density, and also an unstable breakpoint at a relatively low density.
The MSY is obtained at H M because it just touches the peak of the recruitment curve (at a
density N M ): populations greater than N M are reduced to N M , but populations smaller than N M
are driven to extinction. (After Begon et al., 2006.)

individuals are consistently being taken than can be replenished by recruitment. In other words, if
we overestimate the MSY, even slightly, the population will be driven extinct. The lowest harvesting
rate shown ( H L ) crosses the recruitment curve at two points - at a relatively low population density
and at a relatively high density quite close to carrying capacity. Where the lines cross, the harvest
is, by defi nition, sustainable but it is not as big as it could be. Of particular interest, then, is har-
vesting rate H M , which just touches the recruitment rate curve at its peak. This is the highest har-
vesting rate that the population can match with its own recruitment - in other words, the MSY
- the largest harvest that can be removed from the population regularly and indefi nitely. The MSY
is obtained from the population by depressing it to the density at which the recruitment curve
reaches its peak.
There are some profound diffi culties in using the MSY as a basis for harvest management, which
will be discussed in the light of real harvests in Section 7.2. For now, just one of the problems will
be highlighted. The MSY density ( N m ) is an equilibrium (gains = losses), but when harvesting is
based on the removal of a fi xed quota ( H M in Figure 7.2), the equilibrium is very fragile. If, by chance,
the actual density exceeds the MSY density, then H M exceeds the recruitment rate and the popula-
tion declines towards N m . This, in itself, is satisfactory. But if the actual density is ever so slightly
less than N m , then H M will again exceed the recruitment rate so that density will decline even further
- indeed, if the fi xed quota is maintained the population will decline to extinction (see direction of
arrows along the H M line in Figure 7.2). Things are not so bad at the lower harvesting rate ( H L ): in
this case there is a stable equilibrium where the lines cross at high density, but an unstable one
where they cross at low density (so only if actual density were much lower than assumed would
the population drop to extinction). But H L does not provide an MSY.
In the quest for an MSY, in other words, a fi xed quota strategy is reasonable if you have perfect
knowledge and the world is wholly predictable. In the real world of fl uctuating environments and
imperfect data sets, though, this is a very risky approach.

Fixed effort
The risk can be reduced if instead of taking a fi xed quota we regulate harvesting effort (e.g. in
terms of the number of 'boat-days' in a fi shery or 'gun-days' in a hunted waterfowl population). If
harvesting effort is constant, the yield will simply be proportional to the population size (e.g. 50