Environmental Engineering Reference
In-Depth Information
e
r
max
c
MSY
1
e
r
max
1
E
MSY
q
These discrete time equations are conservative in that they give lower maximum
catches than the continuous time versions. However, there is no simple population
size reference point in this case because the population fluctuates over the year in
response to breeding and harvest pulses.
N
MSY
might therefore be substantially
more or less than half
K
, depending on when in the year it is measured.
Simple reference points of this kind are often used to define biological sustain-
ability because they are easy to apply and require relatively little information. The
downside of the approach is that it requires strong assumptions about the under-
lying processes, which are rarely fully justified (see text for discussion of these
assumptions). The approach must therefore be used with great caution.
population size. In the management of many commercially exploited species, MSY
has historically been interpreted as a goal in itself, usually with the result of disastrous
overexploitation because of the unstable nature of the equilibrium at MSY, coupled
with natural stochastic fluctuations and flawed information on catch and species bio-
logy (Punt and Smith 2001). A common way to deal with this risk is to set the ref-
erence point below MSY. For example, Roughgarden and Smith (1996) proposed that
an offtake of three-quarters MSY is a robust target for long-term sustainability.
However, there is no rigorous basis for defining the proportion of MSY that can safely
be caught in any given case. In general, a higher degree of caution is appropriate when
the population has a low productivity rate or is naturally highly variable, when catch
estimates are imprecise or biased, or when there is little certainty about the basic model
parameter values. In the end, though, the choice will primarily be driven by the degree
of risk that you are prepared to accept, which cannot be defined objectively.
The reference points in Box 4.1 are based on the
logistic model
. However, the
parameter values
on which the logistic model depends,
r
max
and
K
, are problematic
to estimate, as is
q
, the catchability coefficient. Although
r
max
has an intuitive
meaning, it is difficult to obtain data to estimate it from natural hunted popula-
tions, and so it is often estimated by allometry or from simple equations based on
survival and productivity rates (see Section 2.4.1). Estimating carrying capacity
requires either an allometric approach or data from an unexploited population in
the same environmental conditions as the hunted population. This is usually diffi-
cult to obtain, because often the reason why an area is unexploited is remoteness or
difficult terrain, which is likely to correlate with different habitat types. Allometric
relationships are useful, but they are derived from the same flawed data and the
variation around the relationship may be both large and biologically meaningful.
The catchability coefficient
q
is usually estimated from data, but as it is not easily
observed directly, it is usually necessary to assume an underlying model to derive
it, which may be incorrect. All three parameters can be estimated jointly from
