Environmental Engineering Reference
In-Depth Information
A fitted catch value is then calculated for each period as a function of the fitted
population size and observed catch and abundance index:
C
ˆ
t
qN
ˆ
t
C
t
/
a
t
where
q
estimates the size of the population index relative to true population size.
If CPUE from full catch and effort totals is used as the population index, this
becomes:
C
ˆ
t
qN
ˆ
t
E
t
and the parameter
q
can now be interpreted as a catchability coefficient, defining
the proportion of the population harvested per unit effort. Having calculated the
full series of fitted abundance and catch values, the best estimates of the initial
population size and catchability coefficient can be found by minimising the sum
of squared deviations between observed and fitted catches. This
least squares fit-
ting procedure
can be carried out in an Excel spreadsheet using the solver add-in
module. Using this function to retrieve known parameters from simulated data is
an excellent way to get a feel for how the procedure works, and to understand the
limits to its utility. When it comes to analysing real data, the package CEDA
(Catch Effort Data Analysis, Section 2.7.1) provides a more sophisticated range
of options for fitting models to catch and abundance index data in order to esti-
mate true abundance, including a facility for calculating bootstrap confidence
intervals for parameter estimates. Alternatively Bishir and Lancia (1996) provide
a maximum likelihood method for catch-effort abundance estimation.
Lancia
et al
. (1996) used this approach to estimate the abundance of intro-
duced wild pigs
Sus scrofa
in Great Smokey Mountain National Park, south-east
USA. Park staff control the pig population by intensive trapping and shooting
during part of the year, and the catch totals can be used along with effort data to
monitor the effectiveness of the cull. The table below shows the weekly catch
totals for 1987, along with the hunting effort, measured in man-hours per week,
and the resulting catch per unit effort. The table also shows the fitted population
sizes and catches, and the squared deviations, at the point of minimum sum of
squares. Figure 2.8 give a visual feel for the goodness of fit by comparing observed
with fitted catch and CPUE values over time.
Initial population size is estimated at 303 pigs (bootstrap confidence interval
272-366), with an estimated catchability coefficient of
q
0.00126. Given a
total catch of 266, this suggests 88% hunting mortality over the entire period. In
fact, this probably underestimates population size, hence overestimates hunting
mortality, as a result of several likely assumption violations. First, the relatively
long sampling period means that significant natural mortality may have taken
place, violating the closure assumption. Second, hunting occurred during spring,
when increasingly dense vegetation may have caused a decline in catchability,
perhaps leading to hyperdepletion (Figure 2.7). This may explain the sudden
slump in CPUE seen around week seven. Finally, it is very likely that there was
