Environmental Engineering Reference
In-Depth Information
When either of the sampling approaches is used, it is, as always, important to
ensure your sample is
representative
of the population as a whole. A common
cause of bias arises if non-breeding individuals are segregated from the breeding
population, making it difficult to ensure that they have an equal chance of being
sampled. In this case, the best way to obtain an unbiased estimate may be to calcu-
late first a productivity rate solely for the breeding portion of the population, then
multiply this by an estimate of the proportion of the population breeding.
2.4.3.2 Using marked individuals
Because population size from one year to the next is a function of survival and
productivity rates, and there is a strict theoretical relationship between these
variables, if you know survival rate and population size over a period of time, you
can derive productivity rate. The mark-recapture methods described earlier in
this chapter are ideal for this, and in fact methods have been developed that build
the estimation of productivity into the analysis of mark-recapture data. These
methods fall broadly into two categories, robust design, and Jolly-Seber and
related methods.
Robust design
(Pollock 1982; Williams
et al
. 2002) combines open (Section
2.4.2.2) and closed population (Section 2.3.4) mark-recapture methods, using the
former to estimate population size, the latter to estimate survival, and deriving
recruitment from these. This requires a design in which periods of closely spaced
capture occasions are interspersed with longer gaps. The population is assumed to
be closed during each set of close-spaced occasions, but can undergo turnover
between each set.
Jolly-Seber
and related methods (Jolly 1965; Seber 1965; Williams
et al
.
2002) are essentially extensions of the open population methods used to estimate
survival rate, described in Section 2.4.2.2. If we can reasonably assume that
the marked portion of the population is a representative, random sample of the
whole, the estimated recapture probability can be interpreted as an estimate of
the proportion of the population observed on a given occasion. If, in addition
to this, we record the numbers of unmarked as well as marked individuals seen or
captured, we can then estimate population size, and hence recruitment, as well as
survival.
The key
assumptions
for these approaches, and the practical considerations for
sampling to provide the necessary data, are largely the same as those highlighted in
Sections 2.3.4 and 2.4.2.2. In addition, the assumption of representative sampling
required by Jolly-Seber methods necessitates a careful field design to ensure that
marked individuals are not targeted for recapture or resighting, either deliberately
or inadvertently. Also, when recording the numbers of unmarked individuals for
this approach, it is important that there is no possibility of double-counting.
Jolly-Seber methods generally result in productivity estimates with low precision,
and which are vulnerable to bias due to heterogeneous capture probabilities. In
addition, Jolly-Seber methods are generally unable to estimate key parameters for
the first and last occasions of a survey.
