Geoscience Reference
In-Depth Information
N
ˆ
532. By comparison, the regression method gives
=
350
with an esti-
mated standard error of 87.6 (Table 5.2).
The CAPTURE program also provides the possibility of relaxing the
assumption that capture probabilities are the same at different sample
times. The heterogeneous removal model is denoted by M
bh
and is
widely used, especially in fisheries science. Using this model, the esti-
mated population size is the same as that for the Zippin model, with the
same standard error.
5.3 The Change-in-Ratio Method
The principle behind the change-in-ratio method is that if a population con-
tains two recognizable types of individual, such as males and females, with
estimated proportions at some initial point in time, and the proportions are
estimated again after a fixed number of one of the two types of individual
have been removed, then it is possible to estimate the population size at the
initial point in time on the assumption that population changes are caused
only by the removals. Selective harvest of fish and wildlife for certain sexes
or desired size often results in changes in ratios of the remaining individuals
so that the methods can be applied. For example, a crab fishery may allow
only males of a certain size to be harvested. Ratios of males to females or
large males to small males are expected to change after harvest of a known
number of large males. It is not necessary for animals to be removed from
the population; rather, individuals can be marked or tagged. For example,
the ratio of unmarked males to females would be expected to change as a
known number of males are captured and marked. The first application
seems to have been described by Kelker (1940, 1944) in terms of changes in
the sex ratio resulting from a differential kill of male and female deer in a
harvested population.
The simplest case involves a population partitioned into two subclasses.
Surveys are conducted to estimate the subclass ratios at the beginning of the
study. Known numbers of the subclasses are then removed or marked. Then,
a second survey is conducted to reestimate the subclass ratios. In the fol-
lowing, we refer to removal of animals; however, it is to be understood that
animals are effectively removed if captured and marked.
The critical assumption required for estimation of the population sizes is
that the probability of encountering the two subclasses is the same for the
first and second samples. However, the probability of encounter can change
from the first to the second. Two other assumptions are also necessary:
The number of animals removed (or marked) should be known, although
in practice precise estimates can be used. Finally, the population should be
closed, that is, there is no recruitment, immigration, emigration, or unknown
