Constant probability of capture
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This is called the constant p method in the program (p for probability of capture). It is also known as Zippin's method, although this probably more correctly refers to a method of solution.
Maximum Likelihood (ML) estimates for estimating population size (N) for a constant probability of capture model were first published by Moran, 1951 and developed by Zippin, 1956. To apply the method the following conditions must be satisfied:
Zippin (1956 & 1958) has considered some of the specific effects of failures in the above assumptions. If the probability of capture falls off with time the population will be underestimated, but if the animals become progressively more susceptible to capture, the population will be overestimated. Changes in susceptibility to capture will arise not only from the effect of the experiment on the animal, but also from changes in behaviour associated with weather conditions or a diel periodicity cycle.
The expected number captured on each sampling occasion E(us) is
where p is the probability of capture on each sampling occasion.
Thus, for the first sampling occasion the expected number caught is Np and for the second N(1-p)p, and so on.
The ML estimates for N and p are given by solving numerically the equations:
where T is the total number caught over all k samples and q = 1-p. First R is calculated and then Eq. 7.3 is solved numerically for q. This value is then used in Eq. 7.2 to estimate N.
The standard error of the estimate of N is given by:
where the notation is as above
If the lower confidence interval is less than the total number of captures, T, then T should be taken as the lower confidence interval
It has been shown by Zippin (1956 & 1958) that a comparatively large proportion of the population must be caught to obtain reasonably precise estimates. His conclusions are presented in Table 1, from which it may be seen that, to obtain a coefficient of variation (C.V. = Estimate/Standard error x 100) of 30%, more than half the animals would have to be removed from a population of less than 200.
Table 1: Proportion of total population required to be trapped for specified coefficient of variation of N (after Zippin 1956).