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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:

 

1.The catching or trapping procedure must not lower (or increase) the probability of an animal being caught. For example, the method will not be applicable if animals are being searched for and, as is likely, the most conspicuous ones are removed first.

 

2.The population must remain stable during the trapping or catching period; there must not be any significant natality, mortality (other than by the trapping) or migration. The experimental procedure must not disturb the animals so that they flee from the area.

 

3.The population must not be so large that the catching of one member interferes with the catching of another. This is seldom likely to be a problem with insects or fish where each sample can take many individuals, but may be significant in vertebrate populations where one trap can only hold one animal.

 

4.The chance of being caught must be equal for all animals. This is the most serious limitation in practice. Some individuals of a population, perhaps those of a certain age, may never visit traps and so will not be exposed to collection. In vertebrates, 'trap-shyness' may be exhibited by part of the population such as one sex. In electric fishing, where the method is used extensively, smaller individuals are more difficult to stun, and individuals occupying territories under banks or other obstructions may be particularly difficult to catch.

 

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:

 

 

and

 

 

 

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).

 


Coefficient of variation

30%

20%

10%

5%

200

.55

.60

.75

.90

300

.50

.60

.75

.85

500

.45

.55

.70

.80

1,000

.40

.45

.60

.75

10,000

.20

.25

.35

.50

100,00

.10

.15

.20

.30