Variable probabilities of capture
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Removal Sampling 2 offers a model in which the probability of capture on the first sampling occasion is different from that on subsequent samples.
To use the variable p method, sampling must have been carried out on at least 4 occasions.
It will often be observed that the probability of capture changes during the course of a study. For example, larger fish are more easily caught when electric fishing. Thus the first sweep along a reach of a stream will tend to have a higher rate of capture. Generally the best way to deal with this problem is to divide the population into a number of groups, each of which can be independently estimated with a constant probability model. This is easily done using Removal Sampling 2, as each column can comprise a particular species or size class. An example of such a subdivision is shown in the demonstration data set RemovalDemo.csv.
In an electric fishing survey of a stream it might be appropriate to undertake independent analyses for eel, trout and minnow and to further subdivide the trout into size (age) classes. However, the ability to avoid capture even varies between individuals of a single age or size class, and if this effect is large the mean probability of capture will change in what the observer perceives as a homogeneous population. When a constant probability model has been rejected, and it is not possible to subdivide the population then the generalized removal method of Otis et al. 1978 can be used.
A removal experiment does not generate sufficient information to allow the calculation of a model in which the mean probability of capture on each sampling occasion is different. This is because there are too many parameters to estimate, given the number of observations. Otis et al. (1978) noted that as animals with a higher probability of capture tend to be caught first, the mean probability of capture on sampling occasion k, pk tends to decline with increasing k, so that after, say, m samples, pk can be assumed constant. A family of models can therefore be constructed in which the first 1,2,3 .. k-2 samples are assumed to have different values for p and all later samples a constant p. In the ideal world the logical approach would be to work upwards from m = 1 and stop when a Χ2 test shows that the model can no longer be rejected. In practice it is rarely worth using a model with k >1 because of the short data series typically collected in removal sampling experiments and the increased standard error of the population estimate as the number of estimated parameters increases. In Removal Sampling 2 we therefore only include a model for the situation where capture probability on the first sampling occasion is different. To use the variable p method, sampling must have been carried out on at least 4 occasions.
The probabilities of capture are calculated using ML methods similar to those used for the constant probability of capture model.
There is a third approach that can be taken if the probability of capture during the first few samples is lower than in later samples. This effect is observed when sampling fish such as lampreys which are buried in the substrate and tend to require a number of passes while electric fishing before they are drawn to the surface where they can be captured. Examine the graph of the pattern of capture, and remove from the analysis the initial samples when the probability of capture was low. Then calculate the population size using the remaining samples with a constant probability model. The total population is given by the number of captures in the not-used initial samples, plus the population estimate.