Appendix

Statistical basis for the model

From the first premise that the density and hence probability of encounter remains constant from night to night, and animals are simply remembering bait station locations, we have:

P₁(0) = P₂(0) ----------------------= P_t(0)

where P_t(0) is the probability of non-encounter at time t.

Now n₁/N = n₂/n₁-----------------------------------= n_t/n_t-1

where n_t is the no. of baits remaining at night t, and N is the total bait stations set.

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Thus the probability of non-encounter up to and including night t is and the probability of n encounters during the t nights can be shown to be

This is a Poisson process, obtained from the superimposition of several independent Poisson processes (Bailey 1964, Cox and Miller 1965). The distribution function can be regarded as a composite one of a Poisson density function and an exponential time function (Bailey 1964) representing the time between encounters.

Thus an estimate of density d_t can be obtained from (1):