HOW MANY VICTIMS WILL A PITFALL MAKE

A model for the trapping of animals with a circular pitfall is formulated. The model's assumptions are: (1) The animals move independently according to the same Brownian motions. (2) The boundary of the pitfall acts as an absorbing or elastic barrier. (3) Initially a fixed number of animals is independently homogeneously distributed over a finite study area (a), or the initial positions follow a homogeneous planar Poisson process (b). The model depends on three free parameters: (i) the motility of the animals, (ii) their reaction to the pitfall, (iii) the initial density. It appears that the catches in disjoint time intervals are multinomially (a) or independently Poisson (b) distributed. The parameters of these distributions are obtained by solving certain partial differential equations. Estimation and testing problems are considered, and the data of some laboratory and field experiments are analyzed. It appears that it is possible to estimate both the animals' motility and density from a pitfall experiment. However, the accuracy is very low. To solve this problem at least partially, experiments for the separate estimation of parameters other than the density are discussed. © 1979 Leiden University Press.