A Capture model for moving individuals

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• Ricardo Carrizo Vergara (Swiss Ornithological Institute)
• Wednesday 04 September 2024, 15:50-16:10
• Seminar Room 1, Newton Institute.

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SSDW05 - Modelling and Applications of Anomalous Diffusions

We present a Capture model for individuals moving on a landscape. In this setting, individuals are supposed to move following iid trajectories over the Euclidean space. In a subdomain of the space, called the capture domain, traps are set to retain the individuals. The capture procedure is modelled following three simple axiomatic principles: no-capture posibility; stationary rate of growth of probability of capture while visiting the capture domain; and a capture-position information criterion. From these axioms and mild continuity conditions on the trajectories, it is proven that the density of the capture time must satisfy a certain Volterra integral equation of the second kind. Formulae for the capture position distribution and the mean and covariance structure of the count field of trapped individuals are provided. Simulation methods are developed. A Gaussian pseudo-likelihood method for fitting the model to the generated abundance data is proposed, justified when the number of individuals is large and which respects mean and covariance structures. We illustrate the fitting method over a biological data set of flies being released in a meadow and repeatedly captured in traps. We also show some results from simulation studies.   From a joint work with Marc Kéry (Swiss Ornithological Institute) and Trevor Hefley (Kansas State University).

This talk is part of the Isaac Newton Institute Seminar Series series.

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