New Zealand Statistical Association 2024 Conference

Alec van Helsdingen

University of Auckland

Extending spatial capture-recapture with the Hawkes process

This is joint work with Charlotte Jones-Todd, Russell Millar

Spatial capture-recapture (SCR) is a well-established method used to estimate animal population size from animal sighting or trapping data. Standard SCR methods assume animal movements are independent and consequently cannot incorporate site fidelity (attachment to a particular region) nor the temporal correlation of an animal’s location. Recent work has sought to solve these issues by explicitly modelling animal movement. In this talk we propose an alternative solution for camera trapping surveys based on a multivariate self-exciting Hawkes process. Here the rates of detection of a given animal at a given camera are a function of not only the location and its proximity to the animal’s activity center, but also where and when the animal was most recently detected. Through a mixture of Gaussian distributions, our model expects more detections closer in space to the last detection, and reduces to SCR when an animal is yet to be detected. This formulation, we believe, better reflects animal behaviour because shortly after detection, we expect to next see an individual close to where it was last seen. Thus, our model allows us to account for both site fidelity and the inherent temporal correlation in detections that have not previously been accounted for in SCR-type models.

In this talk, I will:

1) give an overview of Self-Exciting Spatial Capture-Recapture (SESCR) models,

2) demonstrate the additional inference that can be drawn from such models, and

3) apply the framework using a few case studies to compare traditional SCR and SESCR.