For over 15 years, a group of researchers have monitored the male jaguar population in the Cockscomb Basin Wildlife Sanctuary in Belize. Each year, during the dry season, they go out and put up to twenty cameras throughout the sanctuary. The cameras photograph jaguars that pass. From these photographs, researchers can identify each individual by their unique markings, and so construct for each sighted individual an encounter history: whether the individual was seen each year and, if so, how many times they were seen on each camera. 

 

In this seminar, I discuss the statistical modelling of this dataset of encounter histories and how it can lead to inference on the jaguar population's density, movement, and survival. To do this, I present a general model, the open population spatial capture-recapture model, that jointly considers the detection by the cameras, the movement of the animals, the population's density over space, and the population's dynamics over time. The statistical model has three important components: (1) each individual's encounter history is modelled as a hidden Markov model where the individual's life state (unborn, alive, dead) is partially unobserved, but can be inferred from the encounter history; (2) each individual is assumed to have an "activity centre" around which they move during the survey where activity centres are modelled by a spatial point process; (3) individual's activity centres move from one year to the next by Brownian motion. 

 

By considering the application of this general model to the jaguar dataset, advantages and limitations of the method are presented; in particular, I will focus on two aspects of the method. First, the movement of activity centres is latent and so clearly one must marginalise over the trajectories each observed individual followed, but, less commonly, one must also marginalise over the trajectories of those individuals never seen in order to quantify the probability of detection and so estimate population size. This is an uncommon obstacle in usual movement modelling and I discuss how this was handled in the case of simple Brownian motion. The second aspect I consider is parameter identifiability; briefly discussing the future problem of how best to link inference from these models to the real world population processes in a robust way.   

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