Markov‐modulated Poisson processes as a new framework for analysing capture–recapture data

Opportunistic capture–recapture data consists of observations over non‐constant time intervals and so fails to satisfy the basic assumptions of traditional capture‐recapture models. Analysing opportunistic capture–recapture data is often done by discretizing time intervals or summarizing data, but without taking into account the continuous time process of the state and/or the capture. To deal with non‐constant time‐intervals, continuous time closed capture–recapture models have been proposed by Yip, Huggins, and Lin ([Yip, P. S. F., 1996]), Hwang and Chao ([Hwang, W. H., 2002]), Schofield, Barker, and Gelling ([Schofield, M. R., 2017]) for estimating population size. More recently, a continuous time Cormack–Jolly–Seber model has been proposed by Fouchet, Santin‐Janin, Sauvage, Yoccoz, and Pontier ([Fouchet, D., 2016]) to reduce bias in survival rates, and a two‐state process has been proposed by Choquet, Garnier, Awuve, and Besnard ([Choquet, R., 2017]) to estimate reproduction rates and survival rates of young within a season. The aim of the current study is to demonstrate how an approach based on a Markov‐modulated Poisson process (MMPP) (Freed & Shepp, [Freed, D. S., 1982]) allows, in a similar way to a multistate model, to model opportunistic data, using several states. To this end, several multistate models were rewritten as MMPP models, showing, the potential for this approach to address the ecological questions as multistate models, but using an extended data framework. In particular, it is a useful framework for dealing with data that has unordered levels of uncertainty. The methods were illustrated using simulations and analysis of data on the Alpine ibex ( Capra ibex ).