An ecologist's introduction to continuous-time multi-state models for capture-recapture data

Recent technological advances have led to a rapid increase in the collection of capture-recapture data in continuous time. Unlike traditional capture-recapture data, the detection times from these technologies are themselves random variables and analysis of these data, therefore, requires models that properly account for stochasticity in both state transitions and detection times. Despite the ubiquity of continuously collected capture-recapture data, the mathematical concepts needed to fit continuous-time models remain unfamiliar to many ecologists. In this paper, I provide an introduction to continuous-time models, with a focus on multi-state capture-recapture data. After reviewing the basic structure of these models, I describe several variations, including constant parameters, temporal variation in state transition rates and autocorrelation in detections. To aid comprehension, each model is accompanied by code to simulate data and fit the model in Stan. Although the models presented in this guide are only a small subset of the variations that are possible to suit the needs of specific datasets or questions, the concepts and code will hopefully serve as a foundation for future analyses, allowing ecologists to develop new and creative approaches to continuous-time modelling.