Estimation in the multinomial reencounter model - Where do migrating animals go and how do they survive in their destination area?

Abstract

Spatial variation in survival has individual fitness consequences and influences population dynamics. Which space animals use during the annual cycle determines how they are affected by this spatial variability. Therefore, knowing spatial patterns of survival and space use is crucial to understand demography of migrating animals. Extracting information on survival and space use from observation data, in particular dead recovery data, requires explicitly identifying the observation process. We build a fully stochastic model for animals marked in populations of origin, which were found dead in spatially discrete destination areas. The model acts on the population level and includes parameters for use of space, survival and recovery probability. It is based on the division coefficient and the multinomial reencounter model. We use a likelihood-based approach, derive Restricted Maximum Likelihood-like estimates for all parameters and prove their existence and uniqueness. In a simulation study we demonstrate the performance of the model by using Bayesian estimators derived by the Markov chain Monte Carlo method. We obtain unbiased estimates for survival and recovery probability if the sample size is large enough. Moreover, we apply the model to real-world data of European robins Erithacus rubecula ringed at a stopover site. We obtain annual survival estimates for different spatially discrete non-breeding areas. Additionally, we can reproduce already known patterns of use of space for this species.

Keywords: Capture-mark-recovery; Observation process; Parameter estimation; Survival; Use of space.