A new computational framework for speeding up the fitting of multistate capture–mark–recapture models

Matia H. Muller, Jaume-Adria Badia-Boher 

1. Multistate capture–mark–recapture (CMR) models are widely used to estimate the parameters governing demographic processes such as survival, dispersal, and recruitment in animal populations. In Bayesian analyses, the multinomial likelihood of multistate CMR models summarizes individual encounter histories into groups defined by states and capture occasions, and is regarded as a computationally efficient alternative to widely-used state-space models. However, as model complexity increases – through additional states or capture occasions – the conventional multinomial formulation can also reach very long or intractable computation times. Depending on model structure, the multinomial formulation may include many unnecessary calculations that can be removed while preserving an equivalent model, potentially resulting in substantial computational gains.
2. Here, we present an approach to eliminate such unnecessary calculations, and therefore optimize the implementation of multistate multinomial CMR models. First, we describe the modifications needed for optimization under commonly used multistate model variants: movement models where states represent discrete sites, and age-structured models where states represent age classes. We also provide code-based tutorials to facilitate method implementation. To evaluate model performance, we simulated CMR data under both model types with increasing levels of complexity (two to four sites, two to four age classes), fitted conventional and optimized formulations in NIMBLE and JAGS, and compared parameter estimates in terms of bias, coverage, and computational efficiency. In a case study, we also fitted both formulations to a dataset of German White Storks, using a model that combines age structure and movement between regions.
3. The optimized formulation produced equivalent estimates to the conventional formulation across simulations and in the case study, confirming that both formulations implement the same likelihood. Relative gains in computational efficiency increased with model complexity in age-structured models, reaching a factor of 13 in NIMBLE and 18 in JAGS. Gains were more modest in movement models, which was expected as their structure is less optimizable. In the case study, the optimized formulation was 11-fold more efficient in NIMBLE and 5-fold in JAGS.
4. Our results illustrate that Bayesian multistate CMR models can be largely speeded up, permitting the analysis of more complex models and larger datasets.