Computationally efficient Bayesian capture–mark–recapture models with transients, applied to survival of hand‐reared African Penguins

Abstract Mark–recapture models are the primary framework for estimating demographic parameters in wild organisms. Complex life histories and sampling processes demand complex model formulations, yet these are vulnerable to errors in implementation and unanticipated biases. Simulation is a powerful tool to diagnose potential issues, but as the size of models and data increase, the computational cost of simulation‐based model evaluation may discourage its use. A common phenomenon in mark–recapture studies is ‘transients’: the number of individuals that are only captured once exceeds that expected by the model. To avoid biasing survival estimates, transients should be accounted for. Mixture models offer a flexible, extensible and interpretable way to do so, but current implementations of transient mixture models as multievent models can have long runtimes for large datasets. Here, we describe a novel likelihood calculation for transient mixture models, which allows any multistate model with an efficient product‐multinomial likelihood to account for transients at negligible extra computational cost. The resulting ‘extended product‐multinomial’ (EPM) likelihoods are inferentially equivalent to multievent likelihoods, but faster to fit, often by an order of magnitude or more. A guide to implementation in R and Stan is provided. We illustrate our approach with a case study comparing survival of wild‐raised and hand‐reared African Penguins Spheniscus demersus . Facilitated by our EPM likelihood, we used simulation to assess our model's ability to disentangle survival differences from confounding factors whilst accounting for trap dependence and transience in the data. Hand‐rearing was associated with higher juvenile survival and lower adult survival compared with wild‐raised birds.