Using cross-classified multivariate mixed response models with application to life history traits in great tits (Parus major)

Longitudinal observations on known individuals are an important source of data with which to test evolutionary theory within natural populations, in particular, the evolution and maintenance of life-history traits. In this paper, we concentrate on the reproductive behaviour and survival of a small passerine bird, the great tit (Parus major). The dataset we consider is taken from the long-term study of great tits in Wytham Woods in Oxfordshire. The models we consider are designed to relate variation in several phenotypic response variables that are linked to evolutionary fitness, alongside the correlations between them, to both general environmental and individual-specific factors. We fit multivariate cross-classified random effects models using a Markov chain Monte Carlo (MCMC) estimation algorithm described in the paper. Our results show for which traits variability is influenced by environmental factors and for which traits individual bird factors are more important. The partitioning of correlations is particularly illuminating, producing some pairs of 'antagonistic' correlations which are biologically meaningful.