A Bayesian state-space model for seasonal growth of terrestrial vertebrates

The rate of somatic growth determines when individuals transition between life stages, which along with survival and reproduction, are principal factors governing the rate of population change. For short-lived species that inhabit seasonally dynamic environments, accounting for fluctuations in somatic growth is necessary to make reliable inferences about population dynamics. We describe a Bayesian, state-space formulation of a von Bertalanffy growth model that integrates a sinusoidal model to allow for seasonal fluctuations in growth while also accounting for individual heterogeneity and measurement error. We use this model to describe post-metamorphic growth of canyon treefrogs, Hyla arenicolor, based on capture-recapture data from 404 individuals over a two-year period. For simulated data where we assumed growth varies seasonally, our model provides unbiased estimates of growth rate, mean asymptotic length, standard deviation of individual asymptotic lengths, and date of maximum growth. For field data from canyon treefrogs, we found strong evidence of seasonal variation in growth, with maximum growth during the summer monsoon season. Growth rate of females was 19 % lower than males, although on average, females reached asymptotic lengths that were 15 % greater than males. Ignoring systematic intra-annual variation in growth can bias inferences about population dynamics, particularly for fast-growing species that reproduce more than once per year or inhabit environments with strong seasonal signals. We present a straightforward approach for using repeated length measurements from individuals of unknown age to estimate growth while accounting for seasonality and individual heterogeneity, which are sources of variation common in many vertebrate populations.