Combining a Bayesian nonparametric method with a hierarchical framework to estimate individual and temporal variation in growth

Growth modeling has long played an important role in ecology, conservation and management of many species. However, adopting a statistical framework that includes both temporal and individual variability in the growth dynamics has proven challenging. In this paper, we use a Bayesian state space framework (BSSF) to estimate parameters of a discrete time model from a mark-recapture data set of age-1 juvenile Atlantic salmon. We use a Gaussian process (GP) based approach to model variation in seasonal growth potential. In addition, we use auxiliary information on the food environment as prior knowledge of seasonal fluctuations in growth. Parameters for the GP prior and measurement error variances were fixed to speed convergence. Posterior estimates of model parameters were relatively insensitive to these choices. Our model captures the seasonal growth dynamics of juvenile Atlantic salmon as evidenced by close agreement between observed and predicted lengths (r2 = 0.98). In addition, the relatively narrow confidence intervals indicated significant learning in the parameters of interest. Finally, our model approach was able to accurately recover missing data points. Although this model was applied to a mark-recapture dataset of Atlantic salmon, the generality of the approach should make it applicable to a wide variety of size trajectory datasets, and thus, provides a useful tool to estimate individual and temporal variability in growth from datasets with repeated measurements.