Competition is an important process structuring ecological communities. As such, we need to be able to estimate the strength of pairwise specifies-specific competitive interactions. In diverse communities this can be challenging because of the large number of species pairs. One solution to this problem is to use a hierarchical Bayesian approach in which competition coefficients are drawn from a common distribution. This allows all species-pair competition coefficients to be estimated, while accounting for differences in sample size. Here we estimate the specific-specific neighborhood effect of competition on tree diameter growth using such a hierarchical Bayesian approach. The tree growth and spatial arrangement data come from two census, separated by six years, of a 23 ha research plot in a successional oak-hickory forest. Competing models are compared in which competition coefficients are estimated on their own or with a hierarchical structure. We also compare models in which trait and phylogenic information are used to inform the hierarchical structure of the competition coefficients. We obtain posterior estimates using Markov Chain Monte Carlo and compare models with a spatial leave-one-out validation method.
The hierarchical structure of competition coefficients greatly improved the fit of the model compared to one in which competition coefficients were estimated on their own. Further, incorporating either trait or phylogenic information also improved the fit. Overall this shows the power of this hierarchical approach. Individual species-specific competition coefficients were estimated and these gave insights into the successional dynamics within the forest. In this forest the oak-hickory canopy is being replaced by individuals of more shade-tolerant species, for example black cherry and red maple. Estimated coefficients for these species help explain these competitive dynamics.