Parameter fitting
Regression parameters were estimated using a Bayesian Monte Carlo procedure. For growth, the model was based on a Gaussian error term; for survival, the error was binomial. The post burn-in chain of estimates produced a posterior distribution for every parameter, and statistical confidence in every parameter was estimated as 95thpercentiles from the posterior distributions (or 95% credible intervals). Models were run 10000 steps, and the first 2000 discarded as burn in. Chains were examined visually and converged in < 1000 steps. Details of the method are given elsewhere (Condit et al. 2006, 2007).
Results are presented as effect sizes of the four neighborhood predictors and elevation on growth and survival of stems in each of the top three size categories. Results for the smallest size class, 2-5 cm dbh were not reported in detail because the number of trees in this size class declined substantially during the study due to their high mortality rates during the burns (no live small pin oaks remained by the end of the study), making it impossible for the models to yield reliable results for the latter time periods.
In the case of growth, these are partial regression coefficients from the linear regression (i.e., the regression parameters for each predictor); these were divided by standard deviations in each dbh class and species. Since predictors (neighbors and elevation) were standardized so one unit means approximately the entire range, a growth effect of 1.0 means that growth varied by an amount equal to its standard deviation across the full range of the predictor. Survival rates cannot be transformed with a standard deviation, but effect sizes can be transformed so that they display the change in survival across the range of a predictor. We do not report the dbh effect, since the four dbh categories allow conclusions about neighborhood effects and tree size; dbh was in the model only as a precaution to avoid misinterpreting the density effects.