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.