Appendix B. Stepwise modeling procedure.

In all multivariate models, only main
effects and two-way interactions between pairs of explanatory (life history or
habitat) variables were considered. When a two-way interaction involving a
categorical variable was included, the main effect of the variable with which
the categorical variable interacted was also included in the model (even if not
significant), to satisfy marginality restrictions. By contrast, non-significant
main effects of variables that interacted (or appeared as product terms) *only* with continuous variables were not included, as marginality considerations do
not require their inclusion. The modeling process was performed as follows for
each time period separately. An initial model involving main effects only was
fitted. Product terms, i.e., interactions between continuous variables,
and two-way interactions involving categorical variables were added
successively to the model until no further improvement of fit could be
observed. At this stage, optimal models were modified in three ways. First, any
nonsignificant main effects that were not forced into the model because of
their presence in significant interactions were removed. Second, we
investigated whether adding the squares of the continuous variables in the
model would affect the significance of product terms involving these variables.
This would indeed be expected if product terms or correlated explanatory
variables were acting as proxies for the squares of one or both of the
variables included in the product. Finally, random effects whose variance
components were not significantly different from zero were removed from the
model, in order to improve the accuracy of coefficient estimations for the
remaining random and fixed effects. Following this procedure, we obtained
different models for the two time periods. We then fitted the whole data set to
a third model that included as fixed effects the time period and all the terms
that were significant in one or both of the separate models fitted for each
period. Time period was included in two-way and three-way interactions with
environmental variables and life history traits. Random effects for plots were
allowed to differ between time periods, in order to take into account temporal
changes in the plot characteristics which may not have been recorded by our threat
variables. Nonsignificant terms were then removed one at a time from the
overall model until all remaining terms were significant. At this stage, we
investigated the relevance of adding squares of continuous variables in the
model, and we removed random effects whose variance components were not
significantly different from zero.