Natural Selection
The combination of bird and Eurytoma gigantea attack have well known consequences for patterns of selection. When bird attack is more common, selection is negative and favors small galls. WhenEurytoma gigantea attack is common, selection is positive and larger galls are more likely to survive. Accordingly, environmental changes resulting in differences in average attack rate of one or both enemies may change average patterns of selection, and changes to the among-population variation in attack rates should alter among-population differences in the direction and magnitude of selection.
Before relating selection to extreme events or other environmental drivers, I first had to estimate selection in each population. I began by standardizing gall size by subtracting the population mean gall size and dividing by the standard deviation. I similarly relativized fitness by dividing survival (zero or one) by mean survival in the population in that year. Standardizing and relativizing locally assumes soft selection and allows us to compare estimates of selection among populations that differ in mean fitness. After standardizing variables, I calculated a selection coefficient for each year by population combination by regressing individual relative fitness against standardized gall size in a linear model (Lande and Arnold 1983). Note that while data are binary, generalized linear models do not allow for the estimation of standard parameter values commonly used in selection analyses (e.g. selection gradients), requiring the use of linear models.
After calculating selection gradients, I began testing for the effects of extreme events and environmental conditions on natural selection. First, I used a series of linear models to estimate selection coefficients. I began by running an analysis testing for among-year differences while including population as a random effect, applying Tukey’s tests to make pairwise comparisons. I continued by running a separate model including bird and Eurytoma attack rates as main effects. These analyses then test for relationships between selection and increasingly distant processes (e.g. windstorm in a particular yearenvironmental conditionsecological interactionsselection).
I next sought to quantify spatial variation in selection. I first used Levene’s tests to estimate within-year but among-population difference in selection coefficients, again using Tukey’s tests to make pairwise comparisons. I continued this analysis by comparing within-year residual variation in selection coefficients to residual variation in bird attack and survival as main effects. Recall that bird attack shapes the fitness surface, while survival rates are our measure of mean fitness and can therefore inflate or dampen the opportunity for selection and thus the magnitude of selection coefficients (Arnold and Wade 1984, Benkman 2013).