(f) Selection analyses

We tested whether selection differs between urban and rural genotypes at each field site and whether foreign genotypes experienced stronger selection than local genotypes, a pattern consistent with local adaptation. We conducted the selection analyses on four traits (transition to reproductive phase, date of first open male flower, male to female flower, and height), some of which were highly correlated (electronic supplementary material, tables S11 and S12). These traits are all key contributors to plant fitness and are often under strong selection [38]. We estimated selection differentials (net selection) and selection gradients (direct selection) using simple and multiple linear regression, respectively, of male and female relative fitness on standardized traits [39]. Selection differentials measure selection via both direct selection acting on the trait of interest and selection acting through correlated traits; whereas selection gradients provide estimates of selection on a trait after statistically removing indirect selection that results from selection acting on other measured, but not unmeasured, traits. We calculated relative fitness by dividing individual male and female fitness by the site mean. We standardized traits within each site by subtracting the site mean and dividing by the standard deviation. Last, we calculated the genotypic means for relativized fitness metrics and standardized traits. The significance of differentials and gradients were evaluated with Type II sums of squares.

We conducted separate selection analyses on data from each site, and within each site we examined selection separately for urban and rural genotypes. In addition, we asked whether the strength of selection differed between urban and rural genotypes by fitting a linear model with relative male or female fitness as the response variable, source region and the interaction between the two as predictor variables (electronic supplementary material, A4).

We quantified stabilizing and disruptive selection using the same model format but included the square of each trait as an additional variable. When quadratic terms were significant, we fitted nonparametric cubic splines to the data using the smooth.spline function in R to determine where there was a fitness minimum or maximum within the phenotypic range [40].

We quantified selection gradients and tested whether they differ between urban and rural genotypes by fitting a linear model for the three phenology traits following the same format as the selection differential models above: relative male or female fitness as the response variable, source region, the three phenology traits, and interactions between source region and each trait (electronic supplementary material, A5). We omitted height in the selection gradients analyses because it was highly correlated with our estimates of fitness (all r > 0.6). For all quadratic gradients, we multiplied the regression coefficient by two [41].

To test whether selection was stronger on foreign than local genotypes, we calculated local-foreign contrasts and conducted a one-sided Wilcoxon signed-rank test on these contrasts. We calculated the absolute difference in selection differentials and gradients between local versus foreign genotypes (foreign coefficient − local coefficient) at each field site for each trait. We then used a one-sided Wilcoxon signed-rank test (wilcox.test) to determine if the difference in selection was significantly greater than zero, which would indicate stronger selection on the foreign genotype. We also include the results of the two-sided Wilcoxon signed-rank test for comparison. We conducted all selection analyses with the lme4 package [29], and car packages [34], and conducted separate tests for selection differentials and gradients, and for male and female fitness.