2.5 Multivariate analysis of genetic divergence datasets
The table of weighted F ST across all contrasts (genes as columns, contrasts as rows) was subjected to multivariate analysis following De Lisle & Bolnick, 2020. The idea of the method is to subject the table of contrasts to the appropriate form of eigenvalue decomposition to see whether some or all contrasts align with each other in multivariate space (Figure 1). In the graphical representation of the resulting ordination called “correlation biplot,” where eigenvectors are scaled to the square root of their eigenvalues (scaling=2 in R package vegan ; Borcard et al., 201), angles between the original responses in the multivariate space reflect their correlation in the original data (Legendre & Legendre, 2012). Angles less than 90° indicate parallel evolution (i.e., adaptation involving the same genes), while angles near 90° indicate independence.
To obtain appropriate ordination for the F STdata, where only the positive values are informative of evolutionary parallelism, we first set all negative F ST values to 0 and removed genes with zero F ST across all contrasts, leaving 2,124 genes. We then computed a matrix of distances between contrasts based on the square root of Bray-Curtis dissimilarity, which is a metric distance that quantifies the degree of matching between positive values while ignoring matches between zeroes (Borcard, 201; Legendre & Legendre, 2012). The distance matrix was subjected to the principal coordinate analysis using function capscale in package vegan in R, while also inferring the coordinates of each gene in the new multivariate space using comm option in thecapscale function.