Confidence limits for regression relationships between distance matrices: Estimating gene flow with distance

There is growing interest in assessing relationships between two or more distance matrices, where distances are based on genetic, geographical, and/or environmental measures of dissimilarity for all pairwise combinations of n populations. Methods are developed and assessed for estimating confidence limits for the regression relationship between dependent matrix Y and matrix X and for estimating the value of x given critical y. Methods include a regression mixed model that incorporates an additional population effects variance and a jackknife-by-population regression method that omits the (n - 1) distance observations for each population in turn. The approaches are illustrated using data to quantify rates of gene flow with distance between wild plant populations of sea beet and are assessed using simulations.