*4.3. Genetic Diversity and Population Structure*

We calculated the observed heterozygosity (*H*O), expected heterozygosity (*H*E), nucleotide diversity (π), and inbreeding coefficient (*F*IS) for each population using the POP-ULATIONS program in STACKS. Pairwise *F*-statistics (*F*ST) (1000 permutations) among populations were calculated using ARLEQUIN v3.5.2 [43]. Population structure was analyzed using the program STRUCTURE v2.3.5 [44]. The number of genetic clusters (*K*) was set from 1 to 16 for TIL populations and from 1 to 11 for ZA populations, corresponding to the number of sampled populations in each region. Ten independent iterations were conducted for each *K*, with a burn-in of 10,000 and 100,000 Markov chain Monte Carlo replicates, by assuming the admixture model and independent allele frequencies. The optimal *K* value was determined from the ΔK values calculated by STRUCTURE HARVESTER [45]. A Mantel test for genetic differentiation [*F*ST/(1 − *F*ST)] against geographic distance (log10 transformed) was performed in GENALEX v6.1 [46] for each region, to test the pattern of isolation by distance (IBD). Statistical significance was determined with 1000 permutations.

#### *4.4. Gene Flow and Demographic History Analyses*

For each region, we estimated the levels of interpopulation gene flow using the program BAYESASS v3.03 [47]. First, we ran BAYESASS with the default delta values for allelic frequency, migration rates, and inbreeding coefficients. Then, subsequent runs were adjusted with different delta values to ensure that the acceptance rate ranged between 40 and 60% for each parameter [47]. We performed 10 independent runs (1 × 107 iterations with a burn-in of 10<sup>6</sup> generations), each with a different initial seed. Model convergence was assessed by the program TRACER v1.5 [48]. In addition, we also used the DIVMIGRATE function from the DIVERSITY package v1.9.90 in R [49] to calculate the relative direction of the gene flow between island and mainland populations, using Nei's *G*ST method. To test for asymmetric flow (significantly higher in one direction than the other), 95% confidence intervals were calculated from 1000 bootstrap replicates [50].

We used the program BOTTLENECK v1.2.02 [51] to determine whether *H. chrysotricha* populations underwent significant reductions in effective population size (*N*e). We used Wilcoxon's signed rank test, which examines whether populations exhibit a greater level of heterozygosity than predicted in a population at mutation-drift equilibrium, to detect bottlenecks occurring over approximately the last 2–4 *N*e generations. For each *H. chrysotricha* population, we performed 10,000 simulations for each of three mutation models (IAM, infinite allele model; SMM, stepwise mutation model; and TPM, two-phase mutation model, with 95% single-step and 5% multi-step mutations). Statistical significance was set at the 0.05 level.
