2.4. Detection of genetic differentiation associated with temperature

To detect loci underlying local adaptation, a Bayesian approach as implemented in BAYENV2 (Coop et al., 2010; Günther & Coop, 2013) was applied to the entire SNPs dataset. The Bayesian approach considers the effect of population structure, using a covariance matrix based on neutral SNPs to control for demographic effects when testing for correlations between environmental factors and genetic differentiation (Coop et al., 2010). To identify the neutral loci, we first excluded the candidate loci under natural selection detected in BayeScan 2.1 (Foll & Gaggiotti, 2008).

BayeScan decomposes locus‐population F _ST coefficients into a population‐specific component (beta), shared by all loci and a locus‐specific component (alpha) shared by all the populations using a logistic regression (Foll & Gaggiotti, 2008). Loci with a positive value of alpha were considered to be under divergent selection. Prior odds of 100 were used for identifying the candidates of the selected loci, and then BayeScan was run with the settings of 100,000 iterations, a thinning interval of 10, 20 pilot runs of 5000 iterations each with a burn‐in length of 50,000. Loci with a false discovery rate (FDR) of 0.05 were considered under selection. Then, we retained the SNPs within Hardy–Weinberg equilibrium (HWE) at p < .005 and further pruned the SNPs for linkage disequilibrium (LD) using PLINK (Purcell et al., 2007) at a thread of 0.2. The resulting SNPs were determined as “neutral SNPs.” To ensure that the estimated matrix was convergent, four independent runs with different random seeds were run based on neutral loci. The average water temperatures in January (T1) and August (T8) were selected as the cold and warm months, respectively. As environmental factors that may constrain the survival and reproduction of L. anatifera (Patel, 1959), these temperature variables were tested for association with genetic variation. Each environmental parameter was standardized by subtracting the mean and dividing it by the standard deviation of the parameter across all sampling sites. To reduce stochastic errors, the detection of environmental correlation was also run three times independently with different random seeds. SNPs with log₁₀ Bayes factor (BF) >1.5 (Jeffreys, 1961) in the results were identified as loci strongly associated with environmental variables. Candidate genes containing selected SNPs were functionally annotated with the ANNOVAR software (Wang et al., 2010).

To estimate the degree to which the genomic variations among different populations can be explained by temperature heterogeneity and to test the reliability of temperature‐related outliers detected using BAYENV2, redundancy analysis (RDA) was performed based on adaptive data sets associated with temperature using the RDA function from the vegan package (Oksanen et al., 2013). Analyses of variance (ANOVAs) were performed to check the RDA model for significance and marginal ANOVAs (999 permutations) were run to determine whether the two temperature variables were significantly correlated with genetic variations.