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To obtain the matrix of population structure, a total of 42,368 SNPs were analyzed in the 298 germplasm accessions using the Admixture program v. 1.22 [ 58].

After removing monomorphic loci and minor allele with minor allele frequency (MAF) threshold of 0.05, the Q matrix of population structure with number of estimated populations was added.

PCA was carried out using PROC PRINCOMP in SAS using the correlation matrix of population means of the reduced set of traits.

Also, a tree R2 = 0.97 indicates that branch lengths explained a substantial amount of the variation present in the matrix of population distances [ 56].

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To calculate correlations between SNP allele frequencies and current and past climate variables, we used the Bayesian linear model method of Coop et al. (2010), which controls for population history by incorporating a covariance matrix of populations and accounts for differences in sample size between populations.

The Q-matrix of population membership probabilities was served as covariates in MLM.

We model the population dynamics of Pterostichus melanarius (Coleoptera: Carabidae), a carabid beetle often used as indicator species of habitat changes, by a joint model that combined a matrix model of population dynamics including local dispersal with an explicit model of the patchy landscape of the polders of the Bay of Mont St. Michel (Brittany, France).

Matrix models of population growth provide a useful way to quantify the ecological and evolutionary consequences of environmental changes (Caswell 2001), such as the thermal changes caused by dams.

Table S1: Spatially averaged transition matrices of populations of epiphytic orchids.

To test for signatures of isolation by distance (IBD [ 88]), matrices of population-level, standardized genetic differentiation [FST/ 1-FST)] [FST/ 1-FSTeographic distance between localities were constructed using GENEPOP v4.2 and the Geographic Distance Matrix Generator v1.2.3 [ 90], respectively.

We analyzed the weight matrix of each population using a MANCOVA (with size as a covariate to remove isometric size effects, since the reed ecotypes are significantly larger than the stonewort ecotypes).

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