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The eigenvalues resulting from the decomposition of the truncated matrix of geographic distances are linearly related to Moran's I coefficients of spatial autocorrelation [23].
PCNM is based on the eigenvalue decomposition of a truncated matrix of geographic distances among sampling sites that is obtained through principal coordinate analysis.
The same procedure was performed for the similarity matrix of the mean species assemblage per fallow and the distance matrix of geographic positions of the fallows.
The matrix of geographic distances was calculated from the spatial coordinates of each population using the Geographic Distance Matrix Generator [ 65].
For each time trend, PLS regression was performed separately with the ^γsi as the outcomes and the matrix of geographic covariates as the predictors.
We thank the dedicated ADF&G laboratory staff who processed the samples and I. Stewart for facilitating a matrix of geographic distances between populations for the Kvichak subdrainage.
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The other spatial matrices of geographic, trade and capital channels do not affect the significance of the cultural channel, and only trade and geographic weight matrices significantly affect international housing price co-movements, whereas the FDI weight matrix does not significantly affect international housing market linkages.
Multidimensional scaling plots and Mantel tests for correlation between genetic distance matrices and between them and matrices of geographic distances were computed by NTSYS 1.70.
Isolation by distance (IBD) was tested using Mantel tests for correlation between paired population matrices of geographic distances and genetic distances using Arlequin v3.5.1.2 [ 47] with 10,000 permutations for significance tests.
Next, a matrix of pairwise geographic distances between populations was computed from geographic coordinates and the correlation between genetic and geographic matrices was estimated using 999 permutations in GenAlEx.
The same program was used to run a Mantel test (Mantel 1967), with 10 000 permutations, to estimate the correlation of pairwise linearized distances with a matrix of linear geographic distances to test the hypothesis of genetic isolation by geographic distance (isolation by distance, IBD).
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