Estimating Spatial & Dispersal Distances
Pairwise geographic and larval dispersal distances were converted into
site-based metrics to be used as independent variables in our redundancy
analysis (RDA). To represent geographic structure, we estimated
distance-based Moran’s eigenvector maps (dbMEMs; Dray et al. 2006).
Here, site latitude and longitude were transformed into Cartesian
coordinates using the geoXY function of the R package SoDA
(v1.0.6.1; Chambers 2020), which were used to calculate a matrix of
Euclidian distances using the dist function of the stats package.
We then used the pcnm function of the package vegan to transform
the spatial distances into rectangular matrices that describe spatial
structure at multiple scales suitable for constrained ordination
analyses (Borcard & Legendre 2002; Peres Neto & Legendre 2010).
To account for the asymmetric directionality of ocean current-mediated
larval dispersal between sites we translated larval connectivity
matrices produced by the larval dispersal modelling into asymmetric
eigenvector maps (AEMs; Blanchet et al. 2008, 2011). Connectivity
matrices were used to construct a node-to-edge matrix representing
direct and indirect connectivity between our 12 sites using theaem.build.binary function of the adespatial package in R (v0.3.8;
Dray et al. 2020) (i.e., an edge is present [1] if the probability
of larval connectivity between sites is >0, and not present
[0] if the probability of larval connectivity is 0). This resulted
in a node-to-edge matrix comprised of our 12 sites (nodes) and 66 edges
(connectivity links between sites). This pairwise binary matrix was
translated into site-based AEM vectors using the AEM package (v0.6;
Blanchet et al. 2015), with weights applied to each edge representing
the average probability of connectivity from the larval connectivity
matrix, which was transformed using min-max normalization.