Multivariate redundancy analysis (RDA): assessing spatial &
environmental influences on genetic structure
We used RDAs to estimate the relative influence of spatial and
environmental factors on neutral and putatively adaptive genetic
structure in S. umbilicalis and N. lapillus . Our response
variables were minor allele frequencies (MAF) of each locus, estimated
using the software PLINK (v1.9; Chang et al. 2015), and detrended using
the Hellinger method implemented in the decostand function of
vegan. To account for our large number of molecular markers, we
conducted PCAs on each neutral and outlier dataset and retained only
meaningful PCs (those with eigenvalues >1) as response
variables in our models. Environmental (PCs) and spatial (dbMEM and AEM
vectors) variables were used as predictor variables. We tested for
correlations between these predictors and removed one variable when
correlation exceeded 0.7, resulting in a final predictor variable
dataset of four environmental PCs representing SST, AT and exposure, six
dbMEMs, and three AEMs. As N. lapillus is a direct developer, we
excluded the AEM vectors from our RDA models for this species.
We conducted RDA and partial RDA analyses on our four response variable
datasets (neutral and outlier datasets for N. lapillus andS. umbilicalis ) using vegan. First, we conducted a backwards and
forwards selection procedure using the ordistep function to
determine the combination of predictor variables that best explained
each of our response variable datasets (i.e., the model producing the
highest adjusted R2). From this “best” model, we
conducted partial RDAs, where we conditioned the model to control for
the influence of either geographic structure (dbMEMs), larval
connectivity (AEMs) or environmental variation (PCs) by first estimating
and removing their effects and then performing an RDA on the residual
matrix. Thereby, we were able to partition the variance of our “best”
models, to determine the amount of explainable variation in our dataset
attributed to each set of predictor variables, while controlling for all
other variables. The significance of our models and associated predictor
variables were tested using analyses of variance (ANOVAs), implemented
using the anova function of the stats package in R, with 1,000
permutations.