Covariance {BEDASSLE} R Documentation

## The parametric covariance matrix

### Description

This function parameterizes the decay in covariance of transformed allele frequencies between sampled populations/individuals over their pairwise geographic and ecological distance.

### Usage

Covariance(a0, aD, aE, a2, GeoDist, EcoDist, delta)


### Arguments

 a0 This parameter controls the variance when pairwise distance is zero. It is the variance of the population-specific transformed allelic deviate (theta) when pairwise distances are zero (i.e. when D_{i,j} + E_{i,j} = 0). aD This parameter gives the effect size of geographic distance (D_{i,j}). aE This parameter gives the effect size(s) of ecological distance(s) (E_{i,j}). a2 This parameter controls the shape of the decay in covariance with distance. GeoDist Pairwise geographic distance (D_{i,j}). This may be Euclidean, or, if the geographic scale of sampling merits it, great-circle distance. EcoDist Pairwise ecological distance(s) (E_{i,j}), which may be continuous (e.g. - difference in elevation) or binary (same or opposite side of some hypothesized barrier to gene flow). delta This gives the size of the "delta shift" on the off-diagonal elements of the parametric covariance matrix, used to ensure its positive-definiteness (even, for example, when there are separate populations sampled at the same geographic/ecological coordinates). This value must be large enough that the covariance matrix is positive-definite, but, if possible, should be smaller than the smallest off-diagonal distance elements, lest it have an undue impact on inference. If the user is concerned that the delta shift is too large relative to the pairwise distance elements in D and E, she should run subsequent analyses, varying the size of delta, to see if it has an impact on model inference.

### Examples

#With the HGDP dataset
data(HGDP.bedassle.data)

#Draw random values of the {alpha} parameters from their priors
alpha0 <- rgamma(1,shape=1,rate=1)
alphaE <- matrix(rexp(1,rate=1),nrow=1,ncol=1)
alpha2 <- runif(1,0.1,2)

#Parameterize the covariance function using the HGDP dataset distances (Geo and Eco)
GeoDist = HGDP.bedassle.data$GeoDistance, EcoDist = list(HGDP.bedassle.data$EcoDistance),
plot(HGDP.bedassle.data$GeoDistance, example.covariance, pch=19,col=HGDP.bedassle.data$EcoDistance+1,