# Covariance: The parametric covariance matrix In BEDASSLE: Quantifies Effects of Geo/Eco Distance on Genetic Differentiation

 Covariance 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),
delta = 0.001)

#Plot the example covariance against geographic distance
plot(HGDP.bedassle.data\$GeoDistance,
example.covariance,
pch=19,col=HGDP.bedassle.data\$EcoDistance+1,
main="Covariance in allele frequencies across the Himalayas")
legend(x="topright",pch=19,col=c(1,2),
legend=c("same side of Himalayas",
"opposite sides of Himalayas"))
```

BEDASSLE documentation built on April 11, 2022, 1:07 a.m.