Covariance: The parametric covariance matrix

Description Usage Arguments Author(s) Examples

Description

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

Usage

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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.

Author(s)

Gideon Bradburd

Examples

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#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)
	alphaD <- rexp(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)
	example.covariance <- Covariance(a0 = alpha0,aD = alphaD,aE = alphaE,a2 = alpha2,
				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"))

Example output



BEDASSLE documentation built on May 2, 2019, 6:10 a.m.