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 |

`aD` |
This parameter gives the effect size of geographic distance ( |

`aE` |
This parameter gives the effect size(s) of ecological distance(s) ( |

`a2` |
This parameter controls the shape of the decay in covariance with distance. |

`GeoDist` |
Pairwise geographic distance ( |

`EcoDist` |
Pairwise ecological distance(s) ( |

`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

```
#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"))
```

*BEDASSLE*version 1.6.1 Index]