R: Likelihood-based estimation of inbreeding

Inbreeding estimation {adegenet} | R Documentation

## Likelihood-based estimation of inbreeding

### Description

The function `inbreeding` estimates the inbreeding coefficient of an individuals (F) by computing its likelihood function. It can return either the density of probability of F, or a sample of F values from this distribution. This operation is performed for all the individuals of a genind object. Any ploidy greater than 1 is acceptable.

### Usage

    inbreeding(x, pop = NULL, truenames = TRUE,
               res.type = c("sample", "function", "estimate"), N = 200, M = N * 10)

### Arguments

`x` | an object of class genind.
`pop` | a factor giving the 'population' of each individual. If NULL, pop is seeked from `pop(x)`. Note that the term population refers in fact to any grouping of individuals'.
`truenames` | a logical indicating whether true names should be used (TRUE, default) instead of generic labels (FALSE); used if res.type is "matrix".
`res.type` | a character string matching "sample", "function", or "estimate" specifying whether the output should be a function giving the density of probability of F values ("function"), the maximum likelihood estimate of F from this distribution ("estimate"), or a sample of F values taken from this distribution ("sample", default).
`N` | an integer indicating the size of the sample to be taken from the distribution of F values.
`M` | an integer indicating the number of different F values to be used to generate the sample. Values larger than N are recommended to avoid poor sampling of the distribution.

### Details

Let F denote the inbreeding coefficient, defined as the probability for an individual to inherit two identical alleles from a single ancestor.

Let p_i refer to the frequency of allele i in the population. Let h be an variable which equates 1 if the individual is homozygote, and 0 otherwise. For one locus, the probability of being homozygote is computed as:

F + (1-F) ∑_i p_i^2

The probability of being heterozygote is: 1 - (F + (1-F) ∑_i p_i^2)

The likelihood of a genotype is defined as the probability of being the observed state (homozygote or heterozygote). In the case of multilocus genotypes, log-likelihood are summed over the loci.

### Value

A named list with one component for each individual, each of which is a function or a vector of sampled F values (see `res.type` argument).

### Author(s)

Thibaut Jombart t.jombart@imperial.ac.uk
Zhian N. Kamvar

### See Also

`Hs`: computation of expected heterozygosity.

### Examples

    ## Not run:
    ## cattle breed microsatellite data
    data(microbov)

    ## isolate Lagunaire breed
    lagun <- seppop(microbov)$Lagunaire

    ## estimate inbreeding - return sample of F values
    Fsamp <- inbreeding(lagun, N=30)

    ## plot the first 10 results
    invisible(sapply(Fsamp[1:10], function(e) plot(density(e), xlab="F",
    xlim=c(0,1), main="Density of the sampled F values")))

    ## compute means for all individuals
    Fmean=sapply(Fsamp, mean)
    hist(Fmean, col="orange", xlab="mean value of F",
    main="Distribution of mean F across individuals")

    ## estimate inbreeding - return proba density functions
    Fdens <- inbreeding(lagun, res.type="function")

    ## view function for the first individual
    Fdens[[1]]

    ## plot the first 10 functions
    invisible(sapply(Fdens[1:10], plot, ylab="Density",
    main="Density of probability of F values"))

    ## estimate inbreeding - return maximum likelihood estimates
    Fest <- inbreeding(lagun, res.type = "estimate")
    mostInbred <- which.max(Fest)
    plot(Fdens[[mostInbred]], ylab = "Density", xlab = "F",
         main = paste("Probability density of F values\nfor", names(mostInbred)))
    abline(v = Fest[mostInbred], col = "red", lty = 2)
    legend("topright", legend = "MLE", col = "red", lty = 2)

    ## note that estimates and average samples are likely to be different.
    plot(Fest, ylab = "F", col = "blue",
         main = "comparison of MLE and average sample estimates of F")
    points(Fmean, pch = 2, col = "red")
    arrows(x0 = 1:length(Fest), y0 = Fest,
           y1 = Fmean, x1 = 1:length(Fest), length = 0.125)
    legend("topleft", legend = c("estimate", "sample"), col = c("blue", "red"),
           pch = c(1, 2), title = "res.type")

    ## End(Not run)

[Package adegenet version 2.1.4 Index]