Inbreeding estimation | R Documentation |

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.

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

`x` |
an object of class genind. |

`pop` |
a factor giving the 'population' of each individual. If NULL,
pop is seeked from |

`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. |

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.

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).

Thibaut Jombart t.jombart@imperial.ac.uk

Zhian N. Kamvar

`Hs`

: computation of expected heterozygosity.

## 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)

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