Likelihood-based estimation of inbreeding
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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.