kimura

The goal of kimura is to provide functionality related to the Kimura distribution from statistical genetics (Kimura, 1955), often applied to the study of mitochondrial DNA heteroplasmy.

❗ If you are looking to fit a Kimura distribution to a heteroplasmy sample to provide evidence of selection (or neutrality), please read the notes below and Giannakis et al. (2023) ❗

Installation

You can install the development version of kimura from GitHub with:

# install.packages("devtools")
library("devtools")
devtools::install_github("lbozhilova/kimura")

Example

This package contains functionality for extracting probabilities and generating data from the Kimura distribution.

# Initialise Kimura parameters
p <- 0.6
b <- 0.95

# Probability of allele loss
dkimura(0, p, b)
#> [1] 1.989732e-05
# Probability of fixing an allele
dkimura(1, p, b)
#> [1] 9.694172e-06

# Kimura(p, d) CDF at 0.1 intervals
pkimura(seq(0, 1, 0.1), p, b)
#>  [1] 1.989732e-05 2.165073e-05 1.345668e-04 3.560559e-03 3.773170e-02
#>  [6] 1.840206e-01 4.908528e-01 8.136989e-01 9.711726e-01 9.989777e-01
#> [11] 1.000000e+00

# Random number generation
rkimura(10, p, b)
#>  [1] 0.6837089 0.7312714 0.5824325 0.4693752 0.3754452 0.5464930 0.6789625
#>  [8] 0.6312104 0.7449587 0.5605141

This package also contains functionality for fitting a Kimura distribution to a heteroplasmy sample using the method of moments. This has in the past been used to carry out a Kolmogorov-Smirnov test to assess discrepancy between the sample and the fitted distribution (Wonnapinij et al., 2008).

❗ However, since Wonnapinij et al. (2008), it has been found that a method-of-moments fit does not provide the best-fitting version of the Kimura distribution for a given heteroplasmy sample. Such a fit will often produce a distribution that is a bad fit to the data, and therefore a false positive signal of selection, whereas a differently fitted distribution would given no such signal. This issue is described in Giannakis et al. (2023).

❗ It is not recommended to assess selection by fitting a Kimura distribution to snapshot heteroplasmy data -- time series data is more appropriate for this task. This repository github.com/kostasgian21/heteroplasmy contains functions to identify better Kimura fits than method of moments.

References

Wonnapinij, Passorn, Patrick F. Chinnery, and David C. Samuels. “The distribution of mitochondrial DNA heteroplasmy due to random genetic drift.” The American Journal of Human Genetics 83.5 (2008): 582-593.

Kimura, Motoo. “Solution of a process of random genetic drift with a continuous model.” Proceedings of the National Academy of Sciences of the United States of America 41.3 (1955): 144.

Giannakis, K., Broz, A.K., Sloan, D.B. and Johnston, I.G., 2023. Avoiding misleading estimates using mtDNA heteroplasmy statistics to study bottleneck size and selection. G3: Genes, Genomes, Genetics, 13(6), p.jkad068.

This package started out as a toy reimplementation of lbozhilova/Kimura-Distribution.