LEADMIX is a Fortran program written by Jinliang Wang to estimate the admixture proportions and genetic drift using data on genetic markers, based on the likelihood method described in:
Wang, J. (2003) Maximum Likelihood Estimation of Admixture Proportions from Genetic Data. Genetics 164: 747-765.
It assumes (see Figure above) that ξ + ψ generations ago an ancestral population P0 was split into 2 parental populations (denoted by P1 and P2) which then evolved independently for ξ generations. At that point, a hybrid population, Ph, was instantaneously created by combining genes of proportions of p1 and 1– p1 taken at random from parental populations P1 and P2, respectively. After the hybridization (admixture) event, the 3 populations evolve independently for ψ generations, when a sample is taken from the hybrid and each of the 2 parental populations. The samples are then analysed for some markers (e.g. DNA sequence, microsatellites) and are used to estimate the admixture proportions p1 and the genetic drift occurred to each population.
In this model, there are 8 parameters involved. They are the admixture proportions (p1), the 2 periods of time (ξ and ψ, in generations), the 2 average effective sizes of the parental populations during period ξ (n1, n2), and the 3 average effective sizes of the parental and hybrid populations during period ψ (N1, N2, Nh). Rescaling time by the effective size of each population reduces the number of parameters to only 6, which are p1, ti = ξ /(2ni) (for i=1, 2) and Tj = ψ /(2Nj) (for j=1, 2, h). The parameter of particular interest is the admixture proportion p1. However, the other parameters (ti, Tj) are also important because they give information about the extent of genetic drift occurred to each population. LEADMIX can be used to obtain maximum likelihood estimates and 95% confidence intervals of all the 6 parameters jointly using a sample from each of the current hybrid and parental populations. The method and program apply to the case of more than 2 parental populations contributing to the admixture.