Can evolutionary rate matrices be estimated from allele frequencies?

This paper is a work in progress in which aims to combine the principles of population genetics and continuous-time Markovian evolutionary models to estimate evolutionary rate matrices from the current observed state of a single genome. A model is proposed in which sections of the genome which are not susceptible to natural selection are considered to be a statistical ensemble of individual genomic sites. Each site is a representative from a stationary distribution of allele frequencies 0 < 8 < 1 within the population. Simulations of this distribution via a finite-state Markov model based on a finite effective population size are compared with the stationary solution to the continuum Fokker-Planck equation. Parameters of the evolutionary rate matrix introduced via mutation rates within the Fokker-Planck equation are estimated for simulated data in a number of exploratory examples