Asymptotic behavior of mean fixation times in the Moran process with frequency-independent fitnesses

TL;DR

This paper derives asymptotic formulas for mean fixation times in the Moran process with frequency-independent fitnesses, providing more accurate results for large populations and extending previous work to new initial conditions.

Contribution

It introduces new asymptotic formulas for fixation times in the Moran process, improving accuracy and covering additional initial conditions beyond prior studies.

Findings

More accurate asymptotic formulas for fixation times

Extension to initial conditions with fixed fractions of types

Results applicable to large population limits

Abstract

We derive asymptotic formulae in the limit when population size N tends to infinity for mean fixation times (conditional and unconditional) in a population with two types of individuals, A and B, governed by the Moran process. We consider only the case in which the fitness of the two types do not depend on the population frequencies. Our results start with the important cases in which the initial condition is a single individual of any type, but we also consider the initial condition of a fraction x, 0<x<1, of A individuals, where x is kept fixed and the total population size tends to infinity. In the cases covered by Antal and Scheuring (Bull Math Biol 68(8):1923-1944, 2006), i.e. conditional fixation times for a single individual of any type, it will turn out that our formulae are much more accurate than the ones they found. As quoted, our results include other situations not treated by them.