Organelle gene diversity under migration, mutation, and drift: equilibrium expectations, approach to equilibrium, effects of heteroplasmic cells, and comparison to nuclear genes.

TLDR

Approximate equilibrium equations for organelle gene diversity and GST can be derived by substituting effective gene numbers and migration rates into nuclear gene equations, but these approximations fail when within‑individual diversity exceeds between‑individual diversity, as often occurs in the animal mtDNA D‑loop. The study develops stochastic population‑genetic theory for mitochondrial and chloroplast genes using an infinite‑alleles model suited to molecular data. The authors modeled mutation, drift, and migration in a finite island framework, derived recurrence equations for gene diversity within and between colonies, and used computer solutions to examine the approach to equilibrium across parameters such as colony size, migration rates, sex ratios, paternal transmission, germ‑line divisions, effective organelle genome number, and mutation rate. They found that gene diversities equilibrate slowly while GST equilibrates rapidly; organelle genes often show greater subdivision than nuclear genes, yet for certain sex‑ratio ranges nuclear genes exhibit higher subdivision, and overall nuclear gene diversities exceed organelle diversities over a broader range of sex ratios in subdivided versus panmictic populations.

Abstract

Abstract We developed stochastic population genetic theory for mitochondrial and chloroplast genes, using an infinite alleles model appropriate for molecular genetic data. We considered the effects of mutation, random drift, and migration in a finite island model on selectively neutral alleles. Recurrence equations were obtained for the expectation of gene diversities within zygotes, within colonies, and between colonies. The variables are number and sizes of colonies, migration rates, sex ratios, degree of paternal transmission, number of germ line cell divisions, effective number of segregating organelle genomes, and mutation rate. Computer solutions of the recurrence equations were used to study the approach to equilibrium. Gene diversities equilibrate slowly, while GST, used to measure population subdivision, equilibrates rapidly. Approximate equilibrium equations for gene diversities and GST can be obtained by substituting Neo and me, simple functions of the numbers of breeding or migrating males and females and of the degree of paternal transmission, for the effective numbers of genes and migration rates in the corresponding equations for nuclear genes. The approximate equations are not valid when the diversity within individuals is large compared to that between individuals, as is often true for the D-loop of animal mtDNA. We used the exact equations to verify that organelle genes often show more subdivision than nuclear genes; however, we also identified the range of breeding and migrating sex ratios for which population subdivision is greater for nuclear genes. Finally, we show that gene diversities are higher for nuclei than for organelles over a larger range of sex ratios in a subdivided population than in a panmictic population.