Mendel's First Law: partisan interests and the parliament of genes

Abstract

Mendel's First Law requires explanation because of the possibility of 'meiotic drivers', genes that distort fair segregation for selfish gain. The suppression of drive, and the restoration of fair segregation, is often attributed to genes at loci unlinked to the drive locus-such genes cannot benefit from drive but do suffer its associated fitness costs. However, selection can also favour suppressors at loci linked to the drive locus, raising the question of whether suppression of drive usually comes from linked or unlinked loci. Here, I study linked and unlinked suppression in a two-locus model with initial stable polymorphism at the drive locus. I find that the invasion rate of suppressors is a decreasing function of the recombination fraction between the drive and suppressor loci. Surprisingly, the relative likelihood of unlinked vs. linked suppression increases with the strength of drive and is insensitive to the fitness costs of the driver allele. I find that the chromosomal position of the driver influences how rapidly it is suppressed, with a driver in the middle of a chromosome suppressed more rapidly than a driver near the tip. When drive is strong, only a small number of chromosomes are required for suppression usually to derive from unlinked loci. In contrast, when drive is weak, and especially when suppressor alleles are associated with fitness costs, suppression will usually come from linked loci unless the genome comprises many chromosomes.

Fig. 1. Average establishment probability of a suppressor allele appearing at various recombination distances from the drive locus.

Dots are values from simulations; dashed lines are analytical predictions [Eqs. (2), (5), and (7)]. Parameters: s = 0.1, δ = 0.05.

Fig. 2. For various positions of the drive locus along a chromosome, the average establishment probability of a linked suppressor appearing at a random position on the chromosome (with each position assumed to be equally likely).

Results are displayed for several genetic lengths of the chromosome, assuming a uniform recombination rate and no crossover interference. Parameters: s = 0.1, δ = 0.05.

Fig. 3. The likelihood that suppression of drive derives from loci unlinked to the drive locus, rather than from linked loci, for various chromosome numbers and per-chromosome genetic lengths.

Chromosomes are assumed to be equally sized—relaxing this assumption will tend to increase the number of chromosomes required for suppression usually to be unlinked, for reasons explained in the text.