Selection-mutation balance in polysomic tetraploids: impact of double reduction and gametophytic selection on the frequency and subchromosomal localization of deleterious mutations

Abstract

We modeled the behavior of recessive mutations with deleterious effects to either the sporophyte or the gametophyte, or both, in polysomic tetraploid populations by allowing for varying levels of double reduction, mutation, and self-fertilization. Double reduction causes a decrease of the equilibrium frequencies of deleterious alleles, and it has much more influence on genes subjected to gametophytic selection than on genes solely under sporophytic selection. With gametophytic selection, low frequencies of double reduction are enough to reduce equilibrium frequencies severalfold. Double reduction occurs when sister alleles migrate to the same gamete during meiosis. It depends on the frequency at which a locus recombines with its centromere, and on the frequency of multivalent formation. Therefore, a greater accumulation of deleterious mutations should occur on polysomic chromosomes with a prevalence of bivalent pairing and in chromosomal regions between centromeres and proximal chiasmata. Proximal loci should have a greater impact in reducing the fitness of a polyploid population being inbred. This prediction can explain observations that homozygosities at different subchromosomal regions have distinct effects on inbreeding depression in polyploids. Furthermore, even mildly deleterious alleles can lead to large amounts of inbreeding depression because of their high equilibrium frequencies. Molecular studies correlating level of heterozygosity and degree of heterosis should take into account this nonuniform distribution of deleterious alleles in polyploid genomes. Preservation or enhancement of heterozygosity would be more critical at proximal regions than at other chromosome regions in polysomic polyploid species.

Figure 1

Equilibrium frequencies, q_a, of the deleterious allele a in the absence of selfing or gametophytic selection. The frequency of double reduction is α, the mutation rate is μ, and the fitness of the aaaa genotype is 1 − s. For a diploid species under similar selection and mutation pressures the equilibrium allele frequencies are less than 0.35%.

Figure 2

Equilibrium frequencies, q_a, of a gametophytic lethal allele in the absence of selfing. The range of double reduction values, α, shown is only from 0 to 0.01, at which point most of the reduction in frequency has already taken place. The equilibrium frequencies for α = 0.17 are 5 × 10⁻⁵ and 5 × 10⁻⁶ when the mutation rates, μ, are 10⁻⁵ and 10⁻⁶, respectively.

Figure 3

Ratio of equilibrium frequencies of the deleterious allele (q_a) at a locus not subjected to double reduction compared with a locus subjected to a double reduction of 0.04 and of 0.17, upon different amounts of selfing. A applies in the absence of gametophytic selection (1 − g = 1), and B applies when the aa genotype is lethal to the gametophyte (1 − g = 0). For all cases we chose a mutation rate, μ, of 10⁻⁶ and lethality of the aaaa sporophytic genotype (1 − s = 0).

Figure 4

Change of fitness during the first three generations of selfing diploid and tetraploid populations in equilibrium (assuming a mutation rate of 10⁻⁶, random mating, and a deleterious allele lethal to homozygous sporophytes and double reduction rates α = 0, 0.04, and 0.17). The inbreeding coefficient F_i is obtained from the recurrence relations F_i = (1 + F_i−1)/2 and F_i = (1 + 2α + (5 − 2α)F_i−1)/6 for the diploid and the tetraploid populations, respectively (where i represents the number of generations of selfing and α the is rate of double reduction) (51). At generation 0 we stipulate an inbreeding coefficient of 0 and a fitness of 1.

Figure 5

Change of gametophytic viability under selfing of tetraploid populations in equilibrium (assuming a mutation rate of 10⁻⁶, random mating, and a deleterious allele lethal to homozygous sporophytes or gametophytes). The value of 1 is given to the gametophytic viability of generation 0.