Selection against heteroplasmy explains the evolution of uniparental inheritance of mitochondria

Abstract

Why are mitochondria almost always inherited from one parent during sexual reproduction? Current explanations for this evolutionary mystery include conflict avoidance between the nuclear and mitochondrial genomes, clearing of deleterious mutations, and optimization of mitochondrial-nuclear coadaptation. Mathematical models, however, fail to show that uniparental inheritance can replace biparental inheritance under any existing hypothesis. Recent empirical evidence indicates that mixing two different but normal mitochondrial haplotypes within a cell (heteroplasmy) can cause cell and organism dysfunction. Using a mathematical model, we test if selection against heteroplasmy can lead to the evolution of uniparental inheritance. When we assume selection against heteroplasmy and mutations are neither advantageous nor deleterious (neutral mutations), uniparental inheritance replaces biparental inheritance for all tested parameter values. When heteroplasmy involves mutations that are advantageous or deleterious (non-neutral mutations), uniparental inheritance can still replace biparental inheritance. We show that uniparental inheritance can evolve with or without pre-existing mating types. Finally, we show that selection against heteroplasmy can explain why some organisms deviate from strict uniparental inheritance. Thus, we suggest that selection against heteroplasmy explains the evolution of uniparental inheritance.

Fig 1. Uniparental inheritance replaces biparental inheritance for all tested parameter values.

(A) The three fitness functions when c _h = 1. Unless indicated otherwise, the parameters for B-F are n = 20, μ = 10⁻⁷, c _h = 0.2 and concave fitness. (B) U ₁ replaces B ₁. (C) U ₁ takes longer to replace B ₁ as n increases. (D) U ₁ takes longer to replace B ₁ as μ decreases. (E) U ₁ replaces B ₁ under all three fitness functions. (F) Number of generations for U ₁ to replace B ₁ across a range of costs of heteroplasmy. U ₁ replaces B ₁ even if the cost of heteroplasmy is extremely low.

Fig 2. Fitness and distribution of cell types.

Parameters: n = 20, μ = 10⁻⁴, c _h = 0.2 and concave fitness. U ₁ B ₂ cells appear at generation 0, which is the point at which the B ₁ and B ₂ gametes reach mutation-selection equilibrium. (A) Relative advantage of each genotype through time (see Model for details). For B-E, the relative proportion is the sum of a particular cell type divided by the sum of all cells that carry the same genotype. The heteroplasmic category includes all cells with any level of heteroplasmy. B-C shows the distribution of cells carrying the U ₁ B ₂ genotype (B) and the B ₁ B ₂ genotype (C). D-E show a more detailed distribution of cell types carrying the B ₁ B ₂ genotype at generation 1350 (D) and at generation 1820 (E). The decrease in heteroplasmy in B ₁ B ₂ cells between generations 0–100 is an artifact of introducing U ₁ at a frequency of 0.01 (the influx of U ₁ gametes homoplasmic for the wild type haplotype converts some heteroplasmic B ₁ and B ₂ gametes into homoplasmic gametes, which increases the proportion of homoplasmic B ₁ B ₂ cells). From generations 1350–1820, the proportion of heteroplasmic B ₁ B ₂ cells decreases (C) but the level of heteroplasmy increases (compare D with E). This more than offsets the decrease in the proportion of heteroplasmic cells and ${\overline{w}}_{B_1{B}_2}$ continues to decrease (A).

Fig 3. Fitness and distribution of gamete types.

Parameters: n = 20, μ = 10⁻⁴, c _h = 0.2 and concave fitness. U ₁ gametes appear at generation 0, which is the point at which the B ₁ and B ₂ gametes reach mutation-selection equilibrium. (A) Relative advantage of each gamete through time (see Model for details). For B-F, the relative proportion is the sum of a particular gamete type (e.g. a homoplasmic wild type U ₁ gamete) divided by the sum of all cells carrying that allele (all gametes carrying the U ₁ allele). Thus, the relative proportion describes how an allele is distributed across different gamete types but it does not show their actual frequencies in the population. The heteroplasmic category combines all gametes with any level of heteroplasmy. B-D show the distribution of gametes carrying the U ₁ allele (B), B ₁ allele (C) and the B ₂ allele (D). E-F show a more detailed distribution of gametes carrying the B ₁ allele at generation 1350 (E) and generation 1820 (F). The decrease in heteroplasmy in B ₁ and B ₂ gametes between generations 0–100 is an artifact of introducing U ₁ at a frequency of 0.01 (the influx of U ₁ gametes homoplasmic for the wild type haplotype converts some heteroplasmic B ₁ and B ₂ gametes into homoplasmic gametes). From generations 1350–1820, the proportion of heteroplasmic B ₁ and B ₂ gametes decreases (C and D) but the level of heteroplasmy increases (compare E with F). This more than offsets the decrease in the proportion of heteroplasmic cells and ${\overline{w}}_{B_1}$ continues to decrease (A). Around generation 1350, B ₂ gametes homoplasmic for mutant mitochondria begin to appear, which causes ${\overline{w}}_{B_2}$ to increase and eventually converge with ${\overline{w}}_{U_1}$.

Fig 4. Recombination and no mating types scenarios.

Parameters: n = 20, μ = 10⁻⁴, c _h = 0.2. (A) As the U allele initially spreads (generations 0–1700), the U ₁ B ₂/U ₂ B ₁ genotypes increase in frequency. But, because U ₁ B ₂ and U ₂ B ₁ cells lead to B ₁ B ₂ cells through meiosis and random mating, the U ₁ U ₂ genotype soon takes over and uniparental inheritance becomes fixed. Additional parameters: P _r = 0.5 and concave fitness. (B) Biparental inheritance dominates when U × U matings are biparental and fitness is concave. (C) Uniparental inheritance invades to its maximum value (0.5) when U × U matings are biparental and fitness is linear or convex. (The frequency of uniparental inheritance is the sum of U ₁ U ₂ and U ₂ B ₁.) Additional parameters: linear fitness. (D) U × U matings have a mixture of uniparental and biparental inheritance. Unlike in B, U ₁ U ₂ no longer becomes fixed because some U × U matings now have biparental inheritance and further increasing U ₁ U ₂ would only increase the overall level of biparental inheritance. Additional parameters: P _b = 0.1 and linear fitness. (E) Lines represent the frequency of uniparental inheritance in separate simulations with linear fitness and varying probabilities of biparental inheritance (P _b) when U × U matings have a mixture of uniparental and biparental inheritance. As P _b increases, U × U matings are more likely to lead to biparental inheritance, which decreases the frequency of uniparental inheritance at equilibrium. (F) No mating types scenario under concave fitness. F is identical to A except that the frequency of UB in F is the sum of the U ₁ B ₂ and U ₂ B ₁ freqencies in A.