Genetic Incompatibilities Between Mitochondria and Nuclear Genes: Effect on Gene Flow and Speciation

Abstract

The process of speciation is, according to the biological species concept, the reduction in gene flow between genetically diverging populations. Most of the previous theoretical studies analyzed the effect of nuclear genetic incompatibilities on gene flow. There is, however, an increasing number of empirical examples suggesting that cytoplasmically inherited genetic elements play an important role in speciation. Here, we present a theoretical analysis of mitochondrial driven speciation, in which genetic incompatibilities occur between mitochondrial haplotypes and nuclear alleles. Four population genetic models with mainland-island structure were analyzed that differ with respect to the type of incompatibility and the underlying genetics. Gene flow reduction was measured on selectively neutral alleles of an unlinked locus and quantified by the effective migration rate. Analytical formulae for the different scenarios were derived using the fitness graph method. For the models with haploid genetics, we found that mito-nuclear incompatibilities (MtNI) are as strong as nuclear-nuclear incompatibilities (NNI) in reducing gene flow at the unlinked locus, but only if males and females migrate in equal number. For models with diploid genetics, we found that MtNI reduce gene flow stronger than NNI when incompatibilities are recessive, but weaker when they are dominant. For both haploid and diploid MtNI, we found that gene flow reduction is stronger if females are the migrating sex, but weaker than NNI when males are the migrating sex. These results encourage further examination on the role of mitochondria on genetic divergence and speciation and point toward specific factors (e.g., migrating sex) that could be the focus of an empirical test.

Keywords: effective migration rate; fitness graph; gene flow; mathematical model; mitochondria; nuclear-cytoplasmic incompatibility; speciation.

Figure 1

Basic model structures. Model A: The island population initially consists only of individuals of genotype mt₁N₁, whereas the mainland is homogeneous for genotype mt₂N₂ (haploid genetics). After secondary contact, mating incompatibilities can occur between the mitochondrial haplotype (mt_i) and the nuclear genotype (N_j). Model B: The island population initially consists of individuals of genotype A₁B₁, whereas the mainland is homogeneous for genotype A₂B₂ (haploid genetics). After secondary contact, nuclear-nuclear incompatibilities (NNI) between A_i and B_j reduce the number of offspring in intergroup matings. Model C: The island population initially consists of individuals of genotype mt₁N₁N₁, whereas the mainland is homogeneous for genotype mt₂N₂N₂ (diploid genetics). After secondary, mating incompatibilities can occur between the mitochondrial haplotype (mt_i) and the nuclear genotype (N_jN_k). Model D: The island population initially consists of individuals of genotype A₁A₁B₁B₁, whereas the mainland is homogeneous for genotype A₂A₂B₂B₂ (diploid genetics). After secondary contact, nuclear incompatibilities (NNI) between A_iA_j and B_kB_l can occur. For all four models, gene flow was measured by allele frequency changes at a neutrally selected marker locus that is unlinked to the incompatibility loci (Methods). Before secondary contact, the marker allele is at fixation on the mainland, but absent on the island.

Figure 2

Fitness graph for haploid MtNI. Shown is the fitness graph for Model A (mito-nuclear incompatibilities, haploid genetics). There are eight genetic classes. Class transitions are indicated by black arrows and attached weighting factors. The edges correspond to the proportion of offspring after a cross with a resident individual, weighted by the fitness of the resulting genotype. The graph describes gene flow of rare male and female migrants of genotype mt₂N₂ in an island population consisting of mostly mt₁N₁ individuals. Blue indicates the migrant genotypes, gray the hybrid genotypes, and white the resident genotypes. Gene flow is measured at a neutrally selected nuclear marker locus, which is not shown in the graph (Methods).

Figure 3

Gene flow reduction for models with haploid genetics. Shown is the gene flow factor (values below 1 indicate a reduction of gene flow) for an unlinked neutral locus as a function of the level of incompatibility. (A) Model A with symmetric MtNI and varying incompatibility level s₁ = s₂. (B) Model A with asymmetric MtNI of type I (s₁ = 0) and varying incompatibility level s₂. (C) Model A with asymmetric MtNI of type II (s₂ = 0) and varying incompatibility level s₁. (D) Model B with symmetric (s_A = s_B) and asymmetric (s_B = 0) NNI. For the former, the gene flow factor is shown as a function of s_A = s_B, for the latter as a function of s_A.

Figure 4

Gene flow reduction for models with diploid genetics. Shown is the gene flow factor for an unlinked neutral locus as a function of the level of incompatibility. (A) Model C with recessive symmetric MtNI and varying incompatibility level s₁ = s₂. (B) Model C with recessive asymmetric MtNI of type I (s₁ = 0) and varying incompatibility level s₂. (C) Model C with recessive asymmetric MtNI of type II (s₂ = 0) and varying incompatibility level s₁. (D) Model D with symmetric (s_A = s_B) and asymmetric (s_B = 0) NNI. For the former, the gene flow factor is shown as a function of s_A = s_B, for the latter as a function of s_A. Parameters: h = h_A = 0.

Figure 5

Effect of dominance on gene flow reduction. Shown is the gene flow factor as a function of the dominance levels for Models C and D. (A) Symmetric MtNI vs. symmetric NNI for s = s₁ = s₂ = s_A = 0.5. (B) Symmetric MtNI vs. symmetric NNI for s = s₁ = s₂ = s_A = 1. (C) Asymmetric MtNI vs. asymmetric NNI for s = s₁ = s₂ = s_A = 0.5. (D) Asymmetric MtNI vs. asymmetric NNI for s = s₁ = s₂ = s_A = 1. The number of male and female migrants is equal for Model C, i.e., m_f = 0.5.