THE DYNAMICS OF MITOCHONDRIAL MUTATIONS CAUSING MALE INFERTILITY IN SPATIALLY STRUCTURED POPULATIONS

Mitochondria, often referred to as the “power house of the cell,” are organelles responsible for the majority of ATP production in eukaryotic cells. From an evolutionary perspective, mitochondria are interesting because they are derived from free-living bacteria and carry their own genome. In animals, this genome is particularly prone to mutations (Lynch et al. 2006), and these mutations can cause mitochondrial dysfunction that may lead to a variety of diseases (Taylor and Turnbull 2005). Given the crucial role of mitochondria in sperm development and function (e.g., Mitchell et al. 1976; De Martino et al. 1979; Cardullo and Baltz 1991; Mackenna et al. 1995), it is not surprising that mutations in mitochondrial DNA can also cause male infertility. In humans, mtDNA point mutations have been identified whose presence strongly correlates with low sperm motility or number (Spiropoulos et al. 2002; Selvi Rani et al. 2006), and male infertility can be associated with a distinct mtDNA haplogroup (Ruiz-Pesini et al. 2000; but see also Pereira et al. 2005; Bandelt 2007). Similarly, a mtDNA haplotype was found to be associated with low male fertility in a population of European hares (Smith et al. 2010). Mitochondrial mutations that impact male fertility have also been reported in mice (Nakada et al. 2006), the seed beetle Callosobruchus maculatus (Dowling et al. 2007), and Drosophila melanogaster (Clancy 2008; Clancy et al. 2011). Interestingly, in the latter two species sexually antagonistic fitness effects of mitochondrial genotypes were reported, that is, fitness effects were of opposite sign in males and females (Dowling et al. 2007; Rand et al. 2001).

Unlike nuclear genes, mitochondria are exclusively transmitted from mother to offspring in most species. This means that selection only acts on mtDNA variants that result in fitness variation in females. Mitochondrial mutations that cause male infertility but are neutral in females will therefore not be selected against and can spread in a population through random genetic drift (Frank and Hurst 1996), a phenomenon sometimes referred to as “mother’s curse” (Gemmel et al. 2004). However, this argument applies only when individuals mate randomly within the population. When there is inbreeding, we can expect that females harboring the mitochondrial mutation will also suffer to some extent from this mutation because they tend to mate more often with infertile males (e.g., their brothers) than females carrying the wild-type mitochondria. This effect can produce selection against male infertility mitochondrial mutations in inbreeding populations (Unckless and Herren 2009; Wade and Brandvain 2009). Conversely, with outbreeding (inbreeding avoidance) there can be even weak positive selection for male-deleterious mutations because males carrying the mutation reduce the fitness of wild-type females more than that of mutant females (Engelstädter and Charlat 2006). Recently, Hedrick (2011) generalized these models to arbitrary levels of assortative mating and obtained results that are in agreement with the earlier findings.

All of the above theoretical studies assume a single, undivided population. By contrast, a feature of virtually all natural populations is a certain degree of geographical population structure where individuals form subpopulations connected by migration. Population structure is well known to influence the rates of inbreeding and outbreeding in local populations (Wright 1951, 1978) and the efficacy of selection. On the one hand, population structure leads to an increased rate of inbreeding, which increases the probability of expressing recessive mutations in homozygotes and thereby increases the efficacy of selection against deleterious recessive mutations (e.g., Whitlock 2002). On the other hand, one important effect of population subdivision is local random genetic drift, which will reduce the efficacy of natural selection (e.g., Cherry and Wakeley 2003; Roze and Rousset 2003; Whitlock 2003). However, this effect is not expected to change the fixation probability of a beneficial mutation with additive effects (Maruyama 1970) unless populations are very small (Roze and Rousset 2003) or population extinctions occur (Whitlock 2003). This is because the reduced efficacy of selection is outweighed by the increased total effective population size of subdivided populations. Nevertheless, the rate of fixation of such mutations is slowed compared to a single undivided population (Cherry and Wakeley 2003; Whitlock 2003). Based on these earlier findings, we expect that population subdivision will have a major effect on the evolutionary dynamics of sexually antagonistic mutations by both impeding and enhancing selection, depending on the trade-off of selection pressures in each sex.

Here, we investigate the influence of spatial structure on the spread of mitochondrial mutations that influence male fertility. Our model covers both mutations that induce infertility in males but are neutral in females, and sexually antagonistic mutations. We derive analytical results for a limiting case of Wright’s island model (assuming an infinite number of demes) and study the full model through extensive computer simulations. In addition, we study the impact of sex-specific migration rates and of nearest-neighbor dispersal (i.e., stepping-stone models). Our results show that across a wide range of scenarios, male fertility effects in concert with pronounced population structure can strongly affect the spread of mitochondrial mutations.

Methods

Results

ANALYTICAL RESULTS

To obtain analytical insights into our model, we studied the special case of a population with infinitely many demes of finite size. For simplicity, we assumed equal migration rates in males and females. In what follows, we give the main results of this investigation; the full derivations are detailed in the Appendix.

Under the assumption of weak selection (i.e., both s_f and s_m are small), the effective selection coefficient acting on the mitochondrial mutant genotype was derived as

(1)

(2)

(see eqs. A11 and A12). Here, is the probability of within-deme coalescence of two individuals sampled from a deme without replacement. Equation 1 shows that the effective selection coefficient consists of two terms. The first term describes how population subdivision decreases the efficacy of selection on female fecundity through the effects of local genetic drift. Population subdivision causes increased homogeneity in allele frequencies within demes, thereby reducing this component of selection by a factor . By contrast, marked population subdivision—as quantified by a high value of —increases the weight of the second component of selection that captures the effect of male fertility. This is because a high value of implies a high degree of inbreeding within demes, so that the fitness of mutant females will be strongly affected by the reduced fertility of the mutant males.

From equation 2 it follows that the condition for the mutation to spread, , can be expressed as

(3)

It can be seen that for every value of s_f there is a minimum value of s_m above which the mutation is selected for and below which it is selected against. When s_m=0, the mutation will be selected for whenever s_f>0, and equation 1 recovers the form previously found for nuclear mutations in diploids with additive fitness effects (e.g., Whitlock 2003). Conversely, when s_f=0, the mutation will spread if and only if s_m>0. Thus, in contrast to panmictic populations, a mutation without effects on female fecundity that reduces the fertility of males (s_f=0 and s_m<0) will be selected against in a structured population. Sexually antagonistic mutations that increase female fecundity but decrease male fertility (s_f>0, s_m<0) may also be selected against if population structure is sufficiently strong (i.e., N and m are both sufficiently small). Figure 1A and B illustrate equation 3 for different values of N and m.

We can also ask under what conditions population subdivision enhances the spread of a mitochondrial mutation compared to the spread in a panmictic population. This will be the case when , which simplifies to s_mm(2−m)>s_f. Figure 1C shows that for sexually antagonistic mutations, population structure always inhibits the spread of the mutation when s_f>0, s_m<0, but always enhances spread when s_f<0, s_m>0. When the sign of the selection coefficient is the same in females and males, the effect of population subdivision in enhancing or inhibiting mutation spread depends on the migration rate m, but, interestingly, not on deme size N.

SIMULATION RESULTS: ISLAND MODEL WITH SEX-INDEPENDENT MIGRATION

Because the full model, assuming a finite number of demes of arbitrary size, was not tractable analytically we resorted to computer simulations. We first investigated the spread of a mitochondrial mutation that affects male fertility but is neutral in females (Fig. 2). As expected, this type of mutation behaves as a neutral mutation in an unstructured population (n=1), exhibiting a fixation probability of 1/N. However, in a structured population, the fixation probability of mutations decreasing male fertility (s_m<0) is reduced and the fixation probability of mutations increasing male fertility is increased relative to that of a neutral mutation (as expected from eq. 3). This effect becomes more pronounced with decreasing deme size when the total population size is kept constant. In a highly structured population consisting of n=120 demes with 2N=100 males and females in each deme, the fixation probability is strongly altered even with moderate negative effects on male fertility.

Figure 2 also shows that especially for a large number of small demes, the analytical approximation obtained from equation 3 is in very good agreement with the simulation results. Here, we inserted our expression for the effective selection coefficient (eq. 2) into Kimura’s (1962) formula for the fixation probability. In this case, this formula reads

(4)

where the effective population size is given by (e.g., Whitlock 2003). Interestingly, for s_f=0, equation 4 simplifies to

(5)

which indicates that the normalized fixation probability in that case (i.e., pnN) does not depend on deme size N, but only on deme number and migration rate.

We next considered mitochondrial mutations with sexually antagonistic effects. Figure 3 shows the estimated relative fixation probabilities for such mutations for different deme sizes, migration rates, and male fertility effects. The spread of a mutation that moderately increases female fecundity but substantially reduces male fertility is strongly impeded when the demes are small and the migration rate not too high (Fig. 3A). When the mutation is neutral in males (Fig. 3B), the fixation probability is similar to that in a panmictic population. Finally, when the mutation is beneficial in both females and males, population structure has a positive effect on the fixation probability, which, interestingly, is strongest for intermediate migration rates (Fig. 3C). Note that in all plots in Figure 3, the case of m=1 and N=3000 (i.e., n=2) is a special case in which the mutation can never become fixed because the individuals in the two demes are merely swapped in their entirety in every generation.

SIMULATION RESULTS: ISLAND MODEL WITH SEX-BIASED MIGRATION

In many species, females and males exhibit a different propensity to migrate. For example, migration is often male biased in mammals, whereas the opposite trend is found in birds (Greenwood 1980). It is therefore important to also consider the impact of such sex-biased migration on the spread of mitochondrial mutations.

Figure 4 shows estimates of the normalized fixation probability of different mitochondrial mutations for a wide range of female and male migration rates, m_f and m_m. When the mutation reduces male fertility, the fixation probability is strongly reduced unless either the male or the female migration rate is extremely high (Fig. 4A). As expected, when s_m=0, the male migration rate is of no consequence for the fixation probability (Fig. 4B). Finally, when the mutation is beneficial in males, a very high male migration rate leads to a slightly reduced fixation probability, but in general, male migration rate has little effect on the fixation probability (Fig. 4C).

Overall, our results show that, in contrast to standard mitochondrial population genetics, the male migration rate can have an influence on the fixation probability of mitochondrial variants (although with the parameter combinations screened here this effect is only seen for very high rates of male migration). This effect arises because both male and female migration rates influence the inbreeding rate within demes and thus the degree to which male fertility influences effective selection on the mitochondrial mutation. In the extreme case where m_m=1, all male offspring will leave their natal deme so that no inbreeding occurs within demes.

SIMULATION RESULTS: MIGRATION MODELS OTHER THAN WRIGHT’ ISLAND MODEL

So far, we have assumed Wright’s island model of migration only, in which migration is equally likely between all demes. To ascertain the robustness of our results with respect to this assumption, we obtained simulation results for two other, isolation-by-distance migration models: the stepping stone model (a one-dimensional string of demes connected by migration between adjacent demes) and the lattice model (two-dimensional version of the stepping stone model). In both cases, we assume that there are no border demes, that is, a ring or torus structure, respectively.

Our simulations indicate that the migration model has only weak effects on the fixation probability of mitochondrial mutations. For mutations that are neutral in females, the fixation probabilities of deleterious and neutral mutations in males do not depend on the migration model, as expected. For male beneficial mutations, increased population structure in the models of isolation by distance favors the spread of the mutation compared to the island model (Fig. 5) when the migration rate is high. This is expected from equation 1 because is higher in the isolation-by-distance models than in the island model. For low migration rates (), the fixation probabilities converge in the three models, as expected from the fact that in models of isolation by distance converges to that of the island model (Rousset 2004). A slightly lower fixation probability can still be observed in the stepping-stone model at low migration rates and with very small demes (Fig. 5). Under such circumstances, stochastic deme extinctions occur throughout the population, which impedes the spread of the mitochondrial mutation more in the isolation-by-distance models than in the island model. This effect, however, is seen only for a restricted set of parameter values and for cases of extreme population structure with a large number of very small demes and limited female fecundity (e.g., 2N=10, n=1200, f=6, in Fig. 5). Fixation probabilities for the lattice model are always intermediate between those of the stepping-stone and island models.

Discussion

Mutations in mtDNA that affect male fitness only are generally thought to be selectively neutral due to the maternal inheritance of mitochondria (Frank and Hurst 1996). Using both analytical methods and simulations, we have demonstrated here that mitochondrial mutations that reduce the fertility of males can be selected against when (1) the reduction in male fertility translates into a reduction in offspring number of the females that the male mates with, and (2) the population is subdivided into demes of small or moderate size. We will discuss both of these conditions in turn.

We have assumed that male fertility directly impacts offspring production: a female mating with a mutant male has (1+s_m) times as many offspring as the same female mating with a wild-type male. Whether this is a realistic assumption will depend on the mating system as well as other factors. When females have only a single mating partner during their lifetime as assumed in our model, male fertility translates directly into female offspring production. Thus, this is the mating system where we can expect the strongest effects with respect to selection on mitochondria through their male fitness component. With sequential monogamy, male infertility may also directly impair offspring production. However, in this as in other systems where females mate with several males, females may also compensate to some extent for the low fertility of one of their mating partners. For example, females may save resources from producing fewer offspring in one breeding season, and then produce more offspring in the next breeding season when mating with a fully fertile male. Similarly, where females mate with multiple males in the same breeding season, they may compensate low sperm number or mobility from one male with normal sperm from another male. In the extreme case, a female that mates with both a mutant and a wild-type male may not suffer any reduction in her offspring production through infertility of the mutant male. In line with this reasoning, remating by a female has been shown to lead to increased offspring production in several species of Drosophila, which can be interpreted as an insurance against male sterility and subfertility (Singh et al. 2002). In spite of these and related effects, we expect the results of our model to be robust with respect to the details of the mating system as long as the term (1+s_m) is interpreted not as the fertility of a male per se, but as the average change in offspring number of his female mating partners.

The second condition for selection on male-infertility mitochondrial mutations is that males carrying the mutation mate nonrandomly with females carrying the same mutation. The most straightforward scenario where this will happen is when females have a mating preference for related (inbreeding) or unrelated males (outbreeding or inbreeding avoidance). Inbreeding, modeled as nonrandom mating within a single population, has been shown to produce selection against male infertility mitochondrial mutations (Unckless and Herren 2009; Wade and Brandvain 2009), whereas outbreeding produces weak positive selection for such mutations (Engelstädter and Charlat 2006). In our model, inbreeding is a natural consequence of geographical population structure: with small demes and low migration rates, females are more likely to mate with relatives carrying the same mitotype than in a large panmictic population. As our results show, this can produce strong selection against male-infertility mutations even though mating is completely random within demes.

In contrast to male infertility mitochondrial mutations, population structure reduces the strength of selection on mutations that affect female fitness only. This is in accord with existing theory of nuclear genes (e.g., Maruyama 1970; Roze and Rousset 2003; Whitlock 2003). Putting the two components of selection through female and male effects together, it can be seen that population structure has a twofold effect on the fate of sexually antagonistic mutations: it reduces the efficacy of the female component but increases the efficacy of the male component of selection (see eq. 1). As a result, when both deme size and migration rate are sufficiently small, a large negative fitness effect on males can outweigh a small positive effect in females. Specifically, a female-beneficial but male-deleterious mutation will be selected against when the ratio of selection coefficients −s_m/s_f is larger than the number of females per deme (see eq. 3).

Mitochondrial mutations that impair male fertility have been reported in many animals as well as in humans (Gemmell et al. 2004; St. John et al. 2005; O’Flynn O’Brien et al. 2010). Because there is no direct selection on mitochondria through male fitness effects, this observation raises the question of what evolutionary forces keep these mutations in check. One obvious explanation is that these mutations are also deleterious in females. If these fitness effects in females are weak, these mutations may be maintained at a low frequency in the population through mutation-selection balance. Our model shows that in this case, population structure either weakens or strengthens selection against such mutations, depending on the migration rate (see Fig. 1C). A second explanation that applies for male infertility mutations that are neutral in females is that there will be strong selection at nuclear loci for compensatory mutations that ameliorate the male deleterious effect of the mitochondrial mutations. This notion is supported by reports of mitonuclear epistasis in animals (Rand et al. 2004; Dowling et al. 2008), and in particular the recent finding that mtDNA variation strongly impacts nuclear gene expression in male Drosophila, especially in the testes and accessory glands (Innocenti et al. 2011). Finally, our model offers the alternative explanation that population structure, acting in concert with deleterious effects of male infertility on female fecundity, can produce immediate selection against male infertility mitochondrial mutations that are neutral in females. Given that pronounced population structure as well as limited numbers of mates are common features of many species, we speculate that this effect could also contribute substantially to preventing mtDNA mutations from spreading. For humans, where ancient societies lived in small groups, this explanation might be especially attractive.

Associate Editor: N. Perrin