Proc. NatI. Acad. Sci. USA Vol. 81, pp. 1764-1767, March 1984 Genetics Mitochondrial gene flow (population genetics/interspedfic gene flow/mitochondrial DNA) NAOYUKI TAKAHATA*t AND MONTGOMERY SLATKIN Department of Zoology, NJ-15, University of Washington, Seattle, WA 98195 Communicated by W. T. Edmondson, November 28, 1983 ABSTRACT To account for the transmission of mitochon- drial genotype because of the linkage disequilibrium between drial DNA between Nonspecific species Drosophila pseudoob- them. This could be important for interspecific gene flow scura and D. pprsimilis in sympatry reported by J. R. Powell especially, because it is reasonable to expect some selection [Powell, J. R. (1983) Proc. Nail. Acpd. Sci. USA 80, 492-495], against hybrids. Powell (1) proposes selection against het- a simple model of gene flow and selection in infinite popula- erozygotes as one mechanism for preventing the interchange tions is analyzed. The model assumes two alleles at each of two of nuclear genes among the two Drosophila species. Another loci, one of which is coded by an autosome and the other' by mechanism Powell suggests is assortative mating. If the hy- mitochondrial DNA. Viability selection is'presumed to be un- brids are able to mate with only one of the parental species derdominant-i.e., heterozygous inferiority to the homozy- and the backcrosses tend to mate with the same parental spe- gotes- at an autosomal locus, and neutral or deleterious at a cies, then nuclear and mitochondrial gene flow between spe- mitochondrial locus, with'the combined action being multipli- cies could be lower than expected on the basis of'the number cative. Extremely strong selection against heterozygotes may of hybrids observed. We will not consider this possibility prevent the transmission of mitochondrial DNA between two here, but we will show that the available data are consistent species, but otlerwise the transmission can easily occur over with a model that does not incorporate this effect. species bptindaries. The rate of opproach to equilibrium is de- termined by the level of gene flow and is not affected much by Model and Analysis selection against an autosomal locus. The divergence'of the nu- We consider a simple model of two loci. One locus is carried clear genomes of thp two species is reexamined. Based on pub- lished data on enzyme loci, we conclude that there has been by an autosomal' chromosome and the other is carried by an mitochondrial gene flow between these species for a long extranuclear (mitochondrial or chloroplast) chromosome. enough time that several nuclear loci examined could diverge We assume two alleles at each locus and denote them A and because of accumulation of neutral mutations. a for autosomal alleles and M and m for extranuclear alleles. Assuming the completely maternal inheritance of extranu- clear chromosomes (8), we can treat the extranuclear locus Three recent studies have shown that the geographic pat- as haploid and represent the types of female gametes by AM, terns exhibited by mitochondrial DNA do not necessarily co- Am, aM, and am and the male gametes by A and a. The incide with the geographic patterns of anatomical traits and genotypes of the individuals are, therefore, represented by of nuclear genes. Powell (1) has suggested the interspecific the pairs of these gametes as given in Table 1. transfer of mitochondrial DNA between Drosophila pseu- We consider a randomly mating population that is of effec- doobscura and D. persimilis in their region of sympatry, tively infinite size but that exchanges only females with a even though the two species are distinguishable on cytologi- population (representing the other species) consisting of aam cal and behavioral grounds (2) and have differentiated at sev- individuals. Immigration of males does not alter the follow- eral nuclear loci (3, 4). Ferris et al. (5) have found a similar ing treatment by much, but we assume that hybrid males are pattern in two subspecies of Mus musculus: M. m. musculus sterile, as is usually observed in conspecific matings (see ref. in Scandinavia contains mitochondrial DNA of the species 1 and refs. therein). We assume that selection occurs only M. m. domesticus. Yonekawa'et al. (6) showed there is mito- through the difference in viability. For the autosomal locus, chondrial gene flow between two subspecies of M. muscu- we assume underdominance (the heterozygote inferior to the lus. In Japan, only one subspecies is found, M. m. molos- homozygotes) to model a locus assumed'to be responsible sinus, which is homogeneous in morphology and in electro- for the reproductive isolation between the two populations in phoretically detectable nuclear loci. In the northern part of question. Thus, we consider only the case s > 0, but we do Honshu and in Hokkaido, however, the mitochondrial DNA not exclude the possibility of a large s, which may be as large is apparently the same as that in another subspecies, M. m. as 0.5 or more because of lowered viability of F1 hybrids and castaneus, which occurs in southern China and the Philip- because of backcross progeny. For the extranuclear locus, pines. In light of these findings, it is appropriate to investi- on the other hand, we assume neutrality or selective disad- gate the theory of. mitochondrial gene flow with particular vantage of the m Allele (t . 0). The selection regime is also reference to the conditions under which the geographic pat- given in Table 1. Immigration of females, random mating, terns exhibited by mitochondrial and nuclear genes differ. and selection are assumed to occur in this order, and the In this paper we will analyze a simple model of gene flow generations are nonoverlapping and discrete. and selection affecting both mitochondrial and nuclear Let g be the immigration rate of females per generation, genes, and we use this model to discuss the data of Powell and P1, P2, P3, and P4 be the gamete frequencies ofAM, Am, (1). We will consider, in particular, the association between aM, and am in females, and Pt and PI be the frequencies of mitochondrial and autosomal loci generated by gene flow A and a in males. (7). It is possible, at least, that selection at an autosomal lo- cus could the establishment of a neutral mitochon- prevent *Permanent address: National Institute of Genetics, Mishima, 411 Shizuoka-ken, Japan. The publication costs of this article were defrayed in part by page charge tPresent address (until Aug. 31, 1984): Center for Demographic & payment. This article must therefore be hereby marked "advertisement" Population Genetics, University of Texas at Houston, Houston, in accordance with 18 U.S.C. §1734 solely to indicate this fact. TX 77225. 1764 Downloaded by guest on September 24, 2021 Genetics: Takahata and Slatkin Proc. Natl. Acad. Sci. USA 81 (1984) 1765 Table 1. Combinations of female gametes (AM, Am, aM, and W am) and male gametes (A and a) _ q" = (1 - t)(2 (1) ) )+ sq q AM Am aM am [6b] t A 1 1 - t 1 - S (1 - S)(1 - t) + -f(1 - s - 2q)p + (1 - s)qr] a 1 - S (1- S)(1 - t) 1 1 - t 2 Relative viabilities of the six genotypes are shown, assuming mul- tiplicative action of nuclear and extranuclear genes and underdomi- 1 g r" = s(2q - 1)p + (1 - sq)r, [6c] nance at the nuclear locus; 1 - s is the relative viability ofautosomal heterozygotes and 1 - t is the relative viability of individuals carry- ing the m extranuclear allele. where After immigration, the gamete frequencies in females change from Pi (i = 1, 2, 3, 4) to W = A0(q) + Al(q)p + A2(q)r, AO(q) = (1 - t)[1 - s(q + q' - 2qq')], [q' = (1 - g)q] [7] P! = (1 - g)Pi (i = 1, 2, 3) Al(q) = st(1 - g)(2q - 1), [1] 1~~~~~~~= A2(q) = t(l - g)(1 - sq). P4 + ( - 9)P4 I pi= l , Neutral Mitochondrial Genes (t = 0) but no change occurs in males-i.e., P*' = P* (i = 1, 2), where the primes denote the frequencies after immigration. We study first the case in which the extranuclear genes are Random mating and the subsequent viability selection selectively neutral to find the effect of an underdominant nu- change the gamete frequencies in the next generation. The clear gene on an extranuclear one. In this case, Eq. 6b be- mean fitness of the population is given by comes W = Pt'[P' + (1 - t)P2 + (1 - s)P3 + (1 - s)(1 - t)P4] wo q,, = [(2 g)(1 s) + sq1q + P2*'[(1 - S)PW + (1 - s)(1 - t)P2 + P [2] [8] 1 g 2( 1- g) + (1 - t4], in which and the gamete frequencies in females become WO = 1 - s[q + q' - 2qq']. WP'X = PiPt' + (1 - s)(PiPt' + P'Pt')/2 [3a] On the other hand, Eqs. 6a and 6c do not change except for the replacement of W by W0. WP2 = (1 - t)[P2Pt' + (1 - S)(P2PI' + P'Pt')/2] [3b] We first examine their equilibrium properties. From Eq. 8, WP'3 = P3PS' + (1 - S)(PiPl' + P3Pt')/2 [3C] it is readily seen that there are three equilibria for q, denoted qo, q_, and q+. Clearly, one equilibrium is WP'4 = (1 - t)[P4Pl' + (1 - S)(P2Pt' + P4Pt')/2]. [3d] Ao = 0 In a similar way, we can calculate the gamete frequencies in males and obtain the following relationship. and the other two are the solutions of Pt" = P'1 + P'2 (P2*" = P'3 + Pf4)- [4] g 4(1 g) q2 - 2(3 - 2g)q + + 2 - g = 0 [9] S Therefore, after one generation the frequencies of the auto- somal genes become the same in both sexes. Although only when s > 4g(1 - g).