Heredity (2009) 102, 214–217 & 2009 Macmillan Publishers Limited All rights reserved 0018-067X/09 $32.00 www.nature.com/hdy ORIGINAL ARTICLE Dobzhansky–Muller incompatibilities and adaptation to a shared environment RL Unckless and HA Orr Department of Biology, University of Rochester, Rochester, NY, USA Natural selection might drive the evolution of postzygotic We show that the probability of evolving a DMI falls as reproductive isolation even when allopatric populations adapt selection coefficients among beneficial alleles become less to identical environments, an idea first suggested by Muller similar. The reason is that if one locus is under much (1942). Here, we analyze this scenario mathematically, stronger selection than the other, that locus is much more focusing on the evolution of a Dobzhansky–Muller incompat- likely to experience a substitution first in both populations. ibility (DMI) between populations. Our results identify a This precludes the development of a DMI, which requires potential problem with Muller’s scenario: adaptation to different substitutions in the two populations. identical environments can often involve substitution of the Heredity (2009) 102, 214–217; doi:10.1038/hdy.2008.129; same alleles, precluding formation of a hybrid incompatibility. published online 14 January 2009 Keywords: Dobzhansky–Muller model; hybrid sterility; reproductive isolation; speciation There can now be little doubt that natural selection plays later cause incompatibilities in hybrids formed between an important role in the evolution of postzygotic the populations. Second, allopatric populations might reproductive isolation. Over the last decade or so, adapt to the same environment but in different ways considerable work has shown that positive natural genetically. As populations can respond to identical selection plays a part in the evolution of both extrinsic selection pressures in different ways, two populations (ecological inviability or behavioral sterility) and intrin- might still arrive at different genotypes. If so, their sic postzygotic (hybrid inviability or sterility) isolation hybrids might still suffer incompatible gene combina- (reviewed by Coyne and Orr, 2004). Although the former tions. This scenario was first described by Muller (1942). role is perhaps not surprising—it seems intuitively clear Here, we point out a potential problem with this that selection shapes divergence in characters of ecolo- identical environment scenario. The problem is that it is gical significance—the latter role was less expected. It harder than it might first seem for two populations to was not obvious that substitution at the genes causing adapt to an identical environment in different ways, intrinsic hybrid sterility or inviability is driven by thereby allowing the evolution of postzygotic isolation. positive natural selection. Nonetheless, molecular popu- The reason is that natural selection, although not lation genetic analysis of several genes known to cause deterministic, can often cause the substitution of the hybrid sterility or inviability, for example, OdsH, Nup96, same mutations in two populations. This can lower Lhr and Hmr, shows strong evidence of positive dramatically the chance of forming a hybrid incompat- Darwinian selection (reviewed by Coyne and Orr, 2004; ibility. This problem does not arise when incompatibil- Orr et al., 2007). It seems clear, then, that many of the ities result from adaptation to different environments. substitutions underlying genic (Dobzhansky–Muller) In this note, we calculate the probability of evolving a incompatibilities are driven by selection. (This selection DMI when natural selection drives adaptation to an was not, of course, selection for postzygotic isolation but identical environment. We consider the simplest scenario for some other character; this evolution pleiotropically in which allopatric populations evolve by substitution of gives rise to lowered fitness in hybrids.) recurrent new mutations. Natural selection might drive the evolution of Dobz- hansky–Muller incompatibilities (DMIs) in two ways. First, allopatric populations might adapt to their respec- The model tive—and different—environments and hybrid sterility We begin by considering two allopatric populations that or inviability might arise as a pleiotropic side effect of experience no gene flow. These populations begin with this divergent selection. One population, for example, identical genotypes (both are fixed for wild-type alleles might adapt to a dry environment and another to a wet. at all relevant loci) and experience identical environ- The genes underlying these ecological adaptations might ments. At some point in time this shared environment changes and the populations begin to adapt to the new, Correspondence: RL Unckless, Department of Biology, University of but still shared, environment. (Environments need not be Rochester, 485 Hutchison Hall, Rochester, NY 14627, USA. E-mail: [email protected] strictly identical; formally, our calculations assume only Received 29 August 2008; revised 26 November 2008; accepted 7 that those aspects of the environment that affect selection December 2008; published online 14 January 2009 coefficients at the loci we follow are the same.) Mutation Hybrid incompatibilities in a shared environment RL Unckless and HA Orr 215 is recurrent and evolution involves the substitution of genotypes, is one minus the probability that all a popu- aÀ1 new mutations. We assume that all mutations have lations arrive at the same genotype: PDM ¼ 1À1/2 . independent effects on fitness. Following Gillespie (1984, 1991), we consider the strong selection (Nsb1) and weak Selection: two loci mutation (Nm51) domain. Results involving weak selection and/or strong mutation (for example, NmB1) Now consider the evolution by natural selection. In the might well differ. special case in which sA ¼ sB, matters are again simple. Following Nei (1976), we can simplify our analysis by Because A1 and A2 are equally likely to fix first in a considering haploids. This captures the essence of our population, there is again a one-fourth chance both problem without requiring us to deal with unnecessary populations evolve to be A1B0 and a one-fourth chance details about the dominance of incompatibilities. In the both evolve to be A0B1; the probability that two populations case of a two-locus DMI, both populations initially have arrive at different genotypes, causing postzygotic isolation, 1 genotype A0B0. In the new environment, mutations A1 is thus again PDM ¼ 2, as noted by Gavrilets (2004). Finding and B1 are beneficial. But, when brought together, A1 and the probability of incompatibility with arbitrary sA and sB is B1 cause an in compatibility. Relative fitnesses among not so straightforward, however. genotypes are: To find this probability, we take advantage of several results obtained by Gillespie (1984, 1991). Gillespie A B 1 considered a large population in which beneficial 0 0 5 A1B0 1+sA mutations are sufficiently rare (Nu 1) to have indepen- A0B1 1+sB dent fates (that is, clonal interference does not occur) and A1B1 1Àt, in which beneficial mutations have definite fitness advantages (Nsb1). Standard population genetic theory where sA, sB, and t are all positive. shows that a new beneficial mutation has a probability of PE Note that, once A1 is fixed in a population, B1 cannot fixation of 2s, where the approximation assumes that be fixed as this would yield the unfit A1B1 genotype; s is fairly small (Haldane, 1927). Because most new similarly, once B1 is fixed, A1 cannot be fixed. We assume mutations are lost accidentally, it takes time before that rates of mutation to A1 and B1 are equal; back- recurrent mutation produces a copy of a beneficial allele mutation to A0 and B0 is not allowed. that is destined to sweep to fixation. Gillespie showed A DMI arises if one population evolves the A1B0 that the waiting time to the appearance of such a genotype and the other evolves the A0B1 genotype, mutation is geometrically distributed with a mean of allowing formation of unfit A1B1 hybrids if the popula- 1/(2Nus) generations (in diploids, 1/(4Nus)). For a A0B0 tions were to come into contact. A DMI cannot occur if population, the mean waiting time to fixation of A1 is both populations evolve the same genotype, either A1B0 1/(2NusA) generations and the mean waiting time to or A0B1. In this case, hybrids between the populations fixation of B1 is 1/(2NusB) generations. As each of these would retain a pure-population genotype and would be times is approximately exponentially distributed, the perfectly fit. probability that A1 fixes first in a population equals the We calculate the ultimate probability that two loci probability that an exponential random variable with a form a DMI, PDM, that is, the probability that populations mean of 1/(2NusA) is smaller than an exponential arrive at incompatible genotypes after an extended random variable with a mean of 1/(2NusB). Gillespie (essentially infinite) period of time; in effect, then, we shows that this probability is PA ¼ sA/(sA þ sB). Conver- assume that taxa remain allopatric for very long periods sely, the probability that B1 fixes before A1 is PB ¼ of time. Note also that the loci we follow are capable of sB/(sA þ sB). Note that these values are independent of causing a hybrid incompatibility if they evolve in the population size (so long as it is large). P P ¼ ‘right’ way in our populations. PDM represents, therefore, As A and B are identical in our a 2 populations, a conditional probability: given that the loci we follow the probability that one population becomes A1B0 and are capable of causing a hybrid incompatibility, what is the other A0B1, yielding a DMI, is the probability that they do so? 2sAsB PDM ¼ 2 ð1Þ ðÞsA þ sB The neutral case Though mathematically trivial, it is worth first consider- This probability is maximized when sA ¼ sB and ing the case in which the evolution is neutral: sA ¼ sB ¼ 0. PDM ¼ 1/2. This maximum probability of incompatibility We will see that this scenario represents a limit in the is identical to the probability of incompatibility under case of evolving a hybrid incompatibility by natural neutrality.