A Test of the Snowball Theory for the Rate of Evolution of Hybrid Incompatibilities

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Science  17 Sep 2010:
Vol. 329, Issue 5998, pp. 1518-1521
DOI: 10.1126/science.1193440


Hybrids between species are often sterile or inviable because the long-diverged genomes of their parents cause developmental problems when they come together in a single individual. According to the Dobzhansky-Muller (DM) model, the number of genes involved in these “intrinsic postzygotic incompatibilities” should increase faster than linearly with the divergence time between species. This straightforward prediction of the DM model has remained contentious owing to a lack of explicit tests. Examining two pairs of Drosophila species, we show that the number of genes involved in postzygotic isolation increases at least as fast as the square of the number of substitutions (an index of divergence time) between species. This observation verifies a key prediction of the DM model.

Biological speciation involves the evolution of barriers to gene flow between two populations (1, 2). One of the most effective of those barriers, because it is considered irreversible, is “intrinsic postzygotic isolation,” the developmentally based inviability or sterility of species hybrids. Dobzhansky (1) and Muller (3) proposed a simple two-locus model showing how this form of isolation can result from the accumulation of genes that function normally in a pure-species genome but produce epistatic interactions in hybrids.

The classic version of the Dobzhansky-Muller (DM) model, a population-genetics theory for the evolution of reproductive isolation (2), begins with two loci in an ancestral species having genotype A1A1B1B1 (the model can be expanded to more than two loci). The ancestral species then splits into two geographically isolated descendant species that eventually evolve genotypes A1A1B2B2 and A2A2B1B1 through natural selection, genetic conflict, or sexual selection—or (less likely) genetic drift—that fixes allele A1 in one species and B1 in the other. The DM model posits that postzygotic isolation arises as a collateral effect of this evolutionary divergence. In this case, although species having genotypes A1A1B2B2 and A2A2B1B1 at two loci are fit, in hybrids, where the B2 and A2 alleles first encounter each other, they interact abnormally, producing sterility or inviability (15).

Although several studies have identified genes causing hybrid incompatibilities (48), little is known about the evolutionary rate at which these incompatibilities arise (9, 10). Mathematical modeling has shown that the expected number of two-locus DM incompatibilities should increase as fast as the square of the number of substitutions between two species, the “snowball effect” (11, 12). (Three-way interactions should increase as fast as the cube of the number of substitutions between two species, and so on.) This is because DM interactions occur between two or more genes from different species, and if individual gene substitutions accumulate at a constant rate within each species, the number of negative epistatic interactions involving at least one gene from each species should grow at least with the square of time elapsed. Because this prediction requires counting genes causing hybrid incompatibilities in at least two different hybridizations between taxa of known divergence times, it cannot be tested in most groups of plants or animals (2, 1315).

We took advantage of the fact that Drosophila melanogaster females (mel) produce hybrid females when crossed with D. simulans (sim) and D. santomea (san) males (6, 1618) to test the snowball prediction of DM theory. We counted the number of incompatibilities that evolved since the divergence of each pair of species; the two pairs have divergence times differing by roughly 2.4 [mel-sim: 5.4 million years ago (Ma) and mel-san: 12.8 Ma (19)].

If we assume that DM interactions occur between pairs of loci, the snowball hypothesis leads us to expect at least six (~2.42) times as many incompatibilities between the older than between the younger species pair. We tested this prediction through fine-scale mapping and counting of the gene regions causing inviability in hybrid females (the only sex produced by both the mel × sim and mel × san crosses).

We crossed females from D. melanogaster stocks containing known genomic deletions, or “deficiencies” [Bloomington Drosophila Fly Stock Center (19)], maintained as heterozygotes against a balancer (Bal) chromosome carrying a dominant homozygous lethal mutation, to san and sim males. We determined the effect of each hemizygous region (presumably expressing recessive alleles from san or sim) on the viability of hybrid female offspring from the two interspecific crosses (Fig. 1). If a D. melanogaster deficiency uncovered a recessive region of the other species’ genome producing hybrid lethality when hemizygous in hybrids with D. santomea, this cross would produce Bal/san but not Df/san hybrid females (or, in hybrids with D. simulans, Bal/sim but not Df/sim) (Fig. 1) (6, 16). We considered “inviability regions” to be those yielding relative viability (i.e., the ratio of hybrid progeny carrying the chromosome deficiency to the total number of offspring from that cross) significantly below 0.5 (χ2 test; P < 0.05). This approach detects epistatic interactions between a recessive allele of D. santomea (exposed when hemizygous) and a dominant factor in the mel genome. Although it is not clear whether we uncovered genes directly involved in speciation—for their divergence may have occurred after speciation was complete—they do represent an evolutionary accumulation of hybrid incompatibilities and thus constitute a test of the snowball effect.

Fig. 1

Crossing scheme used to produce two classes of hybrid female offspring, one of which is hemizygous for a section of D. santomea genome uncovered by a deficiency from D. melanogaster. This example shows the cross of a mel female to a san male. If the deficiency does not uncover any lethal allele, half of the progeny will carry the FM6 balancer paired with a san X chromosome; the other half will carry the deficiency paired with a san X chromosome. Lethality or semilethality results in a dearth of deficiency-carrying offspring.

The mel/san crosses tested about 92.0% of the D. melanogaster genome (calculated as the proportion of total chromosome bands covered in our deficiency screening); the mel/sim crosses tested about 79.4% of D. melanogaster genome. Finally, to establish whether the deficiencies had an effect on within-species viability when heterozygous in D. melanogaster females, we measured the relative viability of deficiency-carrying females in crosses between D. melanogaster Df/Bal (mel Df/Bal) females and D. melanogaster ArkLa males (a stock founded by females from wild populations collected in Arkansas and Louisiana).

The interspecific deficiency screening in san/mel hybrids shows 71 nonoverlapping chromosomal regions containing genes involved in DM incompatibilities (Fig. 2 and table S1). In contrast, in sim/mel hybrids, we found just 10 regions involved in DM incompatibilities (Fig. 2 and table S2). None of the deficiencies that caused hybrid lethality showed reduced viability in intraspecific crosses, suggesting that the heterozygous-lethal effects are specific to hybrid backgrounds (table S3).

Fig. 2

Chromosomal locations of hybrid lethal regions (on a D. melanogaster cytological map) for D. melanogaster × D. santomea and D. melanogaster × D. simulans crosses. All lethal regions detected contain at least one gene involved in an epistatic interaction between a recessive element in the D. santomea (or D. simulans) genome and one or more dominant or semidominant factors in the D. melanogaster genome. Regions reducing viability in mel/san hybrids are shown in blue; those in mel/sim hybrids in red.

When possible, we used overlapping deficiencies to further localize inviability genes in each cross. This also ensured that the inviability observed with each lethal deficiency could be reproduced with an independent deficiency in the same chromosome region. Of the 71 regions that caused hybrid inviability in mel/san hybrids, 61 had overlapping deficiencies, and for each one of these 61 regions, at least one overlapping deficiency showed hybrid inviability. This shows that hybrid inviability is not an artifact of a stock’s genetic background and allowed us to further refine the mapping position of each inviability allele (Fig. 2 and tables S1 and S4).

We used Orr’s theoretical framework (4) to determine the existence of the snowball effect predicted by the DM model, that is, whether the number of genes causing inviability in these two pairs of crosses increased quadratically (or even faster) with their relative divergence times. Because there is no fossil record for these species, we estimated relative divergence times using a genetic proxy: the average number of synonymous substitutions per gene (Ks) between each of the two pairs across the whole genome (20). Under the assumption of an approximate molecular clock, Ks increases linearly with divergence time, and, unlike phylogeny-based estimates, the Ks-based estimates of divergence time need not be transformed with calibrations from fossils and make no assumptions about generation times (20).

We estimated Ks by counting the number of synonymous substitutions for the sim-mel (Ks sim-mel) and san-mel (Ks san-mel) species pairs for every sequenced gene shared by these species. These values were then averaged among genes to find the overall Ks (and its standard error, or SEM) for each pair of genomes (Ks sim-mel = 0.101, SEM = 4.03 × 10−4; and Ks san-mel = 0.242, SEM = 8.17 × 10−4). To establish whether the observed data fulfill theoretical expectations, we calculated the expected number of incompatibilities under two models: one in which incompatibilities accumulated linearly with the number of substitutions (i.e., absence of a snowball effect, which could reflect reproductive isolation caused by nonepistatic factors such as accumulated chromosomal rearrangements), and a model in which the expected number of incompatibilities was proportional to the square of the total number of DNA substitutions (i.e., the presence of a snowball effect involving two-locus interactions). In these calculations we included viability data only for deficiency stocks tested in both sets of crosses (65 incompatibilities in the mel × san cross and 10 in the mel × sim cross). To determine which model was more likely to explain the data, we used the AIC [Akaike Information Criterion (21)] scores of each model and calculated the evidence ratio of Akaike weights for the quadratic model over the linear model. These scores were then converted to the normalized probability that the quadratic model is preferred over the linear model (21).

The Ks values, the observed number of incompatibilities, the expected number of incompatibilities, and the results for all the model comparisons are shown in Fig. 3. These data show that the number of incompatibilities does not accumulate linearly with divergence time and is more consistent with a quadratic increase, as expected if the evolution of those incompatibilities obeys the snowball effect. This result holds regardless of which estimate of divergence time we use (Fig. 1 and figs. S1 to S3). We thus conclude that hybrid incompatibilities between these species accumulate substantially faster than linearly with respect to their divergence time.

Fig. 3

Number of observed and expected hybrid incompatibilities in san/mel and sim/mel F1 female hybrids. We fitted the linear and quadratic model that had lowest AIC values and forced the models through the origin (the assumption here is that at time zero, when there are no genetic substitutions between populations, there are no incompatibilities). P values are the normalized probability that each model is to be preferred over the other one (e.g., the quadratic model is to be preferred over the linear model and vice versa) according to the evidence ratio of Akaike weights. Deviations are highly significant for the linear model but not for the quadratic model, regardless of how we quantify “viability”; and in all cases the quadratic model explains the data better than the linear model. Different panels represent the four different definitions of “inviability”: (A) Lower than 0.5; (B) lower than 0.3; (C) lower than 0.1; and (D) equal to 0.

In addition to fitting the linear and quadratic models to regions that caused a relative viability lower than 0.5, we used more stringent criteria for inviability, fitting the two models to regions that showed relative viabilities lower than 0.3, 0.1, and 0. The results were similar in all cases (Fig. 1 and figs. S1 to S3) and revealed that, regardless of their size, deleterious epistatic interactions accumulate faster than linearly with divergence time.

Besides counting incompatibilities, our results can be used to identify and isolate genes causing reproductive isolation between species. Deletion mapping in D. melanogaster/D. simulans hybrids has identified two “hybrid inviability” genes with function in nuclear transport and whose divergence occurred via natural selection (6, 8, 22).

By confirming a key prediction of the DM theory and showing a snowball effect of the accumulation of genetic incompatibilities causing reproductive isolation, we support the view that postzygotic reproductive isolation often results from deleterious interactions in hybrids between genes that behave normally within species.

Supporting Online Material

Materials and Methods

Figs. S1 to S3

Tables S1 to S4


References and Notes

  1. Materials and methods are available as supporting materials on Science Online.
  2. We thank D. C. Presgraves, T. D. Price, R. Unckless, D. Kennedy, M. A. Sprigge, and M. Przeworski for discussions and reading of the manuscript; P. Andolfatto, T. Hu, and K. Thornton for sharing data; and A. Harris and J. Gladstone for technical help. Funded by NIH grant R01GM058260 (J.A.C.).
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