Hybrid Incompatibility “Snowballs” Between Solanum Species

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Science  17 Sep 2010:
Vol. 329, Issue 5998, pp. 1521-1523
DOI: 10.1126/science.1193063


Among the reproductive barriers that can isolate species, hybrid sterility is frequently due to dysfunctional interactions between loci that accumulate between differentiating lineages. Theory describing the evolution of these incompatibilities has generated the prediction, still empirically untested, that loci underlying hybrid incompatibility should accumulate faster than linearly with time—the “snowball effect.” We evaluated the accumulation of quantitative trait loci (QTL) between species in the plant group Solanum and found evidence for a faster-than-linear accumulation of hybrid seed sterility QTL, thus empirically evaluating and confirming this theoretical prediction. In comparison, loci underlying traits unrelated to hybrid sterility show no evidence for an accelerating rate of accumulation between species.

The Dobzhansky-Muller model of hybrid incompatibility [after (1, 2)] proposes that hybrid sterility and inviability are due to negative genetic interactions between two or more loci [commonly called “Dobzhansky-Muller incompatibilities” (DMIs)] that have accumulated substitutions in diverging lineages. When brought together in hybrids, alleles in each divergent lineage interact dysfunctionally, which results in reduced hybrid fitness (3). The action of DMIs is supported by empirical observation of the segregation of sterility in recombinant populations, and the molecular genetic description of individual interacting loci underlying hybrid incompatibility phenotypes (4, 5). The Dobzhansky-Muller model (3, 69) has produced empirically testable predictions including the “snowball effect”—the number of DMIs accumulating between lineages is expected to “snowball” (increase faster than linearly) with increasing time since lineage divergence (3, 6). Formally, because DMIs are due to gene interactions (epistasis), the number of expected DMIs increases with the square of the number of substitutions differentiating two lineages, when DMIs are due to pairwise epistasis; DMIs due to interactions among more than two loci are expected to accumulate even faster (6). Previous attempts to detect the snowball effect by measuring the strength of reproductive isolation between lineages, rather than the number of genes involved, have failed to find a greater-than-linear increase in sterility over time (1012). However, testing this theoretical prediction requires information on the number of DMIs contributing to specific isolating barriers among multiple closely related species, rather than simply their phenotypic effects on hybrid sterility (3, 6).

To evaluate the expected snowball of DMIs, we used data from three quantitative trait loci (QTL) mapping experiments among species in the plant genus Solanum (1315). Each QTL experiment used a unique library of hybrid introgression lines [near-isogenic lines (NILs)] in which all or most of the genome of a wild (undomesticated) Solanum species (Solanum pennellii, Solanum habrochaites, or Solanum lycopersicoides) was represented as short individual chromosomal regions serially introgressed into the genetic background of domesticated tomato (Solanum lycopersicum). These three experiments are comparable in the mean and distribution of heterospecific introgression sizes and the generations of crossing used to create the lines, and they have similar statistical power for detecting pollen and seed sterility QTL (Table 1) (15). Each experiment identified the number, genomic location, and phenotypic effect–size of chromosomal regions associated with two separate postzygotic sterility phenotypes (pollen sterility and seed sterility) acting between two species (15). In each population, we also analyzed morphological traits unrelated to hybrid sterility (fruit shape and size of fertile seeds) as an internal control. As a proxy for time since lineage splitting, we estimated pairwise species molecular divergence as the number of synonymous substitutions per synonymous site (Ks) at six unlinked loci distributed throughout the genome (15).

Table 1

Experimental details of three Solanum QTL mapping experiments. Ks is synonymous site divergence between species; genome coverage is the percentage of the wild species’ genome represented in introgression lines; gens of crossing are the number of generations of crossing used to generate lines; introgression lengths are the mean and range of heterospecific introgression sizes, in centimorgans (cM) and as a percentage of the donor species genome (% genome); n is the experimental population size; min. detectable effect size is the average minimum detectable standardized effect size [d (22)], across all four traits (SSS, PF, FSH, and SSZ) for each experiment (15).

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To evaluate evidence for the nonlinear accumulation of DMIs, we compared regression models describing linear and nonlinear relations between molecular divergence (time since lineage splitting) and the minimum number of sterility QTLs observed between species pairs (Fig. 1). Under the snowball prediction, there should be a greater-than-linear increase in DMIs with increasing molecular divergence between species pairs. We evaluated the relative goodness of fit of linear (y = a1x), and two different quadratic models (quad1: y = a1x + a2x2; quad2: y = a1x2) (Table 2). The last two models are nonlinear and consistent with the snowball prediction; we evaluated both because the exact form of nonlinear accumulation can vary with the complexity of gene interactions underlying DMIs [e.g., pairwise versus greater than pairwise (6)], which is not known in this or any other empirical system. Models were evaluated separately for pollen and seed sterility isolating barriers. All models were forced through the origin, because taxa that do not differ by any molecular substitutions are not expected to have accumulated any reproductive isolation loci. Because linear and quad1 models are hierarchically nested, we compared them with parametric statistics; linear and quad2 models were compared with the Akaike Information Criterion (AIC) (15).

Fig. 1

Patterns of accumulation of QTL over evolutionary divergence between Solanum species. Accumulation of seed sterility QTL is significantly nonlinear; pollen sterility QTL accumulation is consistent with linear (Table 1). In comparison, accumulation of seed size and fruit shape QTL is slower and no greater than linear (table S4).

Table 2

Linear versus nonlinear models for the accumulation of hybrid incompatibility and other QTL between Solanum species. SSS, self seed set (seed sterility); PF, pollen fertility (arcsine square-root transformed); FSH, fruit shape; SSZ, fertile seed size. Model comparison 1: linear and quad1 (y = a1x + a2x2) models were compared using Zar Eq. 21.4 (23). Where P < 0.05, the more complex (quadratic) model provides a significantly better fit. Model comparison 2: linear and quad2 (y = ax2) models were compared by using AIC (24); the model that minimizes the AIC is considered the better fit [see (15)]. For results from least-squares regressions for each model (linear, quad1, and quad2) see table S4.

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For seed sterility, we detected significantly greater-than-linear accumulation of hybrid sterility loci, consistent with a snowball effect. This was true regardless of whether a linear model was compared with either quadratic fit (Table 2). In comparison, a linear model outperformed both nonlinear fits for pollen sterility data (Table 2); therefore, our analysis did not support an accelerating increase in DMI accumulation over time for pollen sterility as an isolating barrier.

The snowball prediction applies specifically to traits determined by epistatic interactions. However, many trait differences between species are not expected to be invariably epistatic; rather, they often contribute additively to interspecific differentiation (16). As such, the accumulation of loci for postzygotic isolation versus nonisolation traits can also be used to assess the unique nonlinearity expected for postzygotic isolation. We assessed the pattern of accumulation of fruit shape (FSH) and seed size (of fertile seeds; SSZ) between the same species pairs. In both cases, we found no evidence for an accelerating accumulation of QTL contributing to species trait differences; for seed size, we also found no evidence for a linear accumulation over time (15). In comparison with sterility traits, therefore, loci for “normal” interspecific quantitative trait differences do not appear to snowball with evolutionary time (Fig. 1).

Although we identified the signal of a snowball effect, it was significant only for seed sterility. The failure to detect a snowball for pollen sterility could be due to several, nonexclusive contributing factors, which we currently cannot differentiate (15). For example, DMIs for pollen sterility might accumulate noncombinatorically [unlike in Orr's (3) original snowball model], which could result in a more linear relation between the number of DMIs and the time since divergence. This could occur, for example, if substitutions contributing to pollen sterility DMIs over time were not independent of each other, as might happen if isolating barriers evolve as the result of genetic conflicts (17). Alternatively, an attenuated snowball for pollen sterility could be due to bias against QTL detection in the cross with the greatest genetic distance, and/or rate heterogeneity in the accumulation of sterility loci (15). Finally, if there is a systematic difference in the complexity of genetic interactions underlying male versus female hybrid sterility, we may have differing abilities to detect them with our introgression line approach, which can detect DMIs due to pairwise epistatic interactions but not DMIs requiring more than one chromosomal segment from each species, i.e., multilocus interactions (4, 15). Current data, although sparse, suggest that DMIs responsible for male sterility might frequently be due to complex multilocus interactions (1820). In Solanum, hybrid introgression lines show progressively more pollen sterility depending on whether they carry one, two, or three conspecific introgressions from the donor species, which suggests that multilocus interactions are necessary for the expression of some hybrid pollen sterility (21); there is no equivalent increase in seed sterility with number of conspecific introgressions.

Overall, our results indicate that the accumulation of sterility loci follows a different trajectory from the accumulation of loci for other quantitative species differences (Fig. 1), consistent with the unique genetic basis expected to underpin species reproductive isolating barriers. Our analysis examines the accumulation of loci contributing to individually evaluated hybrid sterility traits (pollen sterility and seed sterility); therefore, we explicitly evaluate the accumulation of genetic loci rather than sterility phenotypes, and we do not conflate the accumulation of loci underlying genetically and developmentally distinct isolating barriers [for example, by examining the accumulation of both male and female sterility as a single “total isolation” phenotype (12)]. In doing so, we uncover direct empirical support for the Dobzhansky-Muller model of hybrid incompatibility, and the snowball prediction in particular.

Supporting Online Material

Materials and Methods

Tables S1 to S5


References and Notes

  1. Materials and methods are available as supporting material on Science Online.
  2. M. Fryska, E. Graham, E. Lines, and K. Wolt contributed to collection of the data. C. Muir drew Figure 1. M. Hahn, C. Muir, and M. Turelli provided comments on the manuscript. Supported by National Science Foundation grants DEB-0532097 and DEB-0849157 (LCM).
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