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Keywords:

  • hybrid inviability;
  • postmating reproductive isolation;
  • reaction norm;
  • sterility;
  • underdominance

Abstract

  1. Top of page
  2. Abstract
  3. Introduction
  4. Extension of a single-locus hybrid incompatibility model to include GEI
  5. Extension of a multilocus hybrid incompatibility model to include GEI
  6. Discussion
  7. Conclusions
  8. Acknowledgments
  9. References

The Dobzhansky–Muller (D–M) model of reproductive isolation (RI) posits that hybrid sterility and inviability result from negative epistatic interactions between alleles at a minimum of two genes. This standard model makes several implicit assumptions, including a lack of environmental effects and genotype-by-environment interactions (GEI) involving hybrid sterility and hybrid inviability loci. Here we relax this assumption of the standard D–M model. By doing so, several patterns of the genetic architecture of RI change. First, a novel single-locus model of postzygotic RI emerges. Several indirect lines of evidence are discussed in support of the model, but we conclude that this new single-locus model is currently no more supported than previous ones. Second, when multilocus D–M models incorporating GEI are considered, we find that the number of potential negative epistatic interactions increases dramatically over the number predicted by the standard D–M model, even when only the most simple case of two-allele interactions are considered. Third, these multilocus models suggest that some previous generalizations about the evolutionary genetics of postzygotic RI may not necessarily hold. Our findings also suggest that the evolution of postzygotic RI may be more likely when the expression of traits driving speciation is affected by the environment, since there appears to be a greater spectrum of potential hybrid incompatibilities under the D–M model incorporating GEI.


Introduction

  1. Top of page
  2. Abstract
  3. Introduction
  4. Extension of a single-locus hybrid incompatibility model to include GEI
  5. Extension of a multilocus hybrid incompatibility model to include GEI
  6. Discussion
  7. Conclusions
  8. Acknowledgments
  9. References

Traditionally it has been argued that at least two interacting genes underlie the traits intrinsically involved in postzygotic reproductive isolation: hybrid sterility and inviability (Bateson, 1909; Dobzhansky, 1937; Muller, 1942). Consider a one-locus, two-allele model in which a substitution in a population of genotype aa yields a derived population with genotype AA (Fig. 1A). A hybrid formed between these two populations (Aa) is unlikely to be sterile or inviable, because AA evolved from this heterozygous genotype, which would have been an evolutionary dead end had it been maladaptive. Even if heterozygotes are only partially sterile, they would not persist in the population, since they would enter at a frequency of 1/2N, where N is the population size, and are therefore likely to be lost by genetic drift. In addition, they would be disfavoured by natural selection if they drifted to an appreciable frequency.

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Figure 1.  (A) The traditional single-gene model for the evolution of a hybrid incompatibility. C = compatible hybrid genotype, I = incompatible hybrid genotype. (B) The ‘standard’ Dobzhansky–Muller (D–M) two-locus model for the evolution of a hybrid incompatibility. After initial divergence of the two populations, one incompatible interaction is possible (A-B).

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The problem then is to explain how hybrid sterility or inviability evolves if the genes causing such hybrid incompatibilities do not pass through a maladaptive intermediate step. Bateson (1909), Dobzhansky (1937) and Muller (1940) proposed an answer – the addition of a second interacting locus bypasses the maladaptive intermediate step of a one-locus model (Fig. 1B). Assume aabb is the genotype of the ancestral lineage, which consists of two allopatric populations. In the first population, a substitution at the A locus yields genotype AAbb, which is compatible with the ancestral lineage. In the second population, a substitution at the B locus yields another derived lineage with genotype aaBB, likewise compatible with the ancestral line. The hybrid genotype formed from crosses between individuals from different populations, AaBb, can now be unfit by the following reasoning: The derived A and B alleles function normally within their own, nonhybrid, genetic background, but epistatically interact in a hybrid background to produce either sterility or inviability. In this case, the term ‘epistatic’ denotes the between-locus nonadditive component of the genetic variance of a trait (Wade, 1992).

Genetic analyses of interspecific hybrid sterility and inviability are generally consistent with this two-locus model, commonly known as the Dobzhansky–Muller (D-M) model, which we will refer to as the ‘standard’ D-M model (reviewed in Orr, 1997; Naviera & Maside, 1998; Wu & Hollocher, 1998; Johnson, 2000). A particularly clear example of sterility or inviability being caused by complementary gene interactions is the extensive work on the genetics of hybrid male sterility between Drosophila simulans and D. mauritiana, in which numerous alleles only have a large effect on hybrid sterility when brought together in specific combinations (reviewed by Wu & Hollocher, 1998). Such experiments provide strong evidence that epistatically interacting loci can cause reproductive isolation.

The standard D–M model makes a number of specific predictions about the evolution of postzygotic RI (Muller, 1942; Orr, 1995). These include the following: (1) All hybrid incompatibilities must initially be asymmetric, since the derived alleles (A-B) can cause a hybrid incompatibility, but the ancestral alleles (a-b) cannot. (2) Derived alleles are involved in incompatible interactions in hybrids more often than ancestral alleles. The reason is that of the three types of allelic interactions, derived–derived, derived–ancestral and ancestral–ancestral, only the latter type cannot be incompatible. (3) Later substitutions are more likely to be involved in hybrid incompatibilities than earlier ones, since the Kth substitution can negatively interact with K − 1 loci from the other population. For example, while the second substitution (e.g. B) can negatively interact with an allele at one locus (e.g. A), the third substitution (e.g. C) can interact with alleles at two loci (e.g. B and a), and so forth. (4) The total number of possible negative epistatic interactions leading to hybrid incompatibilities increases at least as fast as the square of the number of substitutions separating two taxa, for the same reason as prediction (3).

Because of the standard D–M model’s great utility for explaining the origin and evolution of RI, and its wide acceptance, it is important to test the robustness of the above predictions. Indeed, one may consider the standard D–M model to be the null hypothesis for genetic studies of postzygotic isolation. The model makes a number of implicit assumptions, among which are the following: (1) alleles at interacting ‘speciation loci’ are fixed within populations, (2) alleles at a given speciation locus are limited to two – one ancestral allele and one derived allele, (3) only two-locus interactions causing sterility or inviability are allowed and (4) hybrid incompatibilities are not subject to specific environmental influences. While the first three assumptions have been theoretically investigated (Orr, 1995; Johnson & Porter, 2000), assumption (4) has not been considered to our knowledge. Given the prevalence of environmental influences and genotype-by-environment interactions (GEI) for a wide variety of characters in laboratory, domesticated and natural populations (Lynch & Walsh, 1998, chapter 22, and references contained therein), we suggest that studying the effects of these sources of environmental variation in the D–M model is both warranted and important.

Environmental variation in hybrid incompatibilities can be broadly divided into two categories, which are based upon whether hybrid genotypes and nonhybrid genotypes demonstrate the same or a different degree of environmental sensitivity for fertility and viability. First, genotypes may show parallel responses to environmental change, meaning that individuals of different genotypes react equally in their degree of fertility, for example, in a second environment. This source of environmental variation is characterized as a parallel reaction norm (Gordon, 1992; Roff, 1997). In contrast, nonparallel reaction norms, when different genotypes respond to environmental change in different ways, indicate the existence of GEI. Two examples are (a) when certain hybrid genotypes react either more or less strongly to an environmental change than others, and (b) when the inferior hybrid genotype in one environment is superior to some or all other genotypes in a second environment. There have been few studies of GEI for hybrid traits (but see Wade et al., 1999), though observations of natural animal and plant hybridizations demonstrate that hybrid zone evolution is typically influenced by environmental components, and that GEI can fashion the genetic structure of hybrid zones (Arnold, 1997).

The aim of this paper is to explore how GEI can affect the evolution of both single- and multilocus (Dobzhansky–Muller) hybrid incompatibilities. We first examine the evolution of single-locus hybrid incompatibilities that are conditional on the environment. We make several predictions related to the single-locus model and survey the literature to compile cases in support of these predictions. Likewise, we extend the Dobzhansky–Muller model to include GEI and analyse several issues related to the genetics of postzygotic isolation, including the asymmetry of hybrid incompatibilities, the proportion of derived vs. ancestral alleles conferring hybrid sterility or lethality, and the involvement of late vs. early substitutions in hybrid incompatibilities.

Extension of a single-locus hybrid incompatibility model to include GEI

  1. Top of page
  2. Abstract
  3. Introduction
  4. Extension of a single-locus hybrid incompatibility model to include GEI
  5. Extension of a multilocus hybrid incompatibility model to include GEI
  6. Discussion
  7. Conclusions
  8. Acknowledgments
  9. References

The model

Our one-locus model of postzygotic isolation is depicted in Fig. 2(A). It differs from the standard D–M model in that it relaxes the assumption that the intermediate hybrid state is maladaptive when a new allele arises in the population at the locus under consideration. After a lineage AA evolves by selection or drift from an ancestor aa, an environmental change may induce a maladaptive phenotypic alteration in heterozygotes. This alteration does not occur in either homozygote. In this specific case, Aa hybrids are fertile until the environmental change triggers a hybrid incompatibility that renders Aa hybrids fully or partially sterile. As a simple example, Aa hybrids could be fertile at 19 °C, yet sterile at 26 °C.

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Figure 2.  (A) A single-locus model for the evolution of a hybrid incompatibility following an environmental change. An incompatibility does not arise between the derived populations until a change in the environment causes a change in the hybrid phenotype, e.g. sterility or inviability. ΔE = environmental change, C = compatible hybrid genotype, I = incompatible hybrid genotype. (B) A modified two-locus model of the evolution of hybrid incompatibilities. After initial divergence of the two populations, only one incompatible interaction is possible (A-B). Following the change in environment, there are four potential incompatible interactions (A-B, A-a, B-b and a-b).

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Predictions of the model

This new single-locus model makes at least three predictions that can be tested with our current knowledge of environmentally influenced genetically based characters. The first prediction follows from the key assumption of the model: expression of hybrid sterility or inviability, regardless of genetic basis, should be subject to environmental influence. While the conditionality of hybrid incompatibilities has not been widely investigated, every case study that we found confirms this assumption of our model. The second prediction is that levels of sterility and inviability caused by a single locus should change across systematic changes in the environment. A survey of Mendelian mutants shows that many alleles which cause sterility or inviability display reaction norms for these phenotypes. The third prediction is that single-locus heterozygous genotypes (regardless of the trait they express) should also have reaction norms. Such cases would imply that the phenotypes produced by within-locus allelic interactions are sensitive to the environment. We found a remarkable amount of evidence in support of single-locus heterozygote reaction norms. Notable among these are heterozygotes that yield sterility or inviability phenotypes. In sum, a survey of the literature lent support to the three predictions of the model presented here. However, we caution that support of these predictions only reveals the plausibility of the model.

Prediction 1: the environment influences postzygotic isolation between populations or species

We compiled cases in which the environmental sensitivity of hybrid incompatibilities was specifically tested. Our criteria for selecting cases were the following: (1) the organisms considered must be sexually reproducing diploids or haplodiploids, (2) hybrid sterility or inviability must be genetically based, and (3) hybrid sterility or inviability was measured in more than one environment. We define the environment as any extrinsic factors which may affect the fitness of the organism. Most studies relevant to these criteria and the predictions tested below have investigated the effects of temperature changes on hybrid incompatibilities. This bias is likely due to the practical ease of manipulating temperature in a laboratory setting, rather than an indication that temperature is the dominant environmental influence on hybrid incompatibilities.

Table 1 shows the results of our literature survey. The findings are striking: all 19 case studies found significant environmental effects on hybrid incompatibilities, particularly in F1 hybrids. Although the genetic basis of each of these characters is probably not due to a single locus, these findings are persuasive evidence against the notion that hybrid incompatibilities are unconditional. Indeed, Darwin (1859) writes: ‘The fertility … of hybrids is more easily affected by unfavourable conditions than is the fertility of pure species … their [the hybrids’] degree of fertility is often found to differ greatly in the several individuals raised from seed out of the same capsule and exposed to exactly the same conditions’ (Chapter VIII, p. 256), though he of course found it mechanistically confusing at the time. We note that these data in Table 1 pertain as well to a multilocus D–M model (see below).

Table 1.   Examples of environmentally influenced postzygotic hybrid incompatibilities. Thumbnail image of
Prediction 2: single-locus homozygotes causing sterility or inviability have reaction norms

The key point of this second prediction is that we can assess whether intrinsic postzygotic isolation having a simple genetic basis (i.e. a single locus) is conditional on the environment. To test this prediction, we surveyed the Drosophila melanogaster genes in Lindsley & Zimm (1992) for loci that have at least one known allele that when homozygous, or, for X-linked genes, male hemizygous, are (1) associated with a sterile or lethal phenotype and (2) display a reaction norm for that sterility or inviability phenotype. We found 37 D. melanogaster genes which show temperature-related reaction norms for sterility, and 156 genes which show temperature- or diet-related reaction norms for inviability (detailed gene information is available from the corresponding author). Virtually all of the examples are either spontaneous Mendelian mutants or those generated by mutagenesis; such genotypes are most certainly not the ‘stuff’ of speciation. Nevertheless, the numerous examples in support of this second prediction show that maladaptive phenotypes (of which the genetic basis is known and simple) are sensitive to environmental conditions. [We note that of the sets of 37 sterility and 156 inviability loci, there are 8 loci that are common to both data sets].

Prediction 3: single-locus heterozygotes have reaction norms

Our model posits that underdominances caused by interallelic interactions can be influenced by the environment. Due to a lack of fine-scale genetic analyses measuring the conditions associated with this phenomenon, we cannot directly assess the validity of environmentally sensitive underdominances. However, there is a comparable prediction that can be tested: single locus heterozygotes (regardless of the trait) should show reaction norms. The key point of this prediction is that we can assess the degree of environmental influences on within-locus allelic interactions – the types of interactions that may be involved in hybrid sterility or inviability. Our evidence for heterozygote reaction norms comes from two organisms: Culex pipiens and D. melanogaster.

Plasticity of dominance in C. pipiens.

Dominance of an insecticide-resistance gene (Ace) was characterized under several different environmental conditions, such as concentration of insecticide and type of larval food (Bourguet et al., 1996). Resistance was scored through mortality assays, from which the ratio of heterozygous to homozygous mortality was used as a measure of dominance of resistance to the insecticide. Dominance relationships dramatically changed with systematic changes in the environment. In particular, the resistance phenotype tended to be recessive in more demanding environments. The findings support the notion that variation in dominance levels, and thus intralocular interactions, can be caused by environmental conditions. Dominance, a phenotype by definition only manifested in heterozygotes, is thus not an unconditional trait.

Heterozygote reaction norms in D. melanogaster.

We surveyed all of the D. melanogaster genes in Lindsley & Zimm (1992) for loci which have at least one heterozygous reaction norm. Examples of D. melanogaster loci which have environment-dependent phenotypes in the heterozygous state are shown in Table 2. Table 2 includes all such heterozygotes except those which cause sterility or inviability, which are shown in Table 2.

Table 2. Drosophila melanogaster genes at which a heterozygote genotype displays a norm of reaction for its phenotype. For some loci listed here, multiple combinations of alleles meet these criteria. ‘Ancestral’ alleles are ‘wild-type’ alleles and ‘derived’ alleles are ‘mutant’ alleles. Most loci are affected by the change in environment at the developing (preadult) stage, but a minority are affected at the adult stage. All data are taken from Lindsley & Zimm (1992). Detailed information is available from the corresponding author. (A) Heteroallelic combinations with nonsterile and nonlethal phenotypes. (B) Heteroallelic combinations with sterile or lethal phenotypes. Thumbnail image of

In sum, the heterozygote norms of reaction in Table 2 confirm the third prediction of our model. While they are not direct evidence for our model’s relevance to natural populations (only extremely fine-scale genetic experiments on hybrid incompatibilities in different environments could provide direct evidence for our model), they, along with the evidence for Predictions 1 and 2, reveal the plausibility of an environmentally sensitive single-locus underdominance.

Extension of a multilocus hybrid incompatibility model to include GEI

  1. Top of page
  2. Abstract
  3. Introduction
  4. Extension of a single-locus hybrid incompatibility model to include GEI
  5. Extension of a multilocus hybrid incompatibility model to include GEI
  6. Discussion
  7. Conclusions
  8. Acknowledgments
  9. References

The model

Figure 2(B) depicts a two-locus model of hybrid incompatibility incorporating a single environmental change after population divergence. Although only one incompatible interaction is possible following initial divergence of the two populations, an environmental change that affects the hybrid phenotype allows for four incompatible allelic interactions (Fig. 2B), increasing the likelihood that divergence will occur. Under the standard D–M model, the one possible interaction which causes a hybrid incompatibility is that of A-B (Figs 1B and2B). Under our model, which incorporates GEI after the divergence of two populations, the four possible incompatible interactions are A-B, A-b, a-B and a-b. Thus, A-B may be the least fit genotype under the standard D–M model in environment 1, but when GEI is considered, a-b, for example, may be the least fit of the four genotypic classes in environment 2. The key point is that the alleles not shared between the derived populations all have the potential to negatively interact in a particular environment.

The two-locus model outlined above can be extended to multilocus incompatibility systems. Assuming two alleles at each locus, as the number of loci involved increases, the number of possible two–allele incompatible interactions increases as the square of the number of loci. For example, with three loci A, B and C, there are six alleles, A, a, B, b, C and c, which can interact with each other in hybrid individuals after an environmental change, in nine combinations: A-a, A-B, A-c, b-a, b-B, b-c, C-a, C-B and C-c (Fig. 3; This assumes that the two diverged populations are of fixed genotypes AAbbCC and aaBBcc. The number of interactions remains the same but the precise interactors change with different divergent population genotypes. This assumes solely two-way allelic interactions). With four diallele loci, there are 16 possible two-allele interactions, and so forth. In contrast, under the standard D–M model, only six interactions are possible given the same assumptions. In fact, the difference between the number of potential interactors of the two models, when K divergent loci are considered, is equal to the number of possible interactions under the standard D–M model with K + 1 divergent loci. Therefore with GEI, there can be a dramatically greater number of incompatible genotypes. The contrast between Orr’s (1995) Fig. 1 and our Fig. 3 reveals a more complex web of potential negative interactions when loci conferring sterility and inviability phenotypes are subject to GEI. In addition, the simplifying assumption that only two-allele interactions are possible does not necessarily hold, and so the square of the number of loci is an underestimate of the total number of possible interactions conferring hybrid incompatibility. There is in fact empirical evidence for higher-level allelic interactions from studies of both sterility (Cabot et al., 1994) and inviability (Carvajal et al., 1996).

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Figure 3.  The differential fixation of alleles in two populations, and the evolution of incompatible interactions between them, allowing for GEI. Following Orr (1995; Fig. 1), time runs upward, lowercase letters represent ancestral allelic states, and capital letters represent newly arising and fixed allele states. Arrows show potential incompatibilities between two alleles. Horizontal arrows are drawn in an arbitrary direction.

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Evaluation of predictions of the standard D–M model

Incorporating GEI into the standard D–M model also changes several previous conclusions concerning the population genetics of speciation (Orr, 1995), among which are: (1) Following Muller (1942), all incompatibilities are initially asymmetric – both A-B and a-b cannot be incompatible because one of the two combinations was present in either the common ancestor of the two populations or in an intermediate evolutionary step (Fig. 1B). (2) Evolutionarily derived alleles are involved more often in hybrid incompatibilities than ancestral ones, because no ancestral–ancestral interactions are possible. (3) More incompatibilities result from later substitutions rather than earlier ones. When the environment influences the expression of hybrid incompatibilities, these three conclusions are not necessarily general patterns of the evolution of RI. We discuss these predictions below.

Standard D–M Prediction 1: all incompatibilities are initially asymmetric

Consider a two-locus, two-allele model, with ancestral population aabb and subsequent diverged populations AAbb and aaBB. A-B and a-b cannot both negatively epistatically interact in hybrid individuals, because one of these combinations necessarily existed in an ancestral or transitional state of the populations. In this case, a-b is a combination which existed in the ancestor. Under the standard D–M model, this reasoning is correct; however, we demonstrate below that this line of reasoning does not hold when GEI is considered. Imagine the following scenario: ancestral population aabb in Environment 1 (E1) diverges into populations AAbb and aaBB, both located in E1 but allopatric to each other. Now, the two diverged populations meet and form a hybrid zone in E2, a geographical area separating their populational ranges. The combination of either A-B or a-b could be incompatible, because a-b could be fit in E1 but sterile or inviable in E2. Hence, incompatibilities are not necessarily asymmetric as the standard D–M model predicts. In fact, this example shows that the direction of the asymmetry could even swing the other way –a-b interactions may arise before those of A-B.

The amount of asymmetry (summed across all loci) in these two epistatic interactions, A-B and a-b, will depend upon whether one arises more often than the other. For simplicity, assume that the derived hybrid genotype, AABB, has a certain probability (d) of being sterile or inviable, given some arbitrary divergence time, and that its fitness in E1 and E2 is the same. For the same amount of time, we would like to calculate the likelihood that the ancestral hybrid genotype, aabb, is sterile or inviable in E2. This value will be precisely related to the product of the probability of an environmentally sensitive hybrid incompatibility (s), and the probability of being present in a new environment where that hybrid incompatibility will be expressed (e). If se=d, then there is no asymmetry since one of these epistatic interactions is just as likely to arise as the other. If se does not equal d, then the asymmetry holds, but the predicted direction of the asymmetry depends upon the value of the product. For example, if se > d, then there will be more incompatibilities caused by a-b interactions than by A-B ones. Furthermore, even if the predicted direction of the asymmetry holds (d > se), the scale of the asymmetry will likely be different than that predicted by the standard D–M model, in which the product of s and e is implicitly assumed to equal 0.

Standard D–M Prediction 2: derived alleles are involved in negative epistatic interactions conferring hybrid incompatibilities more often than ancestral ones

This prediction follows from the fact that only derived–derived and derived–ancestral epistatic incompatibilities can occur under the standard D–M model (Orr, 1995). However, in a model that incorporates GEI for hybrid incompatibilities, ancestral–ancestral interactions are also possible.

Following Orr (1995), we calculate the probabilities of various incompatibilities under the standard D–M model, as well as under a D–M model incorporating GEI. Consider two populations incurring independent substitutions. A fraction f of these substitutions occur in population 1 and a fraction 1 – f occur in population 2. In the same way, a fraction 1 – f of these loci in population 1 and a fraction f in population 2 are ancestral alleles. Under the standard D–M model, the probability that a derived allele in population 1 (D1) will be incompatible with an ancestral allele in population 2 (A2) is equal to f2, the product of the proportion of derived alleles in population 1 (f), and the proportion of ancestral alleles in population 2 (f). Thus, the probabilities of hybrid incompatibilities under the standard D–M model are simply

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When the model is extended to include ancestral–ancestral incompatibilities, that result from GEI, a fourth probability is added that depends upon the probability of environmentally sensitive hybrid incompatibilities (s) and the probability of occurring in an environment where that incompatibility will be expressed (e). In addition, since the probability of these incompatibilities is independent of the probability of standard D–M model incompatibilities (which is assumed to equal 1 in the above equations), the probability of a D–M hybrid incompatibility (d) also must be added to the equations. It then follows that under a D–M model with GEI,

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With these probabilities, we can calculate the expected frequency of derived and ancestral alleles involved in hybrid incompatibilities:

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We then obtain the intuitive result that P(D1) + P(A1)=P(D2) + P(A2), since every incompatibility results from an interaction between an allele from each species (Orr, 1995). In other words, the total frequency of population 1 alleles involved in hybrid incompatibilities must equal that of population 2 alleles.

Using these frequencies, we can calculate the amount of asymmetry in derived vs. ancestral alleles involved in hybrid incompatibilities. The ratio P(D):P(A) for hybrid incompatibilities is

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This finding means that the number of derived and ancestral alleles involved in postzygotic isolation depends upon the fraction of substitutions that occur in each population, the probability of a standard D–M hybrid incompatibility (d), and the probability of an environmentally sensitive hybrid incompatibility (i.e. the product of s and e). Under the standard D–M model, when there are equal rates of allelic substitution in the two populations (f=0.5) and no environmentally sensitive incompatibilities (se=0), the asymmetry of D:A is 3:1 (eqn 4; see also Orr, 1995). Put simply, derived alleles are three times more likely to be involved in incompatibilities than ancestral alleles. However, whenever d=se, f can take on any value and the ‘asymmetry’ of D:A is 1:1. There is no asymmetry under these conditions. From this we conclude that derived alleles are not necessarily involved in more hybrid incompatibilities than ancestral alleles. In fact, when se > d, the asymmetry swings the other way. For example, when f=0.5, d=0.25 and se=1, the P(D):P(A) ratio is 1:3, the reciprocal of the asymmetry predicted by the standard D–M model. With values of se < d, the asymmetry holds, but the amount of asymmetry depends upon the precise value of se. For example, when f=se=0.5, and d=1, then P(D):P(A) is 3:2. Since se is unlikely to equal d, we conclude that the scale and/or direction of the asymmetry will tend to differ from that predicted by the standard D–M model, in which the product of s and e is implicitly assumed to equal 0.

Standard D–M Prediction 3: later allelic substitutions are involved in negative epistatic interactions conferring hybrid incompatibilities more often than earlier ones

Similar to Prediction 2 (above), Orr (1995) concluded that later allelic substitutions (L) are involved in postzygotic RI more often than earlier substitutions (E). This is because under the standard D–M model, the Kth substitution in one diverging population can be incompatible with K – 1 loci from the other population. Hence, the greater the rank-order of a given substitution, the more epistatic incompatibilities the substitution could be involved in. In our model, however, the number of incompatibilities that an allele could be involved in is equal to K (Fig. 3). Therefore, later substitutions are not necessarily involved in more incompatible interactions than are earlier substitutions.

Here we have a conclusion similar to that for Prediction 2. If se=d, then L and E substitutions have an equal likelihood of being involved in hybrid incompatibilities (Fig. 3). If se < d, then the asymmetry will hold, but the amount of asymmetry of L and E alleles expressing a hybrid incompatibility depends upon the value of se. Notably, this does not change an additional, secondary, conclusion – the strength of RI between two populations increases faster than linearly with time (Orr, 1995). In fact, our model predicts that RI should increase over time faster than the standard D–M model, and hence the general conclusion concerning the rate of speciation remains true.

Predictions of the multilocus D–M model incorporating GEI

Our model of the evolution of postzygotic isolation makes at least two predictions that can be tested with our current knowledge of the genetic basis of hybrid sterility and inviability.

Prediction 1: The environment influences postzygotic isolation between populations or species

This prediction is identical to Prediction 1 of our single-gene model. A literature survey of studies which tested the conditionality of hybrid incompatibilities revealed 19 out of 19 studies which found a positive result. That is, all 19 studies found environmentally sensitive hybrid incompatibility phenotypes (Table 1). We note that the evidence presented in support of this particular prediction is more relevant to multilocus RI than single locus RI (see above), because although the genetic architecture of RI in the systems is largely unknown (but see Sawamura et al., 1993 and Carracedo et al., 2000, for example), multilocus epistatic incompatibilities tend to be the rule rather than the exception (Orr, 1997; Naviera & Maside, 1998; Wu & Hollocher, 1998). Hence, the studies in Table 1 which detected environmental effects on hybrid incompatibilities constitute strong evidence for the notion that hybrid incompatibilities are sometimes, and perhaps often, influenced by the environment.

Prediction 2: the ratio of D:A alleles involved in hybrid incompatibilities will be smaller than that predicted by the standard D–M model

The reason is that as shown above, a model incorporating GEI allows for ancestral–ancestral interactions to contribute to hybrid sterility and/or inviability, thereby increasing the number of ancestral alleles involved in hybrid incompatibilities. Indeed, the fraction of ancestral alleles involved in hybrid sterility or inviability may be greater than that of derived alleles if the probability of an environmentally sensitive incompatibility (se) is greater than that of a standard D–M incompatibility (d). Unfortunately, to our knowledge there exists no direct empirical evidence to assess this prediction.

Very little is known about specific genes (and hence allelic substitutions) which cause sterility or inviability in hybrids between populations or species. Consequently, we also have very little information about the ancestral vs. derived states of alleles at such genes. The abundance of genetic data that will emerge on postzygotic isolation in the next decade will undoubtedly make this prediction testable.

Discussion

  1. Top of page
  2. Abstract
  3. Introduction
  4. Extension of a single-locus hybrid incompatibility model to include GEI
  5. Extension of a multilocus hybrid incompatibility model to include GEI
  6. Discussion
  7. Conclusions
  8. Acknowledgments
  9. References

Alternative single-locus models of RI

We explored how single- and multilocus models of speciation can change when postzygotic isolating barriers are conditional on the environment. We presented a novel model for the evolution of single locus hybrid incompatibilities which incorporates environmental influences on ‘underdominances’. A ‘contracomplementation’ model of single-locus incompatibilities was proposed by Portin (1974) and Nei et al. (1983), who each suggested that multiple substitutions at a single locus could bypass the maladaptive intermediate step of single gene speciation. Briefly, after divergence at locus A between Populations 1 and 2 (e.g. Population 1 has a substitution at A from allele A1 to A2, and Population 2 has a similar substitution, but from A1 to A3), these ‘derived’ alleles could then interact in hybrids to cause postzygotic isolation. Portin supported his model with data from crosses between several D. melanogaster strains that carried different alleles of the sex-linked Abruptex locus (see below). Single-locus models of ecological underdominance, in which hybrids (e.g. Aa) are competitively inferior in either environment of the nonhybrids (AA or aa), have also been developed (Pimm, 1979; Udovic, 1980). While ecological underdominances exist (Rohwer & Manning, 1990; Grant & Grant, 1993; Schluter, 1996; Hatfield, 1997), resolving their genetic basis is still in its infancy. Admittedly, direct support for any single-locus model of the evolution of postzygotic isolation is marginal at best (Portin, 1974; Li et al., 1997; Axenovich et al., 1998).

Molecular mechanisms of single-locus hybrid incompatibilities

How might within-locus allelic interactions occur on a biochemical scale? One example of biochemical interactions at a single locus contributing to RI are those which occur at the Abruptex (Ax) locus of D. melanogaster to cause postzygotic RI between laboratory strains harbouring different Ax alleles (Portin & Ruohonen, 1972; Portin, 1974, 1975). Portin (1974, 1975) demonstrated that while strains which are fixed for alleles Ax 28, Ax 16172, Ax 71d, Ax E2 and Ax 9B2 are fully viable, the trans-heterozygotes Ax 28/Ax 16172, Ax 28/Ax 71d, Ax 9B2/Ax E2, Ax 9B2/Ax 16172 and Ax 9B2/Ax 71d are lethal (and genotype Ax 28/Ax E2 is semilethal, i.e. some proportion <1 die). Additional within-locus allelic interactions causing postzygotic isolation (lethality) are seen at the lesser-studied D. melanogaster X-linked short wing (sw) locus, which has four known trans-heterozygote lethal combinations. Alleles sw 1, sw 2, sw 5, sw 6 and sw 7 are homozygous viable below 31 °C, but combinations of sw 2, sw 5, sw 6 and sw 7 with sw 1 are unconditionally lethal within the same temperature range.

What is occurring at these loci on a biochemical level? Studies of the Ax locus provide some insight. Portin & Ruohonen (1972) suggest that heterozygote lethality at Ax is ‘due to an active process, probably some kind of interaction between two different mutant gene products’ (p. 70). One could argue that lethality is due to lack of function of the mutant protein products, but it is known that the Ax alleles involved in the hybrid–lethal interactions are not lack-of-function, or ‘null’, alleles (Portin, 1975; Flybase, 1999). Portin (1975) proposes three nonmutually exclusive molecular mechanisms for negative complementation at Ax: (1) Because Ax acts at two distinct times during development, if one mutation causes a deficiency at one time in development, and another mutation similarly causes a deficiency at the other, the combined effect causes a lethal negative complementation. (2) If Ax is a tandem repeat coding for two subunits of a molecule, then hybridization of two mutant proteins might reduce that enzyme’s activity below a critical threshold, resulting in lethality. (3) If Ax has a regulatory function, then a trans-heterozygote of hypo- and hypermorphic alleles (those with less-than and greater-than wild-type phenotypes, respectively) could cause a canalization imbalance, again resulting in lethality. While the basis of negative complementation at Ax is not currently known (P. Portin, personal communication), any of these three mechanisms may be general explanations of within-locus allelic interactions which result in sterility or lethality. Kerr (1997) discusses additional mechanistic hypotheses for interallelic interactions, specifically in relation to single-locus sex determination, which is common in certain insect groups, particularly the Hymenoptera. Single-locus sex determination is a solid demonstration of how novel phenotypes can be caused by intralocular interactions. H. J. Muller independently foresaw the plausibility of single-locus hybrid incompatibilities through this reasoning as well:

‘It is true that a special type of allelic interaction does sometimes occur where the combined action of two different alleles is enabled to transcend these limits of effect, as in the production of the “femaleness” reaction by heterozygous sex alleles in Habrobracon [ = Bracon] (Whiting) … Thus it is conceivable that lethality and sterility also may on rare occasions result from heterozygosis in respect to alleles that by themselves would have no such influence.’ (1942, p. 84)

GEI in nature may diminish the scarcity of such ‘rare’ allelic interactions.

Evolution of hybrid incompatibilities subject to GEI

How might our single- or multilocus model incorporating GEI explain naturally occurring RI? One scenario is when two divergent allopatric populations come into contact and subsequently hybridize in a new environment. We will simplify the genetics of the following scenario by only considering a single-locus, two-allele model; however, it is important to note that the genetics may be extended to any number of loci with similar results. Consider the case in which AA and aa individuals occur separately in a pair of allopatric populations, but upon hybridization in a new environment (i.e. a hybrid zone), Aa individuals may suffer from hybrid sterility or inviability. In other words, the Aa heterozygote and the AA and aa homozygotes are fit in the environments of the allopatric populations, but Aa individuals are unfit in the hybrid zone. Alternatively, the reciprocal is possible: Aa individuals are fit only in the relatively narrow hybrid zone, and are unfit outside of it (i.e. in the ‘parental’ habitats). Hence, hybrids may persist but not spread, essentially maintaining the genetic boundaries of developing species. Indirect evidence for the latter scenario exists in a hybrid zone between two plant species, Ipomopsis aggregata and I. tenuituba, in Poverty Gulch, Gunnison County, Colorado. Briefly, there are significant differences in survival between hybrid individuals from reciprocal parental crosses in both species’ habitats, but this survival difference disappears in the hybrid zone between the species (Campbell & Waser, 2001). In fact, both types of F1 hybrids have higher survival in the hybrid zone than the nonhybrids of I. aggregata. Although the genetic basis of hybrid survival in this species pair is unknown, this is a clear example of variation in hybrid fitness across naturally varying environments. More relevantly for this population genetic model, for hybrids derived from one of the parental cross directions, hybrid fitness is highest within the hybrid zone and lower when in either of the parental habitats. As implied above, hybrid zone size should be limited by the size of the habitat which is favourable to the hybrids, and this will help to reinforce isolation between the forming species. Arnold (1997) has comprehensively reviewed the literature on this topic and has amassed many examples where hybrids and specific hybrid genotypes show varying degrees of fitness in and outside of natural hybrid zones. He shows that the genetic architecture of hybrid populations is not unconditional and can depend upon the availability of environments for those hybrids.

Conclusions

  1. Top of page
  2. Abstract
  3. Introduction
  4. Extension of a single-locus hybrid incompatibility model to include GEI
  5. Extension of a multilocus hybrid incompatibility model to include GEI
  6. Discussion
  7. Conclusions
  8. Acknowledgments
  9. References

We conclude by suggesting a few lines of research relevant to testing aspects of our models. First, while field studies of hybrid incompatibilities encompass a broad range of environments that may demonstrate environmental influences on hybrid traits, laboratory studies are needed in most cases to classify GEI precisely. Hybrid genotypes must be reproducible (e.g. through sibship analysis, hybrid inbred lines, or marker-assisted introgression lines) and tested in well-defined environments. Studies of GEI for hybrid incompatibilities should be tractable in many systems by characterizing nonparallel reaction norms for hybrid sterility and inviability (e.g. Wade et al., 1999). Second, researchers investigating species pairs with genetic tools can test specific hybrid genotypes for nonparallel reaction norms to characterize which loci are involved in GEI more precisely. Additionally, mapping of QTL for hybrid incompatibilities in different environments may reveal that the genetic architecture of hybrid incompatibility can vary across environments. To our knowledge, no such QTL mapping studies have been performed. Finally, once the resolution of genetic studies of RI moves from loci to genes, we will be able to determine the derived vs. ancestral state of alleles involved in hybrid incompatibilities, and therefore whether ancestral–ancestral incompatibilities arise during the evolution of RI.

It is clear that much work needs to be done concerning the population genetics of speciation. The relative importance of GEI in the speciation process is not currently known. The combination of increasingly realistic population genetic models of the evolution of reproductive isolation and more detailed empirical genetic studies of incipient species pairs will greatly increase our knowledge of the process of speciation.

Acknowledgments

  1. Top of page
  2. Abstract
  3. Introduction
  4. Extension of a single-locus hybrid incompatibility model to include GEI
  5. Extension of a multilocus hybrid incompatibility model to include GEI
  6. Discussion
  7. Conclusions
  8. Acknowledgments
  9. References

We thank S. Frank, C. Kennedy, N. Leung, T. Long, A. Peek, P. Portin, D. Presgraves, S. Schrodi and J. Werren for helpful discussions and suggestions. We thank D. Campbell for sharing her unpublished data with us. We thank N. Johnson and an anonymous referee for helpful comments on an earlier version of this manuscript.

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  4. Extension of a single-locus hybrid incompatibility model to include GEI
  5. Extension of a multilocus hybrid incompatibility model to include GEI
  6. Discussion
  7. Conclusions
  8. Acknowledgments
  9. References
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