© 2002 by The Society for Integrative and Comparative Biology
Effects of Wolbachia on Genetic Divergence Between Populations: Mainland-Island Model1
1 Institute for Theoretical Biology, Humboldt University, Invalidenstraße 43, 10115 Berlin, Germany
2 Department of Biology, University of Rochester, Rochester, New York 14627
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Cytoplasmic incompatibility (CI) induced by intracellular bacteria is a possible mechanism for speciation. Growing empirical evidence suggests that bacteria of the group Wolbachia may indeed act as isolating factors in recent insect speciation. Wolbachia are cytoplasmically transmitted and can cause uni- or bidirectional CI. We present a mainland-island model to investigate how much impact Wolbachia can have on genetic divergence between populations. In the first scenario we assume that the island population has diverged at a selected locus and ask whether genetic divergence will be maintained after introduction of migration from the mainland. In the second we explore whether divergence will originate under migration. For simplicity, the host organisms are modeled as haploid sexuals. Simulations show that if each population is initially infected with a different strain of Wolbachia, then higher levels of divergence occur at the locally selected locus than in the absence of Wolbachia. A weaker effect is seen when there is only unidirectional CI caused by a single strain of Wolbachia on the island. CI increases divergence because it reduces effective migration between mainland and island. Migrants suffer from being confronted with the wrong CI system and this also applies to their matrilineal descendants. Moreover, there is a strong linkage disequilibrium between host genotype and infection state, which helps to maintain Wolbachia differences between the populations in the face of migration A sex bias in migration can either increase or decrease the effect of Wolbachia on divergence. Results support the view that Wolbachia has the potential for increasing divergence between populations and thus could enhance probabilities of speciation.
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INTRODUCTION |
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Wolbachia are widespread cytoplasmically inherited bacteria, found in approximately 20% of insects (Werren and Windsor, 2000
), and also commonly in isopods (Bouchon et al., 1998), mites (Breeuwer, 1997) and nematodes (Bandi et al., 1998). These bacteria cause a number of reproductive alterations in their hosts, including induction of parthenogenesis, feminization of genetic males, male-killing, and cytoplasmic incompatibility (for reviews of Wolbachia see Werren, 1997; Stouthamer et al., 1999). Wolbachia are predominantly inherited through the egg cytoplasm, but not via sperm. As a result, transmission is maternal, and the induced reproductive alterations are generally advantageous to the bacteria because they either increase the fitness or proportion of the transmitting (female) sex (Werren and O'Neill, 1997).
Cytoplasmic incompatibility (CI) is an incompatibility between the sperm and egg (see Hoffman and Turelli, 1997 for a review). Cytologically, the paternal chromosomes condense improperly during the first and subsequent mitoses (O'Neill and Karr, 1990; Breeuwer and Werren, 1990; Reed and Werren, 1995), which typically results in death of the developing zygote. There are two basic forms of CI. Unidirectional CI occurs when males from an "infected" population mate with females from an "uninfected" population. Bidirectional incompatibility can occur when two populations are infected with different strains of Wolbachia. CI can be interpreted as a "modification-rescue" system (Werren, 1997). The bacteria modify the sperm, and the same (or similar) strain of bacteria must be present in the egg to rescue the modification. The modification-rescue model can explain the basic patterns of CI (Fig. 1). Unidirectional incompatibility occurs when the sperm is modified but bacteria are not present in the egg to rescue the modification, whereas the reciprocal cross (uninfected male x infected female) is compatible. Bidirectional incompatibility presumably occurs when different strains of Wolbachia have different modification-rescue systems. However, the biochemical mechanisms of CI remain unknown.
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Cytoplasmic incompatibility has attracted attention as a possible mechanism for rapid speciation (Laven, 1959
, 1967; Powell, 1982; Werren, 1998; Hurst and Schilthuizen, 1998; Bordenstein et al., 2001). The basic idea is that CI may sufficiently prevent or reduce gene flow between populations to permit divergence and eventual speciation. The discovery that CI is caused by a widespread group of bacteria (Wolbachia) has revitalized interest in its potential role in speciation. However, this idea is controversial (Hurst and Schilthuizen, 1998; Wade, 2001). Empirical studies are accumulating that are consistent with a possible role of Wolbachia in speciation, including evidence that Wolbachia is a major isolating mechanism in some recent speciation events (Breeuwer and Werren, 1990; Shoemaker et al., 1999; Bordenstein et al., 2001), and growing evidence that many insect species harbor different strains of Wolbachia, often in different geographic populations (Mercot et al., 1995). Surprisingly, there have been virtually no theoretical investigations of the effect of Wolbachia on genetic divergence between populations. Here we investigate this topic, and specifically explore the interactions between migration, selection and Wolbachia induced CI using a mainland-island model. Our results show that Wolbachia induced CI (both unidirectional and bidirectional) can have significant effects on the level of divergence at a selected locus between populations and over a wide range of parameters. A crucial point is that Wolbachia induced CI reduces the effective migration rate between the populations.
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THE BASIC MODEL |
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The model is designed to investigate the effect of Wolbachia on levels of genetic divergence between a mainland and island population, where there is one-way gene flow (from the mainland to island) and positive selection at a single locus on the island (Fig. 2). The basic question is whether presence of Wolbachia, causing either unidirectional or bidirectional incompatibility, affects the level of divergence between the mainland and island population under different levels of selection and migration. For simplicity, we assume a haploid sexual organism. Selection occurs at a single locus with two alleles (G and g), where the G allele is under positive selection (s) on the island. We assume that the G allele is absent or at extremely low frequency on the mainland (e.g., is selected against on the mainland).
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We assume the following order of events each generation: migration, selection, reproduction. This scenario would be most appropriate, for example, for traits that are subject to selection in life stages after dispersal. Initially, we also assume that migration is equal in both sexes, but later we investigate the effects of sex-biased migration. Either one or two different strains of Wolbachia occur within the populations (without double infections), and there are therefore up to three cytoplasm types: A Wolbachia infected (A), B Wolbachia infected (B), and uninfected (0). Cytoplasmic type is inherited through the egg cytoplasm and therefore from females, but not paternally through males. Both Wolbachia types have the same transmission proportion through females, denoted by t. Those offspring that do not receive the Wolbachia revert to uninfected (0). All the offspring of uninfected females are uninfected. In addition, both Wolbachia types have the same characteristic cytoplasmic incompatibility level, l, which is the proportion of offspring that die in an incompatible mating. Cytoplasmic incompatibility occurs mainly when an infected male mates with an uninfected female or a female infected with a different Wolbachia type. Therefore, A males are incompatible with B females and 0 females, and B males are incompatible with A females and 0 females. 0 males are compatible with all three female types. But note that because of the incomplete transmission, infected females may produce some uninfected eggs. These eggs are assumed to be incompatible with the sperm from infected males (A or B).
To investigate the effects of Wolbachia, three starting situations (Fig. 2) were considered. Case 0 treats the situation without Wolbachia. Case A involves unidirectional incompatibility in which the mainland is initially uninfected and a Wolbachia A infection has spread on the island to its equilibrium frequency (see below). Case A + B involves bidirectional CI, Wolbachia A is initially present only on the island, and Wolbachia B only on the mainland. Both have reached their equilibrium frequencies. We do not consider the case where Wolbachia are present on the mainland but absent on the island because this configuration would not be stable to migration from the mainland.
The No Wolbachia case serves as a "control." That is, we initially determine the island frequency of the G allele under different levels of migration and selection in the absence of Wolbachia, and then compare the result with its equilibrium frequency in the other two scenarios. It should be kept in mind that the situations in case A and case A + B are only starting conditions for the selection process. Due to migration from the mainland, Wolbachia B can become established on the island, and in fact (as will be seen), when migration rates are sufficiently high, Wolbachia B can replace Wolbachia A on the island. Note also that because transmission rates of the infection are not necessarily 100%, both the island and the mainland will have uninfected (0) as well as infected individuals.
Finally, we consider two different classes of models that are relevant to the question of whether presence of Wolbachia either promotes the origin or the maintenance of divergence. The first class (Maintenance of Divergence Model) assumes that the two populations have diverged in allopatry with no migration, so that the G allele has gone to fixation on the island. Migration is then introduced from the mainland, and the equilibrium frequency of G is determined in presence or absence of Wolbachia. In the second class (Origin of Divergence Model) the two populations are initiated with migration and allowed to reach equilibrium frequencies of the different cytotypes on the island in the presence of migration. The positive selected G allele is then introduced and the spread of this initially rare G allele determined in the presence of migration. Under most parameter values tested, the two models give the same equilibrium result. However, this was not the case under all conditions (see below).
In the basic model, individuals are described by both nuclear genotype and cytotype. These two types cannot be treated separately because of nonrandom associations between them (linkage disequilibrium) caused by selection and CI. Since there are 3 possible cytotypes (A, B and 0) and two genotypes (G and g), we have six different nucleo-cytotypes. The selection equations (2)–(4) keep track of how the frequencies of these types change from generation to generation. The transition is described by a recursion formula (see below). Because we assume that the selection coefficient, s, is the same in both sexes, it is unnecessary to treat male and female frequencies separately.
The recursion has the following structure. We denote by pi,j the frequency of nucleo-cytotype (i, j), where i = 0 means uninfected, i = 1 infected with Wolbachia A, i = 2 infected with Wolbachia B; j = 0 means genotype g and j = 1 genotype G. To get 
, that is the frequency of nucleo-cytotype (i, j) in the next generation, the effects of migration and selection have to be taken into account (equation 2 and 3). Finally, we sum over all possible matings. But not all pairings contribute to nucleo-cytotype (i, j). So we have to weigh the output of each mating by factors that measure the inheritance of nuclear genes, the transmission of Wolbachia and the cytoplasmic incompatibility induced by Wolbachia (equation 4). In order to state the equations explicitly, we first define parameters and weighting factors:
m = proportion of the island population that are migrants from the mainland, defined each generation at the time of migration.
s = selective advantage of the G allele on the island (fitness of G individuals is 1 + s, that of g individuals 1).
t = proportion of A or B infected females' eggs that inherit the infection.
l = proportion of uninfected eggs that survive if fertilized by sperm from an A or B infected male.
The weighting factors that represent transmission of Wolbachia are denoted by Ti,j (defined in Table 1a). Ti,j is that fraction of offspring of a mother with infection state i that has infection state j. For example, Ti,0 is the uninfected part of offspring of a mother with infection state i; Ti,1 is the part of the same mother's offspring which is infected with Wolbachia A. Furthermore, expressions Li,j are weighting factors for cytoplasmic incompatibility. Li,j is the probability of survival of an egg with infection status j fertilized by sperm of a male with infection state i (defined in Table 1b). Finally, the factors that represent nuclear gene inheritance are denoted by Ii,j,k. Expressions Ii,j,0 and Ii,j,1 are the probabilities that an offspring has genotype 0, 1, respectively if the maternal and paternal genotypes are i, j, respectively. These probabilities are defined in Table 1c.
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Concerning migration, we assume that all migrants from the mainland have genotype g and are either uninfected or infected with Wolbachia type B. Further we assume that the infection has reached equilibrium on the mainland. Let ß be the equilibrium frequency of infected mainland individuals. This equilibrium depends on transmission t and incompatibility level l and can be calculated analytically (Turelli 1994
):
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We are now able to state the recursion formula for nucleo-cytotypes on the island. The intergenerational transition of these frequencies is split into three steps: migration, selection, reproduction. We start with the frequencies of nucleo-cytotypes in one generation, pi,j at the juvenile life stage. In the first step, equation (2), we obtain the frequencies after migration, denoted by 
. In the second step, selection acts via equation (3), yielding the frequencies after selection, 
. The last step, formalized by (4), is reproduction. After that, we have the frequencies of every nucleo-cytotype in the next generation on the island, .
Migration: First, migration takes place.
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The remaining four equations are for j = 1, i = 0, 1, 2 and j = 0, i = 1.
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Selection: Selection is described by equation (3). 
1 denotes the sum of all six numerators in (3); i = 0, 1, 2.
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Reproduction: Equation (4) describes reproduction. 2 denotes the sum of all six square brackets in (4); i = 0, 1, 2 and j = 0, 1.
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Solutions of this equation were calculated by at least 106 numerical iterations using Mathematica 4 and Visual C++ 6.0. A state was considered to be an equilibrium state if (a) subsequent frequencies differed by less than 10–4 and if in addition (b) the same result—within this degree of precision—was obtained by starting from two different states with lower and higher allele frequency of G.
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RESULTS |
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Equilibrium allele frequencies without Wolbachia
We first consider the basic selection scenario in the absence of Wolbachia. Allele G is advantageous on the island where its selective value is 1 + s and that of g is 1. Allele g reaches the island via migration at rate m. Using the standard population genetics approach we derived the island migration-selection equilibrium frequency of G analytically. The frequency p of allele G changes according to recursion equation
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This equilibrium is achieved whether the frequency of G evolves from above or below the equilibrium value. The G allele can only persist on the island if m < s/(1 + s)(note that this means that G is eliminated if m > s). As soon as migration exceeds s/(1 + s), the G allele will be driven to extinction by the steady influx of g from the mainland, so that the scope for local adaptation is indeed very limited. This analytical result was used to establish our "control" expectations for divergence in the absence of Wolbachia-induced CI. The result was also used to test the computer program that calculated numerical solutions of (2)–(4). In the absence of Wolbachia, the frequency of G evolved numerically to the expected equilibrium under all parameter values tested.
Maintenance of divergence model
First, we investigated the effect of Wolbachia on Maintenance of Divergence between the island and mainland populations. This involved a starting situation in which complete lack of gene flow between island and mainland had already led to allopatric divergence with fixation of G on the island and g on the mainland. We investigated the population genetics of the G allele on the island population after introduction of migration from the mainland (m proportion migrants per generation). In this model, either a single strain of Wolbachia was present at the initial island equilibrium (case A) or we had initially two different strains on mainland and island (case A + B).
We examined the model (2)–(4) for a set of parameter values that seemed biologically realistic. Since most Wolbachia have rather high probabilities of being passed on from a female to her eggs, transmission rates of t = 0.99 and t = 0.90 were used for both Wolbachia types. CI levels are more variable, and range from very low in Drosophila melanogaster to complete incompatibility in Nasonia vitripennis (Hoffman and Turelli, 1997; Breeuwer and Werren, 1990). CI levels of l = 0.99, l = 0.90, l = 0.80 and l = 0.50 were examined, since these encompass the range from nearly complete CI to rather weak CI. Very weak CI, as in D. melanogaster, can also effect the divergence between the populations, but the effects are much less pronounced and therefore not discussed in the paper.
Stability of the CI system. We first investigated the stability of the CI system. By this we mean whether the Wolbachia A infection is maintained on the island population despite migration from the mainland. In general we found that the island Wolbachia type remained at relatively high frequency across the range of migration rates until the migration rate approached a "threshold," above which the Wolbachia A went to extinction. Additionally we found that selection at the G-g locus stabilized the CI system at higher migration rates than when there was no selection at this locus. Figure 3 shows the equilibrium frequencies of Wolbachia A and the G allele as a function of migration for fixed selection coefficient and CI-level. Figure 3a, b compares case 0 (No Wolbachia) to case A (unidirectional CI) and to case A + B (bidirectional CI) whereas Figure 3c, d shows the corresponding cytotype frequencies. The island Wolbachia can be maintained at relatively high migration rates. At low-to-moderate migration rates (e.g., 0 < m < 0.15 for l = 0.9) in case A + B, Wolbachia B become established on the island, but generally remained at low frequencies. This is due to their CI disadvantage—the less common cytotype (uninfected or infected with Wolbachia B) on the island suffers a greater relative frequency of CI than does the common type (Turelli, 1994). However, there is a threshold migration level where the system collapses and Wolbachia A goes to extinction. In case A this led to an uninfected island and in case A + B to spread of the mainland Wolbachia B on the island.
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Also shown in Figure 3 are the equilibrium frequencies of G in the two populations for different migration rates and CI levels (but a fixed selection coefficient s = 0.01 or s = 0.1). As can be seen, the presence of uni- or bidirectional CI increases genetic divergence between the two populations at the selected locus, over a broad range of migration rates. This can be interpreted as a reduction of the effective migration rate caused by Wolbachia. When both Wolbachia have a CI level of l = 0.9, presence of Wolbachia A and B increases G allele frequency on the island from zero to 26% (for s = 0.01) or 91% (for s = 0.1), even when migration rates are as high as 10% per generation. Figure 4 shows that the threshold migration rate (i.e., the migration rate that causes collapse of Wolbachia A type) depends, to a good approximation, linearly on the selection coefficient s. For instance, if both CI levels are l = 0.9 and t = 0.99, the threshold migration rate is approximately 0.19 + 0.15s (Fig. 4a). Both the slope and constant are high if CI level is high. The threshold migration rate is higher for the unidirectional case A compared to case A + B. Threshold migration rates for lower transmission rate of t = 0.9 are shown in Figure 4b. As can be seen, lower transmission rate has only a small effect in case A + B, but results in a significant reduction of threshold migration rates in case A.
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The presence of the selected locus stabilizes the CI system at higher migration rates than in the absence of the selected locus. This can be explained by linkage disequilibrium between the selected locus and cytotype (Clark, 1984
; Asmussen et al., 1987; Sanchez et al., 2000) which is created by the combination of migration, selection and CI. The positively selected allele (G) is associated with the resident cytotype (A) and this association between two locally favored genetic elements boosts the frequency of both the G allele and the A cytotype. In conclusion, the presence of cytoplasmic differences between the mainland and island population can be maintained under a relatively wide range of migration rates. These cytoplasmic differences can, in turn, reduce the effective migration rate and cause a nucleo-cytoplasmic linkage disequilibrium. This results in maintenance of appreciable G allele frequency differences between mainland and island. However, if migration rates exceed a threshold value, then Wolbachia A collapses on the island. In case A the island becomes uninfected, and in case A + B the B Wolbachia replaces Wolbachia A, resulting in decline of the G allele.
Effects of selection level and CI interactions. Figures 5 and 6 show more clearly how the equilibrium frequency of G depends on the joint effect of selection level s for the G allele and CI level l. In Figure 5 all three cases with no, one and two strains of Wolbachia are presented for comparison. We can see two qualitative effects. First, the presence of Wolbachia enhances the G allele frequencies compared to case 0. Second, the presence of Wolbachia allows G to persist at lower s than without Wolbachia. Even in the case of a single Wolbachia type, the G allele can achieve consistently higher frequencies than in the absence of Wolbachia, over a wide range of selection values. But for case A + B both effects are much more pronounced than for case A.
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Figure 5a, c shows the frequencies of G for low migration (m = 0.01). When selection is weak, the positive effect of A + B on the G frequency can be dramatic, raising it, for example, from zero to 93%. Similarly, the range for which G persists can be rather large. An example is shown in Figure 5a, where the G allele is lost for s = 0.01 in the No Wolbachia case but still present for s = 0.001 at 45% in case A + B when both Wolbachia strains have a high CI level of l = 0.9. Also shown in the graphs is the unidirectional case A. We see the same qualitative effect that the G allele frequency is enhanced compared to the No Wolbachia situation, raising it, for example, from zero to 33%. Similar results can be obtained for high migration (m = 0.1) as long as the CI level is also high (Fig. 5b, l = 0.9). Different results occur for lower CI level of l = 0.5 in the bidirectional case A + B because Wolbachia A is driven to extinction. The loss of one cytotype leads to the convergence of the G allele frequency to values found in the No Wolbachia situation.
In Figure 6 we examine the effect of selection strength on maintenance of the G allele under bidirectional CI. We compare case A + B with case 0 for four different levels of CI (l = 0.99, l = 0.90, l = 0.80 and l = 0.50). This is presented on a logarithmic scale. In general, the figure shows that under a wide range of values for the selected locus, presence of bidirectional CI can lead to appreciably higher frequencies of the selected allele. As expected, the effects are most pronounced under high levels of CI (l = 0.99). With that high CI level we can see that the G allele can persist even for extremely low selection advantage s, one that is 100 times smaller than needed for persistence in case 0. Interestingly, this seems more or less independent of migration and transmission rates. These effects persist when CI levels are lower (e.g., l = 0.80 i.e., 20% "leakage"), the G allele can persist even when selection is 1/10 that which would allow persistence in the absence of CI. This means that the locally selected allele will be maintained in the presence of CI where it would be eliminated in its absence.
In summary, the results show that presence of both unidirectional incompatibility (Wolbachia only on the island) and bidirectional incompatibility (different "resident" Wolbachia on mainland and island) can increase the level of divergence at a selected locus, sometimes causing very large differences in allele frequencies between the two populations. There are two important contributing factors. First, CI reduces the "effective migration rate" by causing incompatibility between migrants (and their progeny) and the resident island genotypes. Second, a nucleo-cytoplasmic linkage disequilibrium stabilizes the cytoplasmic differences between the populations due to the combined effects of migration, selection and CI.
Origin versus maintenance of divergence
The treatment above explored the equilibrium frequency of a differentially selected allele when two populations come into contact after divergence. However, another reasonable scenario would be that the two populations would first come into contact via migration, achieve a cytotype equilibrium, and subsequently differential selection arises (Origin of Divergence Model). The questions then become "Can divergence occur?" and "Is the same equilibrium reached as for migration following divergence?" To simulate this, we first introduced migration without selection at the G-g locus. The g allele is fixed on both mainland and island. The two populations were allowed to evolve to equilibrium frequencies of the different cytotypes. Then the G allele was introduced with the low frequency of 0.01% on the island population. After that the system was allowed to evolve to equilibrium again.
Under most parameter values for the Origin of Divergence Model, the same equilibrium frequencies of G were achieved as for the Maintenance of Divergence Model. There is a simple rule for this. If the A-B (or A-0) incompatibility system does not collapse, then the G-locus spreads to the same equilibrium as in the Maintenance of Divergence Model (at least in all parameter values tested). Differences in the G allele equilibrium frequencies between the origin and the maintenance of divergence models can be seen in Figure 3. This figure shows the threshold migration rate that causes extinction of Wolbachia A on the island. The threshold depends on the selection coefficient. For the Origin of Divergence scenario the threshold migration rate can be found by looking at the case s = 0 in Figure 3. Differences in the G allele frequency occur due to differences in stability of the Wolbachia system under the two scenarios. For example, in case A + B if m = 0.17 and l = 0.9; then Wolbachia B spreads on the island in the Origin of Divergence Model before the G allele is introduced, eliminating the Wolbachia A. But if the G allele was fixed on the island with s = 0.2 prior to commencement of migration (Maintenance of Divergence Model), then the Wolbachia A infection persists in spite of high migration due to its association with the positively selected allele.
The explanation for this difference between the "origin" and "maintenance" models is as follows. If divergence has already evolved prior to the onset of migration, the linkage of the island resident Wolbachia A with the selected allele G allows Wolbachia A to persist in the island population at migration rates which are higher than in the absence of selection for G. In contrast, if the cytotype equilibrium is achieved under migration, but prior to selection, then moderate migration rates can result in elimination of the A cytotype on the island, and subsequently divergence of the G allele is not favored. However, if migration does not lead to elimination of the A cytotype, then Wolbachia permits selected alleles to increase to frequencies higher than those otherwise obtained. This result indicates that cytoplasmic differentiation between populations can occur in the presence of migration, and then effectively "wait" for differential selection to arise (Werren, 1997).
Effect of sex-dependent migration rates
Knowing that Wolbachia acts differently in males and females, we would expect sex differences in migration to influence divergence. Therefore, the basic model was extended to include migration bias. Three scenarios were modeled for case A and case A + B, (1) only females migrate, (2) 50% of the migrants are females and (3) only males migrate. These are compared with the No Wolbachia situation. The same parameter sets as in the previous section were used to numerically solve the Maintenance of Divergence Model. Total migration rate remains the same, but is allocated differently to males and females. Figure 7 shows how the frequency of G was influenced by sex differential migration. Our main finding was that the reduction of effective migration rate depends positively on the percentage of females among migrants.
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Before discussing the results, we want to remark that the higher the CI disadvantage of the migrants, the higher will be the frequency of G. In case A all migrants are uninfected. So females have a CI disadvantage, whereas males do not. This asymmetry leads to the large effects of sex differences in migration on G allele frequency, with the highest G allele frequencies if only females migrate (Fig. 7a, b). The two-Wolbachia situation shows the same general finding that the G allele frequency is highest if only females migrate (Fig. 7c, d). G allele frequencies are also higher than in case A. However, in contrast to case A, both male and female migrants have a CI disadvantage because they both carry the non-resident B Wolbachia. Females have an additional disadvantage compared to males because they transmit the mainland Wolbachia to their offspring whereas the offspring of male migrants do not inherit this Wolbachia from the father. So the frequency of G was highest if only females migrate and lowest if only males migrate.
In summary, sex differences in migration can strongly influence divergence between the populations; the higher the percentage of females on the migrants the higher is the G allele frequency on the island and the larger the parameter zone, where the G allele can persist in the face of migration.
Nuclear versus cytoplasmic incompatibilities
Here we compare the effects of nuclear and cytoplasmic incompatibilities on the divergence of the populations. Probably the most generally accepted genic model for hybrid sterility and inviability is the epistatic interaction model of Dobzhansky (1937) and Muller (1942). In the simplest form, it assumes two interacting genes, e.g., T1-T2. Divergence in these interacting loci in the two populations can then result in negative epistatic interactions in hybrids. If the negative interactions are recessive, then this will not be expressed until the F2 or subsequent generations; dominant or codominant effects will occur in F1. Recessive interactions are believed to evolve earlier and more readily during the speciation process (Turelli and Orr 2000). Nuclear based post mating incompatibilities appear to be common in plant and animal species (Rieseberg, 2001; see Turelli et al., 2001; for a review). To investigate the effect of nuclear based post mating incompatibility (NI) on Maintenance of Divergence between the populations, we extended our previous model (2)–(4). In addition to the G-g locus, two loci, T1-t1 and T2-t2, were added. Adapting the model for sexual haploids, we investigate the effects of recessive deleterious interactions between the loci, and assume that both recombinant genotypes (T1-t2 and t1-T2) suffer a fitness detriment. Relative fitness is 1 for the genotypes t1t2 and T1T2 and 1-sh for t1T2 and T1t2. This extended model was iterated at least 106 times to reach equilibrium frequencies. We used a starting situation in which complete lack of gene flow between the populations had already led to allopatric divergence with fixation of genotype GT1T2 on the island and gt1t2 on the mainland. We investigated the G allele frequency in the island population after introduction of migration from the mainland. Note that the maximal loss of offspring caused by NI is 0.5 sh, which contrasts to the maximal loss of offspring caused by bidirectional CI which is equal to the CI level l. This is because NI is modeled by two loci in a sexual haploid. This same difference would not occur in a model with diploid genetics.
Figure 8 compares the G allele equilibrium frequencies for nuclear and cytoplasmic incompatibilities. We see that the following scenarios result in the same frequencies: (1) the bidirectional CI with level l and a transmission rate of 100%, and (2) the NI with sh = 2l. This is shown in Figure 8a for l = 0.5 and sh = 1, and in Figure 8b for l = 0.25 and sh = 0.5. Both graphs also show the G allele frequencies for the bidirectional CI scenario with reduced transmission rate t = 0.99, which results in slightly reduced G allele frequencies. In other words, for recessive negative epistatic interactions (in haploid sexuals), a nuclear locus must have twice the negative fitness effect as CI to accomplish the same affect on G allele frequency. To examine dominant hybrid incompatibilities, we assumed a nuclear incompatibility with fitness cost sh in the diploid phase for heterozygotes at a locus (Tt). T is initially fixed on the island and t on the mainland. This form of incompatibility has the same effect on divergence at the selected locus G as does CI with level l = sh (data not shown).
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DISCUSSION |
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SYNOPSISINTRODUCTIONTHE BASIC MODELRESULTSDISCUSSIONReferences |
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The possibility that Wolbachia-induced cytoplasmic incompatibility could play a role in genetic divergence and speciation has been discussed for some time, but there have been few quantitative models. Here we have presented a "mainland-island" model that explores the evolutionary effects of Wolbachia on origin and maintenance of genetic divergence at a single locus. The model describes one-way migration from the mainland to the island, with positive selection for an allele in the island population. We considered two different cytoplasmic starting circumstances (a) Wolbachia only on the island and (b) different bidirectionally incompatible Wolbachia on the island and mainland. It should be emphasized that, because migration occurred from mainland to island, the "mainland Wolbachia" also occurred in the island populations. Further, because we assumed that transmission of Wolbachia was not perfect, uninfected individuals were also present in these simulated populations.
Our results show that under a wide range of conditions presence of cytoplasmic incompatibility results in significant divergence between the island and mainland at a selected locus. This can occur even when migration rates are substantial (e.g., 10% per generation). An unexpected result was that when there was only unidirectional incompatibility (Wolbachia on the island but not the mainland), significant levels of divergence could nevertheless result. However, divergence between mainland and island was most likely and most pronounced when two bidirectionally incompatible Wolbachia were present in the system. It should be emphasized that bidirectional incompatibility did not need to be complete (i.e., 100% mortality). Divergence occurred even with levels as low as 50%, although it was much more likely and stronger when CI was 80% or higher.
An explanation for why Wolbachia can maintain and promote divergence, even when CI is not complete, is that it reduces the "effective" migration rate between populations. This reduction not only occurs in the first migrant generation, but occurs in successive generations, as the progeny of female migrants will retain the "foreign" cytoplasm that is subject to elevated rates of CI. This coincides with our findings by analyzing sex differential migration. We could show that effective migration rate depends positively on the percentage of female migrants.
However, reduction of "effective" number of migrants is not the complete explanation for the effects of Wolbachia on divergence. Linkage disequilibrium between cytotypes and the locus under selection is also important. Basically, the "resident" Wolbachia in a population is strongly associated with the allele under positive selection. As a result, elevated frequencies of both the selected allele and the "resident" Wolbachia type were maintained, even in the face of substantial levels of migration into the population. The linkage disequilibrium effect explains why divergence between the populations could be maintained in the presence of migration at levels that would not have permitted divergence to evolve after the onset of migration between the populations. Our analysis indicates that these special circumstances occur when the level of migration would lead to "collapse" of the two-Wolbachia system by replacement of the island "resident" Wolbachia type with that from the mainland. If divergence has already occurred, the linkage disequilibrium between selected allele and resident Wolbachia resists this process over a certain range of migration or selective values. It should be emphasized, though, that under most circumstances where divergence occurs, it achieves the same equilibrium frequencies whether migration commences before divergence or afterwards. This finding is important, because it implies that when Wolbachia frequency or type differences occur between populations, these differences can persist until divergent selection begins to act upon them, and presence of Wolbachia will permit divergence under a broader range of selected values than in the absence of Wolbachia.
We compared bidirectional CI with nuclear based post mating incompatibility (NI) and found that for recessive nuclear incompatibilities, a fitness detriment 2x greater than that caused by CI was needed to cause an equivalent divergence at the selected locus. This result is strongly influenced by the sexual haploid genetics modeled here. Recessive epistatic interactions would result in much less divergence in diploids, due to the absence of recombinant homozygotes among the progeny of migrants and much reduced frequencies of double homozygotes among descendents. Thus, we expect that CI will have much larger affects than recessive incompatibility loci in diploids. Dominant genic incompatibilities should be similar in effect to CI in diploids. However, dominant incompatibilities are believed to evolve on average later than recessive incompatibilities in the speciation process (Turelli and Orr, 2000; Turelli et al., 2001). More complex patterns (e.g., recessives on the X and autosomes) have yet to be compared to CI effects on genetic divergence.
Bidirectional CI needs two different Wolbachia in different populations. Several studies suggest that around 20% of insect species are infected with Wolbachia (Werren et al., 1995; Werren and Windsor, 2000), although other authors put the frequency as high as 76% (Jeyaprakash and Hoy, 2000). Furthermore, there is accumulating empirical evidence that different populations of the same or closely related species are often infected with different strains of Wolbachia, including Drosophila simulans (Clancy and Hoffmann, 1996), Nasonia wasp's (Bordenstein et al., 2001), Trichopria drosophilae (Werren et al., in review), Protocaliphora flies (Werren et al., unpublished), Chelymorpha alternans tortoise beetles (Keller et al., in preparation), fire ants (Shoemaker et al., 2000), leaf-mining lepidoptera (West et al., 1998) and fig wasps (Shoemaker et al., in preparation). In some of these it was shown that Wolbachia causes bidirectional incompatibility. Additionally, some models suggest that new CI types could evolve relatively easily (Frank, 1997; Charlat et al., 2001).
Although our model shows that Wolbachia can affect genetic divergence between populations, and over a range of circumstances, it is also clear that the scope of these models needs to expanded. Some obvious areas to explore are: (a) two-way migration between populations, (b) effect of stochastic processes, (c) presence of multiple loci under selection, (d) interactions between mate-preference loci (i.e., reinforcement) and CI. Under models of two-way migration, it is much less likely that the single Wolbachia scenario will result in maintenance or evolution of divergence between the populations. The reason for this is that the Wolbachia is likely to become established in both populations (Turelli and Hoffmann, 1991), and therefore will not become differentially associated with the selected locus. It is less clear what the effects of two-way migration will be when there is bidirectional incompatibility in the system. Recent models for reinforcement of mate discrimination actually show that two-way migration is more effective at promoting divergence than one-way migration (Servedio and Kirkpatrick, 1997; Servedio, 2000). However, this needs to be explored for CI in more detail.
More theoretical work needs to be done to determine the range of circumstances under which Wolbachia affects divergence between populations. Nevertheless, the initial foray into this topic presented here provides theoretical support for the view that Wolbachia and cytoplasmic incompatibility can promote genetic divergence between populations, and therefore may play a role in speciation.
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ACKNOWLEDGMENTS |
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We thank Edward Hagen and two anonymous reviewers for helpful comments on earlier drafts of this paper. Work of JHW was supported by the NSF (DEB 9707665 and DEB 9981634), work of PH and AT by the Deutsche Forschungsgesellschaft (Innovationskolleg Theoretische Biologie). JHW and PH thank the Alexander von Humboldt Society for support of a sabbatical visit of JHW to Germany, where the original ideas for this collaboration were developed.
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FOOTNOTES |
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1 From the Symposium Living Together: The Dynamics of Symbiotic Interactions presented at the Annual Meeting of the Society for Integrative and Comparative Biology, 3–7 January 2001, at Chicago, Illinois.
2 E-mail: werr{at}mail.rochester.edu
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SYNOPSISINTRODUCTIONTHE BASIC MODELRESULTSDISCUSSIONReferences |
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