Adaptive Chromosomal Divergence Driven by Mixed Geographic Mode of Evolution

Adaptive chromosomal divergence driven by mixed geographic mode of evolution

Jeffrey L. Feder1,2Richard Gejii3Tom Powell1Patrik Nosil2,4

1Dept. of Biological Sciences, University of Notre Dame, Notre Dame, IN 46556, USA.

email: , .

2Institute for Advanced Study, Wissenschaftskolleg, Berlin, 14193, Germany.

3Dept. of Mathematics, University of Notre Dame, Notre Dame, IN 46556, USA.

email: .

4Department of Ecology and Evolutionary Biology, University of Boulder, Colorado, 80309, USA; email:

Corresponding author: Jeffrey L. Feder

Dept. of Biological Sciences, University of Notre Dame, Notre Dame, IN 46556, USA

e-mail:

Tel: (574)-631-4159

Fax: (574)-631-7413

Chromosomal inversionsare ubiquitous in nature and are of great significance for understanding adaptation and speciation (1-7). Here, we show that a mixed geographic mode of evolutioninvolving allopatric separation followed by secondary contact and gene flow generateschromosomal divergenceby natural selectionunder wider conditions than previoushypotheses (6-13). Moreover, the mixed model accounts for several patterns in the geographic distribution of inversions, includingincreased polymorphism in the center of species ranges(14), inversion differences in small populations (15), maladaptive inversions in allopatric populations(6, 7, 16, 17), and high frequencies of inversions in sympatric populations (10).As inversion differences often separate closely related taxa (6, 7), mixed modes of divergence couldbe common during adaptation and speciation.

Inversions have played a central role in evolutionary biology (18). Inversions werethe first markers used to investigate the genetic structure of natural populations, leading to the concept of coadapted gene complexes (1). Inversionshave also played a keyrole in advancingtheories concerning stochasticprocesses in evolution (6,7). Because of the presumed underdominance of inversions (3, 10, 16), it was argued that their fixation generally required pronounced genetic drift in small, isolated populations(6, 7; but see 19).

In contrast to underdominance models, more recentgenic hypotheses based on the allelic content and reduced recombination ofinversions have shown that inversions can spread without drift (8-13). In one class of ‘allopatric origins’ models, an inversioninitially rises to high frequency or fixation in a geographically isolated population. On secondary contact, populations remain differentiated for inversions, whereascollinear regions homogenize,due todifferences in the effectiveness of selectionin regions of low versushigh recombination (10, 11). There are theoretical difficulties, however, with allopatric origins models (12, 20). First, it is hardto explain howinversions arise and initially spreadin allopatric populations experiencing homogenous selection pressures (12), except perhaps by meiotic drive (6, 7). Second, if inversions oftenfixin allopatry prior to secondary contact, then they should commonly distinguish allopatric populations. In contrast to this prediction, five of six sympatric pairs of Drosophila sister species display inversion differences, whereaseight of nine allopatric pairs do not (10).

A’sympatric origins’ scenariounder which newly formed inversions capture locally adapted genes in hybridizing populations could explain the high incidence of inversions in sympatric populations (12). With gene flow, a newly derivedinversion canbe favored over the ancestral, collinear arrangementby keeping well-adapted genotypes intact due to reduced recombination between loci in inversion heterokaryotypes. The sympatrichypothesis is somewhat restricted, however, to conditions where migration between hybridizing populations ismuch lower than selectionfavoring locally adapted alleles (ms) (12). Lower migration rates are needed to avoid locally favored genes being swamped out by gene flow,andto ensure thata new inversioncapturesessentially allof the favorable alleles segregating in a population, a condition required for the inversion to spread (12). Butifmigration rates are too low, selection favoring reduced recombination for a new inversion is low becausewell-adapted genotypes arealreadypresent at high frequenciesin the collinear region. Consequently, new inversions will often be lost through stochastic processes and not establish in populations.

Here, we propose a novel mechanism that extends past genic theories to allow for the spread of inversions under more general conditions. The basic premise is that speciation may often involve multiple geographic modes of divergence, for example being initiated in allopatry and then completed with gene flow in sympatry following secondary contact (21-23). Under such a ‘mixed geographic mode’, the strengths of the allopatric and sympatric origins modelscomplement, while their inherent weaknessesare alleviated. Although it is difficult for rearrangements to spread in allopatry(12), for example due totheir being slightly deleterious because of alterations in gene expression patterns and meiotic irregularities in heterokaryotypes (3, 16, 23), inversions are nonetheless often present at low frequencies in allopatric populations (5, 17). These inversions are likely retained due to mutation-purifying selection balance (see below). However, these low frequency inversions will often contain the full complement of locally adapted genes, because allopatricpopulations are well-adapted across the genome due to lack of gene flow(Fig 1). Thus, following secondary contact, the selective advantage of reduced recombination can overpowerany slightly deleterious meiotic effect in heterokaryotypes, resulting in thespread of the inversion.Moreover, the highergene flow levels permissibleunder the mixed than sympatric model createa stronger selective advantage for reduced recombination, increasing the chances that an inversion becomes established.

The mixed geographic mode model has profoundevolutionarily implicationsbecause inversions are predicted to harbor genes causing adaptive divergence and reproductive isolation. Thus,mechanisms that facilitate the spread of inversions, such as the mixed mode model, likely also promote the creation of new species (10, 11, 20). Numerous other implications exist, including that in contrast to the sympatric origins model, chromosomal evolution inthe mixed model can happen without a waiting time for new mutation: selection will act immediately following secondary contact to increase the frequency of rearrangements whenever they exist in a populationand where-ever they occur in the genome, driving rapid chromosomal divergencefrom standing genetic variation (24). The mixed model applies to any taxa undergoing introgression (not just sister taxa) and the implications are not limited to inversions: the arguments apply to any structural factor or mutation reducing recombination rates.

Theverbal argument above raises a number of quantitative questions. For example, what levels of migration and recombination are conducive to the spread of inversions under a mixed model? How do these values compare to a model with pure sympatric divergence? How many copies of inversions are required in allopatry for the mixed model to work effectively? How do population sizes and selection coefficientsaffect the spread of inversions, and how might asymmetry in these parameters affect outcomes? Most critically, how well can the mixed model explain empirical patterns in nature?To address these issues, we performedpopulation genetic simulations examining the spread of inversions underboth thesympatric and the mixed modelhypotheses (25). The simulation results illustrate several general points.

First, the parameter values most conducive to the spread of an inversion by the mixed mode model are high migration rate, high recombination rate among loci in collinear arrangements, and moderately strong divergent selectionrelative to migration (Fig. 2). High migration and recombination rates favorthe spread ofan inversionby increasing the frequencies of locally maladapted alleles in the collinear arrangement following secondary contact and introgression. Divergent selection favoring the inversion in the range of 2 to 5 times the migration rate generally works best for establishing a rearrangement under the mixed model: when selection is too weaklocally adapted alleles are swamped out by gene flow, whereas when selection is too strong locally favored alleles are present in high frequency in collinear regions, lessening the advantage of reduced recombination for inversions.

Second,prestanding copies of an inversion that existin allopatry prior to secondary contact increasethe efficacy of the mixed model. Fig. 3illustrates how the probability of spread of an inversion in the mixed model increases with increasing copy number of standing inversions. The keyconsideration is that with multiple standing rearrangements, all copies of an inversion must be lost for a rearrangement not to establish. Thus, if a rearrangement does not greatly affect the chance that any other copy of the rearrangement is lost (a conservative assumption), then the relative probabilities for establishment of an inversion polymorphism under the mixed vs. sympatry origins models are ~ 1-(1-2s)k versus2s, where k = the copy number of the inversionat the time of contact, and s = the selective advantage of an inversion heterokaryotype.

What is the expected frequency of a standing inversion in an allopatric population? Under mutation-purifying selection balance, the mean expected frequency of a dominant deleterious inversionis~ u/s(= mutation rate/selection coefficient against heterokaryotypes) (26). Thus, for example, if the mutation rate per gamete is 10-9to generate a slightly deleterious inversion with s values in the range of 10-5to 10-6, we expect to see inversion frequencies from 0.001 to 0.0001 in allopatric populations. Such levelsare observed in nature (5, 17). For a population of n = 100,000diploid individuals,this would translateinto a copy number (k) of from 20 to 200, resulting in a much higher probability that an inversionis established in the mixed mode than the sympatric origins model (Fig. 3). In addition to mutation-selection balance, many slightly deleterious inversions may drift to modest frequency in small allopatric populations. Thus, the effects of standing inversions prior to contact can be significant in relation to the waiting time required for a new, favorable inversion to arise under the sympatric origins model.

Third, the mixed model relaxes the conditions for an inversion to establishrelative to those forthe sympatric origins model. As noted above, low migration rates can constrain the spread of an inversion. However, this constraint can be overcome by unequal migration rates, unequal population sizes, and to some degree unequal divergent selection coefficients.These inequalities have greater effect for the mixed than for the sympatric origins model. The mixed model therefore more strongly predicts that inversions will be preferentially established in smallerpopulations and can thusexplain inversion fixationin peripheral(peripatric pattern)or centrally located (stasipatric pattern) isolates without the need to invoke special circumstances such as founder effects and drift.In addition, when central populations are larger and migration rates modest, they can accumulate higher levels of inversion polymorphism due to gene flow from surrounding populations, helping explain why the centers of species ranges are often more variable for rearrangements (14).

Fourth,spreading the same overallamount of disruptive selection over greater numbers of loci enhances the mixed model, but restricts the sympatric originsmodel (Fig. S ). The mixed model thus predicts that smallinversions harboring few selected lociwill be rarer in nature.

Fifth,the mixed model makes a clearprediction that distinguishes it from the sympatric origins model. Specifically, the mixed model predicts that inversions in different regions of the genome will often share similar estimated times of origins based on DNA sequence divergence. This is because sequence divergencebetween taxa will tend to mark the time of original allopatric separation between the populations, rather than the time of origin of the different chromosomal rearrangements themselves. Such patterns have been reported in Rhagoletis flies (21), Drosophila (27), and Anopheles mosquitoes (28).

Finally, the mixed model has implications for addressing a classic and ongoing debated in evolutionary biology: did divergence occur in sympatry or allopatry (23)? Empirical data able to distinguish sympatric from allopatric divergence is notoriously difficult to obtain, and patterns of inversion polymorphism for presently allopatric taxa might provide insight into the biogeography of divergence. Specifically, if allopatric populations differ by fixed inversion differences, then they may have gone through a cycle of initial separation, contact, and secondary isolation. If inversion differences are not observed (as appears to be the case for the Drosophila species pairs discussed above), then populations may have been allopatric during their entire history of divergence, because fixing inversions without a period of gene flow can be difficult.

In conclusion, we have shown that a mixed geographic mode of divergence greatly enhances the opportunities for inversions to become established and differentiate taxa. We stress that such a model is not based on evolution occurring solely in sympatry or allopatry. Rather, it is the complementary combination of conditions occurring successively in allopatry and sympatry that makes chromosomal divergence likely. Our results also highlight the significance of standing genetic variation (24). The establishment of an inversion polymorphism, in addition to serving as an immediate seed for speciation, could also function as a reservoir of adaptive variation to foster exploration of populations of novel ecological niches that open in the future, leading to differentiation (e.g., Rhagoletis) (21). Thus, inversion spread via the mixed model could strongly facilitate rapid evolution from standing genetic variation (24) and have similar consequences for hybridization during hybrid speciation (11, 29, 30). As related taxa frequently display inversion differences (1-11), mixed geographic modes of divergence may be fairly common during speciation.

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31. We thank J. Mallet, A. Meyer, F. Ubeda de Torres. The idea for the manuscript was developed while JLF and PN were fellows at the Institute for Advanced Study, Wissenschaftskolleg, Berlin. This work was supported by grants to JLF from the National Science Foundation and the United States Dept. of Agriculture.

Figure Legends

Fig. 1. Schematic diagram of the A) mixed mode and B) sympatric origins models for the adaptive spread of chromosomal inversions. Populations 1 and 2 are shown by large boxes. When boxes touch the populations are exchanging genes, when they do not touch there is no gene flow (i.e., allopatry). Horizontal lines represent chromosomes and letters below the lines two alleles, ‘a’ and ‘b’, differentially adapted to local conditions in populations 1 and 2, respectively. Light grey boxes surrounding chromosomal regions represent inversions.

Fig. 2. The conditions for the spread of an inversion under the ‘mixed mode model’ (25).

Fig. 3. Copy number variation and the probability of fixation of an inversion (25).

Fig. 4. The effect of unequal population sizes on the probability of fixation of an inversion under the sympatric versus mixed models (25).

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Online Materials and Methods

General approach and assumptions. We used discrete generation, two-island population genetic computer simulations written in Matlab™ for a diploid, hermaphroditically reproducing organism to estimate the probabilities of establishment of inversions under the mixed geographic modeand sympatric origins models. The simulations reported in the manuscript text and Figures 2-4 assumed: 1) no gene flux (no effective recombination or gene conversion) between collinear and inverted regions , 2) multiplicative fitness interactions between loci with no epistasis, 3) a life cycle in which divergent selection followed migration between populations and occurred prior to mating, and 4) meiotic irregularities in heterokaryotypes due to single exchange events resulting in a baseline deleterious effect of s = 10-5. In the Extensions and Caveats section below, we examine the consequences of relaxing some of these assumptions.

Mixed Mode Simulations.For the mixed mode model, we considered the two island populations to initially be geographically isolated and not exchanging genes. Thus, at the start of a simulation run, populations 1 and 2 were alternately fixed for different locally adapted alleles a and b, respectively,at each locus under divergent selection. We initially considered population 1 to contain a single copy of an inversion that had a selective disadvantage of 10-5 in a heterokaryotype, reflecting problems in meiosis due to single exchange events(see below for discussion of the effects of meiotic irregularitieson the simulations).As in past inversion models,no gene flux was assumedbetween inverted and collineararrangements.However, recombination occurred at a rate of r between loci in homokaryotypes (inverted/inverted and collinear/collinear karyotypes). After secondary contact, individuals migrated from population 1 into population 2 with a probability ofm12 each generation and from population 2 into populations 1 with a probability ofm21. Population densities were assumed to be independently regulated in the two demes (i.e., soft selection), with a total of n1 and n2zygotes (newborn offspring) produced in each population each generation.We considered a life cycle with selection following migration and preceding mating (newborn offspring > dispersal between populations viability selection within populations > recombination/meiosis in parentsrandom matingand fusion of gametes within populationsnext generation of zygotes in populations). We then followed the fate of the inversion until it was either lost or retained as a polymorphism (see below for details of the criterion used to determine inversion establishment).