SELECTION IN HETEROGENEOUS ENVIRONMENTS MAINTAINS THE GENE ARRANGEMENT POLYMORPHISM OF DROSOPHILA PSEUDOOBSCURA

Authors

  • Stephen W. Schaeffer

    1. Department of Biology and Institute of Molecular Evolutionary Genetics, The Pennsylvania State University, University Park, Pennsylvania 16802
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E-mail: sws4@psu.edu

Abstract

Chromosomal rearrangements may play an important role in how populations adapt to a local environment. The gene arrangement polymorphism on the third chromosome of Drosophila pseudoobscura is a model system to help determine the role that inversions play in the evolution of this species. The gene arrangements are the likely target of strong selection because they form classical clines across diverse geographic habitats, they cycle in frequency over seasons, and they form stable equilibria in population cages. A numerical approach was developed to estimate the fitness sets for 15 gene arrangement karyotypes in six niches based on a model of selection–migration balance. Gene arrangement frequencies in the six different niches were able to reach a stable meta-population equilibrium that matched the observed gene arrangement frequencies when recursions used the estimated fitnesses with a variety of initial inversion frequencies. These analyses show that a complex pattern of selection is operating in the six niches to maintain the D. pseudoobscura gene arrangement polymorphism. Models of local adaptation predict that the new inversion mutations were able to invade populations because they held combinations of two to 13 local adaptation loci together.

Chromosomal rearrangements may contribute to how a species adapts to a heterogeneous environment (Otto and Barton 2001; Kirkpatrick and Barton 2006). When a population expands into a heterogeneous environment, modifiers that increase recombination can increase positive epistatic interactions among genes on chromosomes. Negative recombination modifiers such as inversions may evolve later to maintain the associations among positively interacting genes (Otto and Barton 2001). A newly arisen inversion chromosome may be lost or persist due to stochastic processes, however, if the new inversion captures a gametic combination whose marginal fitness is greater than the mean fitness of the population, it may be favored to invade a population (Charlesworth and Charlesworth 1973). Alternatively, chromosomal inversions may be favored to invade in models of migration–selection balance if two or more loci contribute to local adaptation in heterogeneous environment (Kirkpatrick and Barton 2006). Without inversions, migration introduces nonadaptive gene combinations into a population that can recombine with locally adapted chromosomes generating new gene combinations with lower fitnesses. If inversions capture locally adapted alleles, then the new gene arrangement will be favored because the suppression of recombination between local and migrant chromosomes prevents fitness losses.

Dobzhansky and Sturtevant (1938) discovered a rich gene arrangement polymorphism in Drosophila pseudoobscura that has served as a model system for the study of genetic diversity for over 70 years. In collections of D. pseudoobscura from across its geographic range, over 30 different gene arrangements of the third chromosome have been documented and the names of the chromosomes such as Arrowhead, Chiricahua, and Pikes Peak were derived from the locations where the chromosomes were first discovered (Dobzhansky and Sturtevant 1938). The gene arrangements can be related one to another through a series of single overlapping paracentric inversions. The single exception to this rule requires two inversion events to convert the Santa Cruz chromosome into the Standard arrangement through a yet to be discovered Hypothetical arrangement. This system was the first case in which genetic data were used to infer an evolutionary phylogeny.

All evidence suggest that the D. pseudoobscura gene arrangement polymorphism is under strong selection. The gene arrangement frequencies form classical clines in the southwestern United States (Dobzhansky 1944) that have been stable for over 60 years (Dobzhansky 1944; Anderson et al. 1991; Schaeffer et al. 2003) (Fig. 1). Gradients of inversion frequency occur across different altitudes and in some populations the gene arrangement frequencies cycle with the seasons (Dobzhansky 1948a). Genotypic frequencies were found to be in Hardy–Weinberg equilibrium when tested within populations (Dobzhansky 1944). Laboratory cage experiments reached stable equilibria depending on their population of origin suggesting that balancing selection played a role in the maintenance of the chromosomal polymorphism in nature (Wright and Dobzhansky 1946; Dobzhansky 1950). Dobzhansky also interpreted the cage experiments as evidence for coadapted gene complexes in which chromosomes from within populations had positive epistatic combinations, whereas chromosomes from different populations had negative interactions among genes (Dobzhansky 1949). Molecular genetic data reject the strict coadaptation model (Schaeffer et al. 2003).

Figure 1.

Map of the southwestern United States showing the frequencies of the major third chromosome arrangements of D. pseudoobscura estimated in three different decadal samples (Dobzhansky 1944; Anderson et al. 1991). The populations fall into six major niches in which migration within the niche is not likely to alter the inversion frequencies, but migration between the niches will cause frequencies to change. The localities in which gene arrangement frequencies were estimated are: Niche 1: 1. Kerby, OR; 2. Mendecino, CA; 3. Mt. St. Helena, CA; 4. Davis, CA; 5. Monterey, CA; 6. Santa Lucia Mts., CA; 7. San Rafael Mts. and Santa Barbara, CA; 8. Santa Cruz and Santa Rosa Islands, CA; 9. Santa Monica, Pasadena, and San Gabriel Mts, CA; 10. Riverside, CA; 11. San Jacinto Mts., CA; 12. Anza Borrego State Park, CA; Niche 2: 13. Deer Creek, CA; 14. Georgetown, CA; 15. Placerville and Tahoe, CA; 16. Mather, CA; 17. Southern Sierra Mts., CA; Niche 3: 18. Lamoille Canyon, NV; 19. Lehman Caves National Monument, NV; 20. Death Valley National Monument, CA; 21. Lone Pine Canyon, Inyo National Forest, CA; 22. China Ranch, Tecopa, CA; 23. Charleston Mts., NV; 24. Mojave and Colorado deserts, CA; 25. Prescott, AZ; 26. Tempe, AZ; 27. Organ Pipe National Monument, AZ; 28. Tucson, Huachuc, and Sonoita, AZ; Niche 4: 29. Ferron, UT; 30. Bryce Canyon, UT; 31. Mesa Verde, CO; 32. Betatakin, AZ; 33. Grand Canyon National Park, AZ; 34. Flagstaff, AZ; 35. Grant County, NM; 36. Chiricahua Mts., Cochise County, AZ; Niche 5: 37.Raton, NM; 38. Capitan, Hondo, Ruidoso, and Lincoln, NM; Niche 6: 39. Plains area, TX; 40. Trans-Pecos area, Marfa and Davis Mts., TX; 41. Austin, TX; 42. South-central, TX; 43. Valley area, TX.

Levels of gene flow are critical to understanding the genetic forces that introduce and maintain gene arrangement frequencies in populations. Neutral processes would be the likely explanation for the gene arrangement cline if new gene arrangement mutations diffused to new populations through low levels of gene flow. On the other hand, selection would be the likely explanation for the D. pseudoobscura gene arrangement frequency cline if migration levels are extensive because selection would need to be quite strong to overcome the homogenizing effects of gene flow. Extensive migration would also call into question the strict coadaptation model, which assumed homosequential chromosomes from different populations were differentiated from one another.

Initial direct estimates of dispersal in D. pseudoobscura suggested that gene flow was limited among optimal habitats (Dobzhansky and Wright 1943), however, later studies showed that dispersal was more extensive when flies were released in nonoptimal habitats (Coyne et al. 1987). Indirect molecular methods have estimated the migration parameter (Nem, where Ne is the effective population size and m is the neutral migration rate) to vary between 1.52 and 29.33 for genes distributed across all chromosomes of the D. pseudoobscura genome (Riley et al. 1989; Schaeffer and Miller 1992; Kovacevic and Schaeffer 2000; Schaeffer et al. 2003). The gene arrangement frequencies should be homogeneous among populations of the southwestern United States given that Nm is > 1 (Wright 1931). When Dobzhansky's (1944) genotypic data are combined across different populations, which is appropriate given the extensive gene flow, the genotypic frequencies reject Hardy–Weinberg equilibrium. We now ask what karyotypic fitnesses are necessary to differentiate gene arrangement frequencies among D. pseudoobscura populations in opposition to the homogenizing effect of migration.

A wide variety of population genetics models have been developed to analyze migration–selection balance in heterogeneous environments (for a review see Karlin 1982). Levene (1953) developed a model in which individuals in the migrant pool are distributed among different niches where local selection takes place. Survivors from the local niches make up the migrant pool in the next generation. The Levene (1953) model showed that a stable nontrivial equilibrium could be maintained over a meta-population without overdominance in any niche. The Levene (1953) model is unrealistic for the gene arrangement polymorphism of D. pseudoobscura because it is unlikely that all individuals will be randomly distributed among all niches each generation. Deakin (1966) explored a more realistic model in which a small fraction of migrants move among local niches each generation and selection alters allele frequencies within the niche. Deakin's (1966) model demonstrated that a protected polymorphism could be maintained if Vi < (1 −m+mci) in any niche, where Vi is the fitness of homozygous genotypes in the ith niche, m is the migration rate among niches and ci is the proportion of the population in the ith niche. Haldane (1948) developed a model to estimate selection coefficients for recessive deleterious alleles based on frequency differences among populations in a genetic cline. The alleles that comprise the gradient are deleterious recessive in one environment and beneficial in another habitat. The inversion frequency clines in D. pseudoobscura are not likely to fit this model well because it is not clear whether chromosomal rearrangements are deleterious recessive in some populations and not others as is seen in mouse coat color clines associated with dark and light substrates (Hoekstra et al. 2004).

The analytical solution for the fitness sets responsible for the D. pseudoobscura gene arrangement frequency cline is intractable. We present here an alternative numerical approach to infer fitness values for gene arrangement karyotypes in six niches of D. pseudoobscura to determine how selection maintains this chromosomal polymorphism. We tested whether the estimated fitnesses would lead to stable equilibria or protected polymorphisms (Mandel 1959; Deakin 1966). The populations of D. pseudoobscura fall into one of six niches that coincide with major physiographic provinces in the southwestern United States (Lobeck 1948). We assumed that a fraction of D. pseudoobscura from all niches can migrate to a new niche altering the local gene arrangement frequencies. We asked what fitness values for different chromosomal genotypes would be necessary to convert the migrant gene arrangement frequencies into those observed in the local population. We used inversion frequency data from collections in 1940, 1960, and 1980 to infer fitness matrices for the six niches. Migration–selection recursions reach the observed gene arrangement frequencies when estimated fitnesses from the three decadal samples are used. The six niches reach the observed equilibrium frequencies using a variety of initial inversion frequencies and when chromosomes are added sequentially into the recursion. The fitness sets in the different niches show evidence for directional, underdominant, and overdominant selection acting to maintain the D. pseudoobscura gene arrangements across the southwestern United States.

Materials and Methods

THE SIX NICHES WHERE D. PSEUDOOBSCURA LIVE IN THE SOUTHWESTERN UNITED STATES

Surveys of gene arrangement frequencies in D. pseudoobscura were performed every decade beginning in 1940 and ending in 1980 (Dobzhansky 1944; Anderson et al. 1991). We clustered 51 populations from the 1940 sample into different niches using the five most common gene arrangements, Standard, Arrowhead, Chiricahua, Pikes Peak, and Tree Line. These five chromosomes account for 95.1 to 98.3% of all the chromosomes scored in the five decade samples. All other gene arrangements are rare and the homokaryotypic frequencies are less than 1% in most populations. Euclidean distances estimated from gene arrangement frequencies among the pairs of localities were used to generate a dendrogram that clustered populations using the statistical package MiniTab 14.0 (Minitab, State College, PA). The 51 populations were chosen because each had sample sizes greater than 50 chromosomes. We used the clusters within the dendrogram and the locations of the 51 populations within the southwestern physiographic provinces (Lobeck 1948) (Figs. 1 and 2) to define six environmental regions or niches that differed dramatically in gene arrangement frequencies. The six niches are: Niche (1) Pacific Border Province; Niche (2) Sierra Nevada Mountains; Niche (3) Great Basin and Sonoran Desert; Niche (4) Colorado Plateau; Niche (5) Mexican Highland; and Niche (6) Great Plains. Gene arrangement frequencies within each niche are homogeneous such that migration is unlikely to change inversion frequencies, but are heterogeneous between regions. Discriminant analysis was used to determine the reliability of the classification of the D. pseudoobscura populations into the six niches.

Figure 2.

Dendrogram of 51 D. pseudoobscura populations determined from cluster analysis of gene arrangement frequencies. The gene arrangement frequency data can be found in Table 1 (on pages 82 to 88) of Dobzhansky (1944) for locality names. Euclidean distances were estimated among all pairs of populations.

SELECTION–MIGRATION BALANCE MODEL

We estimated the fitness values for the 15 gene arrangement karyotypes in each of the six niches of D. pseudoobscura using the following model. We assumed that the gene arrangements are superalleles at a single genetic locus that are under viability selection. Each discrete generation consists of a migration phase, where we assume that adult flies can move among niches and a selective phase, where survival of eggs, larvae, and pupae are governed by differences in the habitats of different niches. This is a model of soft selection in which the selection acts locally and the proportion of adults contributed from each niche is constant (Karlin 1982). The frequency of the ith gene arrangement in the kth niche was defined by a matrix of piks. We assumed that a pool of migrants composed of individuals from the five other niches arrived in the kth niche each generation based on the recursion,

image(1)

where mik is the migration rate from the ith to the kth niche. We assumed that natural selection altered the migrant frequencies (pik)migrant to the observed frequencies (pik)observed within each niche in one generation. The matrices of fitness values necessary to transform the migrant frequencies to the observed niche frequencies were estimated with a numerical approach. The fitness value for the ith and jth arrangement karyotype in the kth niche is given by wijk and we assumed that wijk=wjik. Let us consider how the fitnesses were estimated for Niche 1. The vector of marginal fitnesses for Niche 1 are estimated by,

image(2)

The average fitness for Niche 1 is given by,

image(3)

where T is the transpose operator. If the fitness values reflect how selection transforms the migrant gene arrangement frequencies into the observed frequencies, then the following recursion will hold:

image(4)

We used an iterative process to determine the matrix of 15 fitness values. Initially, we set all fitness values wij1 to 1 and estimated a vector of (pi1)test values using equation (4). The deviation of the test and observed frequencies was estimated by,

image(5)

If D was greater than 0.0005, then the 15 fitness values for the niche were perturbed. A normal deviant was added to each fitness value, where the normal deviate had a mean of 0.003 and a variance of 1. A new vector of (pi1)test values was reestimated from equations (2–4) to determine if the new D was less than the initial D. If so, then the new fitness matrix was kept. If not, the original fitness matrix was kept. We iterated this process until D was less than or equal to 0.0005. The set of 15 fitness values was standardized by dividing each value by the maximum fitness among the 15 karyotypes. Because we did not demand an exact solution where D= 0, we performed 1000 replicate estimates of the fitness values to determine variances for our estimates. Fitness values were estimated for the 15 genotypes in each niche for each of three decade samples, 1940, 1960, and 1980 (Dobzhansky 1944; Anderson et al. 1991). It should be emphasized that the estimated fitnesses are those that are necessary to change gene arrangement frequencies in a single generation following the homogenization of diversity following migration. This numerical approach is unable to estimate fluctuating fitness values that may have occurred in the historical past.

MIGRATION RATES AND SCHEMES

We assumed that the six niches are structured as in Wright's (1931) island model. The extent that individuals from donor populations or niches migrate into a recipient population within a niche depends on two factors. First, the migration rate m determines the contribution of individuals from donor populations into the recipient population. Second, the migration scheme describes the probability that individuals from the five nonself niches move to the recipient population. We examined the effect different migration rates have on fitness estimates by comparing three values of m, 0.025, 0.050, and 0.075. In addition, we examined the sensitivity of fitness estimates to a wider range of migration rates (see Supporting Information). Three different migration schemes were used to weight the number of nonself individuals that migrate into the target niche. The Uniform migration scheme assumes that the probabilities of migrants moving to any of the five other niches are equal, where the matrix of miks is given by,

image

The second broad class of migration schemes assumes that the probabilities of migrants moving to any of the five other niches are unequal. The most realistic type of model is the isolation by distance model of Wright (1943), where migrants are more likely to move between adjacent niches rather than between more distant niches. We used two different migration schemes to model Wright's isolation by distance (Wright 1943) model. The first scheme used probabilities from a Normal distribution to determine the relative contributions of individuals from nonself niches given by the matrix of miks,

image

The weighting factors were normalized to insure that each row of the matrix summed to 1. The second scheme used the Laplace or double exponential distribution to determine the relative contributions of individuals from nonself niches given by the matrix of miks,

image

The Laplace distribution is more leptokurtic relative to the Normal distribution and is likely to be more realistic in simulating isolation by distance.

STABILITY ANALYSIS

The fitness values estimated from each decadal sample were used in deterministic migration–selection recursions to estimate the number of potential equilibrium points. We used the “broken stick” method to choose 25,000 random initial frequencies for the five gene arrangements in the six niches (MacArthur 1957; Star et al. 2007). The migration–selection recursions were applied to each set of initial frequencies for 4000 generations. The final gene arrangement frequencies after 4000 generations were determined to be at equilibrium if the frequencies did not change from the previous generation. The number and frequency of each equilibrium point was recorded from the 25,000 initial conditions.

We used the criterion of Deakin (1966) to determine if the fitness sets in the six different niches support the hypothesis that the D. pseudoobscura gene arrangement cline represents a protected polymorphism. We also tested each fitness matrix within each niche to determine whether stable nontrivial equilibria were possible for two, three, four, and five alleles (Mandel 1959). To evaluate the two, three, and four chromosome polymorphisms, we took appropriate subsets of the estimated fitness matrices and tested all combinations of chromosomes for potential multiple arrangement equilibria.

DYNAMICS OF GENE ARRANGEMENT FREQUENCY CHANGES

The fitness values estimated from each decadal sample were used in deterministic migration–selection recursions to determine the dynamics of gene arrangement frequency change over time. These recursions assume that fitness values have been constant through time, an assumption that is not likely to be realistic. In this recursion, the different gene arrangements were added sequentially based on the inferred age of the chromosomes. Nucleotide sequences at the vestigial locus (Schaeffer et al. 2003) were the basis for the estimate of gene arrangement ages. The vestigial data show that the TL is the ancestral arrangement so the population began fixed for the TL arrangement, and the next four chromosomes were added according to their inferred age. A new chromosome was introduced into the niche where the new arrangement had the highest marginal fitness (Charlesworth and Charlesworth 1973; Charlesworth 1974). The sequential addition recursions were run for 500 to 2000 generations and the data were plotted to show the dynamics of gene arrangement frequency changes.

ANALYSIS OF CLIMATE DATA

We downloaded climate data from the National Oceanic and Atmospheric Administration Website to determine if any environmental variables show associations with the six niches defined by the D. pseudoobscura gene arrangement frequency data (at the following URL: http://www1.ncdc.noaa.gov/pub/data/ccd-data/Anonymous 2006). We used Principal Components Analysis to determine the major climatic variables that explain the observed variation among the different niches. We also asked how well the genetic classification of regions into six niches was an accurate reflection of climatic differences with Discriminant Analysis.

Results

EFFECTS OF MIGRATION RATES AND MIGRATION SCHEMES ON FITNESS ESTIMATES

Migration rate and scheme have an effect on fitness estimates within karyotypes, but not on the relative fitnesses among karyotypes. As the magnitude of migration m was varied, fitness estimates changed within karyotypes (Fig. 3). Increasing the migration rate caused the estimated fitness values to become more extreme because increasing dispersal rates led to greater disparities between the migrant and observed gene arrangement frequencies. Larger differences between the migrant and observed frequencies required selection pressures to be stronger to alter the migrant frequencies into those of the local niche. Varying the migration rate, however, did not change the relative fitness differences among the 15 karyotypes (Fig. 3). For a more extensive analysis of different migration rates, see the Supporting Information and Supporting Figures S1 and S2.

Figure 3.

The effect of migration rate on estimates of fitness values for 15 gene arrangement karyotypes in six different niches using the 1940 inversion frequencies (Dobzhansky 1944). The three migration rates examined are: L is m= 0.025, M is m= 0.050, and X is m= 0.075. The Uniform migration distribution model was used in these analyses. The vertical segments indicate a 95% confidence interval for the estimates of fitness for each genotype.

The migration schemes have similar effects on fitness estimates as migration rate does (Fig. 4). Shifting from a leptokurtic (Laplace) to a platykurtic (Uniform) migration schemes led to changes in fitness estimates within karyotypes. The Uniform migration model led to the most extreme fitness estimates within karyotype compared to the Laplace distribution model. The explanation for this is that adjacent niches within the cline tend to have more similar gene arrangement frequencies. As the contributions from neighboring niches decreases, migrant gene arrangement frequencies diverge more from that observed in each niche. As a result, selection pressure must be greater to alter the migrant population chromosome frequencies. Varying the migration distribution scheme, however, did not change the relative fitness differences among the 15 karyotypes (Fig. 3).

Figure 4.

The effect of migration distribution model on estimates of fitness values for 15 gene arrangement karyotypes in six different niches using the 1940 inversion frequencies (Dobzhansky 1944). The three migration distribution models examined are: L, Laplace; N, Normal; and U, Uniform. The migration rate used in all estimates was m= 0.025. The vertical segments indicate a 95% confidence interval for the estimates of fitness for each genotype.

Because the migration rate and distribution model did not affect the relative fitness differences among gene arrangement karyotypes, we will use the fitness estimates from the uniform migration scheme for all subsequent analyses. This assumption is justified based on the lack of evidence for isolation by distance in North American populations of D. pseudoobscura (Riley et al. 1989; Schaeffer and Miller 1992; Kovacevic and Schaeffer 2000; Schaeffer et al. 2003).

FITNESS DIFFERENCES AMONG GENE ARRANGEMENT KARYOTYPES WITHIN AND BETWEEN NICHES

The fitness estimates for the six niches of D. pseudoobscura allowed us to examine how selection has operated on these chromosomes in light of historical models. There is not an average overdominance in any of the six niches or across all populations (mean heterozygote advantage as estimated by the formula on page 1628 in Star et al. 2007). More careful examination shows some interesting trends in the fitness sets. In the analysis of the 1940 sample, Niche 1 has three gene arrangements that account for 96.3% of the observed chromosomes, Standard (ST), Arrowhead (AR), and Chiricahua (CH), whereas Pikes Peak (PP) is virtually absent (Fig. 1). Overdominant selection appears to maintain the three major chromosomes because the heterozygotes ST/AR, ST/CH, and AR/CH have higher fitnesses than their respective homozygotes, however, the ST-AR-CH equililibrium is not stable (Fig. 3 and see Stability Analysis below). PP appears to be removed from Niche 1 because of strong underdominant selection on PP heterozygotes rather than selection against the PP homozygote (Fig. 3). Niche 6 also shows this trend, except that ST and CH are selected against in heterozygotes with the more frequent chromosomes AR and PP. The general theme for Niches 1 and 6 is that gene arrangements are modulated by a combination of over- and underdominant selection.

Niche 4, on the other hand, represents a clear case for strong directional selection on the AR chromosome. Arrowhead is nearly fixed in Niche 4 populations and the fitness of the Arrowhead homozygote is greater than any genotype in the niche. Thus, without the influx of migrants, Arrowhead would go to fixation (Fig. 3). The overall combination of fitness sets in the six different niches acts to maintain a larger set of alleles than any single population.

Figure 5 shows a comparison of the fitness estimates from the three decadal samples for the Uniform migration scheme and a migration rate of 0.025. The striking feature in the comparison of the different decade samples is that the estimated fitnesses in some niches have changed dramatically between 1940 and 1960. The strong selection against PP heterozygous genotypes in Niche 1 has disappeared. In addition, the ST/AR genotype has changed from being overdominant to underdominant relative to its two homozygotes. Niche 4 has shown the least change in fitness estimates over the three decades compared to other niches. Selection has favored the AR homozygote over all other genotypes.

Figure 5.

The effect of different decadal samples on estimates of fitness values for 15 gene arrangement karyotypes in six different niches for a migration rate of 0.025 and a Uniform migration distribution model. The three decadal samples are 1940, 1960, and 1980 (Dobzhansky 1944; Anderson et al. 1991). The vertical segments indicate a 95% confidence interval for the estimates of fitness for each genotype.

STABILITY ANALYSIS

We used migration–selection recursions to infer the number and frequency of equilibrium points for each fitness set. The fitness sets estimated from each yearly sample yield multiple stable equilibria based on the random initiation frequencies. We examined the effect of migration rate on the number and frequency of nontrivial equilibria reached using the 1940 fitness sets estimated from m values of 0.025, 0.050, and 0.075. As the migration rate increased in the model, the fitness values for the different karyotypes increased in intensity. With increasing selective intensity, the number of stable nontrivial equilibrium points decreased (Table 1). For each fitness set and migration rate, one equilibrium point was reached for > 94% of the initial frequencies. The most frequent equilibrium point reached had the highest mean fitness across all niches and the final frequencies in each niche of this equilibrium point matched those observed in nature inferred from Nei's (1972) genetic identity (I). Nei's I varies from 0 to 1, where 0 indicates that inversion frequencies are completely different between populations whereas 1 indicates that the gene arrangement frequencies are identical between the two populations.

Table 1.  The number and frequency of stable equilibrium points for fitness estimates based on D. pseudoobscura gene arrangement samples collected in 1940, 1960, and 1980.
YearmEquilibriuminline imageNo. (%)  Nei's IArr. Present
  1. Year=Gene arrangement frequencies from this year were used to estimate karyotype fitnesses, m=migration rate used to estimate fitness values, Equilibrium, label for an equilibrium point reached based on initial frequencies determined using the “broken stick” method, inline image, Average mean fitness across the six niches for the equilibrium point; No., number of initial frequency conditions that reached this equilibrium point along with the percent of 25,000 replicates; Nei's I, estimate of Nei's (eq. 2 in Nei 1972) genetic similarity between the equilibrium point frequencies and the observed gene arrangement frequencies; Arr. Present, gene arrangements present across the six niches for the equilibrium point.

19400.02510.8464 (0.02) 0.291AR PP TL
  20.86714 (0.06) 0.447ST AR CH PP TL
  30.8672 (0.01) 0.497AR PP TL
  40.88840 (0.2)  0.673ST AR PP TL
  50.8927 (0.03) 0.660ST AR CH PP TL
  60.903477 (1.9)  0.823ST AR CH PP
  70.917312 (1.2)  0.809ST AR CH PP TL
  80.917472 (1.9)  0.821ST AR CH PP TL
  90.94323,672 (94.7) 1.000ST AR CH PP TL
 0.05010.8364 (0.02) 0.487AR PP
  20.8672 (0.01) 0.657ST AR CH PP
  30.87829 (0.1)  0.822ST AR CH PP
  40.90115 (0.06) 0.822ST AR CH PP TL
  50.92924,950 (99.8) 1.000ST AR CH PP TL
 0.07510.8382 (0.01) 0.655ST AR CH PP
  20.87825 (0.1)  0.821ST AR CH PP
  30.91624,971 (99.9) 0.999ST AR CH PP TL
19600.02510.9182 (0.01) 0.344AR PP
  20.951410 (1.6)  0.871AR CH PP TL
  30.95924,588 (98.4) 1.000ST AR CH PP TL
19800.02510.88321 (0.08) 0.168ST CH TL
  20.9064 (0.02) 0.297AR PP
  30.938236 (0.9)  0.788ST AR CH PP TL
  40.9531 (0.004)0.904AR PP TL
  50.9541 (0.004)0.912AR PP TL
  60.96524,740 (98.90)1.000ST AR CH PP TL

The fitness sets estimated from the 1960 and 1980 data also found multiple equilibrium points, but the numbers of points were less than those estimated from the 1940 data (Table 1). Again, the most frequent equilibrium point reached for the 1960 and 1980 data had the highest mean fitness across all niches and the final frequencies in each niche of this equilibrium matched those observed in nature. The recursion analysis implies that stable nontrivial equilibria are reached in the six niches and across all niches.

We tested the fitness sets estimated from the 1940, 1960, and 1980 samples in the six niches for all possible nontrivial equilibrium and whether these equilibria would be stable according to the criteria of Mandel (1959). In none of the cases, does a five or four allele nontrivial equilibrium exist in any of the six niches for any decadal sample. The number of niches with four or more arrangements was three in the 1940 sample, six in the 1960 sample, and four in the 1980 sample (Table 2).

Table 2.  Nontrivial and stable equilibria for six niches of D. pseudoobscura.
NichePolymorphism194019601980
  1. Notes: The table presents all cases in which a nontrivial equilibrium exists for the fitness sets estimated for at least one decadal sample. Exists stable, indicates that the nontrivial equilibrium exists and that it is stable (Mandel 1959). Exists, indicates that the nontrivial exists, but that the equilibrium point is unstable. DNE indicates that the nontrivial equilibrium does not exist.

Niche 1Two arrangements   
 ST ARExists stableExistsExists
 ST CHExists stableExists stableExists stable
 ST TLExists stableExists stableExists stable
 AR CHExists stableDNEExists
 AR TLExists stableDNEDNE
 CH TLExists stableExists stableExists stable
Niche 2Three arrangements   
 ST AR CHExists stableDNEDNE
 Two arrangements   
 ST ARExists stableDNEExists stable
 ST CHExists stableDNEDNE
 ST TLExists stableDNEExists stable
 AR CHExists stableExists stableExists stable
 AR TLExists stableExists stableExists stable
 CH TLExists stableExists stableExists stable
Niche 3Two arrangements   
 ST ARExists stableDNEDNE
 ST CHExists stableExists stableExists stable
 AR CHExists stableDNEDNE
Niche 4Two arrangements   
 ST CHExistsExists stableExists
 PP TLExists stableDNEExists
Niche 5Two arrangements   
 AR PPExists stableExists stableExists stable
 CH-TLDNEDNEExists stable
 PP-TLDNEDNEExists stable
Niche 6Two arrangements   
 AR CHExistsExistsExists stable
 AR TLExists stableExists stableExists stable
 CH TLExistsDNEExists stable
 PP TLExists stableDNEDNE

Two and three allele nontrivial and stable equilibria are possible based on the estimated fitness values in the three decadal samples (Table 2). For instance, the ST, AR, and CH polymorphism in Niches 2 and 3 is predicted by the fitness values. This occurs because of global overdominance of the three heterozygotes. The migration that occurs among populations allows more arrangements to be maintained in each niche than is predicted based on the stability analysis of the nontrivial equilibria.

To assess whether the gene arrangement polymorphism would be protected based on the estimated fitnesses in the six different niches, we examined whether the estimated fitness values fit Deakin's (1966) criterion for a protected polymorphism, Vi < (1−m+mci), where Vi is the fitness of homozygous genotypes in the ith niche, m is the migration rate among niches, and ci is the proportion of the population in the ith niche. Under this criterion, the polymorphism will be protected if Vi < (1 −m+mci) holds in any niche i. If we set the migration rate to 0.025, 0.050, or 0.075 and ci to 1/6, which assumes that the proportion of the population in each of the six niches is equal, then 1 −m+mci will equal 0.979, 0.958, or 0.938, respectively. Based on Deakin's (1966) criterion, the gene arrangement polymorphism of D. pseudoobscura is a protected polymorphism because all homozygous genotypes are significantly less than the criterion value in at least one niche in all analyses (Figs. 3 and 5). Although the majority of two, three, four, and five allele nontrivial equilibria are unstable for our estimated fitness sets, the gene arrangement polymorphism of D. pseudoobscura is protected.

RELATIVE AGES OF THE FIVE GENE ARRANGEMENTS

We investigated whether the sequential addition of gene arrangements based on their relative age could lead to the observed chromosomal frequencies in a migration–selection recursion. The sequential addition recursion begins with a population fixed for one gene arrangement and then introduces chromosomes into the population at low frequency based on the inferred gene arrangement's age. We estimated the relative ages of the five chromosomes from nucleotide sequence data from the vestigial locus (Schaeffer et al. 2003; Fig. 6). Schaeffer et al. (2003) determined the nucleotide sequence of 651 nucleotides of intron 1 of the vestigial locus in 92 individuals. The vestigial locus of D. pseudoobscura maps to within 20 kb of the distal breakpoint of the derived Arrowhead gene arrangement (Richards et al. 2005). The close proximity of the locus to the Standard/Arrowhead breakpoint makes it an ideal candidate to estimate the age of the five gene arrangements because recombination is suppressed near the breakpoint and is unlikely to obscure the true relationships of the chromosomes (Navarro et al. 1997, 2000; Machado et al. 2007). The vestigial locus will be near a breakpoint when the Arrowhead arrangement is paired with any of the four other arrangements making it a good candidate to recover the age and relationships among the five arrangements. The phylogeny shows that the five gene arrangements are monophyletic (full data, not shown) and the coalescence time of each chromosome provides an estimate of the time for expansion for each chromosome. The relative ages suggest that we should introduce the Tree Line chromosome first, the Standard arrangement in generation 46, Chiricahua in generation 92, Arrowhead in generation 110, and Pikes Peak in generation 111. When a chromosome was added, it was introduced at a frequency of 1% to simulate the occurrence of a rare mutation and the frequencies of the other chromosomes were adjusted downward to compensate for the added chromosome. Similar recursion dynamics and equilibria were obtained when chromosomes were introduced at the more realistic frequency of 1 × 10−6, however, the recursions took more generations to reach equilibrium.

Figure 6.

Phylogenetic tree of the five major gene arrangements of D. pseudoobscura determined from 651 aligned nucleotides of intron sequence in the vestigial locus in 92 individuals (5 TL, 15 CH, 14 ST, 42 AR, and 16 PP). The linearized tree was inferred with neighboring-joining (Saitou and Nei 1987) using a Kimura two-parameter model as implemented in Mega 3.0 (Kumar et al. 2004). Bootstrap values were estimated from 1000 D. pseudoobscura-replicates.

DYNAMICS OF GENE ARRANGEMENT FREQUENCY CHANGES

The sequential addition recursion for the 1940 fitness estimates shows that the dynamics of frequency change can be quite complex (Fig. 7). The chromosome frequencies reach nontrivial equilibria in the six different niches with frequencies that match the observed data. Some chromosomes increase in frequency for a period of time, then rapidly decline as is the case for the Standard arrangement in most niches. The Arrowhead chromosome is the only chromosome that has steadily increased in frequency across all populations. Chiricahua and Pikes Peak chromosomes had steady increases in some populations, but not in others.

Figure 7.

Drosophila pseudoobscura gene arrangement frequency changes in six niches over 500 generations using fitness values estimated from the 1940 inversion frequency data (Dobzhansky 1944). The recursion was initiated with populations that were fixed for the Tree Line arrangement and the four other chromosomes were added sequentially according their estimated ages. A migration rate of 0.025 and a Uniform migration distribution model was used in the recursion.

We also used the recursion equations to consider the individual effects of migration and selection on the gene arrangement frequencies in the six niches. When the migration rate is set to zero, but we use the estimated fitness values in the sequential addition recursion, we find that the six niches reach different gene arrangement frequencies than are observed in nature (see Supporting Fig. S3). This suggests that without migration local adaptation would lead to different end points in each population. When all fitness values are set to one, but we use the observed population gene arrangement frequencies and the migration rate used in the estimation procedure, we find that the gene arrangement frequencies reach the same values, which are the mean values across the six niches (see Supporting Fig. S4). This makes intuitive sense because migration is a homogenizing force. These two controls demonstrate that the combination of selection and migration values is required for the recursions to end at the observed population frequencies.

We considered the possibility that the Standard arrangement was the ancestral chromosome (Dobzhansky 1944; Bartolome and Charlesworth 2006) in the recursion analysis. These recursions failed to reach the observed gene arrangement frequencies in any of the six niches (S. W. Schaeffer, unpubl. data). It is not clear whether we should interpret these results to mean that Tree Line is the ancestral arrangement. Further analyses are needed to convince us that Standard cannot be the ancestral arrangement.

Altering the migration rate to estimate the fitness sets has a minor effect on the dynamics of gene arrangement frequency change (Fig. 7, see Supporting Figs. S5 and S6). We used the fitness values estimated from the 1940 sample using the three migration rates of 0.025, 0.050, and 0.075 to compare the dynamics of gene frequency change. The major effect that migration rate has is to change the rates that gene arrangement frequencies expand and contract in the population, but not the eventual equilibrium point that is reached. Examining 25 different migration rates shows that the final outcome of the recursion does not vary significantly even though fitness values change substantially with increasing gene flow levels (see Supporting Information and Supporting Figs. S1 and S2).

The dynamics of gene arrangement frequency change observed in the 1960 and 1980 fitness estimates were remarkably similar in some niches (Fig. 7, see Supporting Figures S7 and S8). For instance, the recursions for Niche 3 show a steady expansion of the ST and PP chromosomes until the AR arrangement is introduced, at which time ST and PP frequencies are reduced dramatically. The major difference between the 1940 data and the two later decadal samples is that the 1960 and 1980 recursions took longer to reach equilibrium points (2000 versus 500 generations). This is largely because the 1960 and 1980 fitness values for all karyotypes were closer to 1 than those estimated from the 1940 sample. The recursions in Niches 1 and 2 were the least similar among the decadal samples perhaps reflecting real changes in the selection that operates in these environments.

A more dramatic method to illustrate which niches show dramatic shifts in gene arrangement frequencies over the 1940 to 1980 interval is to meld the recursions together into one plot. This recursion began with the fitness values from the 1940 sample and sequentially added the chromosomes as before. At generation 480, the 1960 fitness values were used with the 1940 frequencies and the recursion was allowed to proceed for 60 generations, which assumes three generations per year over 20 years. At generation 540, the 1980 fitness values were used with the 1960 frequencies and the recursion was allowed to proceed for an additional 60 generations. Supporting Figure S9 shows the composite gene frequency changes in the six niches. The recursions in Niches 3–6 show relatively smooth transitions when the fitness values change in generations 480 and 540. In addition, the recursions in these niches lack dramatic shifts in the chromosomal frequencies. Niches 1 and 2, however, have some dramatic shifts in gene arrangement frequencies. These results suggest that some niches have shown changes in how selection has operated on the chromosomes whereas others have not.

We examined what happens to average fitness in the six different niches and for all niches as a whole in the migration–selection recursion (Fig. 8). Average fitness within niche fails to be maximized during the course of evolution. Average fitness across all niches is maximized. This indicates D. pseudoobscura populations are likely experiencing migrational load because populations are somewhat maladapted for the local conditions due to the influx of migrants.

Figure 8.

Change in average fitness within six niches and for all niches combined. The average fitnesses were derived for the migration–selection recursions using the 1940 sample (Dobzhansky 1944) and a migration rate of 0.025 and a Uniform migration distribution model.

CLIMATE ANALYSIS

We analyzed eight climatic variables for 34 localities within the six niches occupied by D. pseudoobscura: normal daily mean temperature, normal daily maximum temperature, normal daily minimum temperature, normal precipitation, mean number of days with precipitation 0.01 inch or more, average relative humidity in the morning, average relative humidity in the afternoon, and altitude. We used Principal Components to reduce the dimensionality of the dataset. Four principal components were found to explain 98% of the observed variation in the climatic data and the eigenvectors were heavily loaded by normal daily mean temperature, normal precipitation, mean number of days with precipitation 0.01 inch or more, and altitude. The observed means for these variables can be found in Table 2.

We asked whether the climatic data could correctly identify the six niches that were defined based on the gene arrangement frequencies. When normal daily mean temperature, normal precipitation, mean number of days with precipitation 0.01 inch or more, and altitude are used in a discriminate analysis, they assign the weather data localities into the true niche in 74% of the 34 cases.

Discussion

SELECTION IN HETEROGENEOUS ENVIRONMENTS

The fitness estimates for the six niches of D. pseudoobscura from three decadal samples of gene arrangements in D. pseudoobscura provide a glimpse into the complex selective processes that operate to maintain an inversion frequency cline. The conclusions that we draw from these fitness estimates should be viewed with caution because the collections used to estimate the population frequencies are subject to sampling error due to differences in sample sizes and timing of the collections. Despite these reservations, the dynamics of gene arrangement frequency have consistent features among the decadal samples.

The fitness set analysis of gene arrangement frequencies in the six niches of D. pseudoobscura shows that a genetic polymorphism can be maintained in the absence of global overdominance. Levene's (1953) model demonstrated that a genetic polymorphism can be maintained through selection in heterogeneous environments coupled with complete mixing of genotypes each generation. Star et al. (2007) found that more alleles can be maintained in populations when multiple niches are available even without heterozygote advantage. The numerical analyses presented here found no niche where a stable four or five gene arrangement polymorphism would be maintained based on the estimated fitness values. We found no evidence for global overdominance or overdominance within any niche that could maintain five alleles. The D. pseudoobscura niches, however, reached four and five arrangement equilibria due to migration–selection balance. Niches 2 and 3 are predicted to have stable three allele equilibria (ST, AR, and CH) through an overdominant mechanism, yet Niche 2 also maintains the TL arrangement through migration (Fig. 1 and Table 2). Fitness estimates in Niche 4 predict that directional selection will fix the AR arrangement, yet migration reintroduces the CH and PP chromosomes each generation. Thus, these data demonstrate that global heterosis is not necessary to explain the maintenance of the five major gene arrangements in D. pseudoobscura cline as was suggested by Dobzhansky and Levene (1948).

Underdominant selection plays a role in the observed distribution of gene arrangements. Marginal niches, such as Niches 1 and 6, have distinct fitness sets where subsets of arrangements are maintained by overdominance, while low frequency or absent arrangements are removed by strong underdominant selection in heterozygotes (Fig. 3). Selection in heterozygotes appears more effective than in homozygotes at removing less-fit arrangements because heterozygous karyotypes are more frequent than homozygotes.

The existence of the stable gene arrangement polymorphism based on the Levene (1953) model suggests that D. pseudoobscura experiences its environment as a coarse-grained environment. Levins and MacArthur (1966) envisioned a coarse-grained environment as one in which an individual spends the selective portion of its life history in one of several different niches. This is opposed to a fine-grain environment in which the individual is free to move among the selective regimes of different niches during its life time. Levins and MacArthur (1966) concluded that stable polymorphisms are less likely for an organism that experiences its environment as fine-grained versus coarse-grained. The egg, larval, or pupal stages of the D. pseudoobscura life cycle are the most likely to experience the environment as coarse-grained because these life stages are relatively sedentary within in their habitat. On the other hand, adult flies could experience the environment as fine-grained because flies can move among habitats via long-distance dispersal (Coyne et al. 1987). We conclude that selection on the egg, larval, or pupal stages of the D. pseudoobscura life cycle is driving the diversification of the gene arrangements among the six different niches.

Selection on the early life stages could involve biotic or abiotic factors. Not much is known about the biotic factors that could differentiate the six niches because the breeding sites of D. pseudoobscura are unknown. Carson (1951) suggested that D. pseudoobscura breeds in slime fluxes on oak trees, but the numbers of larvae and pupae isolated from slime fluxes cannot account for the large numbers of endemic individuals that can be trapped when artificial baits are used. The biotic factors that could drive selection on the egg, larva, or pupa could be differences in host plants or microbial diversity in the different niches. Selection on early life stages could also involve abiotic factors such as temperature, moisture, or altitude (Table 3) that are found to vary in meaningful ways among the six niches.

Table 3.  Climatic data for the six niches of D. pseudoobscura.
NichenTemp (°F)Prec. Amt. (in)Prec. DaysAltitude
  1. n, sample size; Temp, normal daily mean temperature; Prec. Amt., normal precipitation; Prec. Days, mean number of days with precipitation of 0.01 inch or more.

1761.9±1.313.5±1.641.1±4.1 209.7±66.4
2456.9±1.3 7.9±1.841.6±6.62986.0±1330.0
3556.8±6.2 7.1±1.452.8±13.03589.0±1124.0
4658.0±4.512.8±2.464.7±8.54090.0±822.0
5451.6±4.511.9±2.267.8±7.95524.0±830.0
6964.5±1.421.4±2.665.4±4.12146.0±418.0

Kirkpatrick and Barton (2006) have suggested that local adaptation is sufficient to allow a new inversion mutation to invade a population in models of migration–selection balance. Their intuitive model shows that new inversions will be favored when they capture genes responsible for local adaptation with the inverted segment. The advantage of an inverted chromosome is that it prevents the loss of fitness associated with recombination between chromosomes that carry different sets of locally adaptive alleles. Kirkpatrick and Barton (2006) have shown that the number of loci that contribute to local adaptation is proportional to the rate of increase of the new inversion given by λ= 1 + (n− 1)m where, λ is the initial rate of increase of the new inverted chromosome, n, is the number of locally adapted alleles, and m is the migration rate. We used the fitness estimates from the 1940 sample to derive estimates of the number of genes responsible for local adaptation within the ST, CH, AR, and PP arrangements. The fitness estimates were used in recursions where each chromosome was sequentially added and was initiated from a frequency of 1 × 10−6, a frequency that is roughly equal to 1/Ne, where Ne is the effective population size in D. pseudoobscura (Schaeffer 1995). λ is estimated from the ratio of allele frequency in generation 2 divided by allele frequency in generation 1. Table 4 shows that the estimates of the number of loci that contribute to local adaptation vary from two to 13 loci, which is consistent with the expectations of Kirkpatrick and Barton (2006) where at least two loci would favor the invasion of the inverted chromosome. The estimates of n are sensitive to the migration rate where higher levels of dispersal lead to lower estimates of selected loci.

Table 4.  Estimates of numbers of loci that contribute to local adaptation within four gene arrangements in D. pseudoobscura.
ArrangementmRatenInverted Genes (%)
  1. Arrangement, D. pseudoobscura gene arrangements Standard (ST), Chiricahua (CH), Arrowhead (AR), and Pikes Peak (PP); m, migration rate, Rate, initial rate of increase of the new gene arrangement from the first to second generation; n, number of loci that contribute to local adaptation within the gene arrangement, Inverted genes, number of genes predicted to be within the inverted segment based on polytene chromosome maps.

ST0.0251.18 8 360 (1.0)
 0.0501.16 4 360 (0.6)
 0.0751.16 3 360 (0.4)
CH0.0251.11 5 334 (0.7)
 0.0501.08 3 334 (0.4)
 0.0751.07 2 334 (0.3)
AR0.0251.18 8 775 (1.0)
 0.0501.17 4 775 (0.5)
 0.0751.13 3 775 (0.4)
PP0.0251.31131309 (1.0)
 0.0501.35 81309 (0.6)
 0.0751.4 61309 (0.5)

The observation of multiple gene arrangements in some populations and not in others suggests that alleles within inverted segments can be deleterious recessive in some habitats and not in others. Kirkpatrick and Barton (2006) have suggested that gene arrangements that harbor deleterious recessive alleles would prevent the chromosome from going to fixation leading to associative overdominance. The AR arrangement is nearly fixed in Niche 4 and would likely go to fixation without recurrent migration suggesting that this chromosome is adapted for this habitat and that the alleles carried on this chromosome are not lethal when homozygous. The AR chromosome, however, does not go to fixation in other habitats because the fitness of the AR homozygote is reduced in the other habitats (Fig. 3) presumably because alleles on the chromosome reduce fitness in different habitats.

Multiple arrangements could be maintained by factors other than those in these natural populations. Two or three gene arrangement equilibria were generated in the laboratory in the absence of environmental heterogeneity (Wright and Dobzhansky 1946; Dobzhansky 1948b, 1950). This suggests that the abiotic and biotic factors that contribute to polymorphism in this system are solely due to local adaptation. Another possibility is that the gene arrangements could be maintained by frequency-dependent selection (Wright and Dobzhansky 1946). The numerical analysis presented here did not consider frequency-dependent selection because the method solved a single generation allele frequency transition. To incorporate frequency dependence would require a multiple generation solution for fitnesses that is beyond the scope of the current set of analyses.

The Kirkpatrick and Barton (2006) model does not require epistasis or coadaptation for the invasion of the new gene arrangement. A new arrangement will invade as long as two or more genes contribute to the local adaptation. Schaeffer et al. (2003) found evidence for epistasis within the gene arrangements of D. pseudoobscura based on long-distance linkage disequilibrium and random association of nucleotide sites over short distances. This would suggest that if local adaptation genes drove the invasion of D. pseudoobscura inverted chromosomes, than the adaptive loci are likely to be acting synergistically.

The predictions of the Kirkpatrick and Barton (2006) model can be tested with future genome-wide scans of nucleotide variation to locate loci that have been targeted by selection. The classic molecular signal of a selective sweep is to detect regions of the genome that show polymorphism deficiencies, which assumes that selection drives a rare allele to high frequency at a rate faster than the neutral fixation rate. Przeworski et al. (2005) have shown that if selection acts on a preexisting, segregating allele, then polymorphism deficiencies may not be found at selective targets. Recombination will introduce variation onto the sweeping chromosome reducing the deficiency signal on the preexisting selected chromosome.

The analysis presented here provided us with information about the past dynamics of gene arrangement frequency change. Some of the gene arrangements have seen dramatic shifts in their frequency both increasing and decreasing during the selective history of the populations making them inappropriate candidates for mapping selective targets. The Arrowhead arrangement is the only chromosome that appears to represent a classical sweep based on the recursion trajectories. Molecular phylogenies are consistent with this view because they show that the Arrowhead chromosome is monophyletic and its phylogeny is star-like. Thus, loci driving the sweep of the Arrowhead chromosome have a higher likelihood of detection because this chromosome fits the classical selective sweep model.

CLINES IN MEXICAN POPULATIONS

The range of D. pseudoobscura extends into Mexico, but we did not consider these populations in our migration–selection balance model. The Santa Cruz, Cuernavaca, Tree Line, and Estes Park are the dominant arrangements in Mexico (Levine et al. 1995). The inclusion of Mexican niches would have likely made our estimates of fitness values more extreme because the differences between migrant and observed gene arrangement frequencies across the Mexican border would have been greater. As a result, the absolute fitness values would have changed, but the relative pattern would have been similar.

IMPLICATIONS FOR ENVIRONMENTAL CHANGES DURING THE LATE 20TH CENTURY

The fitness estimates for the D. pseudoobscura karyotypes have changed from 1940 to 1980. The shift in fitness values in some niches may suggest that D. pseudoobscura is responding to climate changes that have occurred during the sampled decades. The niche that showed the most dramatic shift in genotypic fitnesses is Niche 1, which includes populations in the coastal range of California. One can speculate that environmental changes were brought on by changes in agricultural practice, in pesticide use, in air pollution, or global warming. This suggests that D. pseudoobscura could be used as a biomarker for environmental change.

SUMMARY

In this article, we show that static frequency data from geographic clines can be used to estimate fitness values for different genotypes in models of migration–selection balance. We used this approach to understand the classical gene arrangement polymorphism in D. pseudoobscura. We conclude that selection in heterogeneous environments has maintained the polymorphism where directional, overdominant, and underdominant selection has acted. The data also suggest that environments that D. pseudoobscura inhabits may be changing.

Associate Editor: J. True

ACKNOWLEDGMENTS

The analysis presented here benefited from valuable discussions with J. H. Marden, K. Shea, H. G. Spencer, W. W. Anderson, B. F. McAllister, and T. A. Markow. In addition, the manuscript benefited from the comments of two anonymous reviewers and the Associate Editor John R. True.

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