Simulating genealogies of selected alleles in a population of variable size

An importance-sampling method is presented that allows the simulation of the history of a selected allele in a population of variable size. A sample path describing the number of copies of an allele that arose as a single mutant is generated by simulating backwards from the current frequency until the allele is lost. The mathematical expectation of a quantity or statistic is then estimated by taking averages over replicate simulations, weighting each replicate by the ratio of its probabilities under the Markov chains for the forward and backwards processes. This method was used to find the average age of a selected allele in an exponentially growing population. In terms of the effect on average allele age, selection in favour of an allele is not equivalent to exponential growth. To generate gene genealogies of a sample of copies of a selected allele, the neutral coalescent model is simulated for the subpopulation containing only the selected allele. From the resulting intra-allelic genealogy, it is possible to calculate the likelihood of the selection intensity as a function of the observed level of variability at marker loci closely linked to the selected allele. This method was used to estimate the intensity of selection affecting the delta 32 allele at the CCR5 locus in Europeans and a mutant at the MLH1 locus associated with colorectal cancer in the Finnish population.     

The use of intraallelic variability for testing neutrality and estimating population growth rate

To better understand the forces affecting individual alleles, we introduce a method for finding the joint distribution of the frequency of a neutral allele and the extent of variability at closely linked marker loci (the intraallelic variability). We model three types of intraallelic variability: (a) the number of nonrecombinants at a linked biallelic marker locus, (b) the length of a conserved haplotype, and (c) the number of mutations at a linked marker locus. If the population growth rate is known, the joint distribution provides the basis for a test of neutrality by testing whether the observed level of intraallelic variability is consistent with the observed allele frequency. If the population growth rate is unknown but neutrality can be assumed, the joint distribution provides the likelihood of the growth rate and leads to a maximum-likelihood estimate. We apply the method to data from published data sets for four loci in humans. We conclude that the Delta32 allele at CCR5 and a disease-associated allele at MLH1 arose recently and have been subject to strong selection. Alleles at PAH appear to be neutral and we estimate the recent growth rate of the European population to be approximately 0.027 per generation with a support interval of (0.017-0.037). Four of the relatively common alleles at CFTR also appear to be neutral but DeltaF508 appears to be significantly advantageous to heterozygous carriers.     

Analyses of the age of genes and the first arrival times in a finite population

The age of a mutant gene is studied using the infinite allele model in which every mutant is new and selectively neutral. Based on a time reversal theory of Markov processes, we develop a method of mathematical analysis that is considerably simpler for calculating the various statistics of the age than previous methods. Formulas for the mean and variance and for the distribution of age are presented together with some examples of relevance to cases in natural populations.—Theoretical studies of the first arrival time of an allele to a specified frequency, given an initially monomorphic condition of the locus, are presented. It is shown that, beginning with an allele that has frequency p = 1 or an allele with frequency p = 1/2N, there is an initial lag phase in which there is virtually no chance of an allele with a specified intermediate frequency appearing in the population. The distribution of the first arrival time is also presented. The distribution shows several characteristics that are not immediately obvious from a consideration of only the mean and variance of first arrival time. Especially noteworthy is the existence of a very long tail to the distribution. We have also studied the distribution of the age of an allele in the population. Again, the distribution of this measure is shown to be more informative for several questions than are the mean and variance alone.     

Pedigreed crosses to estimate recessive virulence allele frequencies in natural populations of gall midges

Monitoring changes in rare, recessive allele frequencies in natural populations can be accomplished using pedigreed individuals sampled from these populations. A pedigree keeps track of and limits the mating of sampled individuals, to preserve information about the genotype of the sampled individual in the phenotypes of its descendents. To estimate allele frequencies in a natural population using pedigreed crosses, four relations must be specified: (1) a method to determine whether the pedigreed line carries the desired allele; (2) a method to estimate the phenotypic frequency of the trait among the pedigreed lines and a credibility limit for the estimate; (3) the genetic relation between the phenotype frequency among the lines and the allele frequency in the natural population; and (4) a method to estimate the probability that the first method did not detect the trait, assuming that the allele was present in the sampled individual. Knowledge about the segregation patterns of the allele enables specification of (3) and (4). Bayesian statistics were used to estimate the phenotypic frequency of the trait among the pedigreed lines. The method determining whether the pedigreed line carries the desired allele will vary with the species and trait of concern. We focused on monitoring of vGm1, a recessive autosomal allele, and vGm2, a recessive sex‐linked allele, which provide virulence against certain rice resistance genes in rice gall midge, Orseolia oryzae (Wood‐Mason) (Diptera: Cecidomyiidae). We show how three pedigrees can be used to estimate these allele frequencies. An F₁ field screen challenges the F₁ offspring of sampled individuals on the rice differentials. A P₁ test‐cross mates the sampled individual with a homozygous lab colony for the allele of interest, and evaluates their offspring on the rice differentials. A conditional F₁ test‐cross takes the offspring from pedigrees that were negative in an F₁ field screen, and test‐crosses these offspring with the homozygous laboratory colony. We also indicate how to test for independent assortment when a double (or multiple) homozygote laboratory colony is used in a test‐cross, how to test for differences among samples, and how to pool data to produce a single estimate based on a larger number of pedigreed lines. These methods may encourage the development of a variety of pedigreed monitoring strategies that could improve and prolong the use of scarce plant resistance alleles in rice and other plants.     

Estimating the age of alleles by use of intraallelic variability.

A method is presented for estimating the age of an allele by use of its frequency and the extent of variation among different copies. The method uses the joint distribution of the number of copies in a population sample and the coalescence times of the intraallelic gene genealogy conditioned on the number of copies. The linear birth-death process is used to approximate the dynamics of a rare allele in a finite population. A maximum-likelihood estimate of the age of the allele is obtained by Monte Carlo integration over the coalescence times. The method is applied to two alleles at the cystic fibrosis (CFTR) locus, deltaF508 and G542X, for which intraallelic variability at three intronic microsatellite loci has been examined. Our results indicate that G542X is somewhat older than deltaF508. Although absolute estimates depend on the mutation rates at the microsatellite loci, our results support the hypothesis that deltaF508 arose < 500 generations (approximately 10,000 years) ago.     

An Age-of-Allele Test of Neutrality for Transposable Element Insertions

How natural selection acts to limit the proliferation of transposable elements (TEs) in genomes has been of interest to evolutionary biologists for many years. To describe TE dynamics in populations, previous studies have used models of transposition–selection equilibrium that assume a constant rate of transposition. However, since TE invasions are known to happen in bursts through time, this assumption may not be reasonable. Here we propose a test of neutrality for TE insertions that does not rely on the assumption of a constant transposition rate. We consider the case of TE insertions that have been ascertained from a single haploid reference genome sequence. By conditioning on the age of an individual TE insertion allele (inferred by the number of unique substitutions that have occurred within the particular TE sequence since insertion), we determine the probability distribution of the insertion allele frequency in a population sample under neutrality. Taking models of varying population size into account, we then evaluate predictions of our model against allele frequency data from 190 retrotransposon insertions sampled from North American and African populations of Drosophila melanogaster. Using this nonequilibrium neutral model, we are able to explain ∼80% of the variance in TE insertion allele frequencies based on age alone. Controlling for both nonequilibrium dynamics of transposition and host demography, we provide evidence for negative selection acting against most TEs as well as for positive selection acting on a small subset of TEs. Our work establishes a new framework for the analysis of the evolutionary forces governing large insertion mutations like TEs, gene duplications, or other copy number variants.     

Simulating natural selection in landscape genetics

Linking landscape effects to key evolutionary processes through individual organism movement and natural selection is essential to provide a foundation for evolutionary landscape genetics. Of particular importance is determining how spatially-explicit, individual-based models differ from classic population genetics and evolutionary ecology models based on ideal panmictic populations in an allopatric setting in their predictions of population structure and frequency of fixation of adaptive alleles. We explore initial applications of a spatially-explicit, individual-based evolutionary landscape genetics program that incorporates all factors--mutation, gene flow, genetic drift and selection--that affect the frequency of an allele in a population. We incorporate natural selection by imposing differential survival rates defined by local relative fitness values on a landscape. Selection coefficients thus can vary not only for genotypes, but also in space as functions of local environmental variability. This simulator enables coupling of gene flow (governed by resistance surfaces), with natural selection (governed by selection surfaces). We validate the individual-based simulations under Wright-Fisher assumptions. We show that under isolation-by-distance processes, there are deviations in the rate of change and equilibrium values of allele frequency. The program provides a valuable tool (cdpop v1.0; http://cel.dbs.umt.edu/software/CDPOP/) for the study of evolutionary landscape genetics that allows explicit evaluation of the interactions between gene flow and selection in complex landscapes.     

Effective number of breeding adults in Bufo bufo estimated from age-specific variation at minisatellite loci

Estimates of the effective number of breeding adults were derived for three semi-isolated populations of the common toad Bufo bufo based on temporal (i.e. adult-progeny) variance in allele frequency for three highly polymorphic minisatellite loci. Estimates of spatial variance in allele frequency among populations and of age-specific measures of genetic variability are also described. Each population was characterized by a low effective adult breeding number ( N _b) based on a large age-specific variance in mini-satellite allele frequency. Estimates of N _b (range 21–46 for population means across three loci) were ≊ 55–230-fold lower than estimates of total adult census size. The implications of low effective breeding numbers for long-term maintenance of genetic variability and population viability are discussed relative to the species' reproductive ecology, current land-use practices, and present and historical habitat modification and loss. The utility of indirect measures of population parameters such as N _b and N _e based on time-series data of minisatellite allele frequencies is discussed relative to similar measures estimated from commonly used genetic markers such as protein allozymes.     

Is drift ‘directional’? Unequal breeding sex ratio revisited

Unequal breeding sex ratio can significantly reduce effective population size, allowing a rare neutral allele to jump to a high frequency through genetic drift. However, this one-way alteration to allele frequency appears inconsistent with the concept that drift is non-directional. Based on binomial sampling distribution, this study developed a method to directly and exhaustively measure drift by calculating the mean deviation of change in allele frequency, then applied it to cases of unequal breeding sex ratio. The result shows that, under those cases, (1) the mean deviation can always be divided into two halves that are equal in size but opposite in direction; (2) each half consists of one or several categories represented by various allele proportions in the rare sex; (3) this proportion is another factor that determines the outcome of drift, in addition to effective population size and allele frequency; (4) drift is non-directional on a global scale, but whether an allele will drift up or down can be predicted based on the above factors. This method enables us to dissect every component of the expected change in allele frequency caused by drift and to find out the combined effect of population size, allele frequency and allele proportion in the rarer sex under neutrality but unequal breeding sex ratio.     

Heterozygosity excess at the cattle DRB locus revealed by large scale genotyping of two closely linked microsatellites

A method for MHC DRB typing in cattle based on two closely linked and highly polymorphic microsatellites is described. The two microsatellites DRBP1ms and DRB3ms are located in intron 2 of the corresponding DRB gene. The very strong linkage disequilibrium between the two loci made it possible to establish DRB microsatellite haplotypes. The typing results with this method on reference samples followed closely that obtained with RFLP and direct sequence analysis of DRB3 exon 2. The method is well suited for large scale genotyping and was successfully applied for typing more than 600 unrelated animals representing 23 breeds. The data were used to test whether the observed DRB allele frequency distributions were consistent with that expected for selectively neutral alleles in populations at mutation-drift equilibrium. A significant heterozygosity excess was detected and there was an obvious trend across breeds towards a more even allele frequency distribution than expected. The deviation may be due to balancing selection acting on the DRB locus or by recent population bottlenecks.     

Effective number of breeders and maintenance of genetic diversity in the captive bearded vulture population

We combined pedigree data with data derived from 14 microsatellite loci to investigate genetic diversity and its maintenance in the captive source population for the reintroduction of the bearded vulture into the Alps. We found the captive population to be genetically more variable than the largest natural population in Europe, both in terms of mean number of alleles per locus and mean observed and expected heterozygosity. Allelic diversity of the captive population was higher than, and mean heterozygosity measurements were comparable with the ones found in two large, extinct populations from Sardinia and the Alps represented by museum specimens. The amount of genetic variability recruited with the founders was still present in the captive population of the year 2000, mainly because the carriers of rare alleles were still alive. However, the decline in expected heterozygosity and the loss of alleles over generations in captivity was significant. Point estimates of effective population size, N(e), based on pedigree data and estimates of effective number of breeders, N(b), based on allele frequency changes, ranged from 20 to 30 and were significantly smaller than the census size. The results demonstrate that the amount of genetic variability in the captive bearded vulture population is comparable or even larger than the amount present in natural populations. However, the population is in danger to lose genetic variability over time because of genetic drift. Management strategies should therefore aim at preserving genetic variability by minimising kinship, and at increasing N(e) by recruiting additional founders and enhancing gene flow between the released, the captive and natural populations.     

Demographic Genetics of Brown Trout (Salmo Trutta) and Estimation of Effective Population Size from Temporal Change of Allele Frequencies

We studied temporal allele frequency shifts over 15 years and estimated the genetically effective size of four natural populations of brown trout (Salmo trutta L.) on the basis of the variation at 14 polymorphic allozyme loci. The allele frequency differences between consecutive cohorts were significant in all four populations. There were no indications of natural selection, and we conclude that random genetic drift is the most likely cause of temporal allele frequency shifts at the loci examined. Effective population sizes were estimated from observed allele frequency shifts among cohorts, taking into consideration the demographic characteristics of each population. The estimated effective sizes of the four populations range from 52 to 480 individuals, and we conclude that the effective size of natural brown trout populations may differ considerably among lakes that are similar in size and other apparent characteristics. In spite of their different effective sizes all four populations have similar levels of genetic variation (average heterozygosity) indicating that excessive loss of genetic variability has been retarded, most likely because of gene flow among neighboring populations.     

Empirical Distributions of F ST from Large-Scale Human Polymorphism Data

Studies of the apportionment of human genetic variation have long established that most human variation is within population groups and that the additional variation between population groups is small but greatest when comparing different continental populations. These studies often used Wright’s F _ST that apportions the standardized variance in allele frequencies within and between population groups. Because local adaptations increase population differentiation, high-F _ST may be found at closely linked loci under selection and used to identify genes undergoing directional or heterotic selection. We re-examined these processes using HapMap data. We analyzed 3 million SNPs on 602 samples from eight worldwide populations and a consensus subset of 1 million SNPs found in all populations. We identified four major features of the data: First, a hierarchically F _ST analysis showed that only a paucity (12%) of the total genetic variation is distributed between continental populations and even a lesser genetic variation (1%) is found between intra-continental populations. Second, the global F _ST distribution closely follows an exponential distribution. Third, although the overall F _ST distribution is similarly shaped (inverse J), F _ST distributions varies markedly by allele frequency when divided into non-overlapping groups by allele frequency range. Because the mean allele frequency is a crude indicator of allele age, these distributions mark the time-dependent change in genetic differentiation. Finally, the change in mean-F _ST of these groups is linear in allele frequency. These results suggest that investigating the extremes of the F _ST distribution for each allele frequency group is more efficient for detecting selection. Consequently, we demonstrate that such extreme SNPs are more clustered along the chromosomes than expected from linkage disequilibrium for each allele frequency group. These genomic regions are therefore likely candidates for natural selection.     

Ancient Origin of the Null Allele se 428 of the Human ABO-Secretor Locus (FUT2)

In human populations, a null allele having several nucleotide differences from the wild-type allele is segregating at the FUT2 locus (the ABO-Secretor locus) encoding α(1,2)fucosyltransferase. To estimate the age of the most recent common ancestor (MRCA) of these two alleles, we sequenced FUT2 homologues from chimpanzee, gorilla, orangutan, and green monkey. Since we did not detect acceleration or any heterogeneity in the substitution rate at this locus among these species, the age of the MRCA was estimated to be around 3 MYA, assuming the divergence time of human and chimpanzee to be 5 MYA. We developed a simple test to examine whether or not the old age of the MRCA of the FUT2 is consistent with that expected for two divergent neutral alleles sampled from a random mating population. An application of the test to the data at FUT2 indicated that the age of the MRCA is too old to be explained by the simple neutral assumptions, although our test depends on accurate estimation of the divergence time of human and chimpanzee in units of twice the human population size. Various possibilities including balancing selection are discussed to explain this old age of the MRCA. Received: 9 May 1999 / Accepted: 20 September 1999     

A Bayesian method for jointly estimating allele age and selection intensity.

The problem of jointly estimating the intensity of past selection affecting an allele and the allele's age is formulated in a Bayesian framework. The prior distribution of allele age given its frequency is obtained from existing population genetics theory. The prior distribution of selection intensity is assumed to reflect the fact that positive selection on a new mutant is more likely to be weak than strong. The general approach is illustrated by the development of an importance sampling method applicable to low-frequency alleles. This method can be used either when the haplotypes of closely linked marker loci are known or when the lengths of linked ancestral chromosomal segments can be inferred. The method is illustrated with an application to the A-allele of G6PD in Africa. Because changes in allele frequency and recombination are both intrinsically stochastic, there are limits to the accuracy achievable with any method.     

An investigation of the statistical power of neutrality tests based on comparative and population genetic data

In this report, we investigate the statistical power of several tests of selective neutrality based on patterns of genetic diversity within and between species. The goal is to compare tests based solely on population genetic data with tests using comparative data or a combination of comparative and population genetic data. We show that in the presence of repeated selective sweeps on relatively neutral background, tests based on the d(N)/d(S) ratios in comparative data almost always have more power to detect selection than tests based on population genetic data, even if the overall level of divergence is low. Tests based solely on the distribution of allele frequencies or the site frequency spectrum, such as the Ewens-Watterson test or Tajima's D, have less power in detecting both positive and negative selection because of the transient nature of positive selection and the weak signal left by negative selection. The Hudson-Kreitman-Aguadé test is the most powerful test for detecting positive selection among the population genetic tests investigated, whereas McDonald-Kreitman test typically has more power to detect negative selection. We discuss our findings in the light of the discordant results obtained in several recently published genomic scans.     

Plasminogen activator inhibitor-1 polymorphism in women with pre-eclampsia

We determined whether or not genetic variability in the promoter region of the gene encoding plasminogen activator inhibitor-1 (PAI1) contributes to individual differences in susceptibility to the development of preeclampsia. The study involved 133 preeclamptic and 115 healthy control pregnant women who were genotyped for a single-nucleotide insertion/deletion polymorphism (4G/5G) at position -675 in the PAI1 gene promoter. Furthermore, the frequencies of the alleles in the general middle-aged population are presented for comparison. Chi-square analysis was used to assess genotype and allele frequency differences between preeclamptic women and controls. A similar allelic distribution of PAI1 4G/5G polymorphism was observed in the two groups, with the frequency of the variant 4G allele being 50.4% in the preeclampsia group and 54.3% in the control group (p = 0.377; OR = 0.85, 95% CI = 0.60-1.22). Accordingly, the genotype distribution of the PAI1 4G/5G polymorphism in the preeclamptic and control groups was found to be similar (p = 0.68). Overall, this genotype data on fertile women is almost identical to that in the general middle-aged Finnish population. The 4G/5G polymorphism of the PAI1 gene promoter is unlikely to be a major genetic predisposing factor as regards preeclampsia in subjects from eastern Finland. These results are not suggestive of an important contribution of the PAI1 genotype on preeclampsia across populations.     

Rare alleles and selection

A subpopulation D of rare alleles is considered. The subpopulation is part of a large population that evolves according to a Moran model with selection and growth. Conditional on the current frequency, q, of the rare allele, an approximation to the distribution of the genealogy of D is derived. In particular, the density of the age, T(1), of the rare allele is approximated. It is shown that time naturally is measured in units of qN(0) generations, where N(0) is the present day population size, and that the distribution of the genealogy of D depends on the compound parameters rho=rqN(0) and sigma=sqN(0) only. Here, s is the fitness per generation of heterozygote carriers of the rare allele and r is the growth rate per generation of the population. Amongst more, it is shown that for constant population size (rho=0) the distribution of D depends on sigma only through the absolute value /sigma/, not the direction of selection.     

Adjustment for local ancestry in genetic association analysis of admixed populations

MOTIVATION: Admixed populations offer a unique opportunity for mapping diseases that have large disease allele frequency differences between ancestral populations. However, association analysis in such populations is challenging because population stratification may lead to association with loci unlinked to the disease locus. Methods and results: We show that local ancestry at a test single nucleotide polymorphism (SNP) may confound with the association signal and ignoring it can lead to spurious association. We demonstrate theoretically that adjustment for local ancestry at the test SNP is sufficient to remove the spurious association regardless of the mechanism of population stratification, whether due to local or global ancestry differences among study subjects; however, global ancestry adjustment procedures may not be effective. We further develop two novel association tests that adjust for local ancestry. Our first test is based on a conditional likelihood framework which models the distribution of the test SNP given disease status and flanking marker genotypes. A key advantage of this test lies in its ability to incorporate different directions of association in the ancestral populations. Our second test, which is computationally simpler, is based on logistic regression, with adjustment for local ancestry proportion. We conducted extensive simulations and found that the Type I error rates of our tests are under control; however, the global adjustment procedures yielded inflated Type I error rates when stratification is due to local ancestry difference.     

Patterns of variation within and between Greek populations of Ceratitis capitata suggest extensive gene flow and latitudinal clines

Four natural Greek populations of Mediterranean fruit fly, Ceratitis capitata (Wiedemann), was studied for genetic variability at 25 enzyme loci. The comparison of polymorphism within and between populations shows two loci with high between-population heterozygosity (HT) and very high fixation index (F(ST)) values, suggesting the presence of balancing selection. The gradual decline of common allele frequency of the polymorphic loci tested indicated that latitudinal clines are present in Greece. Indirect estimates of gene flow based both on Wright's method (Nm*) and on the Slatkin's method (Nm*), which depends on the frequencies of rare alleles found in only one population, revealed a substantial amount of gene flow (Nm = 3.493 and Nm* = 3.197). These estimates of gene flow may well explain why the "introduced" Greek populations of C. capitata, in spite of their low genetic variability, display the same polymorphic loci. Gene flow in combination with natural selection and genetic drift may have played an important role to genetic differentiation in this species in Greece.