The evolution of recombination in permanent translocation heterozygotes

The evolution of a selectively neutral locus that controls the degree to which alleles at a single selected locus are linked with a particular set of chromosomes in a permanent translocation heterozygote is studied. With complete selfing and fitness overdominance a new allele at the modifying locus will increase in frequency if it increases the linkage of all alleles at the selected locus to a particular set of chromosomes. With random mating a new allele at the modifying locus will increase when rare if it increases the linkage of alleles at the selected locus to a particular set of chromosomes. In addition, a parameter analogous to the coefficient of linkage disequilibrium in usual two-locus models with random mating must be nonzero if a new allele at the modifying locus is to increase in frequency at a geometric rate when rare. With mixed selfing and random mating a new allele at the modifying locus will apparently increase when rare only if it increases the linkage of alleles at the selected locus to a particular set of chromosomes.     

Ethnic variation in genetic disease: possible roles of hitchhiking and epistasis.

The high incidence of some genetic diseases in certain ethnic groups is important in planning of medical genetic programs. Simple interaction models predict that at least some lethal recessive alleles will have "hitchhiked" to increased frequencies because of linkage to genes whose alleles have been favored by selection for other reasons in certain populations. In the absence of linkage or epistasis with a gene favored by selection, heterozygote advantage for a recessive lethal may produce the same phenomenon. In the hitchhiking model (linkage), the increase in the gene frequency is temporary, but the length of time that the increased gene frequency is at least double the base frequency may be quite long. Changes in gene frequency for the unlinked epistatic model result in a new equilibrium with a possibly higher gene frequency. The most likely chromosomal regions in which hitchhiked lethal recessives would be found are in the vicinity of genes whose allelic frequencies vary substantially among human racial groups (e.g., Gm, Rh, Duffy, lactose tolerance, or HL-A). There will be a hitchhiking effect if recombination distance is less than the selective advantage. The closer the linkage of two loci, the easier hitchhiking effects will be to detect. Hitchhiking is suggested by nonrandom association of the recessive disease and one of the selected markers, as in the case of Gm and cystic fibrosis. However, there is so far insufficient evidence of linkage between them. More pedigree information is necessary than is now available.     

Quantitative genetic models for the balance between migration and stabilizing selection

The evolution of a quantitative trait subject to stabilizing selection and immigration, with the immigrants deviating from the local optimum, is considered under a number of different models of the underlying genetic basis of the trait. By comparing exact predictions under the infinitesimal model obtained using numerical methods with predictions of a simplified approximate model based on ignoring linkage disequilibrium, the increase in the expressed genetic variance as a result of linkage disequilibrium generated by migration is shown to be relatively small and negligible, provided that the genetic variance relative to the squared deviation of immigrants from the local optimum is sufficiently large or selection and migration is sufficiently weak. Deviation from normality is shown to be less important by comparing predictions of the infinitesimal model with a model presupposing normality. For a more realistic symmetric model, involving a finite number of loci only, no linkage and equal effects and frequencies across loci, additional changes in the genetic variance arise as a result of changes in underlying allele frequencies. Again, provided that the genetic variance relative to the squared deviation of the immigrants from the local optimum is small, the difference between the predictions of infinitesimal and the symmetric model are small unless the number of loci is very small. However, if the genetic variance relative to the squared deviation of the immigrants from the local optimum is large, or if selection and migration are strong, both linkage disequilibrium and changes in the genetic variance as a result of changes in underlying allele frequencies become important.     

Evolution of dominance under frequency-dependent intraspecific competition

A population-genetic analysis is performed of a two-locus two-allele model, in which the primary locus has a major effect on a quantitative trait that is under frequency-dependent disruptive selection caused by intraspecific competition for a continuum of resources. The modifier locus determines the degree of dominance at the trait level. We establish the conditions when a modifier allele can invade and when it becomes fixed if sufficiently frequent. In general, these are not equivalent because an unstable internal equilibrium may exist and the condition for successful invasion of the modifier is more restrictive than that for eventual fixation from already high frequency. However, successful invasion implies global fixation, i.e., fixation from any initial condition. Modifiers of large effect can become fixed, and also invade, in a wider parameter range than modifiers of small effect. We also study modifiers with a direct, frequency-independent deleterious fitness effect. We show that they can invade if they induce a sufficiently high level of dominance and if disruptive selection on the ecological trait is strong enough. For deleterious modifiers, successful invasion no longer implies global fixation because they can become stuck at an intermediate frequency due to a stable internal equilibrium. Although the conditions for invasion and for fixation if sufficiently frequent are independent of the linkage relation between the two loci, the rate of spread depends strongly on it. The present study provides further support to the view that evolution of dominance may be an efficient mechanism to remove unfit heterozygotes that are maintained by balancing selection. It also demonstrates that an invasion analysis of mutants of very small effect is insufficient to obtain a full understanding of the evolutionary dynamics under frequency-dependent selection.     

Stable linkage disequilibrium without epistasis in subdivided populations

In a large random mating population stable linkage disequilibrium occurs only when there is epistasis. However if a population is divided into a number of subpopulations among which migration occurs, stable linkage disequilibrium in each subpopulation may be produced without epistasis. In the case of two subpopulations a necessary condition for linkage equilibrium in the absence of epistasis is that at least at one of the two loci under consideration the gene frequency must be the same for the two populations. This condition is rather severe and any violation of this will lead to stable linkage disequilibrium. A similar conclusion can be made with more than two populations. In general the presence of linkage disequilibrium does not necessarily imply the existence of epistasis even in equilibrium populations.     

The Evolution of Recombination: Removing the Limits to Natural Selection

One of the oldest hypotheses for the advantage of recombination is that recombination allows beneficial mutations that arise in different individuals to be placed together on the same chromosome. Unless recombination occurs, one of the beneficial alleles is doomed to extinction, slowing the rate at which adaptive mutations are incorporated within a population. We model the effects of a modifier of recombination on the fixation probability of beneficial mutations when beneficial alleles are segregating at other loci. We find that modifier alleles that increase recombination do increase the fixation probability of beneficial mutants and subsequently hitchhike along as the mutants rise in frequency. The strength of selection favoring a modifier that increases recombination is proportional to λ(2)Sδr/r when linkage is tight and λ(2)S(3)δ r/N when linkage is loose, where λ is the beneficial mutation rate per genome per generation throughout a population of size N, S is the average mutant effect, r is the average recombination rate, and δr is the amount that recombination is modified. We conclude that selection for recombination will be substantial only if there is tight linkage within the genome or if many loci are subject to directional selection as during periods of rapid evolutionary change.     

Finding genes underlying risk of complex disease by linkage disequilibrium mapping

Identification of genes that harbor variation associated with inter-individual differences in risk of complex diseases remains one of the most challenging and important problems in human genetics. For genetic variants that are sufficiently common and have sufficiently large effects, direct tests of association through linkage disequilibrium with anonymous SNPs may prove effective. But the two critical parameters - the frequency of risk-inflating alleles and the magnitudes of their effect on risk - remain largely unknown. In this review we consider the latest information regarding the likely efficacy of the linkage disequilibrium mapping approach.     

Evolution of recombination due to random drift

In finite populations subject to selection, genetic drift generates negative linkage disequilibrium, on average, even if selection acts independently (i.e., multiplicatively) upon all loci. Negative disequilibrium reduces the variance in fitness and hence, by Fisher's (1930) fundamental theorem, slows the rate of increase in mean fitness. Modifiers that increase recombination eliminate the negative disequilibria that impede selection and consequently increase in frequency by "hitchhiking." Thus, stochastic fluctuations in linkage disequilibrium in finite populations favor the evolution of increased rates of recombination, even in the absence of epistatic interactions among loci and even when disequilibrium is initially absent. The method developed within this article allows us to quantify the strength of selection acting on a modifier allele that increases recombination in a finite population. The analysis indicates that stochastically generated linkage disequilibria do select for increased recombination, a result that is confirmed by Monte Carlo simulations. Selection for a modifier that increases recombination is highest when linkage among loci is tight, when beneficial alleles rise from low to high frequency, and when the population size is small.     

Disequilibrium Pattern Analysis. I. Theory

We have developed a method, disequilibrium pattern analysis, for examining the disequilibrium distribution of the entire array of two locus multiallelic haplotypes in a population. It is shown that a selected haplotype will produce a distinct pattern of linkage disequilibrium values for all generations while the selection is acting. This pattern will also presumably be maintained for many generations after the selection event, until the disequilibrium pattern is eventually broken down by genetic drift and recombination. Related haplotypes, sharing an allele with a selected haplotype, assume a value of linkage disequilibrium proportional to the frequency of the unshared allele and have a single negative value of the normalized linkage disequilibrium. The analysis assumes zero linkage disequilibrium for all allelic combinations initially. The same basic results continue to apply if the selection involves a new mutant, the occurrence of which creates linkage disequilibrium for some haplotypes. The disequilibrium pattern predicted under selection is robust with respect to the influence of migration and random genetic drift. This method is applicable to population data having linked polymorphic loci including that determined from protein or DNA sequencing.     

Linkage Disequilibrium in Growing and Stable Populations

Nonrandom associations between alleles at different loci can be tested for using Fisher's exact test. Extensive simulations show that there is a substantial probability of obtaining significant nonrandom associations between closely or completely linked polymorphic neutral loci in a population of constant size at equilibrium under mutation and genetic drift. In a rapidly growing population, however, there will be little chance of finding significant nonrandom associations even between completely linked loci if the growth has been sufficiently rapid. This result is illustrated by the analysis of mitochondrial DNA sequence data from humans. In comparing all pairs of informative sites, fewer than 5% of the pairs show significant disequilibrium in Sardinians, which have apparently undergone rapid population growth, while 20% to 30% in !Kung and Pygmies, which apparently have not undergone rapid growth, show significance. The extent of linkage disequilibrium in a population is closely related to the gene genealogies of the loci examined, with ``starlike' genealogies making significant linkage disequilibrium unlikely.     

Linkage studies on Gilles de la Tourette syndrome: what is the strategy of choice?

For a linkage study it is important to ascertain family material that is sufficiently informative. The statistical power of a linkage sample can be determined via computer simulation. For complex traits uncertain parameters such as incomplete penetrance, frequency of phenocopies, gene frequency and variable expression have to be taken into account. One can either include only the most severe phenotype in the analysis or apply multiple linkage tests for a gradually broadened disease phenotype. Gilles de la Tourette syndrome (GTS) is a chronic neurological disorder characterized by multiple, intermittent motor and vocal tics. Segregation analyses suggest that GTS and milder phenotypes are caused by a single dominant gene. We report here the results of an extensive simulation study on a large set of families. We compared the effectiveness of linkage tests with only the GTS phenotype versus multiple tests that included various milder phenotypes and different gene frequencies. The scenario of multiple tests yielded superior power. Our results show that computer simulation can indicate the strategy of choice in linkage studies of multiple, complex phenotypes.     

Muller''s Ratchet under Epistatic Selection

In a finite asexual population mean fitness may decrease by a process known as Muller's ratchet, which proceeds if all individuals with the minimum number of deleterious alleles are randomly lost. If these alleles have independent effects on fitness, previous analysis suggested that the rate of this decrease either remains constant or, if accumulation of mutations leads to the decline of the population size, grows. Here I show that this conclusion is quite sensitive to the assumption of independence. If deleterious alleles have synergistic fitness effects, then, as the ratchet advances, the frequency of the best available genotype will necessarily increase, making its loss less and less probable. As a result, sufficiently strong synergistic epistasis can effectively halt the action of Muller's ratchet. Instead of being driven extinct, a finite asexual population could then survive practically indefinitely, although with lower mean fitness than without random drift.     

Estimating the minimum rate of genetic transformation in bacteria

Extensive data from multilocus electrophoresis are available for many bacterial populations. In some cases, for example Neisseria gonorrhoeae, these data are consistent with the population being in linkage equilibrium. This raises the following question. What frequency of transformation, or other means of genetic recombination, is needed, relative to mutation, to produce apparent panmixis? Simulation of a finite-population model suggests that, if transformation is at least twenty times as frequent as mutation, the population structure will be indistinguishable from a panmictic one, using the best available data sets. That is, relatively infrequent transformation is sufficient to produce approximate linkage equilibrium.     

Linkage of DNA probe B79a (D7S13) to cystic fibrosis

We have conducted, in 64 affected families, a study of linkage between the anonymous DNA segment pB79a (D7S13) and the locus for cystic fibrosis (CF) on chromosome 7q. The maximum lod score was 12.60 at theta = .08 (confidence bounds .045-.135). Although D7S13 is not sufficiently close to CF for routine use in DNA-based prenatal diagnosis, it will be helpful in certain families when other nearby markers are uninformative. D7S13 will also be useful for refining the linkage map of the CF region.     

A Model of Functional Epistasis and Linkage Disequilibrium in Populations with Overlapping Generations

A model of functional epistasis is proposed in which it is assumed that coupling and repulsion genotypes differ in metabolic efficiency and thus in development time and net fecundity. The implications of this model are investigated for iteroparous populations with fluctuating rates of increase. It is found that the fluctuations in rate of increase can lead to large fluctuations in gamete frequency and D, the coefficient of linkage disequilibrium, but that D will almost always have a value of zero at some point during the populations' demographic cycle. Some of the model populations would be expected to be in a state of linkage disequilibrium only fleetingly: others would exhibit D-cycles interpretable as random fluctuation. Implications of the model for interpretations of existing data on linkage disequilibrium among enzyme loci in Drosophila are discussed.     

Accounting for linkage disequilibrium among markers in linkage analysis: impact of haplotype frequency estimation and molecular haplotypes for a gene in a candidate region for Alzheimer's disease

OBJECTIVES: Linkage disequilibrium (LD) between closely spaced SNPs can be accommodated in linkage analysis by specifying the multi-SNP haplotype frequencies, if known. Phased haplotypes in candidate regions can provide gold standard haplotype frequency estimates, and may be of inherent interest as markers. We evaluated the effects of different methods of haplotype frequency estimation, and the use of marker phase information, on linkage analysis of a multi-SNP cluster in a candidate region for Alzheimer's disease (AD). METHODS: We performed parametric linkage analysis of a five-SNP cluster in extended pedigrees to compare the use of: (1) haplotype frequencies estimated by molecular phase determination, maximum likelihood estimation, or by assuming linkage equilibrium (LE); (2) AD families or controls as the frequency source; and (3) unphased or molecularly phased SNP data. RESULTS: There was moderate to strong pairwise LD among the five SNPs. Falsely assuming LE substantially inflated the LOD score, but the method of haplotype frequency estimation and particular sample used made little difference provided that LD was accommodated. Use of phased haplotypes produced a modest increase in the LOD score over unphased SNPs. CONCLUSIONS: Ignoring LD between markers can lead to substantially inflated evidence for linkage in LOD score analysis of extended pedigrees with missing data. Use of marker phase information in linkage analysis may be important in disease studies where the costs of family recruitment and phenotyping greatly exceed the costs of phase determination.     

The Effect of Linkage on Establishment and Survival of Locally Beneficial Mutations

We study invasion and survival of weakly beneficial mutations arising in linkage to an established migration–selection polymorphism. Our focus is on a continent–island model of migration, with selection at two biallelic loci for adaptation to the island environment. Combining branching and diffusion processes, we provide the theoretical basis for understanding the evolution of islands of divergence, the genetic architecture of locally adaptive traits, and the importance of so-called “divergence hitchhiking” relative to other mechanisms, such as “genomic hitchhiking”, chromosomal inversions, or translocations. We derive approximations to the invasion probability and the extinction time of a de novo mutation. Interestingly, the invasion probability is maximized at a nonzero recombination rate if the focal mutation is sufficiently beneficial. If a proportion of migrants carries a beneficial background allele, the mutation is less likely to become established. Linked selection may increase the survival time by several orders of magnitude. By altering the timescale of stochastic loss, it can therefore affect the dynamics at the focal site to an extent that is of evolutionary importance, especially in small populations. We derive an effective migration rate experienced by the weakly beneficial mutation, which accounts for the reduction in gene flow imposed by linked selection. Using the concept of the effective migration rate, we also quantify the long-term effects on neutral variation embedded in a genome with arbitrarily many sites under selection. Patterns of neutral diversity change qualitatively and quantitatively as the position of the neutral locus is moved along the chromosome. This will be useful for population-genomic inference. Our results strengthen the emerging view that physically linked selection is biologically relevant if linkage is tight or if selection at the background locus is strong.     

Pregnancy termination

During pregnancy, the antiprogestin mifepristone will induce uterine contractions, increase the sensitivity of the myometrium to prostaglandin, and ripen the cervix. These effects indicate that mifepristone can be used for termination of pregnancy. The clinical experience has shown that mifepristone is sufficiently effective for this purpose only if combined with a suitable prostaglandin, e.g. gemeprost or misoprostol. The combined treatment has been used for termination of early pregnancy (up to 63 days of amenorrhea) and for termination of second trimester pregnancy. During early pregnancy, the recommended dose of mifepristone is 600 mg (although 200 mg seems sufficient), followed 36-48 h later by 0.4-0.8 mg misoprostol administered either orally or vaginally, or vaginal administration of 1.0 mg gemeprost. For termination of second trimester pregnancy, the treatment with mifepristone is most commonly combined with 1.0 mg gemeprost repeated at 3-6-h intervals. The combined treatment is as effective and safe during early pregnancy as is the alternative vacuum aspiration and is also equally acceptable if the woman is allowed to choose the method she prefers. During the second trimester, the pretreatment will significantly reduce the duration of labor, dose of prostaglandin, and the frequency of side effects.     

The effect of positive assortative mating at one locus on a second linked locus

Summary A model for positive assortative mating based on genotype for one locus is employed to investigate the effect of this mating system on the genotypic structure of a second linked locus as well as on the joint genotypic structure of these two loci. It is shown that the second locus does not attain a precise positive assortative mating structure, but yet it shares a property that is characteristic of positive assortative mating, namely an increase in the frequency of homozygotes over that typically found in panmictic structures. Given any arbitrary genotypic structure for the parental population, the resulting offspring generation possesses a structure at the second locus that does not depend on the recombination frequency, while the joint structure of course does. In case assortative mating as well as linkage are not complete, there exists a unique joint equilibrium state for the two loci, which is characterized by complete stochastic independence between the two loci as well as by Hardy-Weinberg proportions at the second locus. For the second locus alone, Hardy-Weinberg equilibrium is realized if and only if gametic linkage equilibrium and an additionally specified condition are realized.