The Interactions of Three Widely Separated Loci Controlling Conversion Properties of w Locus I in ASCOBOLUS IMMERSUS

Gene conversion properties of white (w) ascospore locus I in the Pasadena strains of Ascobolus immersus are controlled by complex interactions between three separate conversion control factors ( ccfs), which can give conversion frequencies at wI ranging from less than 1% up to 33%. ccf-2, which has three alleles, is very closely linked to wI but does not usually co-convert with it. ccf-2(K) and ccf-2(91) give lower conversion frequencies than ccf-2(P) and are incompletely dominant to ccf-2(P), with cis/trans position effects on conversion of wI. The "super" factor ( Helmi and Lamb 1979) has two interacting but unlinked components, ccf-3E and ccf-4r, which approximately double the conversion frequency at wI. ccf-2 (linkage group VIII), ccf-3 (linkage group I) and ccf-4 are probably all unlinked but interact and specifically control conversion at wI. ccf-3E could code for a diffusible product that affects the action of different ccf-2 alleles, which probably act by controlling the frequency of initiation of hybrid-DNA, which spreads into the adjacent wI locus. ccf-4R could code for a diffusible inhibitor of ccf-3E product, or be an alternative binding site for ccf-3E product. The dominance of ccf-4R depends on which ccf-2 alleles are present in the cross.     

Hitchhiking: A Comparison of Linkage and Partial Selfing

Genetic hitchhiking occurs when alleles at unselected loci are changed in frequency because of an association with alleles at a selected locus. This association may be mediated either by linkage or partial selfing (inbreeding) and can affect the gene frequency and gametic disequilibrium at the neutral loci. Hitchhiking from partial selfing (unlinked loci) occurs more quickly than linkage hitchhiking and generally has a greater effect. In addition, partial-selfing hitchhiking can cause increases or changes in sign in gametic disequilibrium between neutral loci. The effects of the two types of hitchhiking with different levels of dominance, zygotic frequencies and number of selected loci are also examined. The general conditions for linkage and partial-selfing hitchhiking are outlined and the implications of hitchhiking are discussed for marker or electrophoretic loci.     

Testing Hypotheses about Linkage Disequilibrium with Multiple Alleles

For loci with multiple alleles, hypotheses about linkage disequilibrium may be tested on the complete set of gametic data, or on various collapsed sets of data. Collapsing data into a few alleles at each locus can change the power of the tests, as implied in a recent paper by Zouros, Golding and Mackay (1977). We show that the nature of such changes can be found from properties of the noncentral chi-square distribution, and that the magnitude and direction of these changes depend on the levels of linkage disequilibria, allelic frequencies and degrees of freedom.     

A cladistic analysis of phenotypic associations with haplotypes inferred from restriction endonuclease mapping. I. Basic theory and an analysis of alcohol dehydrogenase activity in Drosophila

Because some genes have been cloned that have a known biochemical or physiological function, genetic variation can be measured in a population at loci that may directly influence a phenotype of interest. With this measured genotype approach, specific alleles or haplotypes in the probed DNA region can be assigned phenotypic effects. In this paper we address several problems encountered in implementing the measured genotype approach with restriction site data. A number of analytical problems arise in part as a consequence of the linkage disequilibrium that is commonly encountered when dealing with small DNA regions: 1) different restriction site polymorphisms are not statistically independent, 2) the sites being measured are not likely to be the direct cause of the associated phenotypic effects, 3) haplotype classes may be phenotypically heterogeneous, and 4) the sites that are most strongly associated with phenotypic effects are not necessarily the most closely linked to the actual genetic cause of the effects. When recombination and gene conversion are rare, the primary cause of linkage disequilibrium is history (mutational origin, genetic drift, hitchhiking, etc.). We deal with historical association directly by producing a cladogram that partially reconstructs the evolutionary history of the present-day haplotype variability. The cladogram defines a nested analysis of variance that simultaneously detects phenotypic effects, localizes the effects within the cladogram, and identifies haplotypes that are potentially heterogeneous in their phenotypic associations. The power of this approach is illustrated by an analysis of the associations between alcohol dehydrogenase (ADH) activity and restriction site variability in a 13-kb fragment surrounding the ADH locus in Drosophila melanogaster.     

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.     

The control of gene conversion properties and corresponding-site interference: the effects of conversion control factor 5 on conversion at locus w9 in Ascobolus immersus

The controls of various aspects and parameters of gene conversion at locus w-9 in the fungus Ascobolus immersus were investigated, along with positive and negative corresponding-site interference in meiotic chromatid pairing. When conversion control factor 5 alleles A and B were heterozygous, conversion frequencies at the closely linked target locus w9 were reduced to 3%, compared with 10.7% when A or B was homozygous, through effects on hybrid-DNA (h-DNA) formation parameters gamma1 and gamma2. In different ways, not related to whether ccf-5 alleles were homozygous or heterozygous, ccf-5 also affected parameters relating to the relative frequencies of asymmetric and symmetric h-DNA, the frequency with which the chromatid bearing the wild-type allele was the invading chromatid in asymmetric h-DNA, and h-DNA correction parameters for the frequency and direction of correction of mispairs. Corresponding-site interference is interference between the two pairs of non-sister chromatids of a bivalent in h-DNA formation at exactly corresponding sites. This interference was positive in the high conversion frequency crosses homozygous for ccf-5 alleles but was strongly negative in the low conversion frequency crosses heterozygous for ccf-5 alleles, through differential effects on parameters gamma1 and gamma2. Models of chromatid pairing are discussed.     

The Effects of Overdominance on Linkage in a Multilocus System

Computer simulations were performed with overdominant multiple alleles among tightly linked multiple loci under a multiplicative fitness model. The quantity X²/N(n — 1) was introduced as a new measure of linkage disequilibrium which, unlike previously available measures, can be applied to multiple allele models, where N is the sample size, and n is the number of alleles at the locus possessing fewest alleles. Simulations showed that (1) With multiple (three or four) alleles, the approach to stable disequilibrium is slower and the amount of disequilibrium established is weaker than in a two allele system. (2) The number of complementary chromosomes is a function of number of alleles and of population size. (3) As population size increases, the rate of the approach to stable disequilibrium is slower. (4) There is an optimum selection coefficient which minimizes the transient fixation probability of alleles when linkage is present. (5) The absence of linkage disequilibrium is in most cases not a practical method of testing the hypothesis of balancing selection of genetic polymorphisms because it depends strongly on population size in determining linkage disequilibria.     

The effect of linkage and population size on inbreeding depression due to mutational load.

Using a stochastic model of a finite population in which there is mutation to partially recessive detrimental alleles at many loci, we study the effects of population size and linkage between the loci on the population mean fitness and inbreeding depression values. Although linkage between the selected loci decreases the amount of inbreeding depression, neither population size nor recombination rate have strong effects on these quantities, unless extremely small values are assumed. We also investigate how partial linkage between the loci that determine fitness affects the invasion of populations by alleles at a modifier locus that controls the selfing rate. In most of the cases studied, the direction of selection on modifiers was consistent with that found in our previous deterministic calculations. However, there was some evidence that linkage between the modifier locus and the selected loci makes outcrossing less likely to evolve; more losses of alleles promoting outcrossing occurred in runs with linkage than in runs with free recombination. We also studied the fate of neutral alleles introduced into populations carrying detrimental mutations. The times to loss of neutral alleles introduced at low frequency were shorter than those predicted for alleles in the absence of selected loci, taking into account the reduction of the effective population size due to inbreeding. Previous studies have been confined to outbreeding populations, and to alleles at frequencies close to one-half, and have found an effect in the opposite direction. It therefore appears that associations between neutral and selected loci may produce effects that differ according to the initial frequencies of the neutral alleles.     

An analysis of linkage disequilibrium in the interleukin-1 gene cluster, using a novel grouping method for multiallelic markers.

In population- and family-based association studies, it is useful to have some knowledge of the patterns of linkage disequilibrium that exist between markers in candidate regions. When such studies are carried out with multiallelic markers, it is often convenient to group the alleles into a biallelic system, for analysis. In this study, we specifically examined the interleukin-1 (IL-1) gene cluster on chromosome 2, a region containing candidates for many inflammatory and autoimmune disorders. Data were collected on eight markers, four of which were multiallelic. Using these data, we investigated the effect of three allele-grouping strategies, including a novel method, on the detection of linkage disequilibrium. The novel approach, termed the "delta method," measures the deviation from the expected haplotype frequencies under linkage equilibrium, for each allelic combination. This information is then used to group the alleles, in an attempt to avoid the grouping together of alleles at one locus that are in opposite disequilibrium with the same allele at the second locus. The estimate haplotype frequencies (EH) program was used to estimate haplotype frequencies and the disequilibrium measure. In our data it was found that the delta method compared well with the other two strategies. Using this method, we found that there was a reasonable correlation between disequilibrium and physical distance in the region (r=-.540, P=.001, one-tailed). We also identified a common, eight-locus haplotype of the IL-1 gene cluster.     

Evidence for Linkage Disequilibrium Maintained by Selection in Two Natural Populations of DROSOPHILA SUBOBSCURA

One island and one mainland population of Drosophila subobscura were found polymorphic at the XDH (xanthine dehydrogenase) and the AO (aldehyde oxidase) loci. It was observed that one allele at the XDH locus, which has a low frequency in both populations, is nonrandomly associated with the alleles at the AO locus. Two lines of evidence support the thesis that this linkage disequilibrium is due to epistasis rather than random drift: (1) D or r, measures of the disequilibrium, have the same sign and magnitude in both populations. (2) The linkage disequilibrium is not due to inversions. Inversions segregating on the chromosome carrying XDH and AO have been separated into two classes, between which exchange of alleles at the two loci is suppressed. Linkage disequilibrium for XDH and AO was observed within each class. In the absence of any exchange of alleles, these disequilibria must have arisen and been maintained independently. The suggestion is made that the epistatic disequilibrium results from the close structural and physiological relationship which exists between the two enzymes.     

The predisposition to type 1 diabetes linked to the human leukocyte antigen complex includes at least one non-class II gene

The human leukocyte antigen (HLA) complex, encompassing 3.5 Mb of DNA from the centromeric HLA-DPB2 locus to the telomeric HLA-F locus on chromosome 6p21, encodes a major part of the genetic predisposition to develop type 1 diabetes, designated "IDDM1." A primary role for allelic variation of the class II HLA-DRB1, HLA-DQA1, and HLA-DQB1 loci has been established. However, studies of animals and humans have indicated that other, unmapped, major histocompatibility complex (MHC)-linked genes are participating in IDDM1. The strong linkage disequilibrium between genes in this complex makes mapping a difficult task. In the present paper, we report on the approach we have devised to circumvent the confounding effects of disequilibrium between class II alleles and alleles at other MHC loci. We have scanned 12 Mb of the MHC and flanking chromosome regions with microsatellite polymorphisms and analyzed the transmission of these marker alleles to diabetic probands from parents who were homozygous for the alleles of the HLA-DRB1, HLA-DQA1, and HLA-DQB1 genes. Our analysis, using three independent family sets, suggests the presence of an additional type I diabetes gene (or genes). This approach is useful for the analysis of other loci linked to common diseases, to verify if a candidate polymorphism can explain all of the association of a region or if the association is due to two or more loci in linkage disequilibrium with each other.     

Association studies under general disease models

There is great expectation that the levels of association found between genetic markers and disease status will play a role in the location of disease genes. This expectation follows from regarding association as being proportional to linkage disequilibrium and therefore inversely related to recombination value. For disease genes with more than two alleles, the association measure is instead a weighted average of linkage disequilibria, with the weights depending on allele frequencies and genotype susceptibilities at the disease loci. There is no longer a simple relationship, even in expectation, with recombination. We adopt a general framework to examine association mapping methods which helps to clarify the nature of case-control and transmission/disequilibrium-type tests and reveals the relationship between measures of association and coefficients of linkage disequilibrium. In particular, we can show the consequences of additive and nonadditive effects at the trait locus on the behavior of these tests. These concepts have a natural extension to marker haplotypes. The association of two-locus marker haplotypes with disease phenotype depends on a weighted average of three-locus disequilibria (two markers with each disease locus). It is likely that these two-marker analyses will provide additional information in association mapping studies.     

Linkage disequilibrium and modification of risk for Huntington disease.

The major limitation in performing predictive testing for Huntington disease (HD) is the unavailability of DNA from crucial family members. In our program approximately 20% (36/183) of persons have been excluded from predictive testing because of this reason. The major aim of this study was to examine whether data derived from linkage disequilibrium could modify risk analysis for persons at risk for HD. As a first step, we assessed whether the previously reported linkage disequilibrium between alleles recognized by probe pBS674E-D at locus D4S95 remained significant in a much larger data set. A total of 1,150 chromosomes from 622 individuals--200 affected and 422 unaffected--from 118 families were assessed. Significant haplotype association was detected with AccI and MboI RFLPs at the locus D4S95, with all the families (P = .00003), as well as for a subset from the United Kingdom (P = .0037). Data derived from linkage disequilibrium studies using D4S95 modifies the risk for HD, especially in persons of U.K. descent. Utilization of this approach for risk modification of HD awaits both validation of these data and additional information concerning ethnic-specific alleles at the D4S95 locus.     

Associative overdominance: Evaluating the effects of inbreeding and linkage disequilibrium

Expressions are obtained for the expected phenotypic values of homozygous and heterozygous genotypes for a neutral marker locus linked to a locus segregating for a recessive deleterious gene. The phenotypic values are functions of the allele frequencies at the marker locus, the inbreeding coefficient and the degree of association of the deleterious gene with the marker alleles. The analysis is extended to more than two alleles at the marker locus. Either linkage disequilibrium or inbreeding alone can produce an apparent superiority of heterozygotes for the marker locus (unless specified otherwise, the terms ‘homozygote’ and ‘heterozygote’ will refer to the marker locus). The effect of linkage disequilibrium on the difference between the heterozygote and homozygote values can be positive (associative overdominance) or negative (associative underdominance), depending on the frequencies of the marker alleles and the degree of their association with the deleterious gene. Inbreeding has always a positive effect. In general, the expected value of a homozygote is a positive function of its allele frequency. When the various homozygous genotypes are combined into one class and the various heterozygous genotypes into another, the phenotypic difference of the two classes is a function of the evenness of the allelic frequency distribution. Inbreeding is a more likely explanation of associative overdominance if the frequency of the deleterious gene is low, but its effect on the character high. Conversely, linkage disequilibrium is more likely if the frequency is high and the effect low. The degrees of association between marker alleles and the deleterious gene can, in principle, be estimated from the observed phenotypic scores and used to calculate expected multi-locus genotype scores. This could provide the basis for statistical tests of the associative overdominance hypothesis as an explanation of observed correlations between multi-locus heterozygosity and phenotypic traits.     

Electrophoretic detection of single-nucleotide polymorphisms

Single-nucleotide polymorphisms (SNPs) represent the most prevalent class of genetic markers available for linkage disequilibrium or cladistic analyses. PCR primers may be labeled with fluorescent dyes and used to rapidly and accurately differentiate among alleles that are defined by a single-nucleotide differences. Here, we describe the primer-mediated detection of SNPs based on primer mismatch during allele-specific amplification of preamplified target sequences. Primers are labeled with different fluors at their 5' nucleotides, with their 3' termini at the transition mutation that defines allelic variation at the target locus. Each primer perfectly matches one of the two available alleles for each locus. Electrophoretic detection permits characterization of the product both by size and fluor. This report demonstrates some of the capabilities of this assay, including heterozygote determination and multiplexed analysis.     

Modeling extent and distribution of zygotic disequilibrium: implications for a multigenerational canine pedigree

Unlike gametic linkage disequilibrium defined for a random-mating population, zygotic disequilibrium describes the nonrandom association between different loci in a nonequilibrium population that deviates from Hardy-Weinberg equilibrium. Zygotic disequilibrium specifies five different types of disequilibria simultaneously that are (1) Hardy-Weinberg disequilibria at each locus, (2) gametic disequilibrium (including two alleles in the same gamete, each from a different locus), (3) nongametic disequilibrium (including two alleles in different gametes, each from a different locus), (4) trigenic disequilibrium (including a zygote at one locus and an allele at the other), and (5) quadrigenic disequilibrium (including two zygotes each from a different locus). However, because of the uncertainty on the phase of the double heterozygote, gametic and nongametic disequilibria need to be combined into a composite digenic disequilibrium and further define a composite quadrigenic disequilibrium together with the quadrigenic disequilibrium. To investigate the extent and distribution of zygotic disequilibrium across the canine genome, a total of 148 dogs were genotyped at 247 microsatellite markers located on 39 pairs of chromosomes for an outbred multigenerational pedigree, initiated with a limited number of unrelated founders. A major portion of zygotic disequilibrium was contributed by the composite digenic and quadrigenic disequilibrium whose values and numbers of significant marker pairs are both greater than those of trigenic disequilibrium. All types of disequilibrium are extensive in the canine genome, although their values tend to decrease with extended map distances, but with a greater slope for trigenic disequilibrium than for the other types of disequilibrium. Considerable variation in the pattern of disequilibrium reduction was observed among different chromosomes. The results from this study provide scientific guidance about the determination of the number of markers used for whole-genome association studies.     

The deviation from linkage equilibrium with multiple loci varying in a stepping-stone cline

The balance between the creation of associations between alleles at different loci by immigration and the convergence to linkage equilibrium due to the recombination process is studied in a theoretical model. The geographical structure of the model is a stepping-stone chain of populations linking two genetically constant source populations. The model assumes an arbitrary number of autosomal loci and considers genetic variation (two alleles at each locus) that is not subject to natural selection. The gene frequencies at each locus will then show a linear cline through the stepping-stone chain of populations. The deviation from linkage equilibrium through the stepping-stone cline is characterized by an equation for linear measures that provide the linkage disequilibrium measures for a given set of loci in terms of the gene frequencies and the linkage disequilibria in the source populations and in terms of the linkage disequilibrium measures through the cline for lower numbers of loci. Numerical examples of this iterative solution are given, and it is shown that the build-up of the higher order Bennett-disequilibria through the cline is considerably more pronounced than the build-up of two-locus disequilibria.     

A genealogical interpretation of linkage disequilibrium

The degree of association between alleles at different loci, or linkage disequilibrium, is widely used to infer details of evolutionary processes. Here I explore how associations between alleles relate to properties of the underlying genealogy of sequences. Under the neutral, infinite-sites assumption I show that there is a direct correspondence between the covariance in coalescence times at different parts of the genome and the degree of linkage disequilibrium. These covariances can be calculated exactly under the standard neutral model and by Monte Carlo simulation under different demographic models. I show that the effects of population growth, population bottlenecks, and population structure on linkage disequilibrium can be described through their effects on the covariance in coalescence times.     

Linkage analysis of "necessary" disease loci versus "susceptibility" loci.

The association of some diseases with specific alleles of certain genetic markers has been difficult to explain. Several explanations have been proposed for the phenomenon of association, e.g. the existence of multiple, interacting genes (epistasis) or a disease locus in linkage disequilibrium with the marker locus. One might suppose that when marker data from families with associated diseases are analyzed for linkage, the existence of the association would assure that linkage will be found, and found at a tight recombination fraction. In fact, however, linkage analyses of some diseases associated with HLA, as well as diseases associated with alleles at other loci located throughout the genome, show significant evidence against linkage, and others show loose linkage, to the puzzlement of many researchers. In part, the puzzlement arises because linkage analysis is ideal for looking for loci that are necessary, even if not sufficient, for disease expression but may be much less useful for finding loci that are neither necessary nor sufficient for disease expression (so-called susceptibility loci). This work explores what happens when one looks for linkage to susceptibility loci. A susceptibility locus in this case means that the allele increases risk but is neither necessary nor sufficient for disease expression. It might be either an allele at the marker locus itself that is increasing susceptibility or an allele at a locus in linkage disequilibrium with the marker. This work uses computer simulation to examine how linkage analyses behave when confronted with data from such a model.(ABSTRACT TRUNCATED AT 250 WORDS)