Effect on linkage disequilibrium of selection for a quantitative character with epistasis

Summary Selection for a character controlled by additive genes induces linkage disequilibrium which reduces the additive genetic variance usable for further selective gains. Additive x additive epistasis contributes to selection response through development of linkage disequilibrium between interacting loci. To investigate the relative importance of the two effects of linkage disequilibrium, formulae are presented and results are reported of simulations using models involving additive, additive x additive and dominance components. The results suggest that so long as epistatic effects are not large relative to additive effects, and the proportion of pairs of loci which show epistasis is not very high, the predominant effect of linkage disequilibrium will be to reduce the rate of selection response.     

On the evolution of epistasis II: a generalized Wright-Kimura framework

The evolution of fitness interactions between genes at two major loci is studied where the alleles at a third locus modify the epistatic interaction between the two major loci. The epistasis is defined by a parameter epsilon and a matrix structure that specifies the nature of the interactions. When epsilon=0 the two major loci have additive fitnesses, and when these are symmetric the interaction matrices studied here produce symmetric viabilities of the Wright [1952. The genetics of quantitative variability. In: Reeve, E.C.R., Waddington, C.H. (Eds.), Quantitative Inheritance. Her Majesty's Stationary Office, London]-Kimura [1956. A model of a genetic system which leads to closer linkage by natural selection. Evolution 10, 278-281] form. Two such interaction matrices are studied, for one of which epistasis as measured by |epsilon| always increases, and for the other it increases when the linkage between the major loci is tight enough and there is initial linkage disequilibrium. Increase of epistasis does not necessarily coincide with increase in equilibrium mean fitness.     

Effects of population size and linkage on optimal selection intensity

Following Robertson (1970a) it is generally considered that for mass selection the selected proportion that maximises ultimate response is 0.5. This prediction has been partly tested by different authors. Here we explicitly address the question using computer simulations of selection in finite populations with linkage. The results show that the response achieved is always lower than the one predicted by standard methods, and that optimum selection intensity may be much lower than predicted unless population size is small.     

Effects of epistasis on phenotypic robustness in metabolic pathways

It is an open question whether phenomena such as phenotypic robustness to mutation evolve as adaptations or are simply an inherent property of genetic systems. As a case study, we examine this question with regard to dominance in metabolic physiology. Traditionally the conclusion that has been derived from Metabolic Control Analysis has been that dominance is an inevitable property of multi-enzyme systems and hence does not require an evolutionary explanation. This view is based on a mathematical result commonly referred to as the flux summation theorem. However it is shown here that for mutations involving finite changes (of any magnitude) in enzyme concentration, the flux summation theorem can only hold in a very restricted set of conditions. Using both analytical and simulation results we show that for finite changes, the summation theorem is only valid in cases where the relationship between genotype and phenotype is linear and devoid of non-linearities in the form of epistasis. Such an absence of epistasis is unlikely in metabolic systems. As an example, we show that epistasis can arise in scenarios where we assume generic non-linearities such as those caused by enzyme saturation. In such cases dominance levels can be modified by mutations that affect saturation levels. The implication is that dominance is not a necessary property of metabolic systems and that it can be subject to evolutionary modification.     

随机交配群体中连锁对世代平均数和方差的影响及其测定

本文以黄花烟草N.rustica的两个品种V_2和V_(12)为材料,人工创造4个随机交配轮次不同的群体,对开花期(FT)和最后株高(FH)两个性状在理论上探讨了随机交配群体中连锁对世代平均数和方差的影响,并用上述材料进行验证。结果指出,在平均数和方差两种水平上都测定出连锁的存在;无论是加性方差还是显性方差,都随着交配轮次的增加而减少,这是相引连锁的表现。本文还讨论了基因连锁强度、基因联合程度对世代平均数和方差的影响。     

On the evolution of epistasis I: diploids under selection

One interpretation of recent literature on the evolution of phenotypic modularity is that evolution should act to decrease the degree of interaction between genes that contribute to different phenotypes. This issue is addressed directly here using a fitness scheme determined by two genetic loci and a third locus which modifies a measure of statistical interaction between the fitnesses due to the first two. The equilibrium structure of such an epistasis-modifying locus is studied. It is shown that under well-specified conditions a modifying allele that increases epistasis succeeds. In other words, genetic interactions tend to become stronger. It is speculated that this occurs because the mean fitness in such models is locally increasing as a function of the degree of epistasis.     

Selective genotyping for determination of linkage between a marker locus and a quantitative trait locus

Summary Selective genotyping is the term used when the determination of linkage between marker loci and quantitative trait loci (QTL) affecting some particular trait is carried out by genotyping only individuals from the high and low phenotypic tails of the entire sample population. Selective genotyping can markedly decrease the number of individuals genotyped for a given power at the expense of an increase in the number of individuals phenotyped. The optimum proportion of individuals genotyped from the point of view of minimizing costs for a given experimental power depends strongly on the cost of completely genotyping an individual for all of the markers included in the experiment (including the costs of obtaining a DNA sample) relative to the cost of rearing and trait evaluation of an individual. However, in single trait studies, it will almost never be useful to genotype more than the upper and lower 25% of a population. It is shown that the observed difference in quantitative trait values associated with alternative marker genotypes in the selected population can be much greater than the actual gene effect at the quantitative trait locus when the entire population is considered. An expression and a figure is provided for converting observed differences under selective genotyping to actual gene effects.     

Combining dependent tests for linkage or association across multiple phenotypic traits

A robust statistical method to detect linkage or association between a genetic marker and a set of distinct phenotypic traits is to combine univariate trait-specific test statistics for a more powerful overall test. This procedure does not need complex modeling assumptions, can easily handle the problem with partially missing trait values, and is applicable to the case with a mixture of qualitative and quantitative traits. In this note, we propose a simple test procedure along this line, and show its advantages over the standard combination tests for linkage or association in the literature through a data set from Genetic Analysis Workshop 12 (GAW12) and an extensive simulation study.     

An integrated genetic linkage map for eucalypts using RFLP,RAPD and isozyme markers

An integrated genetic linkage map for E. nitens was constructed in an outbred three-generation pedigree. Analysis of 210 RFLP, 125 RAPD and 4 isozyme loci resulted in 330 markers linked in 12 linkage groups covering 1462 cM (n=11 in eucalypts). The 12th linkage group is comprised of only 5 markers and will probably coalesce with another linkage group when further linked loci are located. Co-dominant RFLP loci segregating in both parents were used to integrate linkages identified in the male and female parents. Differences in recombination frequencies in the two parents were observed for a number of pairs of loci, and duplication of sequences was identified both within and between linkage groups. The markers were distributed randomly across the genome except for the RFLPs in linkage group 10 and for some loci showing segregation distortion, which were clustered into three regions of the map. The use of a large number of co-dominant RFLP loci in this map enables it to be used in other pedigrees of E. nitens and forms a basis for the detection and location of QTL in E. nitens and other eucalypt species.     

Effects of genetic background and environment on QTLs and epistasis for rice (Oryza sativa L.) panicle number

A double-haploid (DH) population and a recombinant inbred (RI) line population, derived from a cross between a tropical japonica variety, Azucena, as male parent and two indica varieties, IR64 and IR1552, as female parents respectively, were used in both field and pot experiments for detecting QTLs and epistasis for rice panicle number in different genetic backgrounds and different environments. Panicle number (PN) was measured at maturity. A molecular map with 192 RFLP markers for the DH population and a molecular map with 104 AFLP markers and 103 RFLP markers for the RI population were constructed, in which 70 RFLP markers were the same. Six QTLs were identified in the DH population, including two detected from field experiments and four from pot experiments. The two QTLs, mapped on chromosomes 1 and 12, were identical in both field and pot experiments. In the RI population, nine QTLs were detected, five QTLs from field conditions and four from the pot experiments. Three of these QTLs were identical in both experimental conditions. Only one QTL, linked to CDO344 on chromosome 12, was detected across the populations and experiments. Different epistasitic interaction loci on PN were found under different populations and in different experimental conditions. One locus, flanked by RG323 and RZ801 on chromosome 1, had an additive effect in the DH population, but epistatic effects in the RI population. These results indicate that the effect of genetic background on QTLs is greater than that of environments, and epistasis is more sensitive to genetic background and environments than main-effect QTLs. QTL and epistatic loci could be interchangeable depending on the genetic backgrounds and probably on the environments where they are identified. Received: 26 May 2000 / Accepted: 19 October 2000     

Score tests of genetic association in the presence of linkage based on the additive genetic gamma frailty model

Nuclear families with multiple affected sibs are often collected for genetic linkage analysis of complex diseases. Once linkage evidence is established, dense markers are often typed in the linked region for genetic association analysis based on linkage disequilibrium (LD). Detection of association in the presence of linkage localizes disease genes more accurately than the methods that rely on linkage alone. However, test of association due to LD in the linked region needs to account for dependency of the allele transmissions to different sibs within a family. In this paper, we define a joint model for genetic linkage and association and derive the corresponding joint survival function of age of onset for the sibs within a sibship. The joint survival function is a function of both the inheritance vector and the genotypes at the candidate marker locus. Based on this joint survival function, we derive score tests for genetic association. The proposed methods utilize the phenotype data of all the sibs and have the advantages of family-based designs which can avoid the potential spurious association caused by population admixture. In addition, the methods can account for variable age of onset or age at censoring and possible covariate effects, and therefore provide important tools for modelling disease heterogeneity. Simulation studies and application to the data sets from the 12th Genetic Analysis Workshop indicate that the proposed methods have correct type 1 error rates and increased power over other existing methods for testing allelic association.     

Identifying susceptibility genes by using joint tests of association and linkage and accounting for epistasis

Simulated Genetic Analysis Workshop 14 data were analyzed by jointly testing linkage and association and by accounting for epistasis using a candidate gene approach. Our group was unblinded to the "answers." The 48 single-nucleotide polymorphisms (SNPs) within the six disease loci were analyzed in addition to five SNPs from each of two non-disease-related loci. Affected sib-parent data was extracted from the first 10 replicates for populations Aipotu, Kaarangar, and Danacaa, and analyzed separately for each replicate. We developed a likelihood for testing association and/or linkage using data from affected sib pairs and their parents. Identical-by-descent (IBD) allele sharing between sibs was explicitly modeled using a conditional logistic regression approach and incorporating a covariate that represents expected IBD allele sharing given the genotypes of the sibs and their parents. Interactions were accounted for by performing likelihood ratio tests in stages determined by the highest order interaction term in the model. In the first stage, main effects were tested independently, and in subsequent stages, multilocus effects were tested conditional on significant marginal effects. A reduction in the number of tests performed was achieved by prescreening gene combinations with a goodness-of-fit chi square statistic that depended on mating-type frequencies. SNP-specific joint effects of linkage and association were identified for loci D1, D2, D3, and D4 in multiple replicates. The strongest effect was for SNP B03T3056, which had a median p-value of 1.98 x 10(-34). No two- or three-locus effects were found in more than one replicate.     

Accounting for epistasis in linkage analysis of general pedigrees

Complex traits are generally believed to be influenced by multiple loci. Identification of loci involved in complex traits is more difficult for interacting than for additive loci. Here we describe an extension of the program lm_twoqtl in the package MORGAN to handle two quantitative trait loci (QTLs) with gene-gene interaction. We investigate whether parametric linkage analysis that accounts for such epistasis improves prospects for linkage detection and accuracy of localization of QTLs. Through use of simulated data we show that analysis that accounts for epistasis provides higher lod scores and better localization than does analysis without epistasis. In addition, we demonstrate that the difference between lod scores in the presence vs. absence of use of an interaction model in analysis is greater in extended than in nuclear pedigrees.     

Equilibria in an epistatic viability model under arbitrary strength of selection

A class of viability models that generalize the standard additive model for the case of pairwise additive by additive epistatic interactions is considered. Conditions for existence and stability of steady states in the corresponding two-locus model are analyzed. Using regular perturbation techniques, the case when selection is weaker than recombination and the case when selection is stronger than recombination are investigated. The results derived are used to make conclusions on the dependence of population characteristics on the relation between the strength of selection and the recombination rate.     

A simple note on how to save money in linkage analysis

Genetic linkage maps are often based on maximum-likelihood estimates of recombination fractions which are converted into map units by mapping functions. This paper presents a cost analysis of linkage analysis for a segregating F₂␣population with codominant or dominant molecular markers and a qualitative monogenic dominant–recessive trait. For illustration, a disease-resistance trait is considered, where the susceptible allele is recessive. Three sub-populations of the F₂ can be used for linkage analysis [susceptible (= recessive) individuals, resistant (= dominant) individuals, complete F₂]. While it is well-known that recessive individuals are more informative than dominant individuals, it is not obvious a priori, which of the three sub-populations should be preferred, when costs of phenotyping and genotyping are taken into consideration. A comparative economic analysis of alternative procedures of linkage detection based on these three sub-populations does exhibit a clear economic superiority of the sub-population of susceptible (= recessive) individuals, when costs of genotyping are high. This cost-effectiveness is due to the higher information content of this sub-population compared to the sub-population of dominant (= resistant) individuals and also compared to the complete F₂. Our final conclusion/recommendation is as follows: If the cost to genotype an individual is sufficiently large compared with the cost to phenotype an individual, then linkage analysis and genetic mapping should be only based on susceptible (= recessive) individuals. Conversely, if the cost of phenotyping exceeds that for genotyping, it may be preferable to genotype all plants. The exact conditions under which a strategy is preferable are described in the paper.     

Inheritance and linkage relationships of morphological and isozyme loci in chickpea (Cicer arietinum L.)

Inheritance and linkage relationships of several morphological and isozyme loci are described in chickpea (Cicer arietinum L.). Segregation data obtained from several F₂ families confirmed the previously observed mode of inheritance for most of the morphological loci. Additional morphological markers in chickpea are also described. Most of the isozyme loci studied showed codominant expression and fit expected Mendelian segregation ratios. However, distorted ratios were also observed for some loci. Linkage was found betweenPgd-c, the locus encoding the cytosolic form of 6-phosphogluconate dehydrogenase, andHg, the locus controlling plant growth habit. These 2 loci were separated by approximately 18 recombinational map units. A similar linkage between comparable loci was previously reported in pea (Pisum sativum L.) (Weeden and Wolko 1990). Linkage was also detected among 3 isozyme loci; the cytosolic form of phosphoglucomutase (Pgm-c), glucose-1-phosphate transferase (Gpt1), and the plastid specific form of 6-phosphogluconate dehydrogenase (Pgd-p). The linkage of 2 loci (Pgm-c andPgd-p) in this cluster is also conserved in pea and lentil (Lens Miller). The linkage between an acid phosphatase locus (Acp3) and the locus specifying the cytosolic form of glucosephosphate isomerase (Gpi-c) in chickpea suggested another linkage group in common with pea. Additionally, other linkages that were not previously observed in chickpea or related genera included the linkage of the cytosolic form of aconitase (Aco-c) with adenylate kinase (Adk1) and fructokinase (Fk3), and the linkage of a locus encoding the mitochondrial specific aconitase (Aco-m) with a seed protein locus (Spr1). The loci determining flower color (P), epicotyl color (Gst), seed coat color (T ³), and seed surface (Rs) were associated with the locus encoding glucose-1-phosphate transferase (Gpt2). These results, along with previous studies, suggest that pea, lentil and chickpea have several common linkage groups consisting of homologous genes. This also indicates that linkages found in one genus can be used to predict similar linkages in related genera in the development of linkage maps.     

Trait-based analyses for the detection of linkage between marker loci and quantitative trait loci in crosses between inbred lines

Summary Methods are presented for determining linkage between a marker locus and a nearby locus affecting a quantitative trait (quantitative trait locus=QTL), based on changes in the marker allele frequencies in selection lines derived from the F-2 of a cross between inbred lines, or in the high and low phenotypic classes of an F-2 or BC population. The power of such trait-based (TB) analyses was evaluated and compared with that of methods for determining linkage based on the mean quantitative trait value of marker genotypes in F-2 or BC populations [marker-based (MB) analyses]. TB analyses can be utilized for marker-QTL linkage determination in situations where the MB analysis is not applicable, including analysis of polygenic resistance traits where only a part of the population survives exposure to the Stressor and analysis of marker-allele frequency changes in selection lines. TB analyses may be a useful alternative to MB analyses when interest is centered on a single quantitative trait only and costs of scoring for markers are high compared with costs of raising and obtaining quantitative trait information on F-2 or BC individuals. In this case, a TB analysis will enable equivalent power to be obtained with fewer individuals scored for the marker, but more individuals scored for the quantitative trait. MB analyses remain the method of choice when more than one quantitative trait is to be analyzed in a given population.Contribution from the ARO, Bet Dagan, Israel. No. 1698-E, 1986 series     

The effects of linkage and gene flow on local adaptation: a two-locus continent-island model

Population subdivision and migration are generally considered to be important causes of linkage disequilibrium (LD). We explore the combined effects of recombination and gene flow on the amount of LD, the maintenance of polymorphism, and the degree of local adaptation in a subdivided population by analyzing a diploid, deterministic continent–island model with genic selection on two linked loci (i.e., no dominance or epistasis). For this simple model, we characterize explicitly all possible equilibrium configurations. Simple and intuitive approximations for many quantities of interest are obtained in limiting cases, such as weak migration, weak selection, weak or strong recombination. For instance, we derive explicit expressions for the measures and r² (the squared correlation in allelic state) of LD. They depend in qualitatively different ways on the migration rate. Remarkably high values of r² are maintained between weakly linked loci, especially if gene flow is low. We determine how the maximum amount of gene flow that admits preservation of the locally adapted haplotype, hence of polymorphism at both loci, depends on recombination rate and selection coefficients. We also investigate the evolution of differentiation by examining the invasion of beneficial mutants of small effect that are linked to an already present, locally adapted allele. Mutants of much smaller effect can invade successfully than predicted by naive single-locus theory provided they are at least weakly linked. Finally, the influence of linkage on the degree of local adaptation, the migration load, and the effective migration rate at a neutral locus is explored. We discuss possible consequences for the evolution of genetic architecture, in particular, for the emergence of clusters of tightly linked, slightly beneficial mutations and the evolution of recombination and chromosome inversions.     

Asymptotic distribution for epistatic tests in case-control studies

We propose a statistical model for dissecting a multilocus genotypic value into its main (additive and dominant) effects and epistatic effects between different loci in a case-control association study. The model can discern four different kinds of epistasis, additive × additive, additive × dominant, dominant × additive, and dominant × dominant interactions. To test each kind of epistasis, a χ² test statistic was computed for a two by two contingency table derived from combined genotypes in both case and control groups. We derived an analytical approach for estimating the asymptotic distribution of the χ² test statistic for epistatic tests under the null hypothesis, with the result being consistent with that from Monte Carlo simulations. The new model was used to analyze a case-control data set for candidate gene studies of stroke, leading to the identification of several significant interactions between causal SNPs on this disease.     

The genetic interaction between non-nodulation and supernodulation in soybean: an example of developmental epistasis

Summary The interaction between three non-nodulation mutants (nod49, nod772 and nod139) and a supernodulation mutant (nts382) of soybean was studied by analysing the progeny from crosses between these mutants. Previously it had been shown that the non-nodulation mutants arose from single mutation events and that nod49 and nod772 are allelic, whereas nod139 represents another gene required for nodulation. Analysis of progeny from crosses between nts382 and the wild type showed that this mutant also arose from a single mutation. Complementation tests demonstrated that the mutation responsible for supernodulation in nts382 is not allelic to either of these non-nodulation characters, and that it segregates independently. Progeny were identified that were homozygous for both supernodulation and non-nodulation, and these plants were incapable of nodulation. Thus, non-nodulation is epistatic over supernodulation and this is discussed in terms of the developmental blockage in the two mutant types. The identification and confirmation of these double mutants of the supernodulation and non-nodulation mutations are described. Although the non-nodulation mutations behave as recessive characters in a wild-type background, these mutations are incompletely dominant in a genetic background homozygous for supernodulation. The significance of these results to the understanding of nodule ontogeny is discussed.