Inferring linkage disequilibrium between a polymorphic marker locus and a trait locus in natural populations

Three approaches are proposed in this study for detecting or estimating linkage disequilibrium between a polymorphic marker locus and a locus affecting quantitative genetic variation using the sample from random mating populations. It is shown that the disequilibrium over a wide range of circumstances may be detected with a power of 80% by using phenotypic records and marker genotypes of a few hundred individuals. Comparison of ANOVA and regression methods in this article to the transmission disequilibrium test (TDT) shows that, given the genetic variance explained by the trait locus, the power of TDT depends on the trait allele frequency, whereas the power of ANOVA and regression analyses is relatively independent from the allelic frequency. The TDT method is more powerful when the trait allele frequency is low, but much less powerful when it is high. The likelihood analysis provides reliable estimation of the model parameters when the QTL variance is at least 10% of the phenotypic variance and the sample size of a few hundred is used. Potential use of these estimates in mapping the trait locus is also discussed.     

Partial selfing and linkage: the effect of a heterotic locus on a neutral locus

Equilibria are determined for the two-locus model in a partially selfing population when one locus is neutral and the other locus is heterotic. At an equilibrium point, the frequency of heterozygotes at the neutral locus is greater than that expected from one-locus theory, even if the heterotic locus is on a different chromosome. Thus, the neutral locus also appears to be heterotic. The magnitude of this effect is determined for several different proportions of selfing and amounts of recombination.     

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.     

Estimating linkage disequilibrium between a polymorphic marker locus and a trait locus in natural populations.

Positional cloning of gene(s) underlying a complex trait requires a high-resolution linkage map between the trait locus and genetic marker loci. Recent research has shown that this may be achieved through appropriately modeling and screening linkage disequilibrium between the candidate marker locus and the major trait locus. A quantitative genetics model was developed in the present study to estimate the coefficient of linkage disequilibrium between a polymorphic genetic marker locus and a locus underlying a quantitative trait as well as the relevant genetic parameters using the sample from randomly mating populations. Asymptotic covariances of the maximum-likelihood estimates of the parameters were formulated. Convergence of the EM-based statistical algorithm for calculating the maximum-likelihood estimates was confirmed and its utility to analyze practical data was exploited by use of extensive Monte-Carlo simulations. Appropriateness of calculating the asymptotic covariance matrix in the present model was investigated for three different approaches. Numerical analyses based on simulation data indicated that accurate estimation of the genetic parameters may be achieved if a sample size of 500 is used and if segregation at the trait locus explains not less than a quarter of phenotypic variation of the trait, but the study reveals difficulties in predicting the asymptotic variances of these maximum-likelihood estimates. A comparison was made between the statistical powers of the maximum-likelihood analysis and the previously proposed regression analysis for detecting the disequilibrium.     

Detection and estimation of linkage for a co-dominant structural gene locus linked to a gametophytic self-incompatibility locus

Summary The operation of gametophytic self-incompat ibility systems may lead to disturbed segregation ratios for genes at loci linked to the self-incompatibility loci. An exhaustive consideration of the types of crosses, methods of linkage estimation, progeny sizes and controls needed for accurate analysis of disturbed segregation ratios is presented. Examples of the application of these methods are included.     

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

Summary Considerations proceed from a model of positive assortative mating based on genotype at one locus, with an arbitrary number of alleles, assuming no selection, mutation, or migration, hypothetically infinite population size, and discrete non-overlapping generations. From these conditions, inferences are made about the genotypic structure at a linked locus, as well as about the corresponding 2-locus gametic structure.The following main results are presented: in the course of the generations, the genotypic structure at the second locus and the 2-locus gametic structure always tend to a limit responsive to the initial conditions concerning the joint genotypic structure at the two loci and the degree of assortativity and linkage. A complete, analytical representation of the limits is given. In particular, if assortative mating is only partial and at the same time linkage is not complete, a population is not able to maintain a permanent deviation of the gametic structure from linkage equilibrium, and thus the genotypic structure at the second locus tends to Hardy-Weinberg proportions. On the other hand, if initial linkage disequilibrium is combined with partial assortative mating and complete linkage (or with complete assortative mating and unlinked loci) the population maintains this disequilibrium and thus the genotypic structure at the second locus need not tend to Hardy-Weinberg proportions. It turns out that the conditions not only of complete linkage, but also of unlinked loci together with complete assortativity, imply no change in gametic structure from the initial structure.In order to demonstrate the influence of several parameters on the speed of convergence to and the magnitude of the respective limits, several graphs are included.     

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.     

Modeling linkage disequilibrium between a polymorphic marker locus and a locus affecting complex dichotomous traits in natural populations

Linkage disequilibrium is an important topic in evolutionary and population genetics. An issue yet to be settled is the theory required to extend the linkage disequilibrium analysis to complex traits. In this study, we present theoretical analysis and methods for detecting or estimating linkage disequilibrium (LD) between a polymorphic marker locus and any one of the loci affecting a complex dichotomous trait on the basis of samples randomly or selectively collected from natural populations. Statistical properties of these methods were investigated and their powers were compared analytically or by use of Monte Carlo simulations. The results show that the disequilibrium may be detected with a power of 80% by using phenotypic records and marker genotype when both the trait and marker variants are common (30%) and the LD is relatively high (40-100% of the theoretical maximum). The maximum-likelihood approach provides accurate estimates of the model parameters as well as detection of linkage disequilibrium. The likelihood method is preferred for its higher power and reliability in parameter estimation. The approaches developed in this article are also compared to those for analyzing a continuously distributed quantitative trait. It is shown that a larger sample size is required for the dichotomous trait model to obtain the same level of power in detecting linkage disequilibrium as the continuous trait analysis. Potential use of these estimates in mapping the trait locus is also discussed.     

Initial characterization of a protochordate histocompatibility locus

The colonial protochordate, Botryllus schlosseri, undergoes a natural transplantation reaction which is controlled by a single, highly polymorphic locus called the Fu/HC. We are using map-based cloning to identify Fu/HC gene(s), and have currently delineated their location to an approximately 1-cM region of the B. schlosseri genome. The Fu/HC physical map currently consists of 85 sequence-tagged sites mapped on a minimum tiling path of 800 kb which consists of five contigs, with four gaps remaining to be crossed, and is estimated to be 75% completed. Approximately half this region has been sequenced throughout the locus, allowing the first analysis of a metazoan histocompatibility locus outside of vertebrates. This has resulted in the identification of 18 predicted genes, a number of which have been found to be expressed. Several of these genes are well conserved among the chordates; however, none of the predicted or expressed genes are linked within the genome of any organism in the databases. In addition, the Fu/HC is one of the most polymorphic loci ever described, and physical mapping has revealed that the locus is quite dynamic, and includes features such as hotspots of recombination.     

Genetic linkage of a leucine aminopeptidase locus with the Kunitz trypsin inhibitor locus in soybeans

The soybean (Glycine max (L.) Merrill) seed leucine aminopeptidase locus (Lap1) was found to be linked to the Kunitz trypsin inhibitor locus (Ti) with a recombination frequency of 15.3 percent +/- 0.9 percent. The two loci are in linkage group 9. Both Lap1 and Ti loci are inherited independently of the flower color locus (W1) in linkage group 8.     

Characterization of a hemin-storage locus ofYersinia pestis

Summary The pigmentation phenotype (Pgm⁺) ofYersinia pestis refers to temperature-dependent storage of hemin as well as expression of a number of other physiological characteristics. Spontaneous mutation to a Pgm^– phenotype occurs via a large chromosomal deletion event and results in the inability to express the Pgm⁺ characteristics. In this study, we have used transposon insertion mutants to define two regions of a hemin-storage (hms) locus. A clone (pHMSI) encompassing this locus reinstates expression of hemin storage (Hms⁺) inY. pestis spontaneous Pgm^– strains KIM and Kuma but not inEscherichia coli. Complementation analysis using subclones of pHMS1 inY. pestis transposon mutants indicates that both regions (hmsA andhmsB), which are separated by about 4 kb of intervening DNA, are essential for expression of the Hms⁺ phenotype. The 9.1-kb insert of pHMS1 contains structural genes encoding 90-kDa, 72-kDa, and 37-kDa polypeptides. Two-dimensional gel electrophoresis analysis of cells from Pgm⁺, spontaneous Pgm^–, and Hms^– transposon strains, as well as a spontaneous Pgm^– strain transformed with pHMS1, indicated that two families of surface-exposed polypeptides (of about 87 and 69-73 kDa) are associated with the Hms⁺ phenotype.     

A null mutation at the mouse Phosphoglucomutase-1 locus and a new locus,Pgm-3

A null mutation at the phosphoglucomutase locus (Pgm-1) was discovered by electrophoretic analysis of the inbred mouse strain C57 BL/6J. The null allele (Pgm-1 ⁿ) was shown to segregate as a Mendelian unit alternative to the Pgm-1 ^a and Pgm-1 ^b alleles. Mice expressing the Pgm-1 ⁿ allele, either in the heterozygous or homozygous state, are viable, healthy, and fertile. The occurrence of the Pgm-1 ⁿ mutant revealed a previously unreported genetic locus (Pgm-3) that controls the expression of a third phosphoglucomutase. Two electrophoretically expressed alleles of Pgm-3 (inherited without dominance) are found in the inbred mouse strains C57 BL/6J and DBA/2J. Linkage observed between the Pgm-3 locus, the dilute locus (d) and the cytoplasmic malic enzyme locus (Mod-1) has allowed assignment of the Pgm-3 locus to chromosome 9. A striking tissue specific expression of Pgm-1 and Pgm-3 was observed. Products of the Pgm-3 locus were detected in kidney, testes, brain, and heart. In contrast, Pgm-1 controlled isozymes were present in kidney, spleen, ovaries, and erythrocytes.Financial support for this work was provided in part by Contract #263-78-C-0393 from the National Institute of Environmental Health Sciences to the Research Triangle Institute.     

Linkage between an incompatibility locus and a peroxidase isozyme locus (Prx 7) in rye

Summary Under controlled growth chamber conditions of 30 °C, seed set after selfing is possible in normally self-incompatible rye plants. Within selfed progenies produced by this method, plants homozygous at the peroxidase isozyme locus Prx 7 were crossed to heterozygous individuals. Segregation at the Prx 7 locus in progenies of these crosses provides clear evidence of a close linkage between Prx 7 and one of the two incompatibility loci in rye. A recombination fraction in the range of 0–2% was calculated from the segregation data. In rye, Prx 7 is linked with a phosphoglucoisomerase locus (Pgi). The similarity between the observations in Secale cereale and those made in Lolium perenne is discussed.     

Molecular identification of human Ia antigens coded for by a gene locus closely linked toHLA-DR locus

Human Ia(-like) specificities controlled by gene loci other thanHLA-DR were searched for at the molecular level in cells of human B-cell-type cell lines which carrytwo established DR specificities. Chevalier cells of DRw3 and 7 and U698M cells of DRw2 and 4 were used. Their Ia molecules were partially purified, radioiodinated and analyzed for Ia specificities by the direct binding and sequential binding assays with a selected panel of human Ia alloantisera. It was possible in both the cell lines to define a third subset of Ia molecules carrying a new specificity in addition to two Ia subsets carrying the established DR specificities. The new specificity was detected by putative anti-DRw4 and anti-DRw7 antisera and was closely associated with DRw4 and DRw7 at population level. It was thus designated provisionally as BR4X7. These results suggest that the BR4X7 specificity is coded for by a separateIa locus closely linked toHLA-DR locus. The determinant(s) responsible for BR4X7 was located on the small subunit of Ia molecules.