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.     

Gametic equilibrium of four loci on chromosome 1

Summary The present study is the first to investigate gametic disequilibrium of loosely linked loci (recombination >22%) of known map distance in humans. The study population consisted of 302 healthy unrelated individuals of white mixed-European ancestry living in the Denver, Colorado area. Pairwise combinations of four loci on chromosome 1 (Rhesus, Duffy, phosphoglucomutase-1, and amylase-2) were examined for nonrandom association of alleles at different loci. Observed and expected values were compared with chi-square goodness-of-fit tests. There was no evidence of first-order interaction, i.e., gametic disequilibrium. From these findings it seems that gametic disequilibrium may not be important in the genetic organization of chromosome 1.     

Population genetics of the highly polymorphic locus D16S7 and its use in paternity evaluation.

We have developed a DNA RFLP test to resolve paternity cases in which the accused man is included at a low probability of paternity by conventional testing. The DNA probe p79-2-23 was used to determine the allele frequency distribution for the locus D16S7 in the North American black, Caucasian, and Hispanic racial groups. Approximately 3,500 TaqI-digested DNAs were analyzed from the three populations studied. An apparent continuum of alleles was detected varying in size from 2.9 kb to 8.3 kb. Estimates of the average probability of exclusion were found to be .90 and .79 for the North American black and Caucasian populations, respectively. Gene frequency data for common and rare alleles indicated a potential paternity index ranging from 2 to 450.     

Derivation of single-locus relationship coefficients conditional on marker information

The coefficient of relationship is defined as the correlation between the additive genetic values of two individuals. This coefficient can be defined specifically for a single quantitative trait locus (QTL) and may deviate considerably from the overall expectation if it is taken conditional on information from linked marker loci. Conditional halfsib correlations are derived under a simple genetic model with a biallelic QTL linked to a biallelic marker locus. The conditional relationship coefficients are shown to depend on the recombination rate between the marker and the QTL and the population frequency of the marker alleles, but not on parameters of the QTL, i.e. number and frequency of QTL alleles, degree of dominance etc., nor on the (usually unknown) QTL genotype of the sire. Extensions to less simplified cases (multiple alleles at the marker locus and the QTL, two marker loci flanking the QTL) are given. For arbitrary pedigrees, conditional relationship coefficients can also be derived from the conditional gametic covariance matrix suggested by Fernando and Grossman (1989). The connection of these two approaches is discussed. The conditional relationship coefficient can be used for marker-assisted genetic evaluation as well as for the detection of QTL and the estimation of their effects.     

Genetic microstructure in two Spanish cat populations. II: gametic disequilibrium and spatial autocorrelation

In a previous publication, we described some aspects of the microgenetic structure of two Spanish cat populations (in Barcelona and Alicante). In the present study, the possible existence ofgametic disequilibrium and spatial genetic structure for these populations, at the coat colour pattern and length genes O, A, T D, L, S and W, was analyzed. There was little gametic disequilibrium between pairs of these loci, despite certain pairs that showed significant systematic gametic disequilibrium (a-d and O-S), which appears to show the action of natural selection on domestic cat populations. Nevertheless, we believe that the major cause of the small amount of gametic disequilibrium found was probably a combination of gene drift and gene flow. The results obtained here were clearly in disagreement with those of Hedrick (1985), who concluded that epistatic selection was the cause of the gametic disequilibrium that he found in cat populations. We also found that although Hardy-Weinberg equilibrium could not be demonstrated, the gametic disequilibrium statistics were not affected by this fact, adding credence to the estimates obtained. We found no genetic spatial structure inside the city of Barcelona, as shown by analysis of the spatial autocorrelation of the individual loci, and analysis of the coordinates of the two first axes of a multidimensional scale. However, some gametic disequilibrium statistics showed certain spatial patterns, which leads us to consider the possibility of several evolutionary processes acting upon some of Barcelona's cat colonies.     

Dynamics of Correlated Genetic Systems. V. Rates of Decay of Linkage Disequilibria in Experimental Populations of DROSOPHILA MELANOGASTER

The dynamic behavior of four-locus gametic frequency distributions was studied in five replicate cage populations of Drosophila melanogaster for up to 50 generations. The joint frequency distributions were resolved into gene frequencies and various disequilibrium measures. In addition, F statistics for marginal single-locus genotypic frequency distributions were followed through time. The gene frequency, disequilibrium and F statistics were obtained for four chromosome 3 enzyme marker loci [isocitrate dehydrogenase (3–27.1), esterase-6 (3–36.8), phosphoglucomutase (3–43.4) and esterase-C (3–49.0)]. The initial structure of the experimental populations featured random mating proportions, and two complementary gametic types with respect to the marker loci, thus assuring complete pairwise linkage disequilibrium among the markers.——The experimental results indicate: (1) the between-replicate variance in gene frequency varied substantially among loci, with isocitrate dehydrogenase showing the greatest between-replicate variance, and esterase-C the least. (2) The F statistics initially were strongly negative but decayed to the neighborhood of zero for all marker loci except esterase-C. The rate at which the F statistics approached zero varied among the marker loci, indicating substantial differences in the distribution of selective effects along the chromosome. The centromeric region, marked by esterase-C, shows the strongest selective effects. (3) The rate of decay of linkage disequilibrium was much faster than expected for pairs of neutral loci, averaging 1.82 times the neutral rate over all replicates and pairs of loci. This acceleration, which was observed for all six pairwise combinations of loci, was interpreted as resulting from the interaction between selection and recombination. Our experimental results are consistent with many investigations of linkage disequilibrium in natural populations of Drosophila melanogaster that show little or no disequilibrium among enzyme loci. (4) A fortuitous contamination of two cages revealed an apparent regulatory interaction between the migrant and nonmigrant chromosomes at the esterase-C locus. The migrant chromosomes were very rapidly absorbed into the recipient populations, despite this interaction. This result suggests that the dynamics of migration in populations may be phenomenologically richer than anticipated by simple theory.     

The multiple-locus symmetric fertility model

Selection due to variation in the fecundity among matings of genotypes with respect to many loci each with two alleles is studied. The fitness of a mating depends only on the genotypic distinction between homozygote and heterozygote at each locus in the two individuals, and differences among loci are allowed. This symmetric fertility model is therefore a generalization of the multiple-locus symmetric viability model. The phenomena seen in the two-locus symmetric fertility model generalize—e.g., the possibility of joint stability of equilibria with linkage equilibrium and with linkage disequilibrium, and the existence of different types of totally polymorphic equilibria with the gametic proportions in linkage equilibrium. The central equilibrium with genotypic frequencies in Hardy-Weinberg proportions and gametic frequencies in Robbins proportions exists for all symmetric fertility models. For some symmetric fertility regimes additional equilibria exist with gametic frequencies in linkage equilibrium and with genotypic frequencies in Hardy-Weinberg proportions at all except one locus. These equilibria may exist in the dioecious symmetric viability model, and then they will be locally stable. For free recombination the stable equilibria show linkage equilibrium, but several of these with different numbers of polymorphic loci may be stable simultaneously.     

Definition and Properties of Disequilibrium Statistics for Associations between Nuclear and Cytoplasmic Genotypes

We define and establish the interrelationships of four components of statistical association between a diploid nuclear gene and a uniparentally transmitted, haploid cytoplasmic gene: an allelic (gametic) disequilibrium (D), which measures associations between alleles at the two loci; and three genotypic disequilibria (D1, D2, D3), which measure associations between two cytotypes and the three respective nuclear backgrounds. We also consider an alternative set of measures, including D and the residual disequilibrium (d). The dynamics of these disequilibria are then examined under three conventional models of the mating system: (1) random mating; (2a) assortative mating without dominance (the "mixed-mating model"); and (2b) assortative mating with dominance ("O'Donald's model"). The trajectories of gametic disequilibria are similar to those for pairs of unlinked nuclear loci. The dynamics of genotypic disequilibria exhibit a variety of behaviors depending on the model and the initial conditions. Procedures for statistical estimation of cytonuclear disequilibria are developed and applied to several real and hypothetical data sets. Special attention is paid to the biological interpretations of various categories of allelic and genotypic disequilibria in hybrid zones. Genetic systems for which these statistics might be appropriate include nuclear genotype frequencies in conjunction with those for mitochondrial DNA, chloroplast DNA, or cytoplasmically inherited microorganisms.     

Establishment of paternity testing system using microsatellite markers in Chinese Holstein

To estimate the efficiency of microsatellite markers in paternity testing among Chinese Holstein, 30 microsatellite loci were used to differentiate 330 Chinese Holstein genotypes, according to the calculation of the allele frequency, number of alleles, effective number of alleles, genetic heterozygosity, polymorphic information content (PIC), and the exclusion probability in this cattle population. The results demonstrated that the exclusion probability ranged from 0.620 in locus BM1818 to 0.265 in locus INRA005 with the average of 0.472 and 11 microsatellite markers exceeding 0.5. The combined exclusion probability of nine microsatellite markers was over 0.99. The result showed that paternity testing of Chinese Holstein was basically resolved using the nine microsatellite markers selected.     

Gametic Disequilibrium Measures: Proceed with Caution

Five different measures of gametic disequilibrium in current use and a new one based on R. C. Lewontin's D', are examined and compared. All of them, except the measure based on Lewontin's D', are highly dependent upon allelic frequencies, including four measures that are normalized in some manner. In addition, the measures suggested by A. H. D. Brown, M. F. Feldman and E. Nevo, and T. Ohta can have negative values when there is maximum disequilibrium and have rates of decay in infinite populations that are a function of the initial gametic array. The variances were large for all the measures in samples taken from populations at equilibrium under neutrality, with the measure based on D' having the lowest variance. In these samples, three of the measures were highly correlated, D2, D (equal to the correlation coefficient when there are two alleles at each locus) and the measure X(2) of Brown et al. Using frequency-dependent measures may result in mistaken conclusions, a fact illustrated by discussion of studies inferring recombinational hot spots and the effects of population bottlenecks from disequilibrium values.     

Allele frequency distribution of two highly polymorphic DNA sequences in three ethnic groups and its application to the determination of paternity

The allele frequency distribution of two highly polymorphic DNA sequences has been determined in three ethnic groups (American blacks, Caucasoids, and Hispanics) from the New York metropolitan area. The two loci examined were D14S1 and the flanking region of HRAS-1. The former was analyzed in EcoRI-digested DNA and the latter in TaqI-digested DNA. Approximately 700 DNA samples from unrelated individuals were digested with each of these enzymes and hybridized with the appropriate recombinant DNA probes. The size range of the DNA fragments detected for the D14S1 polymorphism varied from 14.3 to 32.5 kilobase pairs (kbp). The number of alleles identified under the experimental conditions used in this study was more than 40. For the HRAS-1 polymorphism, we have detected 18 different alleles varying in size from 1.85 to 4.5 kbp. Although the number of alleles observed in the different ethnic groups examined was very similar, the relative frequency of them varied significantly. The results presented here can be used as the basis for the utilization of DNA RFLP for the purpose of identity, such as paternity determinations or the analysis of forensic material. As an example, we have compared the results of paternity cases analyzed by HLA typing with those obtained with these two DNA polymorphisms. The values of paternity index and power of exclusion were similar by both procedures.     

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.     

Exclusion probabilities obtainable by biochemical polymorphisms in dogs

General formulae are given to calculate the exclusion probabilities in false paternity and parentage cases by means of gene loci with an arbitrary number of alleles whereas in paternity cases an arbitrary number of offspring per litter is considered additionally.
By aid of these formulae and on the basis of the allele frequencies of four blood protein and enzyme systems the probabilities of excluding incorrect paternity and parentage are calculated in seven German dog breeds. The results are tabulated and discussed.
It can be shown that the exclusion probability in false paternity cases increases distinctly with an increasing number of offspring per litter and its maximum is nearly attained if 5 offspring are examined. Therefore it is of value to consider entire litters in paternity controls in dogs.     

Inferences about linkage disequilibrium.

Existing theory for inferences about linkage disequilibrium is restricted to a measure defined on gametic frequencies. Unless gametic frequencies are directly observable, they are inferred from genotypic frequencies under the assumption of random union of gametes. Primary emphasis in this paper is given to genotypic data, and disequilibrium coefficients are defined for all subsets of two or more of the four genes, two at each of two loci, carried by an individual. Linkage disequilibrium coefficients are defined for genes within and between gametes, and methods of estimating and testing these coefficients are given for gametic data. For genotypic data, when coupling and repulsion double heterozygotes cannot be distinguished. Burrows' composite measure of linkage disequilibrium is discussed. In particular, the estimate for this measure and hypothesis tests based on it are compared to the usual maximum likelihood estimate of gametic linkage disequilibrium, and corresponding likelihood ratio or contingency chi-square tests. General use of the composite measure, whether or not random union of gametes is an appropriate assumption, is recommended. Attention is given to small samples, where the non-normality of gene frequencies will have greatest effect on methods of inference based on normal theory. Even tools such as Fisher's z-transformation for the correlation of gene frequencies are found to perform quite satisfactorily.     

Hla-Sharing, Recurrent Spontaneous Abortion, and the Genetic Hypothesis

A number of studies indicates that there is a high sharing of HLA antigens in couples having recurrent spontaneous abortions. The genetic hypothesis to explain this phenomenon suggests that this fetal loss results from homozygosity of recessive lethal or deleterious alleles in gametic disequilibrium with HLA antigens. Theory predicting the lethality rate is derived when antigens are shared at one, two or three loci, given that the disequilibrium is absolute. In addition, the effects of partial disequilibrium, inbreeding, and segregation distortion on the lethal proportion are examined.     

Linkage Disequilibrium and Genetic Variances under Mutation-Selection Balance

I determine the contribution of linkage disequilibrium to genetic variances using results for two loci and for induced or marginal systems. The analysis allows epistasis and dominance, but assumes that mutation is weak relative to selection. The linkage disequilibrium component of genetic variance is shown to be unimportant for unlinked loci if the gametic mutation rate divided by the harmonic mean of the pairwise recombination rates is much less than one. For tightly linked loci, linkage disequilibrium is unimportant if the gametic mutation rate divided by the (induced) per locus selection is much less than one.     

A Two-Locus Neutrality Test: Applications to Humans, E. COLI and Lodgepole Pine

The expected disequilibrium between two loci with k alleles at one locus and l alleles at the other is given for a sample of size n drawn from a population under neutrality equilibrium. Three different measures of disequilibrium with 95% intervals are tabulated for combinations of n, k, l and 4Nc, where N is the effective population size and c is the amount of recombination between the loci. The extent and pattern of disequilibrium are strongly dependent upon 4Nc and are somewhat dependent on n, k and l. The 95% intervals are large, particularly for low numbers of alleles and low values of 4Nc. As examples, observed disequilibrium from histocompatibility loci in humans (HLA) and electrophoretic data in E. coli and lodgepole pine were compared to these theoretical values. Using information about recombination rates, the HLA data showed more disequilibrium than neutrality expectations, whereas electrophoretic data from E. coli and lodgepole pine had somewhat less disequilibrium than neutrality expectations.