Association between a genetic trait and a marker: Discrimination between epistasis and gametic disequilibrium

Summary We reconsider the method of Ott and Falk (1982) for the analysis of genetic linkage and of epistasis in the presence of phenotypic association. Their approach is extended to allow for gametic disequilibrium between marker and trait loci. We show that epistasis and tight linkage with gametic disequilibrium may be indistinguishable as explanations of association even in a very large pedigree.     

A Comparison of the Genetic Infrastructure of the Ye''Cuana and the Yanomama: A Likelihood Analysis of Genotypic Variation among Populations

A general procedure is described for measuring and testing population differences in gametic frequencies. The total dispersion among populations is subdivided in hierarchical fashion. The multiple-locus treatment is simply the sum of the single-locus analyses, provided gametic equilibrium obtains among the loci. In the event that gametic equilibrium does not obtain, correlations among loci need to be dealt with.—The analysis is then used to examine the genetic infrastructure of two Indian tribes from South America, the Ye'cuana (Makiritare) and the Yanomama. From historical evidence, we may identify several "clusters" of villages within each tribe. The demographic and cultural practices affecting village formation and the maintenance of peer integrity are rather different in these tribes, however, and lead us to postulate rather different patterns of genetic variation among villages. Analyses of five codominant two-allele loci, four dominant two-allele loci and two complex loci (with four codominant haplotypes each) demonstrate that Yanomama clusters are more disparate than Ye'cuana clusters, as would have been predicted on sociocultural grounds.     

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.     

PARENTAL AGE,GAMETIC AGE,AND INBREEDING INTERACT TO MODULATE OFFSPRING VIABILITY IN DROSOPHILA MELANOGASTER

In principle, parental relatedness, parental age, and the age of parental gametes can all influence offspring fitness through inbreeding depression and the parental effects of organismal and postmeiotic gametic senescence. However, little is known about the extent to which these factors interact and contribute to fitness variation. Here, we show that, in Drosophila melanogaster, offspring viability is strongly affected by a three‐way interaction between parental relatedness, parental age, and gametic age at successive developmental stages. Overall egg‐to‐adult viability was lowest for offspring produced with old gametes of related, young parents. This overall effect was largely determined at the pupa–adult stage, although three‐way interactions between parental relatedness, parental age and gametic age also explained variation in egg hatchability and larva‐pupa survival. Controlling for the influence of parental and gametic age, we show that inbreeding depression is negligible for egg hatchability but significant at the larva–pupa and pupa–adult stages. At the pupa–adult stage, where offspring could be sexed, parental relatedness, parental age, and gametic age interacted differently in male and female offspring, with daughters suffering higher inbreeding depression than sons. Collectively, our results demonstrate that the architecture of offspring fitness is strongly influenced by a complex interaction between parental effects, inbreeding depression and offspring sex.     

Evolution of Zygotic Linkage Disequilibrium in a Finite Local Population

One crucial feature of zygotic linkage disequilibrium (LD) analysis is its direct use of diploid genotyping data, irrespective of the type of mating system. Previous theories from an evolutionary perspective mainly focus on gametic LD, but the equivalent development for zygotic LD is not available. Here I study the evolution of zygotic LD and the covariances between gametic and zygotic LDs or between distinct zygotic LDs in a finite local population under constant immigration from a continent population. I derive the analytical theory under genetic hitchhiking effects or in a neutral process. Results indicate that zygotic LDs (diploid level) are more informative than gametic LD (haploid level) in indicating the effects of different evolutionary forces. Zygotic LDs may be greater than or comparable to gametic LD under the epistatic selection process, but smaller than gametic LD under the non epistatic selection process. The covariances between gametic and zygotic LDs are strongly affected by the mating system, linkage distance, and genetic drift effects, but weakly affected by seed and pollen flow and natural selection. The covariances between different zygotic LDs are generally robust to the effects of gene flow, selection, and linkage distance, but sensitive to the effects of genetic drift and mating system. Consistent patterns exist for the covariances between the zygotic LDs for the two-locus genotypes with one common genotype at one locus or without any common genotype at each locus. The results highlight that zygotic LDs can be applied to detecting natural population history.     

On supergenes. II. The estimation of gametic excess in natural populations

The behaviour of supergenes (closely linked blocks of co-adapted loci) can be studied by using various parameters of gametic excess (= linkage disequilibrium). Three useful parameters are the gametic determinant (D), the relative determinant (D'), and the log of the eross product ratio. The behaviour of the gametic determinant under mating and recombination is described. Formulae are given for estimating gametic excess in natural populations, Recombination, and the fitness of double heterozygotes, may be estimated from the determinants at different stages of the life cycle; this would be useful in human population genetics.     

Association studies in consanguineous populations.

To study the genetic determinism of multifactorial diseases in large panmictic populations, a strategy consists in looking for an association with markers closely linked to candidate genes. A distribution of marker genotypes different in patients and controls may indicate that the candidate gene is involved in the disease. In panmictic populations, the power to detect the role of a candidate gene depends on the gametic disequilibrium with the marker locus. In consanguineous populations, we show that it depends on the inbreeding coefficient F as well. Inbreeding increases the power to detect the role of a recessive or quasi-recessive disease-susceptibility factor. The gain in power turns out to be greater for small values of the gametic disequilibrium. Moreover, even in the absence of gametic disequilibrium, the presence of inbreeding may allow to detect the role of a recessive factor. Ignoring inbreeding when it exists may lead to reject falsely a recessive model if the mode of inheritance is inferred on the distribution of genotypes among patients.     

Why Parental Sex Ratio Manipulation is Rare in Higher Vertebrates (Invited Article)

The debate over adaptive parental sex ratio adjustment in higher vertebrates appears neither to be resolvable by the current approach, nor does it necessarily make sense. It rests on the a priori supposition of parental manipulation, which is questioned here from first principle. It is considered an unlikely biological hypothesis if we extend our perspective to gametic and offspring optimal strategies, and to the potential mechanisms existing in the avian and mammalian reproductive systems. Evenness of primary sex ratios is expected to be optimal from the gametic point of view and is supposed here to be the more likely evolutionary outcome. Also, manipulations by sex-selective offspring mortality is argued to be unlikely as usually the benefits will be surpassed by the costs incurred. Furthermore, parents can adjust behavioural and energetic investment patterns to their offspring sex (ratio), thereby minimizing any costs of sex ratio control inability. Slight biases in offspring sex ratios are then viewed as resulting from physiological limitations ultimately relating to sex differences in embryonic development. Contrary to recent attempts to understand higher vertebrate sex ratio variation by further refinement of functional models (of parental optima) and data analysis, Bayesian logic precludes those approaches to gain useful new insights. To prove the basic assumption of parental manipulation, apart from defining gametic and offspring optima, the emphasis should lie on identifying control mechanisms by experimental verification.     

Estimation of preferential pairing rates in second-generation autotetraploid pacific oysters (Crassostrea gigas)

Although previously disregarded, polyploidy, and in particular autopolyploidy, is now believed to have played a prominent role in the evolution of plants and animals. We estimated the rate of preferential pairing in second-generation autotetraploid Pacific oysters from gametic frequencies. We found significant levels of preferential pairing in these recently generated autopolyploids, suggesting that genetic variation in standing populations may play a role in meiotic mechanisms of polyploids derived from these populations.     

Gametic differentiation in Chlamydomonas reinhardtii. II. Flagellar membranes and the agglutination reaction

A structural and biochemical study is presented concerning the agglutination of gametic flagella, the initial step in the mating reaction of Chlamydomonas reinhardtii. An alteration in the distribution of the intramembranous particles revealed by freeze-fracturing of flagella membranes is shown to accompany gametic differentiation in both mating types. The isolation and electrophoretic analysis of flagellar membranes and mastigonemes are reported; no electrophoretic differences can be detected when the membrane or mastigoneme glycoproteins from vegative and gametic cells are compared, nor when glycoproteins from the two mating types are compared, and no novel polypeptides are present in gametic preparations. The membrane vesicles, after they are freed of mastigonemes by sedimentation through a discontinuous sucrose gradient, are extremely active as an isoagglutinin, indicating a direct involvement of the membrane in the mating reaction.     

Mating in Chlamydomonas: a system for the study of specific cell adhesion. I. Ultrastructural and electrophoretic analyses of flagellar surface components involved in adhesion

To determine the ultrastructural and biochemical bases for flagellar adhesiveness in the mating reaction in Chlamydomonas, gametic and vegetative flagella and flagellar membranes were studied by use of electron microscope and electrophoretic procedures. Negative staining with uranyl acetate revealed no differences in gametic and vegetative flagellar surfaces; both had flagellar membranes, flagellar sheaths, and similar numbers and distributions of mastigonemes. Freezecleave procedures suggested that there may be a greater density of intramembranous particles on the B faces of gametic flagellar membranes than on the B faces of vegetative flagellar membranes. Gamone, the adhesive material that gametes release into their medium, was demonstrated, on the basis of ultrastructural and biochemical analyses, to be composed of flagellar surface components, i.e., membrane vesicles and mastigonemes. Comparison of vegetative (nonadhesive) and gametic (adhesive) "gamones" by use of SDS polyacrylamide gel electrophoresis showed both preparations to be composed of membrane, mastigoneme, and some microtubule proteins, as well as several unidentified protein and carbohydrate-staining components. However, there was an additional protein of approximately 70,000 mol wt in gametic gamone which was not present in vegetative gamone. When gametic gamone was separated into a membrane and a mastigoneme fraction on CSCl gradients, only the membrane fraction had isoagglutinating activity; the mastigoneme fraction was inactive, suggesting that mastigonemes are not involved in adhesion.     

Constructing the parental linkage phase and the genetic map over distances <1 cM using pooled haploid DNA

A new statistical approach for construction of the genetic linkage map and estimation of the parental linkage phase based on allele frequency data from pooled gametic (sperm or egg) samples is introduced. This method can be applied for estimation of recombination fractions (over distances <1 cM) and ordering of large numbers (even hundreds) of closely linked markers. This method should be extremely useful in species with a long generation interval and a large genome size such as in dairy cattle or in forest trees; the conifer species have haploid tissues available in megagametophytes. According to Mendelian expectation, two parental alleles should occur in gametes in 1:1 proportions, if segregation distortion does not occur. However, due to mere sampling variation, the observed proportions may deviate from their expected value in practice. These deviations and their dependence along the chromosome can provide information on the parental linkage phase and on the genetic linkage map. Usefulness of the method is illustrated with simulations. The role of segregation distortion as a source of these deviations is also discussed. The software implementing this method is freely available for research purposes from the authors.     

Habitat loss and fragmentation reduce effective gene flow by disrupting seed dispersal in a neotropical palm

Habitat loss and fragmentation often reduce gene flow and genetic diversity in plants by disrupting the movement of pollen and seed. However, direct comparisons of the contributions of pollen vs. seed dispersal to genetic variation in fragmented landscapes are lacking. To address this knowledge gap, we partitioned the genetic diversity contributed by male gametes from pollen sources and female gametes from seed sources within established seedlings of the palm Oenocarpus bataua in forest fragments and continuous forest in northwest Ecuador. This approach allowed us to quantify the separate contributions of each of these two dispersal processes to genetic variation. Compared to continuous forest, fragments had stronger spatial genetic structure, especially among female gametes, and reduced effective population sizes. We found that within and among fragments, allelic diversity was lower and genetic structure higher for female gametes than for male gametes. Moreover, female gametic allelic diversity in fragments decreased with decreasing surrounding forest cover, while male gametic allelic diversity did not. These results indicate that limited seed dispersal within and among fragments restricts genetic diversity and strengthens genetic structure in this system. Although pollen movement may also be impacted by habitat loss and fragmentation, it nonetheless serves to promote gene flow and diversity within and among fragments. Pollen and seed dispersal play distinctive roles in determining patterns of genetic variation in fragmented landscapes, and maintaining the integrity of both dispersal processes will be critical to managing and conserving genetic variation in the face of continuing habitat loss and fragmentation in tropical landscapes.     

Transmission ratio distortion in Arabidopsis lyrata: effects of population divergence and the S-locus

We investigated transmission ratio distortion within an Icelandic population of Arabidopsis lyrata using 16 molecular markers unlinked to the S-locus. Transmission ratio distortion was found more often than expected by chance at the gametic level, but not at the genotypic or zygotic level. The gametic effect may be due to meiotic drive or selection acting postmeiotically. At the gametic level, 10.9% of the tests were significant, which is substantially lower than earlier observed in an interpopulation cross (allowing for differences in power)-suggesting that the high level of transmission ratio distortion in the interpopulation cross is due to population divergence. It is also substantially lower than previously observed in intrapopulation crosses at the self-incompatibility locus, suggesting inherent fitness differences of the self-incompatibility alleles. We discuss the possible role of deleterious alleles accumulating at loci under balancing selection. Zygotic effects play a larger role in the interpopulation cross than in the intrapopulation crosses suggesting that Dobzhansky-Muller incompatibilities may be accumulating between the widely diverged populations.     

Use of Multiple Genetic Markers in Prediction of Breeding Values

Genotypes at a marker locus give information on transmission of genes from parents to offspring and that information can be used in predicting the individuals' additive genetic value at a linked quantitative trait locus (MQTL). In this paper a recursive method is presented to build the gametic relationship matrix for an autosomal MQTL which requires knowledge on recombination rate between the marker locus and the MQTL linked to it. A method is also presented to obtain the inverse of the gametic relationship matrix. This information can be used in a mixed linear model for simultaneous evaluation of fixed effects, gametic effects at the MQTL and additive genetic effects due to quantitative trait loci unlinked to the marker locus (polygenes). An equivalent model can be written at the animal level using the numerator relationship matrix for the MQTL and a method for obtaining the inverse of this matrix is presented. Information on several unlinked marker loci, each of them linked to a different locus affecting the trait of interest, can be used by including an effect for each MQTL. The number of equations per animal in this case is 2m + 1 where m is the number of MQTL. A method is presented to reduce the number of equations per animal to one by combining information on all MQTL and polygenes into one numerator relationship matrix. It is illustrated how the method can accommodate individuals with partial or no marker information. Numerical examples are given to illustrate the methods presented. Opportunities to use the presented model in constructing genetic maps are discussed.     

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.     

A Theoretical Model for Estimating Linkage in F2 Populations with Distorted Single Gene Segregation

A model is presented which allows estimation of linkage from dihybrid F₂ populations with distorted single gene segregation by applying the maximum-likelihood method. For different selection processes operating on one locus at either the gametic or the zygotic level, it can be demonstrated that, if the deficit is previously taken into account, testing for free recombination can be carried out without prior knowledge of the causes of this deficit. In the presence of linkage, the expected frequencies of two phenotypic classes depend on whether gametic or zygotic selection is operating. The remaining two classes can be utilized for the estimation of linkage as their frequency ratio is independent of these selection types. The application of this procedure to situations with coupling, incomplete penetrance, gametic and zygotic selection is discussed.     

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.     

Efficient computation of the inverse of gametic relationship matrix for a marked QTL

Best linear unbiased prediction of genetic merits for a marked quantitative trait locus (QTL) using mixed model methodology includes the inverse of conditional gametic relationship matrix (G^-1) for a marked QTL. When accounting for inbreeding, the conditional gametic relationships between two parents of individuals for a marked QTL are necessary to build G^-1 directly. Up to now, the tabular method and its adaptations have been used to compute these relationships. In the present paper, an indirect method was implemented at the gametic level to compute these few relationships. Simulation results showed that the indirect method can perform faster with significantly less storage requirements than adaptation of the tabular method. The efficiency of the indirect method was mainly due to the use of the sparseness of G^-1. The indirect method can also be applied to construct an approximate G^-1 for populations with incomplete marker data, providing approximate probabilities of descent for QTL alleles for individuals with incomplete marker data.     

Heterozygous expression of insulin-dependent diabetes mellitus (IDDM) determinants in the HLA system.

HLA phenotypes of cases with insulin-dependent diabetes mellitus (IDDM) and identity by descent of HLA haplotypes in affected sib-pairs support an intermediate model in which morbid risk is increased by one HLA-linked IDDM determinant, and greatly increased by two determinants, which may be qualitatively different in DR3 and DR4 haplotypes. Linkage analysis allowing for gametic disequilibrium reveals no recombination in pedigrees with a DR3/DR4 propositus, but spurious recombination in the remaining pedigrees. This evidence favors interaction of unlinked IDDM determinants to produce affection in a small proportion of heterozygotes for an HLA-linked determinant. Partition of data by HLA type of the propositus (ideally by DR and the complement types jointly) is a powerful method to resolve etiological heterogeneity for HLA-associated diseases.