Relationship between heterozygosity and quantitative traits: Intralocus interactions and multiple-locus averaging

The dependence of the expression of genotypic values (Y) on gene dosage (X) have been analyzed for four types of intralocus interactions (additivity, dominance, overdominance, and neutrality) using a linear model. Artificial numerical examples have been used to demonstrate that X and Y are positively associated with each other in the cases of additivity, dominance, and overdominance and are not associated in the case of neutrality. The averaging of single-locus genotypic values to obtain multiple-locus genotypes yields different results for different types of intralocus interactions. Genotypic values and individual heterozygosity are positively correlated with each other in the cases of dominance and overdominance and are negatively correlated in the case of additivity. In the case of neutrality, there is still no correlation after averaging. The results obtained and their interpretation suggest a new view on the experimental studies and generalizations on the relationship between heterozygosity and quantitative traits.Translated from Genetika, Vol. 41, No. 1, 2005, pp. 100–111.Original Russian Text Copyright © 2005 by Kartavtsev.     

Gene regulatory networks generating the phenomena of additivity, dominance and epistasis

We show how the phenomena of genetic dominance, overdominance, additivity, and epistasis are generic features of simple diploid gene regulatory networks. These regulatory network models are together sufficiently complex to catch most of the suggested molecular mechanisms responsible for generating dominant mutations. These include reduced gene dosage, expression or protein activity (haploinsufficiency), increased gene dosage, ectopic or temporarily altered mRNA expression, increased or constitutive protein activity, and dominant negative effects. As classical genetics regards the phenomenon of dominance to be generated by intralocus interactions, we have studied two one-locus models, one with a negative autoregulatory feedback loop, and one with a positive autoregulatory feedback loop. To include the phenomena of epistasis and downstream regulatory effects, a model of a three-locus signal transduction network is also analyzed. It is found that genetic dominance as well as overdominance may be an intra- as well as interlocus interaction phenomenon. In the latter case the dominance phenomenon is intimately connected to either feedback-mediated epistasis or downstream-mediated epistasis. It appears that in the intra- as well as the interlocus case there is considerable room for additive gene action, which may explain to some degree the predictive power of quantitative genetic theory, with its emphasis on this type of gene action. Furthermore, the results illuminate and reconcile the prevailing explanations of heterosis, and they support the old conjecture that the phenomenon of dominance may have an evolutionary explanation related to life history strategy.     

Allozyme and RFLP Heterozygosities as Correlates of Growth Rate in the Scallop Placopecten Magellanicus: A Test of the Associative Overdominance Hypothesis

Several studies have reported positive correlations between the degree of enzyme heterozygosity and fitness-related traits. Notable among these are the correlations between heterozygosity and growth rate in marine bivalves. Whether the correlation is the result of intrinsic functional differences between enzyme variants at the electrophoretic loci scored or arises from non-random genotypic associations between these loci and others segregating for deleterious recessive genes (the associative overdominance hypothesis) is a matter of continuing debate. A prediction of the associative overdominance hypothesis, not shared by explanations that treat the enzyme loci as causative agents of the correlation, is that the correlation is not specific to the type of genetic marker used. We have tested this prediction by scoring heterozygosity at single locus nuclear restriction fragment length polymorphisms (RFLPs) in a cohort of juvenile scallops (Placopecten magellanicus) in which growth rate was known to be positively correlated with an individual's degree of allozyme heterozygosity. A total of 222 individuals were scored for their genotypes at seven allozyme loci, two nonspecific protein loci of unknown function and eight nuclear RFLPs detected by anonymous cDNA probes. In contrast to the enzyme loci, no correlation was observed between growth rate and the degree of heterozygosity at the DNA markers. Furthermore, there was no relationship between the magnitude of heterozygote deficiency at a locus and its effect on the correlation. The differences observed between the effects of allozyme and RFLP heterozygosity on growth rate provide evidence against the associative overdominance hypothesis, but a strong case against this explanation must await corroboration from similar studies in different species.     

The role of epistasis in the manifestation of heterosis: a systems-oriented approach

Heterosis is widely used in breeding, but the genetic basis of this biological phenomenon has not been elucidated. We postulate that additive and dominance genetic effects as well as two-locus interactions estimated in classical QTL analyses are not sufficient for quantifying the contributions of QTL to heterosis. A general theoretical framework for determining the contributions of different types of genetic effects to heterosis was developed. Additive x additive epistatic interactions of individual loci with the entire genetic background were identified as a major component of midparent heterosis. On the basis of these findings we defined a new type of heterotic effect denoted as augmented dominance effect di* that comprises the dominance effect at each QTL minus half the sum of additive x additive interactions with all other QTL. We demonstrate that genotypic expectations of QTL effects obtained from analyses with the design III using testcrosses of recombinant inbred lines and composite-interval mapping precisely equal genotypic expectations of midparent heterosis, thus identifying genomic regions relevant for expression of heterosis. The theory for QTL mapping of multiple traits is extended to the simultaneous mapping of newly defined genetic effects to improve the power of QTL detection and distinguish between dominance and overdominance.     

Algebraic regularities of the ratio of heterozygosity with a mean and variance of quantitative character

The relationships of heterozygosity with the mean and variance of quantitative character were considered under neutrality, additivity and overdominance of polymorphic loci. Attention was drawn to dependence of the patterns of relationships on the number of polymorphic loci (which varied from 1 to 10) and on the type of polymorphic loci, both homogeneous (polymorphic loci are of the same type) and heterogeneous (polymorphic loci are of the two types) samples of 10 polymorphic loci and their combination. It is shown that increase in the number of polymorphic loci is accompanied with extension of the limits of corresponding relations, whereas the patterns of these relations depend on the type of connection of separate polymorphic locus with the quantitative character and on the ratio of different loci in the set of polymorphic loci. It is assumed that the relationship of heterozygosity with quantitative characters, displayed in the number of experimental works, may contain a component mediated by similar statistical effects. It is inferred that the discrepancy between different authors' experimental data on existence or lack of some relationships between multiplicative heterozygosity and morphological variability of quantitative characters can be explained by different types of relations of polymorphic loci to quantitative characters encountered in their works.     

Conditions for positive and negative correlations between fitness and heterozygosity in equilibrium populations.

The past decades have witnessed extensive efforts to correlate fitness traits with genomic heterozygosity. While positive correlations are revealed in most of the organisms studied, results of no/negative correlations are not uncommon. There has been little effort to reveal the genetic causes of these negative correlations. The positive correlations are regarded either as evidence for functional overdominance in large, randomly mating populations at equilibrium, or the results of populations at disequilibrium under dominance. More often, the positive correlations are viewed as a phenomenon of heterosis, so that it cannot possibly occur under within-locus additive allelic effects. Here we give exact genetic conditions that give rise to positive and negative correlations in populations at Hardy-Weinberg and linkage equilibria, thus offering a genetic explanation for the observed negative correlations. Our results demonstrate that the above interpretations concerning the positive correlations are not complete or even necessary. Such a positive correlation can result under dominance and potentially under additivity, even in populations where associated overdominance due to linked alleles at different loci is not significant. Additionally, negative correlations and heterosis can co-occur in a single population. Although our emphasis is on equilibrium populations and for biallelic genetic systems, the basic conclusions are generalized to non-equilibrium populations and for multi-allelic situations.     

The joint variability of the growth-weight characteristics and biochemical gene markers in newborn infants

A relationship between heterozygosity of 6 biochemical loci and variability of 4 anthropometric traits at birth has been studied in 304 boys and girls from Moscow population. All 4 traits in boys are positively correlated with the number of loci for which they are heterozygous. The values of all the traits in girls are highest in homozygous individuals. In order to reduce the number of variables the principal component analysis is applied. Boys and girls with average level of heterozygosity turned out to be closest to the corresponding population averages of morphological traits. The results are discussed in terms of 3 models: Lerner's concept of genetical homeostasis, additive and overdominance polygenic models. It is concluded that an average level of heterozygosity is optimal for a population.     

Molecular-Marker-Facilitated Investigations of Quantitative-Trait Loci in Maize. I. Numbers, Genomic Distribution and Types of Gene Action

Individual genetic factors which underlie variation in quantitative traits of maize were investigated in each of two F2 populations by examining the mean trait expressions of genotypic classes at each of 17-20 segregating marker loci. It was demonstrated that the trait expression of marker locus classes could be interpreted in terms of genetic behavior at linked quantitative trait loci (QTLs). For each of 82 traits evaluated, QTLs were detected and located to genomic sites. The numbers of detected factors varied according to trait, with the average trait significantly influenced by almost two-thirds of the marked genomic sites. Most of the detected associations between marker loci and quantitative traits were highly significant, and could have been detected with fewer than the 1800-1900 plants evaluated in each population. The cumulative, simple effects of marker-linked regions of the genome explained between 8 and 40% of the phenotypic variation for a subset of 25 traits evaluated. Single marker loci accounted for between 0.3% and 16% of the phenotypic variation of traits. Individual plant heterozygosity, as measured by marker loci, was significantly associated with variation in many traits. The apparent types of gene action at the QTLs varied both among traits and between loci for given traits, although overdominance appeared frequently, especially for yield-related traits. The prevalence of apparent overdominance may reflect the effects of multiple QTLs within individual marker-linked regions, a situation which would tend to result in overestimation of dominance. Digenic epistasis did not appear to be important in determining the expression of the quantitative traits evaluated. Examination of the effects of marked regions on the expression of pairs of traits suggests that genomic regions vary in the direction and magnitudes of their effects on trait correlations, perhaps providing a means of selecting to dissociate some correlated traits. Marker-facilitated investigations appear to provide a powerful means of examining aspects of the genetic control of quantitative traits. Modifications of the methods employed herein will allow examination of the stability of individual gene effects in varying genetic backgrounds and environments.     

Using dominance relationship coefficients based on linkage disequilibrium and linkage with a general complex pedigree to increase mapping resolution

Dominance (intralocus allelic interactions) plays often an important role in quantitative trait variation. However, few studies about dominance in QTL mapping have been reported in outbred animal or human populations. This is because common dominance effects can be predicted mainly for many full sibs, which do not often occur in outbred or natural populations with a general pedigree. Moreover, incomplete genotypes for such a pedigree make it infeasible to estimate dominance relationship coefficients between individuals. In this study, identity-by-descent (IBD) coefficients are estimated on the basis of population-wide linkage disequilibrium (LD), which makes it possible to track dominance relationships between unrelated founders. Therefore, it is possible to use dominance effects in QTL mapping without full sibs. Incomplete genotypes with a complex pedigree and many markers can be efficiently dealt with by a Markov chain Monte Carlo method for estimating IBD and dominance relationship matrices (D(RM)). It is shown by simulation that the use of D(RM) increases the likelihood ratio at the true QTL position and the mapping accuracy and power with complete dominance, overdominance, and recessive inheritance modes when using 200 genotyped and phenotyped individuals.     

Evidence for the Partial Dominance of Viability Genes Contributing to Inbreeding Depression in Mimulus Guttatus

The relative importance of different modes of gene expression of viability genes contributing to inbreeding depression was investigated in the wild plant, Mimulus guttatus. Viability genes were identified by self-fertilizing 31 outbred plants, each heterozygous for three to nine unlinked allozyme markers, and analyzing segregation ratios of selfed progeny at maturity for deviations from 1:2:1 ratios. In this study, 24 linkages of viability genes to marker loci were detected. To infer the nature of gene action for these viability genes, a ``model-free' graphical method was developed that examines the ``space' of segregation ratios allowed by each of seven selection models (i.e., overdominance, complete recessivity, partial recessivity, additivity, partial dominance, complete dominance and underdominance). Using this method, we found that, of 24 linkages detected, 18 were consistent with either partial dominance, complete dominance or underdominance. Six were consistent with either partial recessivity, complete recessivity or overdominance. This finding indicates that, in these chromosomal segments identified by allozyme markers, partial dominance plays the predominant role in inbreeding depression. This is inconsistent with either the dominance or overdominance hypotheses proposed to account for inbreeding depression.     

Investigation of individual heterozygosity correlated to growth traits in Tongshan Black-boned goat

Ten single nucleotide polymorphisms were used for genotyping of 176 Tongshan Black-boned goats, which are Chinese indigenous goat colony for meat production. The average individual heterozygosity was 0.292. To assess the correlations between individual heterozygosity and growth in Tongshan Black-boned goat individuals, and the potential of using individual heterozygosity as an indicator of growth, the data of growth traits, including body weight, height at withers, body length, chest girth and cannon circumference, were collected. Significant correlations were observed between individual heterozygosity and body weight, height at withers, body length, heart girth, cannon circumference (P < 0.05). All the significant regression showed positive slope with R square values ranged from 0.0251 to 0.0368. These data suggests that individual heterozygosity is positively correlated with growth traits in Tongshan Black-boned goat individuals and associative overdominance may affect Tongshan Black-boned goat growth significantly. Therefore it is possible to use individual heterozygosity as an indicator of growth. Our results also provide a strong support to the overdominance hypothesis.     

DIFFERENTIAL DOMINANCE OF PLEIOTROPIC LOCI FOR MOUSE SKELETAL TRAITS

The term "differential dominance" describes the situation in which the dominance effects at a pleiotropic locus vary between traits. Directional selection on the phenotype can lead to balancing selection on differentially dominant pleiotropic loci. Even without any individual overdominant traits, some linear combination of traits will display overdominance at a locus displaying differential dominance. Multivariate overdominance may be responsible, in part, for high levels of heterozygosity found in natural populations. We examine differential dominance of 70 mouse skeletal traits at 92 quantitative trait loci (QTL). Our results indicate moderate to strong additive and dominance effects at pleiotropic loci, low levels of individual-trait overdominance, and universal multivariate overdominance. Multivariate overdominance affects a range of 6% to 81% of morphospace, with a mean of 32%. Multivariate overdominance tends to affect a larger percentage of morphospace at pleiotropic loci with antagonistic effects on multiple traits (42%). We conclude that multivariate overdominance is common and should be considered in models and in empirical studies of the role of genetic variation in evolvability.     

群体融合对遗传方差的影响

探讨了群体融合对遗传方差的影响,无显性时基因型方差对群体中的基因频率为一凸函数,群体融合将导致它的增加,完全显性时,当群体中显性基因的频率时,群体融合导致基因型方差增加;而当时,融合导致基因型方差减小。超显性时,群体融合导致基因型方差增加,对加性方差和显性方差也分别进行了探讨。     

Relationships of differential gene expression in leaves with heterosis and heterozygosity in a rice diallel cross

Using differential display analysis, we assessed the patterns of differential gene expression in hybrids relative to their parents in a diallel cross involving 8 elite rice lines. The analysis revealed several patterns of differential expression including: (1) bands present in one parent and F₁ but absent in the other parent, (2) bands observed in both parents but not in the F₁, (3) bands occurring in only one parent but not in the F₁ or the other parent, and, (4) bands detected only in the F₁ but in neither of the parents. Relationships between differential gene expression and heterosis and marker heterozygosity were evaluated using data for RFLPs, SSRs and a number of agronomic characters. The analysis showed that there was very little correlation between patterns of differential expression and the F₁ means for all six agronomic traits. Differentially expressed fragments that occurred only in one parent but not in the other parent or in F₁ in each of the respective crosses were positively correlated with heterosis and heterozygosity. And conversely, fragments that were detected in F₁s but in neither of the respective parents were negatively correlated with heterosis and heterozygosity. The remaining patterns of differential expression were not correlated with heterosis or heterozygosity. The relationships between the patterns of differential expression and heterosis observed in this study were not consistent with expectations based on dominance or overdominance hypotheses.     

Heterosis at Allozyme Loci under Inbreeding and Crossbreeding in PINUS ATTENUATA

The dependence of heterosis at isozyme loci on inbreeding and crossbreeding was studied in 10-yr-old trees of knobcone pine (Pinus attenuata Lemm.). Heterozygosity was determined at 24 polymorphic isozyme loci and related to the rate of vegetative growth and cone production. The inbreds, created by selfpollination, had 46% of the heterozygosity of their mothers; the crossbreds, created by interpopulation crossing, had 155% of the heterozygosity of their mothers. Within the crossbreds, heterozygosity was positively correlated with trunk growth, but negatively correlated with cone production. Results in the crossbreds, however, were strongly influenced by a few individuals that showed unusually slow growth, high reproduction and low heterozygosity. Without those individuals, there was no relationship of heterozygosity to either growth or reproduction.—Within the inbreds, heterozygosity was positively correlated with both trunk growth and cone production. Each locus that was heterozygous in the mothers was calculated to mark about 3% of the genome for identity by descent in the inbred progeny; the total proportion of the genome marked was between 10 and 11%. Using these estimates to relate heterozygosity to the inbreeding coefficient (F) gave estimates of inbreeding depression per unit of F that fell within the range of published values for conifers. The strength of heterosis found among the inbreds suggests that single-locus or multilocus overdominance should be exceedingly difficult to detect in natural populations of predominantly outcrossing species.     

Inheritance of reproductive traits of medicinal leeches (Hirudo medicinalis L.)

The phenotype variability and inheritance of reproductive traits were investigated in the medicinal leech. Distribution parameters were determined for the following traits: batch size (X = 4.3 +/- 0.2, sigma = 1.7, CV = 40%, As = 0.23 +/- 0.25, Ex = 0.19 +/- 0.51), number of juveniles in a cocoon (X = 10.9 +/- 0.3, sigma = 4.6, CV = 42%, As = 0.31 +/- 0.15, Ex = 0.23 +/- 0.30), and juvenile weight (X = 32.0 +/- 0.3, sigma = 14.9, CV = 47%, As = 1.38 +/- 0.05, Ex = 3.32 +/- 0.11. A nonlinear negative correlation between the number of juveniles in a cocoon and their weight was found (correlation ratio R = 0.86). It was shown that the environmental variance dominated over the genotypic one in the structure of phenotypic variance of the traits studied. The genetic variability is determined mainly by additive gene interactions and, to a small extent, intralocus dominance. The narrow-sense heritability, h2, for batch size was 0.35-0.40; for the number of juveniles in a cocoon, 0.35; for juvenile weight, 0.42.     

Dominance relationships among male hamadryas baboons (Papio hamadryas)

The concept of dominance has been shown to be useful in describing and predicting social interactions in group-living animals. However, the dominance relationships among adult hamadryas males (Papio hamadryas) are poorly understood, and systematic data are missing from the literature. This study investigated dominance relationships among male hamadryas baboons by applying novel statistical techniques to systematic detailed data on agonistic interactions. We also analyzed the dominance relationship with male age and evaluated the association between dominance and access to mating partners (i.e. the number of adult females per one-male unit (OMU)), food resources (i.e. monopolization of feeding areas), and greeting interactions. The derived dominance indexes showed that, in general, leader males were dominant over followers, and that dominance ability did not correlate with male age. Individual dominance values were very close to each other, suggesting that dominance relationships among hamadryas males were not very rigid. In addition, dominance values were positively correlated with number of adult females per OMU but not with feeding priority. Finally, greeting interactions occurred more frequently between individuals with similar dominance values and with low levels of dominance decidedness. We suggest the need of further studies, especially in wild populations, to confirm our findings.     

Correlations between fitness and heterozygosity at allozyme and microsatellite loci in the Atlantic salmon, Salmo salar L

The relationship between heterozygosity at genetic markers (six allozyme and eight microsatellite loci), and fluctuating asymmetry (FA), length and weight was investigated in two samples of Atlantic salmon (Salmo salar L.) with different timings of first active feeding (early (EA) and late (LA) salmon). This trait had previously been related to fitness. EA fish show smaller values of FA, are longer, heavier and are more heterozygous at allozyme loci than are conspecific LA fish. Also within both samples, heterozygosity at allozyme loci was inversely related to FA and was positively related to weight and length. However, no significant differences in microsatellite diversity (heterozygosity and mean d2 measurements) were observed between samples (EA vs LA). Furthermore, no association was observed between the variability at microsatellite loci and FA, weight or length within each sample. These results suggest that allozyme loci, in themselves, influence fitness components, rather than associations arising from associative overdominance.     

Inherited Biochemical Variation in DROSOPHILA MELANOGASTER: Noise or Signal? I. Single-Locus Analyses

A study was conducted using small effective population size as an experimental design to test selective neutrality of seven isozyme polymorphisms. Loci varied as to the degree to which the decay of heterozygosity over 21 generations was retarded. Selection for heterozygotes, overdominance, is implicated for at least four of seven loci. Of these ADH gave the largest heterozygote excess in the presence of inbreeding. An interaction between the small population size treatment and excess heterozygosity suggests that (1) the loci studied may be selectively neutral and linked to other loci which are under the influence of selection or (2) the selection coefficients for the loci studied are not independent of the background genotype. In either case four of the seven enzymes studied are signaling the operation of selection. The problem of distinguishing the effect of a single marker from that of a chromosome segment is emphasized. The identification of the genetic unit of selection is crucial to any interpretation of the meaning of enzyme polymorphisms.     

The genetic conditions in heterozygous and homozygous populations ofDrosophila I. The fate of alien chromosomes

In experimental populations ofDrosophila melanogaster lethal chromosomes with dominant markers and inversions were introduced and the frequency changes of the markers studied during a period of several generations. The base populations of the various experiments differed from each other with respect to their degree of heterozygosity. Monochromosomal populations were isogenic for a quasinormal + chromosome, dichromosomal populations contained the genetic material of two different + chromosomes, trichromosomal of three, tetrachromosomal of four, hexachromosomal of six and polychromosomal populations of many normal chromosomes. Marker chromosomes with the dominant genesLCy, Cy, Pm orD respectively were added to the populations with an initial frequency of 16,6 per cent. The fate of the dominant markers was different in different populations. In some the marker chromosome reached equilibrium frequencies, in others they were eliminated with variable speed. As a rule the lethal marker chromosomes were accepted by monochromosomal populations; however, they were eliminated from populations with a higher degree of heterozygosity. Since in all populations one genotype, namely the homozygote for the marker chromosome, was lethal, the adaptive values c of the +/LCy, +/Cy, +/Pm or +/D heterozygotes could easily be calculated from the experimental data. This c value can be used as a measure for the combining ability of the marker chromosomes. It could be shown that c depends on the degree of heterozygosity of a population or in other words that the average degree of heterozygosity of the marker free individuals determines the selection processes. An equation can be arrived at which fits the experimental results very well if superiority of heterozygous +/+ individuals over +/+ homozygotes is assumed. From that it was concluded that heterosis is the determining variable in our experiments. An attempt was undertaken in order to decide if in our case the observed heterosis was due to dominance or to overdominance. It was postulated that in di-, tri-, tetra- or hexachromosomal populations the adaptive values of the marker free normals should progressively increase if recessive detrimental genes are the cause of heterosis but not if heterozygosity on many loci leads to overdominance. The a values of the +/+ individuals were ealeulated from the frequency changes of the marker chromosomes for each subsequent two-generation period. Unfortunately only two different dichromosomal populations were available. These showed increasing adaptive values for the normals. The tri-, tetra-, and hexachromosomal populations, however, gave different results, some with increasing, some with fluctuating adaptive values. From that it was concluded that heterosis can be due in one case to dominance and in the other to overdominance. In either case, the recessive genetic load may be rather important as a determinating factor in the dynamics of populations.Dedicated to Prof. Th. Dobzhansky on the occasion of his seventieth birthday in deepest gratitude.