Models to estimate maternally controlled genetic variation in quantitative seed characters

Summary Estimating quantitative contributions to specific traits can be accomplished from a variety of genetic models (Mather 1949; Mather and Jinks 1971; Falconer 1981). Residual genetic effects, those beyond main and interaction effects of the embryo genotype, are often pooled under a single classification, termed maternal effects. Maternal contributions to seed-related traits can originate from various maternal sources (e.g., endosperm, testa and cytoplasm). Quantitative contributions of a maternal nature are not predictable from parental performance and effects are largely non-persistent over generations (Jinks et al. 1972). The methods used to determine maternal effects in quantitative traits often do not measure quantitative genetic parameters, while those that do are either complex or partially resolve potential contributions of individual sources of maternal effects. We present simple genetic models for estimating quantitative genetic parameters which take into account maternal effects expressed in the major seed tissues of higher plants.     

Linkage analysis of quantitative traits in an interspecific cross of tomato (lycopersicon esculentum x lycopersicon pimpinellifolium) by means of genetic markers

Linkage relationships between loci affecting quantitative traits (QTL) and marker loci were examined in an interspecific cross between Lycopersicon esculentum and Lycopersicon pimpinellifolium. Parental lines differed for six morphological markers and for four electrophoretic markers. Almost 1700 F-2 plants were scored with respect to the genetic markers and also with respect to 18 quantitative traits. Major genes affecting the quantitative traits were not found, but out of 180 possible marker x trait combinations, 85 showed significant quantitative effects associated with the genetic markers. The average marker-associated main effect was on the order of 6% of the mean value of the trait. Most of the main effects were apparently due to linkage of QTL to the marker loci rather than to pleiotropy. Fourteen of the traits showed at least one highly significant effect of opposite sign to the overall difference between the parental lines, demonstrating the ability of this design to uncover cryptic genetic variation. Significant variance and skewness effects on the quantitative traits were found to be associated with the genetic markers, suggesting the possible presence of loci affecting the variance and shape of quantitative trait distribution in a population. Most marker-associated quantitative effects showed some degree of dominance, generally in the direction of the L. pimpinellifolium parent. When the significant marker-associated effects were examined in pairs, 12% showed significant interaction effects. The results of this study illustrate the potential usefulness of this type of analysis for the detailed genetic investigation of quantitative trait variation in suitably marked populations.     

QUANTITATIVE GENETIC MODELS FOR DEVELOPMENT,EPIGENETIC SELECTION,AND PHENOTYPIC EVOLUTION

Herein we describe a general multivariate quantitative genetic model that incorporates two potentially important developmental phenomena, maternal effects and epigenetic effects. Maternal and epigenetic effects are defined as partial regression coefficients and phenotypic variances are derived in terms of age-specific genetic and environmental variances. As a starting point, the traditional quantitative genetic model of additive gene effects and random environmental effects is cast in a developmental time framework. From this framework, we first extend a maternal effects model to include multiple developmental ages for the occurrence of maternal effects. An example of maternal effects occurring at multiple developmental ages is prenatal and postnatal maternal effects in mammals. Subsequently, a model of intrinsic and epigenetic effects in the absence of maternal effects is described. It is shown that genetic correlations can arise through epigenetic effects, and in the absence of other developmental effects, epigenetic effects are in general confounded with age-specific intrinsic genetic effects. Finally, the two effects are incorporated into the basic quantitative genetic model. For this more biologically realistic model combining maternal and epigenetic effects, it is shown that the phenotypic regressions of offspring on mother and offspring on father can be used in some cases to estimate simultaneously maternal effects and epigenetic effects.     

Methods for the study of cytoplasmic effects on quantitative traits

Summary The methods used to study cytoplasmic effects in quantitative traits often do not measure quantitative genetic parameters, while those that do are either complicated or do not take into account situations where the expression of cytoplasmic effects does not persist, but decreases in advanced generations. We present two simple models that take cytoplasmic effects and the quantitative genetic parameters into account. One of the models (A) is for cases where cytoplasmic effects remain constant through successive generations, and the second model (B) is for traits where cytoplasm-genotype interactions are present. This model also takes into account the decreasing persistence of cytoplasmic effects with advancing generations, which is often reported in the literature.     

Phenotypic variation and natural selection at catsup, a pleiotropic quantitative trait gene in Drosophila

Quantitative traits are shaped by networks of pleiotropic genes . To understand the mechanisms that maintain genetic variation for quantitative traits in natural populations and to predict responses to artificial and natural selection, we must evaluate pleiotropic effects of underlying quantitative trait genes and define functional allelic variation at the level of quantitative trait nucleotides (QTNs). Catecholamines up (Catsup), which encodes a negative regulator of tyrosine hydroxylase , the rate-limiting step in the synthesis of the neurotransmitter dopamine, is a pleiotropic quantitative trait gene in Drosophila melanogaster. We used association mapping to determine whether the same or different QTNs at Catsup are associated with naturally occurring variation in multiple quantitative traits. We sequenced 169 Catsup alleles from a single population and detected 33 polymorphisms with little linkage disequilibrium (LD). Different molecular polymorphisms in Catsup are independently associated with variation in longevity, locomotor behavior, and sensory bristle number. Most of these polymorphisms are potentially functional variants in protein coding regions, have large effects, and are not common. Thus, Catsup is a pleiotropic quantitative trait gene, but individual QTNs do not have pleiotropic effects. Molecular population genetic analyses of Catsup sequences are consistent with balancing selection maintaining multiple functional polymorphisms.     

Evolutionary quantitative genetics of nonlinear developmental systems

In quantitative genetics, the effects of developmental relationships among traits on microevolution are generally represented by the contribution of pleiotropy to additive genetic covariances. Pleiotropic additive genetic covariances arise only from the average effects of alleles on multiple traits, and therefore the evolutionary importance of nonlinearities in development is generally neglected in quantitative genetic views on evolution. However, nonlinearities in relationships among traits at the level of whole organisms are undeniably important to biology in general, and therefore critical to understanding evolution. I outline a system for characterizing key quantitative parameters in nonlinear developmental systems, which yields expressions for quantities such as trait means and phenotypic and genetic covariance matrices. I then develop a system for quantitative prediction of evolution in nonlinear developmental systems. I apply the system to generating a new hypothesis for why direct stabilizing selection is rarely observed. Other uses will include separation of purely correlative from direct and indirect causal effects in studying mechanisms of selection, generation of predictions of medium‐term evolutionary trajectories rather than immediate predictions of evolutionary change over single generation time‐steps, and the development of efficient and biologically motivated models for separating additive from epistatic genetic variances and covariances.     

Estimation and testing of parent-of-origin effects for quantitative traits

Recent progress in developing family-based association methods has extended their use to the analysis of quantitative traits in the offspring and to the estimation, for dichotomous traits, of the relative contribution of genetic and environmental mechanisms for parent-of-origin effects. However, many traits of interest are not naturally measured on a binary scale yet are suspected or known to be influenced by imprinted genes, and there is consequent interest in seeking evidence for parent-of-origin effects at these loci. Here we show how simple linear models can be used to estimate these parent-of-origin effects for a broad class of phenotypes; in particular, normally distributed quantitative traits are easily dealt with.     

A comparison between methods for linkage disequilibrium fine mapping of quantitative trait loci

We present a maximum likelihood method for mapping quantitative trait loci that uses linkage disequilibrium information from single and multiple markers. We made paired comparisons between analyses using a single marker, two markers and six markers. We also compared the method to single marker regression analysis under several scenarios using simulated data. In general, our method outperformed regression (smaller mean square error and confidence intervals of location estimate) for quantitative trait loci with dominance effects. In addition, the method provides estimates of the frequency and additive and dominance effects of the quantitative trait locus.     

Quantitative trait loci in Drosophila

Phenotypic variation for quantitative traits results from the simultaneous segregation of alleles at multiple quantitative trait loci. Understanding the genetic architecture of quantitative traits begins with mapping quantitative trait loci to broad genomic regions and ends with the molecular definition of quantitative trait loci alleles. This has been accomplished for some quantitative trait loci in Drosophila. Drosophila quantitative trait loci have sex-, environment- and genotype-specific effects, and are often associated with molecular polymorphisms in non-coding regions of candidate genes. These observations offer valuable lessons to those seeking to understand quantitative traits in other organisms, including humans.     

A blocking Gibbs sampling method to detect major genes with phenotypic data from a diallel mating

Diallel mating is a frequently used design for estimating the additive and dominance genetic (polygenic) effects involved in quantitative traits observed in the half- and full-sib progenies generated in plant breeding programmes. Gibbs sampling has been used for making statistical inferences for a mixed-inheritance model (MIM) that includes both major genes and polygenes. However, using this approach it has not been possible to incorporate the genetic properties of major genes with the additive and dominance polygenic effects in a diallel mating population. A parent block Gibbs sampling method was developed in this study to make statistical inferences about the major gene and polygenic effects on quantitative traits for progenies derived from a half-diallel mating design. Using simulated data sets with different major and polygenic effects, the proposed method accurately estimated the major and polygenic effects of quantitative traits, and possible genotypes of parents and progenies. The impact of specifying different prior distributions was examined and was found to have little effect on inference on the posterior distribution. This approach was applied to an experimental data set of Loblolly pine (Pinus taeda L.) derived from a 6-parent half-diallel mating. The result indicated that there might be a recessive major gene affecting height growth in this diallel population.     

Quantitative methods for analysing cumulative effects on fish migration success: a review

It is often recognized, but seldom addressed, that a quantitative assessment of the cumulative effects, both additive and non-additive, of multiple stressors on fish survival would provide a more realistic representation of the factors that influence fish migration. This review presents a compilation of analytical methods applied to a well-studied fish migration, a more general review of quantitative multivariable methods, and a synthesis on how to apply new analytical techniques in fish migration studies. A compilation of adult migration papers from Fraser River sockeye salmon Oncorhynchus nerka revealed a limited number of multivariable methods being applied and the sub-optimal reliance on univariable methods for multivariable problems. The literature review of fisheries science, general biology and medicine identified a large number of alternative methods for dealing with cumulative effects, with a limited number of techniques being used in fish migration studies. An evaluation of the different methods revealed that certain classes of multivariable analyses will probably prove useful in future assessments of cumulative effects on fish migration. This overview and evaluation of quantitative methods gathered from the disparate fields should serve as a primer for anyone seeking to quantify cumulative effects on fish migration survival.     

The coupled variability of quantitative and qualitative traits: a single-locus 3-allele model

Statistics for estimation of additive and non-additive effects of marker gene on quantitative trait are developed from the mad-model of a quantitative trait for three-allelic codominant marker locus. All they may be obtained directly from population data, without any hybridological experiments.     

Additive genetic variation and the distribution of QTN effects among sites

Early quantitative genetic theories emphasize the distribution of gene effects at individual loci or the distribution of mutant effects in maintaining quantitative genetic variation, but infrequently stress the distribution of gene effects among loci. In this study, we analyse the effects of the distribution of quantitative trait nucleotides (QTN) effects among sites under artificial and stabilizing selection. Wright's formula is applied to describing the density distribution of allele frequencies of multiple diallelic QTN at the equilibrium of mutation-drift-selection. Our results demonstrate that the distribution of QTN effects among sites can affect additive genetic variation in terms of total additive variance, average gene diversity, per-class contribution of QTN effects and per-QTN contribution. When the distribution of QTN effects among sites is changed from L-shaped to bell-shaped or to be a flatter, both the total additive variance and the average gene diversity are changed. Per-class and per-QTN contributions exhibit different distribution patterns. The L-shaped distribution indicates the predominant role of the aggregative effects from the QTN of small finite effects. The bell-shaped or flatter distributions indicate the predominance of the QTN of intermediate and large effects. These predictions highlight the significance of the distribution of QTN effects among sites in interpreting the maintenance of quantitative genetic variation at the fine genome scale.     

Quantitative trait locus mapping using human pedigrees

In the past decade phenomenal progress has been made in molecular and statistical genetic methods for localizing quantitative trait loci. Because of these advances, we can anticipate a long period of active genetic research in which the genes influencing human quantitative variability will be mapped and their effects accurately evaluated. Here, we review the current state of the science in statistical genetic methods for quantitative trait linkage analysis. In particular, we detail a variance component-based framework for localizing quantitative trait loci and for accurately estimating their relative effect sizes. Attention is paid to the optimal design of human family studies for localizing genes of small to moderate effect. In addition, methods and strategies are described for dealing with the most important complications of quantitative variation, including the assessment of genotype x environment interaction and epistasis.     

MHC polymorphism and disease resistance to vibrio anguillarum in 8 families of half-smooth tongue sole (Cynoglossus semilaevis)

Background

Most quantitative traits are controlled by multiple quantitative trait loci (QTL). The contribution of each locus may be negligible but the collective contribution of all loci is usually significant. Genome selection that uses markers of the entire genome to predict the genomic values of individual plants or animals can be more efficient than selection on phenotypic values and pedigree information alone for genetic improvement. When a quantitative trait is contributed by epistatic effects, using all markers (main effects) and marker pairs (epistatic effects) to predict the genomic values of plants can achieve the maximum efficiency for genetic improvement.

Results

In this study, we created 126 recombinant inbred lines of soybean and genotyped 80 makers across the genome. We applied the genome selection technique to predict the genomic value of somatic embryo number (a quantitative trait) for each line. Cross validation analysis showed that the squared correlation coefficient between the observed and predicted embryo numbers was 0.33 when only main (additive) effects were used for prediction. When the interaction (epistatic) effects were also included in the model, the squared correlation coefficient reached 0.78.

Conclusions

This study provided an excellent example for the application of genome selection to plant breeding.     

Impact of epistasis and QTL×environment interaction on the developmental behavior of plant height in rice (Oryza sativa L.)

QTLs with epistatic effects and environmental interaction effects for the developmental behavior of plant height in rice were studied by conventional and conditional methods for quantitative trait loci (QTLs) by mapping with a doubled-haploid population of 123 lines from IR64/Azucena in three environments. The results showed that epistatic effects were important and most epistasis could be detected only by conditional QTL mapping, while most non–epistatic QTLs could be detected by both conventional and conditional methods. Many modificative QTLs showed only epistatic effects without their own additive effects at some stages. QTL×environment (QE) interaction effects were detected more often than QTL main effects for plant-height behavior, which might indicate that gene expression could be greatly affected by the environment. No QTLs had effects during the whole of ontogeny. Conditional QTL mapping might be a valid way to reveal dynamic gene expression for the development of quantitative traits, especially for epistatic effects. Received: 19 May 2000 / Accepted: 27 October 2000     

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.     

Tests for major genes affecting quantitative traits in wild radish,Raphanus raphanistrum

The number of gene loci coding for quantitative traits is an important issue in genetics. However, there are still very few empirical data on this point, especially in natural populations. I tested for major gene effects on ten quantitative traits in wild radish, using an indirect method based on the patterns of family means and within and between family variances for traits. This method should reveal whether a single locus is responsible for most of the variation in a trait. Eight of the traits measured were morphological dimensions of leaves and flowers; no strong evidence for major gene effects on these traits was found. In contrast, evidence for major gene effects was found in the other two traits, emergence time and flowering time.     

Indirect genetic effects from ecological interactions in Arabidopsis thaliana

Indirect genetic effects arise when genes expressed in one individual affect the expression of traits in other individuals. The importance of indirect genetic effects has been recognized for a diversity of evolutionary processes including kin selection, sexual selection, community structure and multilevel selection, but data regarding their genetic architecture and prevalence throughout the genome remain scarce, especially for interactions between unrelated individuals. Using a set of 411 Bay-0 x Shahdara Arabidopsis recombinant inbred lines grown with Landsberg neighbours, we examined quantitative trait loci (QTL) having direct and indirect effects on size, developmental, and fitness related traits. Using an interval mapping approach, we identified 15 QTL with direct effects and found that 13 of these QTL had significant indirect effects on trait expression in neighbouring plants. These results suggest widespread pleiotropy, as nearly all direct effect QTL have associated pleiotropic indirect effects. Paradoxically, most indirect effects were of the same sign as direct effects, creating a pattern of nearly universal positive pleiotropy that makes most covariances between direct and indirect effects positive. These results are consistent with a complex genetic basis for intraspecific interactions, but suggest that interactions between neighbouring plants are largely positive, rather than negative as would be expected for competition. In addition to their evolutionary and ecological importance, these pleiotropic relationships between DGE and IGE loci have implications for quantitative genetic studies of natural populations as well as experimental design considerations. Additionally, studies that ignore IGEs may over- or underestimate quantitative genetic parameters, as well as the effect of and variance contributed by QTL.