Varying coefficient models for mapping quantitative trait loci using recombinant inbred intercrosses

There has been a great deal of interest in the development of methodologies to map quantitative trait loci (QTL) using experimental crosses in the last 2 decades. Experimental crosses in animal and plant sciences provide important data sources for mapping QTL through linkage analysis. The Collaborative Cross (CC) is a renewable mouse resource that is generated from eight genetically diverse founder strains to mimic the genetic diversity in humans. The recombinant inbred intercrosses (RIX) generated from CC recombinant inbred (RI) lines share similar genetic structures of F(2) individuals but with up to eight alleles segregating at any one locus. In contrast to F(2) mice, genotypes of RIX can be inferred from the genotypes of their RI parents and can be produced repeatedly. Also, RIX mice typically do not share the same degree of relatedness. This unbalanced genetic relatedness requires careful statistical modeling to avoid false-positive findings. Many quantitative traits are inherently complex with genetic effects varying with other covariates, such as age. For such complex traits, if phenotype data can be collected over a wide range of ages across study subjects, their dynamic genetic patterns can be investigated. Parametric functions, such as sigmoidal or logistic functions, have been used for such purpose. In this article, we propose a flexible nonparametric time-varying coefficient QTL mapping method for RIX data. Our method allows the QTL effects to evolve with time and naturally extends classical parametric QTL mapping methods. We model the varying genetic effects nonparametrically with the B-spline bases. Our model investigates gene-by-time interactions for RIX data in a very flexible nonparametric fashion. Simulation results indicate that the varying coefficient QTL mapping has higher power and mapping precision compared to parametric models when the assumption of constant genetic effects fails. We also apply a modified permutation procedure to control overall significance level.     

Identification of superior parents in a potato breeding programme

Summary An incomplete diallel cross was used to study components of genetic variation in potatoes for a range of characters after early and late harvest. The progenies were also used to evaluate five predictors of progeny performance, namely the mean seedling performance, the mid-parent value and the means of the selfed progenies, of the diploid progenies and of the test-cross progenies. For almost all characters, the general combining ability effects were predominant, although the specific combining ability effects present were greater at late than at early harvests. The seedling performance for tuber yield, number of tubers and average tuber weight did not show any relevant relationship to the field performance. The midparent value provided, in general, satisfactory predictions of the mean progeny performance obtained in the diallel, except for ware tuber yield. The selfed and the diploid progenies did not improve the prediction of progeny means compared to the mid-parent value. The predictions based on the test-crosses surpassed those of the mid-parent value, particularly for tuber yield at ware potato harvest. Methods to identify superior parents are discussed.     

Using mating designs to uncover QTL and the genetic architecture of complex traits

Analysis of quantitative trait loci (QTL) affecting complex traits is often pursued in single-cross experiments. For most purposes, including breeding, some assessment is desired of the generalizability of the QTL findings and of the overall genetic architecture of the trait. Single-cross experiments provide a poor basis for these purposes, as comparison across experiments is hampered by segregation of different allelic combinations among different parents and by context-dependent effects of QTL. To overcome this problem, we combined the benefits of QTL analysis (to identify genomic regions affecting trait variation) and classic diallel analysis (to obtain insight into the general inheritance of the trait) by analyzing multiple mapping families that are connected via shared parents. We first provide a theoretical derivation of main (general combining ability (GCA)) and interaction (specific combining ability (SCA)) effects on F(2) family means relative to variance components in a randomly mating reference population. Then, using computer simulations to generate F(2) families derived from 10 inbred parents in different partial-diallel designs, we show that QTL can be detected and that the residual among-family variance can be analyzed. Standard diallel analysis methods are applied in order to reveal the presence and mode of action (in terms of GCA and SCA) of undetected polygenes. Given a fixed experiment size (total number of individuals), we demonstrate that QTL detection and estimation of the genetic architecture of polygenic effects are competing goals, which should be explicitly accounted for in the experimental design. Our approach provides a general strategy for exploring the genetic architecture, as well as the QTL underlying variation in quantitative traits.     

作物杂种后代基因型值和杂种优势的预测方法

本文提出了利用作物亲本和F_1预测杂种后代基因型值和杂种优势的统计分析方法.该方法运用加性-显性遗传模型,分析双列杂交试验资料,用MINQUE(1)法估算方差分量以及预测遗传效应值.由加性和显性效应预测值可进一步预测F_1,F_2,BC_1,BC_2,等不同世代的基因型值,在预测F_1群体平均优势和群体超亲优势的基础上,可以推导出其它各世代的杂种优势.提出了预测杂种后代保持超亲优势世代数的简单公式,根据杂交组合F_1群体平均优势和双亲相对遗传差异,便可预测该组合能在生产上直接利用的世代数.以棉花六个品种完全双列杂交试验资料为例,分析了各组合F_1和F_2的基因型值、超亲优势和保持5％超亲优势的世代数.     

二棱大麦熟期性状的遗传研究

以甘木二条等7个二棱大麦品种进行不完全双列杂交,对其亲本、F1和F2的抽穗期,灌浆期和成熟期三个性状以1992和1995年（播种年份）的两年资料,采用加性-显性-上位性（ADAA）模型进行遗传分析．遗传方差分量的比率估算表明,三个性状都存在上位性作用．除灌浆期外,其余二性状还受显性和加性效应的作用,并以加性为主．显性效应和加性效应与环境的互作均达显著水平,基因效应的预测值表明采用P3（黔浙1号）和P4（浙农大3号）较易获得早熟后代．     

普通玉米籽粒性状的遗传效应分析

采用二倍体种子遗传模型及其分析方法,研究了５个玉米籽粒性状的直接效应、母体效应和细胞质效应．分析结果表明,各性状的遗传同时受种子直接效应和母体效应的影响,细胞质基因对百粒重和粒宽具有极显著影响．除粒长、粒厚的直接显性效应与母体显性效应间的协方差外,直接效应与母体效应间的协方差均不显著．因此,通过母体植株的表现可对这些性状进行有效的选择．Ｓ_２２和 ８７－１是改良粒重的优良亲本．选择粒较宽的自交系作母本有利于提高后代选系及Ｆ_１的百粒重．     

Bayesian multiple quantitative trait loci mapping for recombinant inbred intercrosses

The Collaborative Cross (CC) is a renewable mouse resource that mimics the genetic diversity in humans. The recombinant inbred intercrosses (RIX) generated from CC recombinant inbred (RI) lines share similar genetic structures to those of F(2) individuals. In contrast to F(2) mice, genotypes of RIX can be inferred from the genotypes of their RI parents and can be produced repeatedly. Also, RIX mice do not typically share the same degree of relatedness. This unbalanced genetic relatedness requires careful statistical modeling to avoid a large number of false positive findings. For complex traits, mapping multiple genes simultaneously is arguably more powerful than mapping one gene at a time. In this article, we describe how we have developed a Bayesian quantitative trait locus (QTL) mapping method that simultaneously deals with the special genetic architecture of RIX and maps multiple genes. The performance of the proposed method is evaluated by extensive simulations. In addition, for a given set of RI lines, there are numerous ways to generate RIX samples. To provide a general guideline on future RIX studies, we compare several RIX designs through simulations.     

High-resolution genetic mapping using the Mouse Diversity outbred population

The JAX Diversity Outbred population is a new mouse resource derived from partially inbred Collaborative Cross strains and maintained by randomized outcrossing. As such, it segregates the same allelic variants as the Collaborative Cross but embeds these in a distinct population architecture in which each animal has a high degree of heterozygosity and carries a unique combination of alleles. Phenotypic diversity is striking and often divergent from phenotypes seen in the founder strains of the Collaborative Cross. Allele frequencies and recombination density in early generations of Diversity Outbred mice are consistent with expectations based on simulations of the mating design. We describe analytical methods for genetic mapping using this resource and demonstrate the power and high mapping resolution achieved with this population by mapping a serum cholesterol trait to a 2-Mb region on chromosome 3 containing only 11 genes. Analysis of the estimated allele effects in conjunction with complete genome sequence data of the founder strains reduced the pool of candidate polymorphisms to seven SNPs, five of which are located in an intergenic region upstream of the Foxo1 gene.     

作物品种间杂种优势遗传分析的新方法

本文提出了分析双列杂交试验资料的两个遗传模型。第一个模型包括加性、显性和母体效应;第二个模型只包括简单的加性和显性效应。还介绍了分析杂种优势、估算遗传方差分量以及预测遗传效应值的相应统计分析方法。用所介绍的遗传模型和分析方法以及常用的Griffing配合力分析方法,分析了棉花6个品种双列杂交的产量性状,并进一步比较了不同方法的分析结果。采用本文所介绍的遗传模型和分析方法,可以克服用Griffing的配合力模型及其方法分析杂种优势和配合力遗传表现所存在的局限性。     

An inclusive fitness model for the sex ratio in a partially sibmating population with inbreeding cost

Summary We construct an inclusive fitness model to find the evolutionarily stable sex ratios in a partially sibmating diploid or haplodiploid population. We assume a constant rate of sibmating with inbred offspring incurring a fitness penalty which, under haplodiploidy, is only suffered by females. We construct a one-locus genetic model for the same problem and observe that when selection is weak it gives the same numerical results as the inclusive fitness model.     

Intergenerational effects of inbreeding in Nicrophorus vespilloides: offspring suffer fitness costs when either they or their parents are inbred

Inbreeding depression is the reduction in fitness caused by mating between related individuals. Inbreeding is expected to cause a reduction in offspring fitness when the offspring themselves are inbred, but outbred individuals may also suffer a reduction in fitness when they depend on care from inbred parents. At present, little is known about the significance of such intergenerational effects of inbreeding. Here, we report two experiments on the burying beetle Nicrophorus vespilloides, an insect with elaborate parental care, in which we investigated inbreeding depression in offspring when either the offspring themselves or their parents were inbred. We found substantial inbreeding depression when offspring were inbred, including reductions in hatching success of inbred eggs and survival of inbred offspring. We also found substantial inbreeding depression when parents were inbred, including reductions in hatching success of eggs produced by inbred parents and survival of outbred offspring that received care from inbred parents. Our results suggest that intergenerational effects of inbreeding can have substantial fitness costs to offspring, and that future studies need to incorporate such costs to obtain accurate estimates of inbreeding depression.     

The collaborative cross: a recombinant inbred mouse population for the systems genetic era

The mouse is the most extensively used mammalian model for biomedical and aging research, and an extensive catalogue of laboratory resources is available to support research using mice: classical inbred lines, genetically modified mice (knockouts, transgenics, and humanized mice), selectively bred lines, consomics, congenics, recombinant inbred panels, outbred and heterogeneous stocks, and an expanding set of wild-derived strains. However, these resources were not designed or intended to model the heterogeneous human population or for a systematic analysis of phenotypic effects due to random combinations of uniformly distributed natural variants. The Collaborative Cross (CC) is a large panel of recently established multiparental recombinant inbred mouse lines specifically designed to overcome the limitations of existing mouse genetic resources for analysis of phenotypes caused by combinatorial allele effects. The CC models the complexity of the human genome and supports analyses of common human diseases with complex etiologies originating through interactions between allele combinations and the environment. The CC is the only mammalian resource that has high and uniform genomewide genetic variation effectively randomized across a large, heterogeneous, and infinitely reproducible population. The CC supports data integration across environmental and biological perturbations and across space (different labs) and time.     

PATERNAL EFFECTS ON THE EXPRESSION OF A MALE POLYPHENISM

Polyphenic traits are widespread, but compared to other traits, relatively few studies have explored the mechanisms that influence their inheritance. Here we investigated the relative importance of additive, nonadditive genetic, and parental sources of variation in the expression of polyphenic male dimorphism in the mite Rhizoglyphus echinopus, a species in which males are either fighters or scramblers. We established eight inbred lines through eight generations of full‐sibling matings, and then crossed the inbred lines in a partial diallel design. Nymphs were isolated and raised to adulthood with ad libitum food. At adulthood, male morph was recorded for all male offspring. Using a Cockerham–Weir model, we found strong paternal effects for this polyphenic trait that could be either linked to the Y chromosome of males or an indirect genetic effect that is environmentally transmitted. In additional analyses, we were able to corroborate the paternal effects but also detected significant additive effects questioning the Cockerham–Weir analysis. This study reveals the potential importance of paternal effects on the expression of polyphenic traits and sheds light on the complex genetic architecture of these traits.     

The Collaborative Cross, a groundbreaking tool to tackle complex traits

Complex traits, like the susceptibility to common diseases, are controlled by numerous genomic regions which individual effect is generally weak. These observations led geneticists to develop an experimental system to dissect the genetic of complex traits in the mouse. The Collaborative Cross (CC) is a genetic reference population of over 300 inbred lines derived from eight inbred strains of three Mus musculus sub-species that captures 90% of the genetic variation known in the mouse genome. We present here the generation and the characteristics of the CC and we report the results of the first experiments with partially inbred CC lines.     

Evolution of Adaptation and Mate Choice: Parental Relatedness Affects Expression of Phenotypic Variance in a Natural Population

Mating between relatives generally results in reduced offspring viability or quality, suggesting that selection should favor behaviors that minimize inbreeding. However, in natural populations where searching is costly or variation among potential mates is limited, inbreeding is often common and may have important consequences for both offspring fitness and phenotypic variation. In particular, offspring morphological variation often increases with greater parental relatedness, yet the source of this variation, and thus its evolutionary significance, are poorly understood. One proposed explanation is that inbreeding influences a developing organism’s sensitivity to its environment and therefore the increased phenotypic variation observed in inbred progeny is due to greater inputs from environmental and maternal sources. Alternatively, changes in phenotypic variation with inbreeding may be due to additive genetic effects alone when heterozygotes are phenotypically intermediate to homozygotes, or effects of inbreeding depression on condition, which can itself affect sensitivity to environmental variation. Here we examine the effect of parental relatedness (as inferred from neutral genetic markers) on heritable and nonheritable components of developmental variation in a wild bird population in which mate choice is often constrained, thereby leading to inbreeding. We found greater morphological variation and distinct contributions of variance components in offspring from highly related parents: inbred offspring tended to have greater environmental and lesser additive genetic variance compared to outbred progeny. The magnitude of this difference was greatest in late-maturing traits, implicating the accumulation of environmental variation as the underlying mechanism. Further, parental relatedness influenced the effect of an important maternal trait (egg size) on offspring development. These results support the hypothesis that inbreeding leads to greater sensitivity of development to environmental variation and maternal effects, suggesting that the evolutionary response to selection will depend strongly on mate choice patterns and population structure.     

Population differentiation in the beetleTribolium castaneum. I. Genetic architecture

We used joint-scaling analyses in conjunction with rearing temperature variation to investigate the contributions of additive, non-additive, and environmental effects to genetic divergence and incipient speciation among 12 populations of the red flour beetle, Tribolium castaneum, with small levels of pairwise nuclear genetic divergence (0.033 < Nei's D < 0.125). For 15 population pairs we created a full spectrum of line crosses (two parental, two reciprocal F1's, four F2's, and eight backcrosses), reared them at multiple temperatures, and analyzed the numbers and developmental defects of offspring. We assayed a total of 219,388 offspring from 5147 families. Failed crosses occurred predominately in F2's, giving evidence of F2 breakdown within this species. In all cases where a significant model could be fit to the data on offspring number, we observed at least one type of digenic epistasis. We also found maternal and cytoplasmic effects to be common components of divergence among T. castaneum populations. In some cases, the most complex model tested (additive, dominance, epistatic, maternal, and cytoplasmic effects) did not provide a significant fit to the data, suggesting that linkage or higher order epistasis is involved in differentiation between some populations. For the limb deformity data, we observed significant genotype-by-environment interaction in most crosses and pure parent crosses tended to have fewer deformities than hybrid crosses. Complexity of genetic architecture was not correlated with either geographic distance or genetic distance. Our results support the view that genetic incompatibilities responsible for postzygotic isolation, an important component of speciation, may be a natural but serendipitous consequence of nonadditive genetic effects and structured populations.     

On the assignment of fitness to parents and offspring: whose fitness is it and when does it matter?

There has been a long‐standing conceptual debate over the legitimacy of assigning components of offspring fitness to parents for purposes of evolutionary analysis. The benefits and risks inherent in assigning fitness of offspring to parents have been given primarily as verbal arguments and no explicit theoretical analyses have examined quantitatively how the assignment of fitness can affect evolutionary inferences. Using a simple quantitative genetic model, we contrast the conclusions drawn about how selection acts on a maternal character when components of offspring fitness (such as early survival) are assigned to parents vs. when they are assigned directly to the individual offspring. We find that there are potential shortcomings of both possible assignments of fitness. In general, whenever there is a genetic correlation between the parental and direct effects on offspring fitness, assigning components of offspring fitness to parents yields incorrect dynamical equations and may even lead to incorrect conclusions about the direction of evolution. Assignment of offspring fitness to parents may also produce incorrect estimates of selection whenever environmental variation contributes to variance of the maternal trait. Whereas assignment of offspring fitness to the offspring avoids these potential problems, it introduces the possible problem of missing components of kin selection provided by the mother, which may not be detected in selection analyses. There are also certain conditions where either model can be appropriate because assignment of offspring fitness to parents may yield the same dynamical equations as assigning offspring fitness directly to offspring. We discuss these implications of the alternative assignments of fitness for modelling, selection analysis and experimentation in evolutionary biology.     

海岛棉F1产量性状的条件遗传分析

调查了海岛棉5×4不完全双列杂交实验的3年产量性状资料,运用包括加性、显性、加性×环境互作、显性×环境互作的遗传模型进行条件和非条件的遗传分析.双列杂交的亲本具有不同果枝类型.非条件遗传方差结果表明,总皮棉产量没有检测到显著的非条件加性效应方差.但是铃重、霜前铃数、霜后铃数以及霜前皮棉产量的条件分析结果发现这些性状的加性效应均对总皮棉产量的加性效应有贡献.因此,可通过这些性状改良总皮棉产量的加性效应表现.当某材料产量构成因素的加性贡献率比较高时,选择该材料作为杂交亲本可望获得具有较好总皮棉产量表现的后代.各产量构成因素的显性效应对霜前皮棉产量和总皮棉产量的杂种优势具有较大的贡献率.产量构成因素之间又相互影响.那些能够检测到显著的正向贡献率的性状将为进一步改良目标性状提供可能.本研究结果显示运用条件分析方法不仅能分析原因性状对目标性状的贡献率,还可以分析特定亲本(或组合)的某一性状对该亲本或组合目标性状的作用大小和正负,据此就可以指导某一亲本后代或组合的目标性状的间接选择.这对实际育种中具体组合的选择具有重要的意义.     

黑米中矿质元素铁、锌、锰、磷含量的遗传效应研究

采用禾谷类作物种子胚乳数量性状模型,分析黑米稻品种双列杂交Ｆ１和Ｆ２种子的Ｆｅ、Ｚｎ、Ｍｎ、Ｐ含量的遗传效应。结果表明,４种矿质元素含量同时受制于种子直接遗传效应、母体效应和细胞质作用影响。其中,Ｆｅ、Ｚｎ、Ｍｎ含量的种子直接效应比母体效应和细胞质效应的作用更大;Ｐ含量则主要受种子直接加性、母体加性和显性效应共同作用。Ｆｅ、Ｚｎ、Ｍｎ含量的种子直接遗传率较高,在杂种早代分别结合农艺性状选择单株上各     

甘蔗生物量育种的ADGE遗传分析

对甘蔗11个亲本品种及不完全双列杂交(NCdesignⅡ)遗传设计的30个组合的F1代实生苗生物量进行加性-显型-随机环境效应模型(ADGE)分析。结果表明:甘蔗的生物量性状遗传主要是由基因的加性、显性及加性×环境互作效应共同决定的,但基因的加性效应作用较大;甘蔗杂交亲本对其后代表型的遗传作用主要为母本的遗传效应影响;甘蔗生物量性状都具有较高的广义遗传率(h2B)和狭义遗传率(h2N),且h2B>h2N,说明了对甘蔗生物量性状在选育种早期阶段的选择效果好;通过对亲本的加性基因随机效应分析的综合,较优良的甘蔗亲本有粤糖72/426、粤糖79/177、粤糖85/177、ROC24和ROC25;根据杂交组合显性随机效应分析,认为粤糖72/426×ROC16、粤糖79/177×ROC24、粤糖79/177×ROC23及粤糖80/101×ROC22是较优良的高生物量甘蔗杂交组合,可以应用于甘蔗的高生物量育种。