Functional Regression Models for Epistasis Analysis of Multiple Quantitative Traits

To date, most genetic analyses of phenotypes have focused on analyzing single traits or analyzing each phenotype independently. However, joint epistasis analysis of multiple complementary traits will increase statistical power and improve our understanding of the complicated genetic structure of the complex diseases. Despite their importance in uncovering the genetic structure of complex traits, the statistical methods for identifying epistasis in multiple phenotypes remains fundamentally unexplored. To fill this gap, we formulate a test for interaction between two genes in multiple quantitative trait analysis as a multiple functional regression (MFRG) in which the genotype functions (genetic variant profiles) are defined as a function of the genomic position of the genetic variants. We use large-scale simulations to calculate Type I error rates for testing interaction between two genes with multiple phenotypes and to compare the power with multivariate pairwise interaction analysis and single trait interaction analysis by a single variate functional regression model. To further evaluate performance, the MFRG for epistasis analysis is applied to five phenotypes of exome sequence data from the NHLBI’s Exome Sequencing Project (ESP) to detect pleiotropic epistasis. A total of 267 pairs of genes that formed a genetic interaction network showed significant evidence of epistasis influencing five traits. The results demonstrate that the joint interaction analysis of multiple phenotypes has a much higher power to detect interaction than the interaction analysis of a single trait and may open a new direction to fully uncovering the genetic structure of multiple phenotypes.     

Methods for Checking Assumptions in Regression Models

The usual assumptions in regression analysis are: The setup is true; the random errors are uncorre-lated (and normally distributed); and the data contain no outliers. Reasoning known recommendations to check these assumptions by inspection of the residuals new proposals are discussed and illustrated by an example.     

Gene-Based Mapping and Pathway Analysis of Metabolic Traits in Dairy Cows

The metabolic adaptation of dairy cows during the transition period has been studied intensively in the last decades. However, until now, only few studies have paid attention to the genetic aspects of this process. Here, we present the results of a gene-based mapping and pathway analysis with the measurements of three key metabolites, (1) non-esterified fatty acids (NEFA), (2) beta-hydroxybutyrate (BHBA) and (3) glucose, characterizing the metabolic adaptability of dairy cows before and after calving. In contrast to the conventional single-marker approach, we identify 99 significant and biologically sensible genes associated with at least one of the considered phenotypes and thus giving evidence for a genetic basis of the metabolic adaptability. Moreover, our results strongly suggest three pathways involved in the metabolism of steroids and lipids are potential candidates for the adaptive regulation of dairy cows in their early lactation. From our perspective, a closer investigation of our findings will lead to a step forward in understanding the variability in the metabolic adaptability of dairy cows in their early lactation.     

Multilocus Population Genetics with Weak Epistasis. I. Equilibrium Properties of Two-Locus Two-Allele Models

Using perturbation techniques, I determine the equilibrium of two-locus two-allele models with overdominance and weak epistasis. To lowest order, the allele frequencies, the mean fitness and the covariance between heterokaryotic and homokaryotic flies arising in the Sturtevant experimental design are independent of the recombination rate, r. The disequilibrium varies as one divided by the recombination rate, in contrast to neutral models. Although the disequilibrium generated by weak epistasis is small, too small to be experimentally detected, it can be large enough to have biological importance.     

Complex Epistasis for Dobzhansky–Muller Hybrid Incompatibility in Solanum

We examined the prevalence of interactions between pairs of short chromosomal regions from one species (Solanum habrochaites) co-introgressed into a heterospecific genetic background (Solanum lycopersicum). Of 105 double introgression line (DIL) families generated from a complete diallele combination of 15 chromosomal segments, 39 (~38%) showed evidence for complex epistasis in the form of genotypic and/or allelic marker transmission distortion in DIL F₂ populations.     

Nonparametric Method for Genomics-Based Prediction of Performance of Quantitative Traits Involving Epistasis in Plant Breeding

Genomic selection (GS) procedures have proven useful in estimating breeding value and predicting phenotype with genome-wide molecular marker information. However, issues of high dimensionality, multicollinearity, and the inability to deal effectively with epistasis can jeopardize accuracy and predictive ability. We, therefore, propose a new nonparametric method, pRKHS, which combines the features of supervised principal component analysis (SPCA) and reproducing kernel Hilbert spaces (RKHS) regression, with versions for traits with no/low epistasis, pRKHS-NE, to high epistasis, pRKHS-E. Instead of assigning a specific relationship to represent the underlying epistasis, the method maps genotype to phenotype in a nonparametric way, thus requiring fewer genetic assumptions. SPCA decreases the number of markers needed for prediction by filtering out low-signal markers with the optimal marker set determined by cross-validation. Principal components are computed from reduced marker matrix (called supervised principal components, SPC) and included in the smoothing spline ANOVA model as independent variables to fit the data. The new method was evaluated in comparison with current popular methods for practicing GS, specifically RR-BLUP, BayesA, BayesB, as well as a newer method by Crossa et al., RKHS-M, using both simulated and real data. Results demonstrate that pRKHS generally delivers greater predictive ability, particularly when epistasis impacts trait expression. Beyond prediction, the new method also facilitates inferences about the extent to which epistasis influences trait expression.     

Ubiquitous Polygenicity of Human Complex Traits: Genome-Wide Analysis of 49 Traits in Koreans

Recent studies in population of European ancestry have shown that 30%∼50% of heritability for human complex traits such as height and body mass index, and common diseases such as schizophrenia and rheumatoid arthritis, can be captured by common SNPs and that genetic variation attributed to chromosomes are in proportion to their length. Using genome-wide estimation and partitioning approaches, we analysed 49 human quantitative traits, many of which are relevant to human diseases, in 7,170 unrelated Korean individuals genotyped on 326,262 SNPs. For 43 of the 49 traits, we estimated a nominally significant (P<0.05) proportion of variance explained by all SNPs on the Affymetrix 5.0 genotyping array (). On average across 47 of the 49 traits for which the estimate of is non-zero, common SNPs explain approximately one-third (range of 7.8% to 76.8%) of narrow sense heritability.The estimate of is highly correlated with the proportion of SNPs with association P<0.031 (r² = 0.92). Longer genomic segments tend to explain more phenotypic variation, with a correlation of 0.78 between the estimate of variance explained by individual chromosomes and their physical length, and 1% of the genome explains approximately 1% of the genetic variance. Despite the fact that there are a few SNPs with large effects for some traits, these results suggest that polygenicity is ubiquitous for most human complex traits and that a substantial proportion of the “missing heritability” is captured by common SNPs.     

The Influence of Matrix Size on Statistical Properties of Co-Occurrence and Limiting Similarity Null Models

Null models exploring species co-occurrence and trait-based limiting similarity are increasingly used to explore the influence of competition on community assembly; however, assessments of common models have not thoroughly explored the influence of variation in matrix size on error rates, in spite of the fact that studies have explored community matrices that vary considerably in size. To determine how smaller matrices, which are of greatest concern, perform statistically, we generated biologically realistic presence-absence matrices ranging in size from 3–50 species and sites, as well as associated trait matrices. We examined co-occurrence tests using the C-Score statistic and independent swap algorithm. For trait-based limiting similarity null models, we used the mean nearest neighbour trait distance (NN) and the standard deviation of nearest neighbour distances (SDNN) as test statistics, and considered two common randomization algorithms: abundance independent trait shuffling (AITS), and abundance weighted trait shuffling (AWTS). Matrices as small as three × three resulted in acceptable type I error rates (p < 0.05) for both the co-occurrence and trait-based limiting similarity null models when exclusive p-values were used. The commonly used inclusive p-value (≤ or ≥, as opposed to exclusive p-values; < or >) was associated with increased type I error rates, particularly for matrices with fewer than eight species. Type I error rates increased for limiting similarity tests using the AWTS randomization scheme when community matrices contained more than 35 sites; a similar randomization used in null models of phylogenetic dispersion has previously been viewed as robust. Notwithstanding other potential deficiencies related to the use of small matrices to represent communities, the application of both classes of null model should be restricted to matrices with 10 or more species to avoid the possibility of type II errors. Additionally, researchers should restrict the use of the AWTS randomization to matrices with fewer than 35 sites to avoid type I errors when testing for trait-based limiting similarity. The AITS randomization scheme performed better in terms of type I error rates, and therefore may be more appropriate when considering systems for which traits are not clustered by abundance.     

家养动物复杂性状基因定位的统计分析和实验设计

复杂性状基因定位的研究是人类、动植物研究中的1个热点领域。在畜禽的研究中,其目的是定位与生产性状、繁殖性状和疾病相关的基因。在人类中,复杂性状基因定位的研究具有极大的挑战性。尽管基因定位的结果积累得很快,但能得以确认的结果却很少。关于畜禽基因定位的研究结果同样也增长很快,目前在鸡、猪、奶牛等物种中几个大尺度的基因定位工作也正在开展中。虽然在不远的将来能够得到新的、可确信的结果,但是如何精确地理解这些复杂性状的基因仍然需要一定的时间。近来,复杂性状基因定位的方法已被用于通过基因表达的数据研究转录调节因子的定位工作中,这是基因定位研究中1个新的领域。基因定位的统计分析和实验设计是基因定位研究中的关键性步骤,研究的目的在于讨论畜禽复杂性状基因定位的统计分析和实验设计的研究进展及今后的发展。     

胚乳性状的遗传模型和世代平均数

谷类作物的胚乳是三倍体组织,胚乳性状受3N遗传控制。本文分析了胚乳性状的遗传特征,建立了相应的遗传模型,推导了世代群体的平均数分量,并提出了研究胚乳性状基因效应的一些简单的交配设计。     

Pleiotropic Models of Polygenic Variation, Stabilizing Selection, and Epistasis

We show that in polymorphic populations many polygenic traits pleiotropically related to fitness are expected to be under apparent ``stabilizing selection' independently of the real selection acting on the population. This occurs, for example, if the genetic system is at a stable polymorphic equilibrium determined by selection and the nonadditive contributions of the loci to the trait value either are absent, or are random and independent of those to fitness. Stabilizing selection is also observed if the polygenic system is at an equilibrium determined by a balance between selection and mutation (or migration) when both additive and nonadditive contributions of the loci to the trait value are random and independent of those to fitness. We also compare different viability models that can maintain genetic variability at many loci with respect to their ability to account for the strong stabilizing selection on an additive trait. Let V(m) be the genetic variance supplied by mutation (or migration) each generation, V(g) be the genotypic variance maintained in the population, and n be the number of the loci influencing fitness. We demonstrate that in mutation (migration)-selection balance models the strength of apparent stabilizing selection is order V(m)/V(g). In the overdominant model and in the symmetric viability model the strength of apparent stabilizing selection is approximately 1/(2n) that of total selection on the whole phenotype. We show that a selection system that involves pairwise additive by additive epistasis in maintaining variability can lead to a lower genetic load and genetic variance in fitness (approximately 1/(2n) times) than an equivalent selection system that involves overdominance. We show that, in the epistatic model, the apparent stabilizing selection on an additive trait can be as strong as the total selection on the whole phenotype.     

Limits to the Relationship among Recombination, Disequilibrium and Epistasis in Two-Locus Models

I determine limits to the equilibrium relationship among epistasis, recombination and disequilibrium in two-locus, two-allele models using linear programming techniques. I show that when allele frequencies are one-half at each locus, the symmetric model is the fitness pattern that generates the most disequilibrium for the smallest level of epistasis. When allele frequencies deviate from one-half much larger levels of epistasis are required to generate similar levels of disequilibrium. I determine the level of epistasis required to generate observed significant levels of disequilibrium in natural populations. The overall implication is that disequilibrium will be large at equilibrium only between strongly interacting, closely linked loci.     

A Model for Transgenerational Imprinting Variation in Complex Traits

Despite the fact that genetic imprinting, i.e., differential expression of the same allele due to its different parental origins, plays a pivotal role in controlling complex traits or diseases, the origin, action and transmission mode of imprinted genes have still remained largely unexplored. We present a new strategy for studying these properties of genetic imprinting with a two-stage reciprocal F mating design, initiated with two contrasting inbred lines. This strategy maps quantitative trait loci that are imprinted (i.e., iQTLs) based on their segregation and transmission across different generations. By incorporating the allelic configuration of an iQTL genotype into a mixture model framework, this strategy provides a path to trace the parental origin of alleles from previous generations. The imprinting effects of iQTLs and their interactions with other traditionally defined genetic effects, expressed in different generations, are estimated and tested by implementing the EM algorithm. The strategy was used to map iQTLs responsible for survival time with four reciprocal F populations and test whether and how the detected iQTLs inherit their imprinting effects into the next generation. The new strategy will provide a tool for quantifying the role of imprinting effects in the creation and maintenance of phenotypic diversity and elucidating a comprehensive picture of the genetic architecture of complex traits and diseases.     

Dominant Genetic Variation and Missing Heritability for Human Complex Traits: Insights from Twin versus Genome-wide Common SNP Models

In order to further illuminate the potential role of dominant genetic variation in the “missing heritability” debate, we investigated the additive (narrow-sense heritability, h²) and dominant (δ²) genetic variance for 18 human complex traits. Within the same study base (10,682 Swedish twins), we calculated and compared the estimates from classic twin-based structural equation model with SNP-based genomic-relatedness-matrix restricted maximum likelihood [GREML(d)] method. Contributions of δ² were evident for 14 traits in twin models (average δ²_twin = 0.25, range 0.14–0.49), two of which also displayed significant δ² in the GREMLd analyses (triglycerides δ²_SNP = 0.28 and waist circumference δ²_SNP = 0.19). On average, the proportion of h²_SNP/h²_twin was 70% for ADE-fitted traits (for which the best-fitting model included additive and dominant genetic and unique environmental components) and 31% for AE-fitted traits (for which the best-fitting model included additive genetic and unique environmental components). Independent evidence for contribution from shared environment, also in ADE-fitted traits, was obtained from self-reported within-pair contact frequency and age at separation. We conclude that despite the fact that additive genetics appear to constitute the bulk of genetic influences for most complex traits, dominant genetic variation might often be masked by shared environment in twin and family studies and might therefore have a more prominent role than what family-based estimates often suggest. The risk of erroneously attributing all inherited genetic influences (additive and dominant) to the h² in too-small twin studies might also lead to exaggerated “missing heritability” (the proportion of h² that remains unexplained by SNPs).     

Rate Limiting Factors in Melanocortin 1 Receptor Signalling Throughthe cAMP Pathway

The melanotropic actions of α‐melanocyte‐stimulating hormone (α‐MSH) and other melanocortins are mediated by activation of the melanocortin 1 receptor (MC1R). This G protein‐coupled receptor is positively coupled to Gs and triggers the cyclic adenosine mono‐phosphate (cAMP) pathway. Mutations of the MC1R gene are associated with skin type and pigmentation phenotypes, and with increased risk of skin cancers. Genetic studies have demonstrated an heterozygote carrier effect for these associations, suggesting the importance of variant allele dosage. This could be accounted for, at least partially, if the number of MC1R molecules, rather than the Gs protein or the effector enzyme, adenylyl cyclase, is limiting for the activation of the signalling pathway. However, the nature of the limiting factor(s) in MC1R signalling has not been investigated. We addressed this question by comparing the cAMP output of clones of human melanoma cell lines enriched in MC1R by stable transfection. We also analysed heterologous cell systems widely used for functional studies of MC1R. We show that cAMP production in clones of Chinese hamster ovary cells stably expressing the MC1R is a linear function of receptor number up to high, supraphysiological levels of approximately 50 000 α‐MSH binding sites per cell. Enrichment of human melanoma cell lines with MC1R also results in increased cAMP levels, with a small leftward shift of the agonist dose–response curves. Therefore, at physiological expression levels second‐messenger generation is dependent on receptor density. Within melanoma cells and also likely in normal melanocytes, MC1R appears the limiting factor controlling the output of the cAMP signalling pathway.