Stevan J. Arnold · 2023
Abstract The phenotypic effect of selection on multiple traits can be assessed by its effects on multivariate trait distributions. As in the case of a single trait, the fundamental approach is to compare the first and second central moments of trait distributions before and after selection. Such a multivariate comparison of moments represents a major statistical improvement over trait-by-trait comparisons. By taking a multivariate approach we may be able to identify which traits are the actual targets of selection. Analysis of selection in natural systems reveals that the effects of selection on actual targets are often obscured by correlations between traits. In addition to identifying targets of selection, multivariate analysis also gives us a way to quantify functional interactions between traits. Measuring the strength of such interactions is especially important because most traits belong to one or more functional complexes.
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Stevan J. Arnold · 2023
Abstract The G-matrix provides a useful way to model inheritance when multiple traits are affected by many genes and genetically coupled. The G-matrix is an m trait × m trait table with genetic variances on its main diagonal and genetic covariances elsewhere. The genetic covariance between two traits summarizes genetic connections arising from linkage disequilibrium and/or pleiotropy. Studies of multiple trait inheritance often reveal appreciable genetic correlations between traits, especially when those traits are size-related. The M-matrix summarizes the patterns of mutational effects on multiple traits. Just as covariances among relatives are the foundation for estimation of the G-matrix, the accumulation of mutations in inbred lines is the foundation for estimation of the M-matrix. Studies of G- and M-matrices suggest that these matrices have almost as many dimensions of variation as the number of characters included in the study. Consequently, these matrices are unlikely to constrain the course of evolution on long evolutionary timescales. The entire G-matrix, as well as its constituent genetic variances and covariances, can be visualized as achieving a stable balance between opposing forces. This stable equilibrium represents a compromise between alternative structures imposed by the processes of selection, mutation, recombination, and migration.
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Sanja Mikić, Ankica Kondić‐Špika, Ljiljana Brbaklić et al. · Chilean journal of agricultural research · 2016
Association analysis is a relatively novel approach in quantitative traits studies that allows high resolution mapping and time efficient and direct application on breeding material. Since the markers, which are close to the quantitative trait loci stable across environments and genetic backgrounds, may be valuable for marker assisted selection, we chose microsatellite markers previously linked to traits of interest in various mapping studies. A set of 36 microsatellite markers positioned near important maize (Zea mays L.) agronomic loci was used to evaluate genetic diversity and determine population structure. To verify the associations between the markers and traits, a panel of diverse maize inbred lines was genotyped with microsatellites and phenotyped for flowering time, yield and yield components. A relatively high level of polymorphism detected in number of alleles per locus (8.2), average polymorphic information content value (0.64), and average gene diversity (0.684) lines showed the analyzed panel of maize inbred contained significant genetic diversity and was suitable for association mapping. The population structure estimated by model-based clustering method grouped maize inbred lines into three clusters. The association analysis using the general linear and mixed linear models determined significant correlations between several agronomic traits and three microsatellites on chromosomes 3, 5, and 8, namely umc1025, bnlg1237, and bnlg162 consistent across the environments, explaining from 4.7% to 18.2% of total phenotypic variations. The results suggest that the chromosome regions containing quantitative trait loci (QTLs) associated with multiple yield-related traits consistently across environments are potentially important targets for selection.
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Maria De Marsico, Riccardo Distasi, Michele Nappi et al. · Studies in computational intelligence · 2010
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Zhenchuan Wang · 2018
This dissertation includes three papers with each distributed in one chapter. In chapter 1, we proposed an Adaptive Weighting Reverse Regression (AWRR) method to test association between multiple traits and rare variants in a genomic region. AWRR is robust to the directions of effects of causal variants and is also robust to the directions of association of traits. Using extensive simulation studies, we compared the performance of AWRR with canonical correlation analysis (CCA), Single-TOW, and the Weighted Sum Reverse Regression (WSRR). Our results showed that, in all of the simulation scenarios, AWRR is consistently more powerful than CCA. In most scenarios, AWRR is more powerful than Single-TOW and WSRR. In chapter 2, we proposed an “optimal” maximum heritability test (MHT-O) to test the association between multiple traits and a single variant. MHT-O includes a procedure of deleting traits that have weak or no association with the variant. Using extensive simulation studies, we compared the performance of MHT-O with MHT, Trait-based Association Test uses Extended Simes procedure (TATES), SUM_SCORE and MANOVA. Our results showed that, in all of the simulation scenarios, MHT-O is either the most powerful test or comparable to the most powerful test among the five tests we compared. In chapter 3, we developed a statistical method by testing an optimally weighted combination of variants with multiple traits (TOWmuT) to test the association between multiple traits and a weighted combination of variants (rare and/or common) in a genomic region. TOWmuT is robust to the directions of effects of causal variants and is applicable to different types of traits. Using extensive simulation studies, we compared the performance of TOWmuT with the following five existing methods: gene association with multiple traits (GAMuT), multiple sequence kernel association test (MSKAT), adaptive weighting reverse regression (AWRR), single-TOW, and MANOVA. Our results showed that, in all of the simulation scenarios, TOWmuT has correct type I error rates and is consistently more powerful than the other five tests. We also illustrated the usefulness of TOWmuT by analyzing a whole-genome genotyping data from a lung function study.
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Shizhong Xu · 2022
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Suzanne J. Rowe (496302), Amy Rowlatt (496303), Gail Davies (107670) et al. · Figshare · 2015
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Stevan J. Arnold · 2023
Abstract Drift of the multivariate mean provides an important baseline against which we can gauge the effects of multivariate selection. Multivariate drift is a function of elapsed time, effective population size, and the G-matrix. In the two-trait case at any given time, we can visualize the trait means of replicate populations as a cloud of points in bivariate trait space. Although each mean takes an erratic path through trait space as time unfolds, the statistical behaviour of the cloud is highly predictable. The dispersion cloud retains its shape and orientation, as it gradually expands in size from generation to generation. Moreover, the cloud shares its characteristic shape and orientation with the G-matrix. Tests of these predictions in natural populations reject drift as an explanation for trait radiation. In particular, the observed dispersion cloud is smaller, sometimes much smaller than expected by neutral drift of the trait means. The need for models that include selection as well as drift is also suggested by the empirical result that the major axis of the dispersion cloud can be aligned with the major axes of inheritance and/or selection.
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Hye K. Pae · Educational Research and Evaluation · 2012
Multiple traits of language proficiency as well as test method effects were concurrently analyzed to investigate interrelations of construct validity, convergent validity, and discriminant validity using multitrait-multimethod (MTMM) matrices. A total of 585 test takers' scores were derived from the field test of the Pearson Test of English Academic. An MTMM confirmatory factor analysis model was parameterized using 4 traits and 3 assessment methods. The 4 traits included listening, reading, speaking, and integrated skills, while the 3 methods included prescribed multiple-choice responses, constructed responses, and summarized responses. The trait factor loadings were systematically greater than those of methods, providing evidence that the indicators were strongly related to their latent constructs, after adjusting for the method effects. The results showed robust convergent validity, moderate discriminant validity, and insignificant method effects. Implications are discussed.
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Christoph Lippert, Franceso Paolo Casale, Barbara Rakitsch et al. · bioRxiv (Cold Spring Harbor Laboratory) · 2014
Abstract Multi-trait mixed models have emerged as a promising approach for joint analyses of multiple traits. In principle, the mixed model framework is remarkably general. However, current methods implement only a very specific range of tasks to optimize the necessary computations. Here, we present a multi-trait modeling framework that is versatile and fast: LIMIX enables to flexibly adapt mixed models for a broad range of applications with different observed and hidden covariates, and variable study designs. To highlight the novel modeling aspects of LIMIX we performed three vastly different genetic studies: joint GWAS of correlated blood lipid phenotypes, joint analysis of the expression levels of the multiple transcript-isoforms of a gene, and pathway-based modeling of molecular traits across environments. In these applications we show that LIMIX increases GWAS power and phenotype prediction accuracy, in particular when integrating stepwise multi-locus regression into multi-trait models, and when analyzing large numbers of traits. An open source implementation of LIMIX is freely available at: https://github.com/PMBio/limix .
Cited by 132Open access
Stevan J. Arnold · 2023
Abstract In the short term, the response of multiple traits to directional selection is a function of the G-matrix and the vector of selection gradients, β. Directional selection on a particular trait is expected to change the mean of that trait, but selection may also induce responses in genetically correlated traits. This phenomenon is familiar to plant and animal breeders, who counteract the undesirable correlated responses to selection by selecting on a special linear combination of traits. In the common case in which natural selection alone acts on the multivariate phenotype, the initial response may be biased towards directions with abundant genetic variation. On longer time scales, evolution may be temporarily constrained for certain kinds of traits, especially those that represent trait combinations with low mutation rates and little standing genetic variation. For most traits, however, evolution in the long term is not constrained by genetic variation. Calculations of minimum selective mortality indicate that only a small amount of directional selection each generation is required to account for even appreciable trait change that is observed in the fossil record.
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Sara J. Larsson (380822), Alexander E. Lipka (102478), Edward S. Buckler (14329) · Figshare · 2015
<p>No clear pattern can be observed between correlation between traits and its association to the 6 bp and 18 bp deletions in <i>d8</i>.</p>
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Christoph Lange, John C. Whittaker, M. C. Denham · Annals of Human Genetics · 1999
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Gil, D., Gahr, M. · Max Planck Digital Library · 2002
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T. Mark, P G Sullivan · Journal of Dairy Science · 2006
International genetic bull evaluations of somatic cell counts (SCC) from 8 different Holstein populations and clinical mastitis from 3 of these populations were inferred simultaneously using a multiple-trait-multiple-country evaluation (MT-MACE) model. This model considered effective independent weighting factors and multivariately deregressed national genetic evaluations for countries with multiple-trait national models. Predictions of genetic merit from MT-MACE and their reliabilities were compared with the corresponding results from 2 separate single-trait-multiple-country evaluations (ST-MACE) for different groups of bulls. The assumed heritabilities for clinical mastitis (h(2) = 0.02 to 0.05) were substantially lower than the heritabilities for SCC (h(2) = 0.08 to 0.27). The predictive ability of MT-MACE was essentially equal to or better than the predictive ability of ST-MACE for all country-trait combinations, but both methods yielded effectively unbiased and consistent consecutive predictions (correlation > 0.93). Both sets of predictions also agreed well with future national genetic evaluations for bulls receiving additional daughter information (correlation > 0.96), except for evaluations for which within-country correlations were utilized internationally, but not nationally (correlation = 0.86 to 0.97). The reliabilities for MT-MACE were essentially equal to or higher than reliabilities for ST-MACE, depending on the trait and group of bulls in question. Reliabilities increased most for young bulls, and for clinical mastitis in countries that did not use the within-country correlations with SCC in the national evaluation (up to a 23% increase in average reliability).
Cited by 23Open access
Sueme Ueno · LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) · 2017
Caracteres quantitativos possuem herança complexa, que envolvem efeitos epistáticos, pleiotrópicos e interação com ambientes. Em razão da importância desses caracteres para o melhoramento genético, diversos estudos sobre sua natureza genética e herança têm sido conduzidos. Nesse contexto, o mapeamento de QTL é uma ferramenta útil, que permite mapear e estimar os efeitos dos locos que controlam os caracteres quantitativos além de obter outras importantes informações, como a ocorrência de QTL pleiotrópicos e interações QTL x ambientes. Os objetivos do presente trabalho foram mapear QTL e obter informações sobre a interação QTL x ambientes, QTL pleiotrópicos e herança de diversos caracteres de importância agronômica em uma população de milho tropical. Foram utilizadas 250 progênies F2:3 retrocruzadas para ambos os genitores conforme proposto no delineamento III, totalizando 500 progênies, as quais foram avaliadas em até seis ambientes. Para o mapeamento de QTL foi empregado o mapeamento por intervalo composto expandido para múltiplos ambientes ou caracteres (mCIM), considerando um mapa genético com 177 marcadores microssatélite. Os caracteres analisados foram produção de grãos (PG), prolificidade (PROL), peso de 500 grãos (P500), número de fileiras da espiga (NF) e de grãos por fileira (NGF), altura de planta (AP) e espiga (AE), dias para o florescimento feminino (FF) e masculino (FM), número de ramificações do pendão (RP) e stay green (SG). Os resultados das análises do delineamento III indicaram sobredominância para o caráter PG, dominância completa para NGF e dominância parcial para os demais caracteres. Estimativas elevadas de correlações genéticas foram obtidas entre os caracteres PG, PROL, NGF, FF, FM, AP e AE, sugerindo ocorrência de pleiotropia entre tais caracteres. No mapeamento considerando múltiplos ambientes foram mapeados 260 QTL para os onze caracteres analisados, distribuídos por todos os cromossomos do milho. O grau médio de dominância dos QTL foi de sobredominância para PG e AP, e dominância completa ou parcial para os demais caracteres. Devido ao desequilíbrio de ligação nesta população e ao modelo de mapeamento empregado, as estimativas que indicaram sobredominância foram, provavelmente, superestimadas. Para os caracteres PG, NF, NGF, P500, AE e SG, a maioria dos QTL mapeados interagiu significativamente com ambientes, indicando que experimentos conduzidos em vários locais e anos são necessários para identificar genótipos e QTL estáveis. Esses resultados sugerem que devido à elevada interação QTL x ambientes dos caracteres avaliados, os programas de melhoramento e a utilização de seleção assistida por marcadores (SAM) devem ser direcionados para ambientes específicos. No mapeamento de múltiplos caracteres foram identificados 43 QTL com efeitos significativos para dois ou mais caracteres analisados, distribuídos em todos os cromossomos do milho. A quantidade de QTL pleiotrópicos para combinações entre pares de caracteres não foi consistente com as magnitudes das correlações observadas. Em geral, para cada caráter, os QTL pleiotrópicos apresentaram magnitudes e graus de dominância distintos. Portanto, embora diversos QTL pleiotrópicos tenham sido mapeados, suas magnitudes e efeitos distintos para cada caráter indicaram grande complexidade da natureza genética das correlações, constituindo-se em um desafio para uso das informações desses QTL na SAM visando o melhoramento de múltiplos caracteres.
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R. W. Doerge, Jun Xie, Riyan Cheng · 2007
Usually, multiple traits are measured on individuals in a quantitative trait locus (QTL) mapping experiment. These traits are typically analyzed separately. Currently, there is great interest in analyzing multiple traits simultaneously (multiple-trait QTL mapping) since more statistical power of QTL detection can be gained by taking advantage of the structure of the residual covariance of the traits. This work studies various multiple-trait QTL mapping methods, including the multiple-trait single-marker approach, the multiple-trait multiple-marker regression approach, the seemingly unrelated regression equations (SURE) approach, and the multiple-trait composite multiple-interval mapping (MTCMIM) approach. While the SURE model has been widely applied in Econometrics and other fields, it has received little attention in QTL mapping applications. By allowing different sets of QTL for different traits, the SURE model provides flexibility for the analysis of multiple traits and multiple QTL. Specific to the MTCMIM model, multiple traits and multiple QTL can be analyzed simultaneously while carefully selected markers are used to control background genetic variation. As an application, these methods are applied to gene expression traits (etraits) in Arabidopsis thaliana gained from Affymetrix microarray technology.
Cited by 1
Jeremy J. Berg, Xinjun Zhang, Graham Coop · bioRxiv (Cold Spring Harbor Laboratory) · 2017
Abstract Our understanding of the genetic basis of human adaptation is biased toward loci of large pheno-typic effect. Genome wide association studies (GWAS) now enable the study of genetic adaptation in polygenic phenotypes. We test for polygenic adaptation among 187 world-wide human populations using polygenic scores constructed from GWAS of 34 complex traits. We identify signals of polygenic adaptation for anthropometric traits including height, infant head circumference (IHC), hip circumference and waist-to-hip ratio (WHR). Analysis of ancient DNA samples indicates that a north-south cline of height within Europe and and a west-east cline across Eurasia can be traced to selection for increased height in two late Pleistocene hunter gatherer populations living in western and west-central Eurasia. Our observation that IHC and WHR follow a latitudinal cline in Western Eurasia support the role of natural selection driving Bergmann’s Rule in humans, consistent with thermoregulatory adaptation in response to latitudinal temperature variation. Author’s Note on Failure to Replicate After this preprint was posted, the UK Biobank dataset was released, providing a new and open GWAS resource. When attempting to replicate the height selection results from this preprint using GWAS data from the UK Biobank, we discovered that we could not. In subsequent analyses, we determined that both the GIANT consortium height GWAS data, as well as another dataset that was used for replication, were impacted by stratification issues that created or at a minimum substantially inflated the height selection signals reported here. The results of this second investigation, written together with additional coauthors, have now been published ( https://elifesciences.org/articles/39725 along with another paper by a separate group of authors, showing similar issues https://elifesciences.org/articles/39702 ). A preliminary investigation shows that the other non-height based results may suffer from similar issues. We stand by the theory and statistical methods reported in this paper, and the paper can be cited for these results. However, we have shown that the data on which the major empirical results were based are not sound, and so should be treated with caution until replicated.
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Keira J. A. Johnston (6836690), Mark J. Adams (2954100), Barbara I. Nicholl (489582) et al. · Figshare · 2019
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Cheng, Riyan · Purdue e-Pubs (Purdue University System) · 2007
Usually, multiple traits are measured on individuals in a quantitative trait locus (QTL) mapping experiment. These traits are typically analyzed separately. Currently, there is great interest in analyzing multiple traits simultaneously (multiple-trait QTL mapping) since more statistical power of QTL detection can be gained by taking advantage of the structure of the residual covariance of the traits. This work studies various multiple-trait QTL mapping methods, including the multiple-trait single-marker approach, the multiple-trait multiple-marker regression approach, the seemingly unrelated regression equations (SURE) approach, and the multiple-trait composite multiple-interval mapping (MTCMIM) approach. While the SURE model has been widely applied in Econometrics and other fields, it has received little attention in QTL mapping applications. By allowing different sets of QTL for different traits, the SURE model provides flexibility for the analysis of multiple traits and multiple QTL. Specific to the MTCMIM model, multiple traits and multiple QTL can be analyzed simultaneously while carefully selected markers are used to control background genetic variation. As an application, these methods are applied to gene expression traits (etraits) in Arabidopsis thaliana gained from Affymetrix microarray technology.
Cited by 0