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Mark W Blows - One of the best experts on this subject based on the ideXlab platform.
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heritable micro environmental variance covaries with fitness in an outbred population of drosophila serrata
Genetics, 2017Co-Authors: Jacqueline L Sztepanacz, Katrina Mcguigan, Mark W BlowsAbstract:The Genetic basis of stochastic variation within a defined environment, and the consequences of such micro-environmental variance for fitness are poorly understood . Using a multigenerational breeding design in Drosophila serrata, we demonstrated that the micro-environmental variance in a set of morphological wing traits in a randomly mating population had significant additive Genetic variance in most single wing traits. Although heritability was generally low (<1%), coefficients of additive Genetic variance were of a magnitude typical of other morphological traits, indicating that the micro-environmental variance is an evolvable trait. Multivariate analyses demonstrated that the micro-environmental variance in wings was Genetically correlated among single traits, indicating that common mechanisms of environmental buffering exist for this functionally related set of traits. In addition, through the dominance Genetic Covariance between the major axes of micro-environmental variance and fitness, we demonstrated that micro-environmental variance shares a Genetic basis with fitness, and that the pattern of selection is suggestive of variance-reducing selection acting on micro-environmental variance.
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accounting for sampling error in Genetic eigenvalues using random matrix theory
Genetics, 2017Co-Authors: Jacqueline L Sztepanacz, Mark W BlowsAbstract:The distribution of Genetic variance in multivariate phenotypes is characterized by the empirical spectral distribution of the eigenvalues of the Genetic Covariance matrix. Empirical estimates of Genetic eigenvalues from random effects linear models are known to be overdispersed by sampling error, where large eigenvalues are biased upward, and small eigenvalues are biased downward. The overdispersion of the leading eigenvalues of sample Covariance matrices have been demonstrated to conform to the Tracy-Widom (TW) distribution. Here we show that Genetic eigenvalues estimated using restricted maximum likelihood (REML) in a multivariate random effects model with an unconstrained Genetic Covariance structure will also conform to the TW distribution after empirical scaling and centering. However, where estimation procedures using either REML or MCMC impose boundary constraints, the resulting Genetic eigenvalues tend not be TW distributed. We show how using confidence intervals from sampling distributions of Genetic eigenvalues without reference to the TW distribution is insufficient protection against mistaking sampling error as Genetic variance, particularly when eigenvalues are small. By scaling such sampling distributions to the appropriate TW distribution, the critical value of the TW statistic can be used to determine if the magnitude of a Genetic eigenvalue exceeds the sampling error for each eigenvalue in the spectral distribution of a given Genetic Covariance matrix.
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The Genetic Covariance between life cycle stages separated by metamorphosis
Proceedings of The Royal Society B: Biological Sciences, 2014Co-Authors: J. David Aguirre, Mark W Blows, Dustin J. MarshallAbstract:Metamorphosis is common in animals, yet the Genetic associations between life cycle stages are poorly understood. Given the radical changes that occur at metamorphosis, selection may differ before and after metamorphosis, and the extent that Genetic associations between pre- and post-metamorphic traits constrain evolutionary change is a subject of considerable interest. In some instances, metamorphosis may allow the Genetic decoupling of life cycle stages, whereas in others, metamorphosis could allow complementary responses to selection across the life cycle. Using a diallel breeding design, we measured viability at four ontoGenetic stages (embryo, larval, juvenile and adult viability), in the ascidian Ciona intestinalis and examined the orientation of additive Genetic variation with respect to the metamorphic boundary. We found support for one eigenvector of G (gobsmax), which contrasted larval viability against embryo viability and juvenile viability. Target matrix rotation confirmed that while gobsmax shows Genetic associations can extend beyond metamorphosis, there is still considerable scope for decoupled phenotypic evolution. Therefore, although Genetic associations across metamorphosis could limit that range of phenotypes that are attainable, traits on either side of the metamorphic boundary are capable of some independent evolutionary change in response to the divergent conditions encountered during each life cycle stage.
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the contribution of selection and Genetic constraints to phenotypic divergence
The American Naturalist, 2010Co-Authors: Stephen F Chenoweth, Howard D Rundle, Mark W BlowsAbstract:Abstract: Although divergent natural selection is common in nature, the extent to which Genetic constraints bias evolutionary trajectories in its presence remains largely unknown. Here we develop a general framework to integrate estimates of divergent selection and Genetic constraints to estimate their contributions to phenotypic divergence among natural populations. We apply these methods to estimates of phenotypic selection and Genetic Covariance from sexually selected traits that have undergone adaptive divergence among nine natural populations of the fly Drosophila serrata. Despite ongoing sexual selection within populations, differences in its direction among them, and Genetic variance for all traits in all populations, divergent sexual selection only weakly resembled the observed pattern of divergence. Accounting for the influence of Genetic Covariance among the traits significantly improved the alignment between observed and predicted divergence. Our results suggest that the direction in which sexu...
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characterizing the evolution of Genetic variance using Genetic Covariance tensors
Philosophical Transactions of the Royal Society B, 2009Co-Authors: Emma Hine, Stephen F Chenoweth, Howard D Rundle, Mark W BlowsAbstract:Determining how Genetic variance changes under selection in natural populations has proved to be a very resilient problem in evolutionary Genetics. In the same way that understanding the availability of Genetic variance within populations requires the simultaneous consideration of Genetic variance in sets of functionally related traits, determining how Genetic variance changes under selection in natural populations will require ascertaining how Genetic variance–Covariance ( G ) matrices evolve. Here, we develop a geometric framework using higher-order tensors, which enables the empirical characterization of how G matrices have diverged among populations. We then show how divergence among populations in Genetic Covariance structure can then be associated with divergence in selection acting on those traits using key equations from evolutionary theory. Using estimates of G matrices of eight male sexually selected traits from nine geographical populations of Drosophila serrata , we show that much of the divergence in Genetic variance occurred in a single trait combination, a conclusion that could not have been reached by examining variation among the individual elements of the nine G matrices. Divergence in G was primarily in the direction of the major axes of Genetic variance within populations, suggesting that Genetic drift may be a major cause of divergence in Genetic variance among these populations.
K Meyer - One of the best experts on this subject based on the ideXlab platform.
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estimating sampling error of evolutionary statistics based on Genetic Covariance matrices using maximum likelihood
Journal of Evolutionary Biology, 2015Co-Authors: David Houle, K MeyerAbstract:We explore the estimation of uncertainty in evolutionary parameters using a recently devised approach for resampling entire additive Genetic variance-Covariance matrices (G). Large-sample theory shows that maximum-likelihood estimates (including restricted maximum likelihood, REML) asymptotically have a multivariate normal distribution, with Covariance matrix derived from the inverse of the information matrix, and mean equal to the estimated G. This suggests that sampling estimates of G from this distribution can be used to assess the variability of estimates of G, and of functions of G. We refer to this as the REML-MVN method. This has been implemented in the mixed-model program WOMBAT. Estimates of sampling variances from REML-MVN were compared to those from the parametric bootstrap and from a Bayesian Markov chain Monte Carlo (MCMC) approach (implemented in the R package MCMCglmm). We apply each approach to evolvability statistics previously estimated for a large, 20-dimensional data set for Drosophila wings. REML-MVN and MCMC sampling variances are close to those estimated with the parametric bootstrap. Both slightly underestimate the error in the best-estimated aspects of the G matrix. REML analysis supports the previous conclusion that the G matrix for this population is full rank. REML-MVN is computationally very efficient, making it an attractive alternative to both data resampling and MCMC approaches to assessing confidence in parameters of evolutionary interest.
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sampling based approximation of confidence intervals for functions of Genetic Covariance matrices
Proceedings of the Twentieth Conference of the Association for the Advancement of Animal Breeding and Genetics Translating Science into Action Napier , 2013Co-Authors: K Meyer, David HouleAbstract:Approximate lower bound sampling errors of maximum likelihood estimates of Covariance components and their linear functions can be obtained from the inverse of the information matrix. For non-linear functions, sampling variances are commonly determined as the variance of their first order Taylor series expansions. This is used to obtain sampling errors for estimates of heritabilities and correlations, and these quantities can be computed with most software performing such analyses. In other instances, however, more complicated functions are of interest or the linear approximation is difficult or inadequate. A pragmatic alternative then is to evaluate sampling characteristics by repeated sampling of parameters from their asymptotic, multivariate normal distribution, calculating the function(s) of interest for each sample and inspecting the distribution across replicates. This paper demonstrates the use of this approach and examines the quality of approximation obtained.
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better estimates of Genetic Covariance matrices by bending using penalized maximum likelihood
Genetics, 2010Co-Authors: K Meyer, Mark KirkpatrickAbstract:Obtaining accurate estimates of the Genetic Covariance matrix \(\mathbf{{\Sigma}}_{\mathrm{G}}\) for multivariate data is a fundamental task in quantitative Genetics and important for both evolutionary biologists and plant or animal breeders. Classical methods for estimating \(\mathbf{{\Sigma}}_{\mathrm{G}}\) are well known to suffer from substantial sampling errors; importantly, its leading eigenvalues are systematically overestimated. This article proposes a framework that exploits information in the phenotypic Covariance matrix \(\mathbf{{\Sigma}}_{\mathrm{P}}\) in a new way to obtain more accurate estimates of \(\mathbf{{\Sigma}}_{\mathrm{G}}\) . The approach focuses on the “canonical heritabilities” (the eigenvalues of \(\mathbf{{\Sigma}}_{\mathrm{P}}^{{-}1}\mathbf{{\Sigma}}_{\mathrm{G}}\) ), which may be estimated with more precision than those of \(\mathbf{{\Sigma}}_{\mathrm{G}}\) because \(\mathbf{{\Sigma}}_{\mathrm{P}}\) is estimated more accurately. Our method uses penalized maximum likelihood and shrinkage to reduce bias in estimates of the canonical heritabilities. This in turn can be exploited to get substantial reductions in bias for estimates of the eigenvalues of \(\mathbf{{\Sigma}}_{\mathrm{G}}\) and a reduction in sampling errors for estimates of \(\mathbf{{\Sigma}}_{\mathrm{G}}\) . Simulations show that improvements are greatest when sample sizes are small and the canonical heritabilities are closely spaced. An application to data from beef cattle demonstrates the efficacy this approach and the effect on estimates of heritabilities and correlations. Penalized estimation is recommended for multivariate analyses involving more than a few traits or problems with limited data.
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perils of parsimony properties of reduced rank estimates of Genetic Covariance matrices
Genetics, 2008Co-Authors: K Meyer, Mark KirkpatrickAbstract:Eigenvalues and eigenvectors of Covariance matrices are important statistics for multivariate problems in many applications, including quantitative Genetics. Estimates of these quantities are subject to different types of bias. This article reviews and extends the existing theory on these biases, considering a balanced one-way classification and restricted maximum-likelihood estimation. Biases are due to the spread of sample roots and arise from ignoring selected principal components when imposing constraints on the parameter space, to ensure positive semidefinite estimates or to estimate Covariance matrices of chosen, reduced rank. In addition, it is shown that reduced-rank estimators that consider only the leading eigenvalues and -vectors of the “between-group” Covariance matrix may be biased due to selecting the wrong subset of principal components. In a Genetic context, with groups representing families, this bias is inverse proportional to the degree of Genetic relationship among family members, but is independent of sample size. Theoretical results are supplemented by a simulation study, demonstrating close agreement between predicted and observed bias for large samples. It is emphasized that the rank of the Genetic Covariance matrix should be chosen sufficiently large to accommodate all important Genetic principal components, even though, paradoxically, this may require including a number of components with negligible eigenvalues. A strategy for rank selection in practical analyses is outlined.
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multivariate analyses of carcass traits for angus cattle fitting reduced rank and factor analytic models
Journal of Animal Breeding and Genetics, 2007Co-Authors: K MeyerAbstract:Summary Multivariate analyses of carcass traits for Angus cattle, consisting of six traits recorded on the carcass and eight auxiliary traits measured by ultrasound scanning of live animals, are reported. Analyses were carried out by restricted maximum likelihood, fitting a number of reduced rank and factor analytic models for the Genetic Covariance matrix. Estimates of eigenvalues and eigenvectors for different orders of fit are contrasted and implications for the estimates of Genetic variances and correlations are examined. Results indicate that at most eight principal components (PCs) are required to model the Genetic Covariance structure among the 14 traits. Selection index calculations suggest that the first seven of these PCs are sufficient to obtain estimates of breeding values for the carcass traits without loss in the expected accuracy of evaluation. This implied that the number of effects fitted in Genetic evaluation for carcass traits can be halved by estimating breeding values for the leading PCs directly.
Mark Kirkpatrick - One of the best experts on this subject based on the ideXlab platform.
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better estimates of Genetic Covariance matrices by bending using penalized maximum likelihood
Genetics, 2010Co-Authors: K Meyer, Mark KirkpatrickAbstract:Obtaining accurate estimates of the Genetic Covariance matrix \(\mathbf{{\Sigma}}_{\mathrm{G}}\) for multivariate data is a fundamental task in quantitative Genetics and important for both evolutionary biologists and plant or animal breeders. Classical methods for estimating \(\mathbf{{\Sigma}}_{\mathrm{G}}\) are well known to suffer from substantial sampling errors; importantly, its leading eigenvalues are systematically overestimated. This article proposes a framework that exploits information in the phenotypic Covariance matrix \(\mathbf{{\Sigma}}_{\mathrm{P}}\) in a new way to obtain more accurate estimates of \(\mathbf{{\Sigma}}_{\mathrm{G}}\) . The approach focuses on the “canonical heritabilities” (the eigenvalues of \(\mathbf{{\Sigma}}_{\mathrm{P}}^{{-}1}\mathbf{{\Sigma}}_{\mathrm{G}}\) ), which may be estimated with more precision than those of \(\mathbf{{\Sigma}}_{\mathrm{G}}\) because \(\mathbf{{\Sigma}}_{\mathrm{P}}\) is estimated more accurately. Our method uses penalized maximum likelihood and shrinkage to reduce bias in estimates of the canonical heritabilities. This in turn can be exploited to get substantial reductions in bias for estimates of the eigenvalues of \(\mathbf{{\Sigma}}_{\mathrm{G}}\) and a reduction in sampling errors for estimates of \(\mathbf{{\Sigma}}_{\mathrm{G}}\) . Simulations show that improvements are greatest when sample sizes are small and the canonical heritabilities are closely spaced. An application to data from beef cattle demonstrates the efficacy this approach and the effect on estimates of heritabilities and correlations. Penalized estimation is recommended for multivariate analyses involving more than a few traits or problems with limited data.
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perils of parsimony properties of reduced rank estimates of Genetic Covariance matrices
Genetics, 2008Co-Authors: K Meyer, Mark KirkpatrickAbstract:Eigenvalues and eigenvectors of Covariance matrices are important statistics for multivariate problems in many applications, including quantitative Genetics. Estimates of these quantities are subject to different types of bias. This article reviews and extends the existing theory on these biases, considering a balanced one-way classification and restricted maximum-likelihood estimation. Biases are due to the spread of sample roots and arise from ignoring selected principal components when imposing constraints on the parameter space, to ensure positive semidefinite estimates or to estimate Covariance matrices of chosen, reduced rank. In addition, it is shown that reduced-rank estimators that consider only the leading eigenvalues and -vectors of the “between-group” Covariance matrix may be biased due to selecting the wrong subset of principal components. In a Genetic context, with groups representing families, this bias is inverse proportional to the degree of Genetic relationship among family members, but is independent of sample size. Theoretical results are supplemented by a simulation study, demonstrating close agreement between predicted and observed bias for large samples. It is emphasized that the rank of the Genetic Covariance matrix should be chosen sufficiently large to accommodate all important Genetic principal components, even though, paradoxically, this may require including a number of components with negligible eigenvalues. A strategy for rank selection in practical analyses is outlined.
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migration and the Genetic Covariance between habitat preference and performance
The American Naturalist, 2006Co-Authors: Patrik Nosil, Bernard J Crespi, C P Sandoval, Mark KirkpatrickAbstract:Abstract: Studies of the Genetic Covariance between habitat preference and performance have reported conflicting outcomes ranging from no Covariance to strong Covariance. The causes of this variability remain unclear. Here we show that variation in the magnitude of Genetic Covariance can result from variability in migration regimes. Using data from walking stick insects and a mathematical model, we find that Genetic Covariance within populations between host plant preference and a trait affecting performance on different hosts (cryptic color pattern) varies in magnitude predictably among populations according to migration regimes. Specifically, Genetic Covariance within populations is high in heterogeneous habitats where migration between populations locally adapted to different host plants generates nonrandom associations (i.e., linkage disequilibrium) between alleles at color pattern and host preference loci. Conversely, Genetic Covariance is low in homogeneous habitats where a single host exists and mi...
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Restricted maximum likelihood estimation of Genetic principal components and smoothed Covariance matrices
Genetics Selection Evolution, 2005Co-Authors: Karin Meyer, Mark KirkpatrickAbstract:Principal component analysis is a widely used 'dimension reduction' technique, albeit generally at a phenotypic level. It is shown that we can estimate Genetic principal components directly through a simple reparameterisation of the usual linear, mixed model. This is applicable to any analysis fitting multiple, correlated Genetic effects, whether effects for individual traits or sets of random regression coefficients to model trajectories. Depending on the magnitude of Genetic correlation, a subset of the principal component generally suffices to capture the bulk of Genetic variation. Corresponding estimates of Genetic Covariance matrices are more parsimonious, have reduced rank and are smoothed, with the number of parameters required to model the dispersion structure reduced from $k(k+1)/2$ to $m(2k-m+1)/2$ for $k$ effects and $m$ principal components. Estimation of these parameters, the largest eigenvalues and pertaining eigenvectors of the Genetic Covariance matrix, via restricted maximum likelihood using derivatives of the likelihood, is described. It is shown that reduced rank estimation can reduce computational requirements of multivariate analyses substantially. An application to the analysis of eight traits recorded via live ultrasound scanning of beef cattle is given.
Karin Meyer - One of the best experts on this subject based on the ideXlab platform.
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WOMBAT A tool for mixed model analyses in quantitative Genetics by restricted maximum likelihood （REML）
Journal of Zhejiang University. Science. B, 2007Co-Authors: Karin MeyerAbstract:WOMBAT is a software package for quantitative Genetic analyses of continuous traits, fitting a linear, mixed model; estimates of Covariance components and the resulting Genetic parameters are obtained by restricted maximum likelihood. A wide range of models, comprising numerous traits, multiple fixed and random effects, selected Genetic Covariance structures, random regression models and reduced rank estimation are accommodated. WOMBAT employs up-to-date numerical and computational methods. Together with the use of efficient compilers, this generates fast executable programs, suitable for large scale analyses. Use of WOMBAT is illustrated for a bivariate analysis. The package consists of the executable program, available for LINUX and WINDOWS environments, manual and a set of worked example, and can be downloaded free of charge from http://agbu.une.edu.au/~kmeyer/wombat.html
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Restricted maximum likelihood estimation of Genetic principal components and smoothed Covariance matrices
Genetics Selection Evolution, 2005Co-Authors: Karin Meyer, Mark KirkpatrickAbstract:Principal component analysis is a widely used 'dimension reduction' technique, albeit generally at a phenotypic level. It is shown that we can estimate Genetic principal components directly through a simple reparameterisation of the usual linear, mixed model. This is applicable to any analysis fitting multiple, correlated Genetic effects, whether effects for individual traits or sets of random regression coefficients to model trajectories. Depending on the magnitude of Genetic correlation, a subset of the principal component generally suffices to capture the bulk of Genetic variation. Corresponding estimates of Genetic Covariance matrices are more parsimonious, have reduced rank and are smoothed, with the number of parameters required to model the dispersion structure reduced from $k(k+1)/2$ to $m(2k-m+1)/2$ for $k$ effects and $m$ principal components. Estimation of these parameters, the largest eigenvalues and pertaining eigenvectors of the Genetic Covariance matrix, via restricted maximum likelihood using derivatives of the likelihood, is described. It is shown that reduced rank estimation can reduce computational requirements of multivariate analyses substantially. An application to the analysis of eight traits recorded via live ultrasound scanning of beef cattle is given.
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Estimates of the complete Genetic Covariance matrix for traits in multi-trait Genetic evaluation of Australian Hereford cattle
Australian Journal of Agricultural Research, 2004Co-Authors: Karin Meyer, David Johnston, H. U. GraserAbstract:Estimates of Covariance components among all 22 traits considered in the current multi-trait Genetic evaluation of Australian Hereford cattle were obtained. Traits included 5 weight traits, 8 traits measured through live ultrasound scanning, 3 traits related to reproductive performance, and 6 carcass traits. Estimates were obtained by restricted maximum likelihood, carrying out a series of bivariate analyses. Data for each analysis were selected attempting to maximise the number of animals or animal-parent pairs that had both traits recorded. Estimates were pooled using a weighted 'iterative summing of expanded part matrices' procedure, which ensured positive semi-definite Covariance matrices. Models of analyses for individual traits closely resembled those used in Genetic evaluation. Results generally agreed with literature results, although estimates of Genetic parameters for carcass traits that had few records available tended to fluctuate. Except for 'days to calving', heritability estimates were moderate to high for all traits. Genetic parameters for early growth were different to those for other breeds, with maternal effects for weaning weight being considerably more important and the heritability somewhat lower. AR K. M eyer et al Hera
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Estimating Genetic Covariance functions assuming a parametric correlation structure for environmental effects
Genetics Selection Evolution, 2001Co-Authors: Karin MeyerAbstract:A random regression model for the analysis of "repeated" records in animal breeding is described which combines a random regression approach for additive Genetic and other random effects with the assumption of a parametric correlation structure for within animal Covariances. Both stationary and non-stationary correlation models involving a small number of parameters are considered. Heterogeneity in within animal variances is modelled through polynomial variance functions. Estimation of parameters describing the dispersion structure of such model by restricted maximum likelihood via an "average information" algorithm is outlined. An application to mature weight records of beef cow is given, and results are contrasted to those from analyses fitting sets of random regression coefficients for permanent environmental effects.
Axel Meyer - One of the best experts on this subject based on the ideXlab platform.
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The Integrated Genomic Architecture and Evolution of Dental Divergence in East African Cichlid Fishes (Haplochromis chilotes x H. nyererei).
G3&#58; Genes|Genomes|Genetics, 2017Co-Authors: C. Darrin Hulsey, Gonzalo Machado-schiaffino, Lara Keicher, Diego Ellis-soto, Frederico Henning, Axel MeyerAbstract:The independent evolution of the two toothed jaws of cichlid fishes is thought to have promoted their unparalleled ecological divergence and species richness. However, dental divergence in cichlids could exhibit substantial Genetic Covariance and this could dictate how traits like tooth numbers evolve in different African Lakes and on their two jaws. To test this hypothesis, we used a hybrid mapping cross of two trophically divergent Lake Victoria species (Haplochromis chilotes × Haplochromis nyererei) to examine genomic regions associated with cichlid tooth diversity. Surprisingly, a similar genomic region was found to be associated with oral jaw tooth numbers in cichlids from both Lake Malawi and Lake Victoria. Likewise, this same genomic location was associated with variation in pharyngeal jaw tooth numbers. Similar relationships between tooth numbers on the two jaws in both our Victoria hybrid population and across the phyloGenetic diversity of Malawi cichlids additionally suggests that tooth numbers on the two jaws of haplochromine cichlids might generally coevolve owing to shared Genetic underpinnings. Integrated, rather than independent, genomic architectures could be key to the incomparable evolutionary divergence and convergence in cichlid tooth numbers.