scholarly journals A robust new metric of phenotypic distance to estimate and compare multiple trait differences among populations

2012 ◽  
Vol 58 (3) ◽  
pp. 426-439 ◽  
Author(s):  
Rebecca Safran ◽  
Samuel Flaxman ◽  
Michael Kopp ◽  
Darren E. Irwin ◽  
Derek Briggs ◽  
...  
Keyword(s):  
Distance Measure ◽  
Cumulative Distribution ◽  
Phenotypic Trait ◽  
Sexually Dimorphic ◽  
Sample Sizes ◽  
Multiple Traits ◽  
Multiple Trait ◽  
Unequal Variances ◽  
Trait Divergence ◽  
Simultaneous Comparisons

Abstract Whereas a rich literature exists for estimating population genetic divergence, metrics of phenotypic trait divergence are lacking, particularly for comparing multiple traits among three or more populations. Here, we review and analyze via simulation Hedges’ g, a widely used parametric estimate of effect size. Our analyses indicate that g is sensitive to a combination of unequal trait variances and unequal sample sizes among populations and to changes in the scale of measurement. We then go on to derive and explain a new, non-parametric distance measure, “Δp”, which is calculated based upon a joint cumulative distribution function (CDF) from all populations under study. More precisely, distances are measured in terms of the percentiles in this CDF at which each population’s median lies. Δp combines many desirable features of other distance metrics into a single metric; namely, compared to other metrics, p is relatively insensitive to unequal variances and sample sizes among the populations sampled. Furthermore, a key feature of Δp—and our main motivation for developing it—is that it easily accommodates simultaneous comparisons of any number of traits across any number of populations. To exemplify its utility, we employ Δp to address a question related to the role of sexual selection in speciation: are sexual signals more divergent than ecological traits in closely related taxa? Using traits of known function in closely related populations, we show that traits predictive of reproductive performance are, indeed, more divergent and more sexually dimorphic than traits related to ecological adaptation.

Pairwise comparisons of means under realistic nonnormality, unequal variances, outliers and equal sample sizes

2011 ◽  
Vol 81 (2) ◽  
pp. 125-135 ◽  
Author(s):  
Philip H. Ramsey ◽  
Kyrstle Barrera ◽  
Pri Hachimine-Semprebom ◽  
Chang-Chia Liu
Keyword(s):  
Pairwise Comparisons ◽  
Sample Sizes ◽  
Unequal Variances

scholarly journals Optimal Reduction of Multivariate Dirac Mixture Densities

2015 ◽  
Vol 63 (4) ◽  
Author(s):  
Uwe D. Hanebeck
Keyword(s):  
Distance Measure ◽  
Cumulative Distribution ◽  
Control Methods ◽  
Continuous Domains ◽  
Estimation And Control ◽  
Von Mises ◽  
And Control ◽  
Optimal Reduction ◽  
Continuous Domain

AbstractThis paper is concerned with the optimal approximation of a given multivariate Dirac mixture, i.e., a density comprising weighted Dirac distributions on a continuous domain, by a Dirac mixture with a reduced number of components. The parameters of the approximating density are calculated by numerically minimizing a smooth distance measure, a generalization of the well-known Cramér–von Mises-Distance to the multivariate case. This generalization is achieved by defining an alternative to the classical cumulative distribution, the Localized Cumulative Distribution (LCD), as a smooth characterization of discrete random quantities (on continuous domains). The resulting approximation method provides the basis for various efficient nonlinear estimation and control methods.

scholarly journals Bayesian mixture structural equation modelling in multiple-trait QTL mapping

2010 ◽  
Vol 92 (3) ◽  
pp. 239-250 ◽  
Author(s):  
XIAOJUAN MI ◽  
KENT ESKRIDGE ◽  
DONG WANG ◽  
P. STEPHEN BAENZIGER ◽  
B. TODD CAMPBELL ◽  
...  
Keyword(s):  
Qtl Mapping ◽  
Structural Equation ◽  
Statistical Power ◽  
Bayes Factor ◽  
Causal Structure ◽  
Mapping Method ◽  
Parameter Estimates ◽  
Detection Accuracy ◽  
Multiple Traits ◽  
Multiple Trait

SummaryQuantitative trait loci (QTLs) mapping often results in data on a number of traits that have well-established causal relationships. Many multi-trait QTL mapping methods that account for correlation among the multiple traits have been developed to improve the statistical power and the precision of QTL parameter estimation. However, none of these methods are capable of incorporating the causal structure among the traits. Consequently, genetic functions of the QTL may not be fully understood. In this paper, we developed a Bayesian multiple QTL mapping method for causally related traits using a mixture structural equation model (SEM), which allows researchers to decompose QTL effects into direct, indirect and total effects. Parameters are estimated based on their marginal posterior distribution. The posterior distributions of parameters are estimated using Markov Chain Monte Carlo methods such as the Gibbs sampler and the Metropolis–Hasting algorithm. The number of QTLs affecting traits is determined by the Bayes factor. The performance of the proposed method is evaluated by simulation study and applied to data from a wheat experiment. Compared with single trait Bayesian analysis, our proposed method not only improved the statistical power of QTL detection, accuracy and precision of parameter estimates but also provided important insight into how genes regulate traits directly and indirectly by fitting a more biologically sensible model.

Type I Error Rates for Welch’s Test and James’s Second-Order Test Under Nonnormality and Inequality of Variance When There Are Two Groups

1994 ◽  
Vol 19 (3) ◽  
pp. 275-291 ◽  
Author(s):  
James Algina ◽  
T. C. Oshima ◽  
Wen-Ying Lin
Keyword(s):  
Degrees Of Freedom ◽  
Type I Error ◽  
Total Sample ◽  
Error Rates ◽  
Second Order ◽  
T Test ◽  
Type I ◽  
Sample Sizes ◽  
Unequal Variances ◽  
Type I Error Rates

Type I error rates were estimated for three tests that compare means by using data from two independent samples: the independent samples t test, Welch’s approximate degrees of freedom test, and James’s second-order test. Type I error rates were estimated for skewed distributions, equal and unequal variances, equal and unequal sample sizes, and a range of total sample sizes. Welch’s test and James’s test have very similar Type I error rates and tend to control the Type I error rate as well or better than the independent samples t test does. The results provide guidance about the total sample sizes required for controlling Type I error rates.

scholarly journals Detecting mosaic patterns in macroevolutionary disparity

2018 ◽  
Author(s):  
Caroline Parins-Fukuchi
Keyword(s):  
Evolutionary Dynamics ◽  
Distinct Pattern ◽  
The Body ◽  
Phenotypic Trait ◽  
Multiple Traits ◽  
Mosaic Pattern ◽  
Phenotypic Data ◽  
Evolutionary Patterns ◽  
Multidimensional Datasets ◽  
Evolutionary Distinctiveness

ABSTRACTEvolutionary biologists have long sought to understand the full complexity in pattern and process that shapes organismal diversity. Although phylogenetic comparative methods are often used to reconstruct complex evolutionary dynamics, they are typically limited to a single phenotypic trait. Extensions that accommodate multiple traits lack the ability to partition multidimensional datasets into a set of mosaic suites of evolutionarily linked characters. I introduce a comparative framework that identifies heterogeneity in evolutionary patterns across large datasets of continuous traits. Using a model of continuous trait evolution based on the differential accumulation of disparity across lineages in a phylogeny, the approach algorithmically partitions traits into a set of character suites that best explains the data, where each suite displays a distinct pattern in phylogenetic morphological disparity. When applied to empirical data, the approach revealed a mosaic pattern predicted by developmental biology. The evolutionary distinctiveness of individual suites can be investigated in more detail, either by fitting conventional comparative models or by directly studying the phylogenetic patterns in disparity recovered during the analysis. This framework can supplement existing comparative approaches by inferring the complex, integrated patterns that shape evolution across the body plan from disparate developmental, morphometric, and environmental sources of phenotypic data.

scholarly journals Test Gene-Environment Interactions for Multiple Traits in Sequencing Association Studies

2019 ◽  
Author(s):  
Jianjun Zhang ◽  
Qiuying Sha ◽  
Han Hao ◽  
Shuanglin Zhang ◽  
Xiaoyi Raymond Gao ◽  
...  
Keyword(s):  
Association Studies ◽  
Complex Diseases ◽  
Error Rates ◽  
Phenotypic Trait ◽  
Type I ◽  
Environment Interaction ◽  
Multiple Traits ◽  
Gene Environment ◽  
Variable Weight ◽  
Protective Variants

AbstractThe risk of many complex diseases is determined by a complex interplay of genetic and environmental factors. Data on multiple traits is often collected for many complex diseases in order to obtain a better understanding of the diseases. Examination of gene-environment interactions (GxEs) for multiple traits can yield valuable insights about the etiology of the disease and increase power in detecting disease associated genes. Most existing methods focus on testing gene-environment interaction (GxE) for a single trait. In this study, we develop novel approaches to test GxEs for multiple traits in sequencing association studies. We first perform transformation of multiple traits by using either principle component analysis or standardization analysis. Then, we detect the effect of GxE for each transferred phenotypic trait using novel proposed tests: testing the effect of an optimallyweighted combination of GxE (TOW-GE) and/or variable weight TOW-GE (VW-TOW-GE). Finally, we employ the Fisher’s combination test to combine the p-values of TOW-GE and/or VW-TOW-GE. Extensive simulation studies based on the Genetic Analysis Workshop 17 data show that the type I error rates of the proposed methods are well controlled. Compared to the existing interaction sequence kernel association test (ISKAT), TOW-GE is more powerful when there are only rare risk and protective variants; VW-TOW-GE is more powerful when there are both rare and common risk and protective variants. Both TOW-GE and VW-TOW-GE are robust to directions of effects of causal GxEs. Application to the COPDGene Study demonstrates that our proposed methods are very powerful.

Ontogeny of a sexual dimorphism in tiger salamanders

2009 ◽  
Vol 87 (7) ◽  
pp. 573-580 ◽  
Author(s):  
Richard D. Howard
Keyword(s):  
Sexual Dimorphism ◽  
Tail Length ◽  
Ambystoma Tigrinum ◽  
Sexually Dimorphic ◽  
Trait Divergence ◽  
Selection Gradients ◽  
Tiger Salamanders ◽  
Allometric Analysis ◽  
Insight Into ◽  
Static Allometry

Sexual dimorphism results when the sexes differ in the degree to which trait elaboration confers a reproductive or survival advantage. Trait size dimorphism is often reported in terms of allometry, typically using adults of varying ages (static allometry). A static allometric analysis of tail length in breeding tiger salamanders ( Ambystoma tigrinum (Green, 1825)) revealed that tail length is a positive allometric trait in both sexes, as well as a sexually dimorphic trait. Although static analyses are common in the literature, ontogenetic allometric analyses in which individuals are measured through time are preferred because they provide insight into the heterochronic process underlying trait divergence between the sexes and which sex is diverging from its earlier growth trajectory. I reared 91 individuals from the zygote stage to sexual maturity. An ontogenetic analysis revealed that tail length was isometric in larvae and young metamorphs of both sexes; however, tail length became allometric in males but not in females prior to sexual maturation. I also present static allometric analyses and show how conclusions differ from those of ontogenetic analyses. Lastly, I discuss how sex differences in selection gradients, as well as resource allocation costs, might influence differences between the sexes in the duration and rate of trait growth.

Is the ANOVA F-Test Robust to Variance Heterogeneity When Sample Sizes are Equal?: An Investigation via a Coefficient of Variation

1977 ◽  
Vol 14 (4) ◽  
pp. 493-498 ◽  
Author(s):  
Joanne C. Rogan ◽  
H. J. Keselman
Keyword(s):  
Type I Error ◽  
Type I ◽  
Variance Heterogeneity ◽  
Sample Sizes ◽  
F Test ◽  
Unequal Variances ◽  
Treatment Groups ◽  
Type 1 Error ◽  
Number Of Treatment

Numerous investigations have examined the effects of variance heterogeneity on the empirical probability of a Type I error for the analysis of variance (ANOVA) F-test and the prevailing conclusion has been that when sample sizes are equal, the ANOVA is robust to variance heterogeneity. However, Box (1954) reported a Type I error rate of .12, for a 5% nominal level, when unequal variances were paired with equal sample sizes. The present paper explored this finding, examining varying degrees and patterns of variance heterogeneity for varying sample sizes and number of treatment groups. The data indicate that the rate of Type 1 error varies as a function of the degree of variance heterogeneity and, consequently, it should not be assumed that the ANOVA F-test is always robust to variance heterogeneity when sample sizes are equal.

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