Estimating sampling error of evolutionary statistics based on genetic covariance matrices using maximum likelihood

@article{Houle2015EstimatingSE,
  title={Estimating sampling error of evolutionary statistics based on genetic covariance matrices using maximum likelihood},
  author={David Houle and Karin Meyer},
  journal={Journal of Evolutionary Biology},
  year={2015},
  volume={28}
}
  • D. Houle, K. Meyer
  • Published 1 August 2015
  • Mathematics
  • Journal of Evolutionary Biology
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… 
Accounting for Sampling Error in Genetic Eigenvalues Using Random Matrix Theory
TLDR
It is shown how using confidence intervals from sampling distributions of genetic eigenvalues without reference to the Tracy–Widom distribution is insufficient protection against mistaking sampling error as genetic variance, particularly when eigen values are small.
A note on simulating null distributions for G matrix comparisons
TLDR
The issue arises from the fact that the method as currently used generates null distributions of statistics pertaining to differences in G matrices across populations by simulating breeding value vectors based on GMatrices estimated from data, randomizing these vectors across populations, and then calculating null values of statistics from G matrix that are calculated directly from the variances and covariances among randomized vectors.
Performance of the No-U-Turn sampler in multi-trait variance component estimation using genomic data
Background Multi-trait genetic parameter estimation is an important topic for target traits with few records and with a low heritability and when the genetic correlation between target and secondary
Variance estimates are similar using pedigree or genomic relationships with or without the use of metafounders or the algorithm for proven and young animals1
TLDR
There was a tendency for higher additive genetic variances and lower permanent environmental variances estimated with A+1 compared with the three H−1 methods, which supports that G−1 is better than A−1 at separating genetic and permanent environmental components, due to a better definition of the actual relationships between animals.
EvolQG - An R package for evolutionary quantitative genetics
TLDR
ThevolQG package provides functions for calculation of relevant evolutionary statistics; estimation of sampling error; corrections for this error; matrix comparison via correlations, distances and matrix decomposition; analysis of modularity patterns; and functions for testing evolutionary hypotheses on taxa diversification.
EvolQG - An R package for evolutionary quantitative genetics.
TLDR
The EvolQG package provides functions for calculation of relevant evolutionary statistics; estimation of sampling error; corrections for this error; matrix comparison via correlations, distances and matrix decomposition; analysis of modularity patterns; and functions for testing evolutionary hypotheses on taxa diversification.
Causes of variability in estimates of mutational variance from mutation accumulation experiments
TLDR
Estimation error, expected to be relatively high due to the low differentiation among lines diverging solely through new mutation, is likely to contribute strongly to variability of estimates of mutational variance.
An assessment of the reliability of quantitative genetics estimates in study systems with high rate of extra-pair reproduction and low recruitment
TLDR
The authors' simulations revealed an important lack of precision in heritability and genetic-correlation estimates for most traits, a low power to detect significant effects and important identifiability problems, and the difficulties of generalizing quantitative genetic estimates reliably from one study system to another.
Can dominance genetic variance be ignored in evolutionary quantitative genetic analyses of wild populations?
  • B. Class, J. Brommer
  • Biology, Psychology
    Evolution; international journal of organic evolution
  • 2020
TLDR
It is found that dominance variance, when estimable, does not statistically differ from zero and represents a modest amount of genetic variance, and the importance of proper model construction for accurately estimating evolutionary potential is highlighted.
Fly wing evolutionary rate is a near-isometric function of mutational variation
TLDR
Simulations and reanalyses of the Drosophilid data set using the Q method suggests that the original estimates of the scaling relationship were close to the true value, and proposes an analytical version of the neutral subset model, which can indeed explain any scaling slope by varying assumptions about the pattern of pleiotropy.
...
...

References

SHOWING 1-10 OF 46 REFERENCES
A Bayesian framework for comparative quantitative genetics
TLDR
It is suggested that a natural summary statistic for G-matrix comparisons can be obtained by examining how different the underlying multinormal probability distributions are, and this work derives a simple Monte Carlo method for computation of fraternity coefficients needed for the estimation of dominance variance.
Sampling based approximation of confidence intervals for functions of genetic covariance matrices.
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
Restricted maximum likelihood estimation of genetic principal components and smoothed covariance matrices
TLDR
It is shown that reduced rank estimation can reduce computational requirements of multivariate analyses substantially and an application to the analysis of eight traits recorded via live ultrasound scanning of beef cattle is given.
Determining the Effective Dimensionality of the Genetic Variance–Covariance Matrix
TLDR
A simulation study indicated that while the performance of Amemiya's method was more sensitive to power constraints, it performed as well or better than factor-analytic modeling in correctly identifying the original genetic dimensions at moderate to high levels of heritability.
ESTIMATING UNCERTAINTY IN MULTIVARIATE RESPONSES TO SELECTION
TLDR
The application of a framework that blends the merits of the Robertson–Price Identity approach and the multivariate breeder's equation to address challenges of natural selection and hypothesis testing about natural selection, genetic constraints, and evolutionary responses is described.
Comparing G: multivariate analysis of genetic variation in multiple populations
TLDR
A cohesive and general analytical framework for the comparative analysis of G is presented that incorporates and extends current methods with a strong geometrical basis, and describes the application of random skewers, common subspace analysis, the 4th-order genetic covariance tensor and the decomposition of the multivariate breeders equation within a Bayesian framework.
Perils of Parsimony: Properties of Reduced-Rank Estimates of Genetic Covariance Matrices
TLDR
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.
WOMBAT—A tool for mixed model analyses in quantitative genetics by restricted maximum likelihood (REML)
  • K. Meyer
  • Biology
    Journal of Zhejiang University SCIENCE B
  • 2007
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
PROPERTIES OF SPONTANEOUS MUTATIONAL VARIANCE AND COVARIANCE FOR WING SIZE AND SHAPE IN DROSOPHILA MELANOGASTER
TLDR
There are significant mutational effects on 19 of 21 possible aspects of wing form, consistent with the high dimensionality of standing genetic variation for wing shape previously identified in D. melanogaster.
Bayesian approaches in evolutionary quantitative genetics
TLDR
This work advocates the use of Bayesian methods to overcome problems arising from the small size of data sets typical of evolutionary studies, and the additional complexity of the questions asked by evolutionary biologists.
...
...