scholarly journals Animal models with group-specific additive genetic variances: extending genetic group models

2018 ◽  
Author(s):  
Stefanie Muff ◽  
Alina K. Niskanen ◽  
Dilan Saatoglu ◽  
Lukas F. Keller ◽  
Henrik Jensen
Keyword(s):  
Animal Model ◽  
Animal Models ◽  
Genetic Variance ◽  
Additive Genetic Variance ◽  
Genetic Group ◽  
Breeding Value ◽  
Sampling Variance ◽  
Implicit Assumption ◽  
Genetic Variances ◽  
Genetic Groups

Abstract1. The animal model is a key tool in quantitative genetics and has been used extensively to estimate fundamental parameters, such as additive genetic variance, heritability, or inbreeding effects. An implicit assumption of animal models is that all founder individuals derive from a single population. This assumption is commonly violated, for instance in cross-bred livestock breeds, when an observed population receive immigrants, or when a meta-population is split into genetically differentiated subpopulations. Ignoring genetic differences among different source populations of founders may lead to biased parameter estimates, in particular for the additive genetic variance.2. To avoid such biases, genetic group models, extensions to the animal model that account for the presence of more than one genetic group, have been proposed. As a key limitation, the method to date only allows that the breeding values differ in their means, but not in their variances among the groups. Methodology previously proposed to account for group-specific variances included terms for segregation variance, which rendered the models infeasibly complex for application to most real study systems.3. Here we explain why segregation variances are often negligible when analyzing the complex polygenic traits that are frequently the focus of evolutionary ecologists and animal breeders. Based on this we suggest an extension of the animal model that permits estimation of group-specific additive genetic variances. This is achieved by employing group-specific relatedness matrices for the breeding value components attributable to different genetic groups. We derive these matrices by decomposing the full relatedness matrix via the generalized Cholesky decomposition, and by scaling the respective matrix components for each group. To this end, we propose a computationally convenient approximation for the matrix component that encodes for the Mendelian sampling variance. Although convenient, this approximation is not critical.4. Simulations and an example from an insular meta-population of house sparrows in Norway with three genetic groups illustrate that the method is successful in estimating group-specific additive genetic variances and that segregation variances are indeed negligible in the empirical example.5. Quantifying differences in additive genetic variance within and among populations is of major biological interest in ecology, evolution, and animal and plant breeding. The proposed method allows to estimate such differences for subpopulations that form a connected meta-population, which may also be useful to study temporal or spatial variation of additive genetic variance.

scholarly journals Genomic estimation of quantitative genetic parameters in wild admixed populations

2021 ◽  
Author(s):  
Kenneth Aase ◽  
Henrik Jensen ◽  
Stefanie Muff
Keyword(s):  
Animal Model ◽  
Animal Models ◽  
Genetic Parameters ◽  
Genomic Data ◽  
Structured Populations ◽  
Genetic Group ◽  
List Type ◽  
Genetic Groups ◽  
Quantitative Genetic ◽  
Quantitative Genetic Parameters

AbstractHeritable genetic variation among free-living animals or plants is essential for populations to respond to selection and adapt. It is therefore important to be able to estimate additive genetic variance VA, which can be obtained using a generalized linear mixed model known as the animal model. An underlying assumption of the standard animal model is that the study population is genetically unstructured, which is often unrealistic. In fact, admixture might be the norm rather than the exception in the wild, like in geographically structured populations, in the presence of (im)migration, or in re-introduction and conservation contexts. Unfortunately, animal model estimators may be biased in such cases. So-called genetic group animal models that account for genetically differentiated subpopulations have recently become popular, but methodology is currently only available for cases where relatedness among individuals can be estimated from pedigrees.To ensure that the animal model remains useful in future applications, there is a clear need to generalize genetic group animal models with heterogeneous VA to the case when exclusively genomic data is available. We therefore introduce such methodology for wild admixed systems by extending methods that were recently suggested in the context of plant breeding. Our extension relaxes the limiting assumptions that currently restrict their use to artificial breeding setups.We illustrate the usefulness of the extended genomic genetic groups animal model on a wild admixed population of house sparrows resident in an island system in Northern Norway, where genome-wide data on more than 180 000 single nucleotide polymorphisms (SNPs) is available to derive genomic relatedness. We compare our estimates of quantitative genetic parameters to those derived from a corresponding pedigree-based genetic groups animal model. The satisfactory agreement indicates that the new method works as expected.Our extension of the very popular animal model ensures that the upcoming challenges with increasing availability of genomic data for quantitative genetic studies of wild admixed populations can be handled. To make the method widely available to the scientific community, we offer guidance in the form of a tutorial including step-by-step instructions to facilitate implementation.

ESTIMATION OF ADDITIVE AND NONADDITIVE GENETIC VARIANCES IN NONINBRED POPULATIONS UNDER SIRE OR FULLSIB MODEL

1989 ◽  
Vol 69 (1) ◽  
pp. 61-68
Author(s):  
C. Y. LIN ◽  
A. J. LEE
Keyword(s):  
Animal Model ◽  
Maximum Likelihood ◽  
Least Squares ◽  
Key Words ◽  
Genetic Variance ◽  
Additive Genetic Variance ◽  
Restricted Maximum Likelihood ◽  
Animal Breeding ◽  
Genetic Variances ◽  
Reml Estimation

The separation of additive and nonadditive genetic variances has been a problem for animal breeding researchers because conventional methods of statistical analyses (least squares or ANOVA type) were not able to accomplish this task. Henderson presented computing algorithms for restricted maximum likelihood (REML) estimation of additive and nonadditive genetic variances from an animal model for noninbred populations. Unfortunately, application of this algorithm in practice requires extensive computing. This study extends Henderson's methodology to estimate additive genetic variance independently of nonadditive genetic variances under halfsib (sire), fullsib nested and fullsib cross-classified models. A numerical example illustrates the REML estimation of additive [Formula: see text] and additive by additive [Formula: see text] genetic variances using a sire model. Key words: Genetic variance, additive, nonadditive, dairy

Genetic variation within and between subpopulations of the Australian Merino breed

2016 ◽  
Vol 56 (1) ◽  
pp. 87 ◽  
Author(s):  
Andrew A. Swan ◽  
Daniel J. Brown ◽  
Julius H. J. van der Werf
Keyword(s):  
Genetic Variation ◽  
Variance Components ◽  
Additive Genetic Variance ◽  
Genetic Correlations ◽  
Fibre Diameter ◽  
Genetic Group ◽  
Additive Variance ◽  
Breeding Values ◽  
Genetic Groups ◽  
Australian Merino

Genetic variation within and between Australian Merino subpopulations was estimated from a large breeding nucleus in which up to 8500 progeny from over 300 sires were recorded at eight sites across Australia. Subpopulations were defined as genetic groups using the Westell–Quaas model in which base animals with unknown pedigree were allocated to groups based on their flock of origin if there were sufficient ‘expressions’ for the flock, or to one of four broad sheep-type groups otherwise (Ultra/Superfine, Fine/Fine-medium, Medium/Strong, or unknown). Linear models including genetic groups and additive genetic breeding values as random effects were used to estimate variance components for 12 traits: yearling greasy and clean fleece weight (ygfw and ycfw), yearling mean and coefficient of variation of fibre diameter (yfd and ydcv), yearling staple length and staple strength (ysl and yss), yearling fibre curvature (ycuv), yearling body wrinkle (ybdwr), post-weaning weight (pwt), muscle (pemd) and fat depth (pfat), and post-weaning worm egg count (pwec). For the majority of traits, the genetic group variance ranged from approximately equal to two times larger than the additive genetic (within group) variance. The exceptions were pfat and ydcv where the genetic group to additive variance ratios were 0.58 and 0.22, respectively, and pwec and yss where there was no variation between genetic groups. Genetic group correlations between traits were generally the same sign as corresponding additive genetic correlations, but were stronger in magnitude (either more positive or more negative). These large differences between genetic groups have long been exploited by Merino ram breeders, to the extent that the animals in the present study represent a significantly admixed population of the founding groups. The relativities observed between genetic group and additive genetic variance components in this study can be used to refine the models used to estimate breeding values for the Australian Merino industry.

scholarly journals Estimation of Genetic Variance in Fitness, and Inference of Adaptation, When Fitness Follows a Log-Normal Distribution

2019 ◽  
Vol 110 (4) ◽  
pp. 383-395 ◽  
Author(s):  
Timothée Bonnet ◽  
Michael B Morrissey ◽  
Loeske E B Kruuk
Keyword(s):  
Natural Selection ◽  
Animal Models ◽  
Normal Distribution ◽  
Genetic Variance ◽  
Additive Genetic Variance ◽  
Relative Fitness ◽  
Parameter Estimates ◽  
Log Normal ◽  
Change In Mean ◽  
Log Normal Distribution

AbstractAdditive genetic variance in relative fitness (σA2(w)) is arguably the most important evolutionary parameter in a population because, by Fisher’s fundamental theorem of natural selection (FTNS; Fisher RA. 1930. The genetical theory of natural selection. 1st ed. Oxford: Clarendon Press), it represents the rate of adaptive evolution. However, to date, there are few estimates of σA2(w) in natural populations. Moreover, most of the available estimates rely on Gaussian assumptions inappropriate for fitness data, with unclear consequences. “Generalized linear animal models” (GLAMs) tend to be more appropriate for fitness data, but they estimate parameters on a transformed (“latent”) scale that is not directly interpretable for inferences on the data scale. Here we exploit the latest theoretical developments to clarify how best to estimate quantitative genetic parameters for fitness. Specifically, we use computer simulations to confirm a recently developed analog of the FTNS in the case when expected fitness follows a log-normal distribution. In this situation, the additive genetic variance in absolute fitness on the latent log-scale (σA2(l)) equals (σA2(w)) on the data scale, which is the rate of adaptation within a generation. However, due to inheritance distortion, the change in mean relative fitness between generations exceeds σA2(l) and equals (exp⁡(σA2(l))−1). We illustrate why the heritability of fitness is generally low and is not a good measure of the rate of adaptation. Finally, we explore how well the relevant parameters can be estimated by animal models, comparing Gaussian models with Poisson GLAMs. Our results illustrate 1) the correspondence between quantitative genetics and population dynamics encapsulated in the FTNS and its log-normal-analog and 2) the appropriate interpretation of GLAM parameter estimates.

Potential biases of incomplete linear models in heritability estimation and breeding value prediction

1999 ◽  
Vol 29 (6) ◽  
pp. 724-736 ◽  
Author(s):  
P X Lu ◽  
D A Huber ◽  
T L White
Keyword(s):  
Genetic Variance ◽  
Linear Models ◽  
Additive Genetic Variance ◽  
Genetic Effect ◽  
Breeding Value ◽  
Additive Genetic Effect ◽  
Unbalanced Data ◽  
Breeding Values ◽  
Incomplete Model ◽  
Heritability Estimation

Potential biases associated with incomplete linear models in the estimation of heritability and the prediction of breeding values have been investigated. Results indicate that estimates of additive genetic variance and heritability as well as predicted parental breeding values from incomplete models will inevitably be biased as long as the true variance components of ignored effects are not zero. While models ignoring the interaction effect of males and females (SCA) × environment (E) interaction downwardly biased the estimates of additive genetic variance and heritability, models ignoring SCA and (or) the additive genetic effect (GCA) × E interaction yielded upward biases. The magnitudes of biases are functions of population genetic architecture, mating design, and field experimental design and can be precisely assessed with formulae derived for balanced data. Numerical simulations using unbalanced data of different mating and field experimental designs suggest that the formulae from balanced data can be used to approximate the minimum biases associated with unbalanced data. Because of the magnitudes of biases for some typical forest genetic scenarios, it is suggested that models ignoring SCA and (or) GCA × E should be avoided when the numbers of test sites and crosses per parent are small. However, incomplete model ignoring SCA × E interaction may be used to reduce computational demand with only negligible consequences.

scholarly journals A guide to using a multiple-matrix animal model to disentangle genetic and nongenetic causes of phenotypic variance

2018 ◽  
Author(s):  
Caroline E. Thomson ◽  
Isabel S. Winney ◽  
Oceane C. Salles ◽  
Benoit Pujol
Keyword(s):  
Animal Model ◽  
Genetic Variance ◽  
Genetic Relatedness ◽  
Additive Genetic Variance ◽  
Phenotypic Traits ◽  
Phenotypic Variance ◽  
Data Types ◽  
Evolutionary Potential ◽  
Recent Developments

AbstractNon-genetic influences on phenotypic traits can affect our interpretation of genetic variance and the evolutionary potential of populations to respond to selection, with consequences for our ability to predict the outcomes of selection. Long-term population surveys and experiments have shown that quantitative genetic estimates are influenced by nongenetic effects, including shared environmental effects, epigenetic effects, and social interactions. Recent developments to the “animal model” of quantitative genetics can now allow us to calculate precise individual-based measures of non-genetic phenotypic variance. These models can be applied to a much broader range of contexts and data types than used previously, with the potential to greatly expand our understanding of nongenetic effects on evolutionary potential. Here, we provide the first practical guide for researchers interested in distinguishing between genetic and nongenetic causes of phenotypic variation in the animal model. The methods use matrices describing individual similarity in nongenetic effects, analogous to the additive genetic relatedness matrix. In a simulation of various phenotypic traits, accounting for environmental, epigenetic, or cultural resemblance between individuals reduced estimates of additive genetic variance, changing the interpretation of evolutionary potential. These variances were estimable for both direct and parental nongenetic variances. Our tutorial outlines an easy way to account for these effects in both wild and experimental populations. These models have the potential to add to our understanding of the effects of genetic and nongenetic effects on evolutionary potential. This should be of interest both to those studying heritability, and those who wish to understand nongenetic variance.

scholarly journals Variance of neutral genetic variances within and between populations for a quantitative character.

Genetics ◽  
1991 ◽  
Vol 129 (2) ◽  
pp. 535-553
Author(s):  
Z B Zeng ◽  
C C Cockerham
Keyword(s):  
Linkage Disequilibrium ◽  
Coefficient Of Variation ◽  
Genetic Variance ◽  
Quantitative Character ◽  
Sampling Variance ◽  
Effective Population ◽  
Identity By Descent ◽  
Multiple Allele ◽  
Genetic Variances ◽  
Parameter Variance

Abstract The variances of genetic variances within and between finite populations were systematically studied using a general multiple allele model with mutation in terms of identity by descent measures. We partitioned the genetic variances into components corresponding to genetic variances and covariances within and between loci. We also analyzed the sampling variance. Both transient and equilibrium results were derived exactly and the results can be used in diverse applications. For the genetic variance within populations, sigma 2 omega, the coefficient of variation can be very well approximated as [formula: see text] for a normal distribution of allelic effects, ignoring recurrent mutation in the absence of linkage, where m is the number of loci, N is the effective population size, theta 1(0) is the initial identity by descent measure of two genes within populations and t is the generation number. The first term is due to genic variance, the second due to linkage disequilibrium, and third due to sampling. In the short term, the variation is predominantly due to linkage disequilibrium and sampling; but in the long term it can be largely due to genic variance. At equilibrium with mutation [formula: see text] where u is the mutation rate. The genetic variance between populations is a parameter. Variance arises only among sample estimates due to finite sampling of populations and individuals. The coefficient of variation for sample gentic variance between populations, sigma 2b, can be generally approximated as [formula: see text] when the number of loci is large where S is the number of sampling populations.

scholarly journals Response in Genotypic and Breeding Value to a Single Generation of Divergent Selection for Fresh Fruit Color in Strawberry

1995 ◽  
Vol 120 (2) ◽  
pp. 270-273 ◽  
Author(s):  
Douglas V. Shaw ◽  
Erik J. Sacks
Keyword(s):  
Genetic Variance ◽  
Breeding Population ◽  
Selection Response ◽  
Fruit Color ◽  
Divergent Selection ◽  
Fresh Fruit ◽  
Breeding Value ◽  
Genetic Variances ◽  
Selection For ◽  
Genotypic Selection

Four sets of selected strawberry (Fragaria ×ananassa Duch.) genotypes were generated from within a single breeding population to evaluate the correspondence between predicted and realized selection response for fresh fruit color traits. Genotypes were selected for extreme phenotypes, dark or light, of either internal or external color value (CIELAB L*). Genotypic selection response was evaluated empirically by scoring fruit from the clonal derivatives of these selected genotypes, and response for breeding value was estimated by scoring the offspring of crosses performed among a subset of the genotypes within each selected set. Realized selection response was slightly larger than predicted for internal and external L* when calculated for selected genotypes. Also, more than half of the selected genotypes had genotypic values for L* outside the range of the original parents, providing evidence for transgressive segregation. Realized selection response for breeding value in exterior and interior color was slightly less than predicted. Compared in a different way, genotypic selection response for external color was significantly greater than selection response for breeding value, whereas genotypic and breeding value responses did not differ for internal color. These observations suggest the presence of some nonadditive genetic variance for external color but support the conclusion that the heritabilities predicted previously were reasonably accurate. Estimates of variance components within each of the offspring populations demonstrated that genetic variances were modified substantially by one generation of selection. Selection for dark fruit color reduced genetic variance to nonsignificant levels, with internal color more affected than external color. The total genetic variances within both of the offspring populations from parents selected for light color were changed little by one generation of selection, but substantial dominance variance was detected that had not been found in the original population. The rapid response to selection and large changes in the distribution of genetic variances may indicate the presence of a few genes with comparatively large effect in strawberry color expression. Additional divergent selection response can be expected, but primarily in the direction of light fruit color.

scholarly journals Estimation of non-additive genetic variance in human complex traits from a large sample of unrelated individuals

2020 ◽  
Author(s):  
Valentin Hivert ◽  
Julia Sidorenko ◽  
Florian Rohart ◽  
Michael E Goddard ◽  
Jian Yang ◽  
...  
Keyword(s):  
Complex Traits ◽  
Genetic Variance ◽  
Additive Genetic Variance ◽  
Sampling Variance ◽  
Analysis Model ◽  
Additive Variance ◽  
Snp Data ◽  
Causal Variants ◽  
The Uk ◽  
Epistatic Variance

AbstractNon-additive genetic variance for complex traits is traditionally estimated from data on relatives. It is notoriously difficult to estimate without bias in non-laboratory species, including humans, because of possible confounding with environmental covariance among relatives. In principle, non-additive variance attributable to common DNA variants can be estimated from a random sample of unrelated individuals with genome-wide SNP data. Here, we jointly estimate the proportion of variance explained by additive , dominance and additive-by-additive genetic variance in a single analysis model. We first show by simulations that our model leads to unbiased estimates and provide new theory to predict standard errors estimated using either least squares or maximum likelihood. We then apply the model to 70 complex traits using 254,679 unrelated individuals from the UK Biobank and 1.1M genotyped and imputed SNPs. We found strong evidence for additive variance (average across traits . In contrast, the average estimate of across traits was 0.001, implying negligible dominance variance at causal variants tagged by common SNPs. The average epistatic variance across the traits was 0.058, not significantly different from zero because of the large sampling variance. Our results provide new evidence that genetic variance for complex traits is predominantly additive, and that sample sizes of many millions of unrelated individuals are needed to estimate epistatic variance with sufficient precision.

scholarly journals Accounting for Genetic Differences Among Unknown Parents in Bubalus bubalis: A Case Study From the Italian Mediterranean Buffalo

2021 ◽  
Vol 12 ◽  
Author(s):  
Mayra Gómez ◽  
Dario Rossi ◽  
Roberta Cimmino ◽  
Gianluigi Zullo ◽  
Yuri Gombia ◽  
...  
Keyword(s):  
Animal Model ◽  
Bubalus Bubalis ◽  
Breeding Value ◽  
Pedigree Information ◽  
Body Depth ◽  
Genetic Groups ◽  
Population Type ◽  
Grouping Strategies ◽  
Type Traits ◽  
Efficiency Of Selection

The use of genetic evaluations in the Water Buffalo by means of a Best Linear Unbiased Prediction (BLUP) animal model has been increased over the last two-decades across several countries. However, natural mating is still a common reproductive strategy that can increase the proportion of missing pedigree information. The inclusion of genetic groups in variance component (VC) and breeding value (EBV) estimation is a possible solution. The aim of this study was to evaluate two different genetic grouping strategies and their effects on VC and EBV for composite (n = 5) and linear (n = 10) type traits in the Italian Mediterranean Buffalo (IMB) population. Type traits data from 7,714 buffalo cows plus a pedigree file including 18,831 individuals were provided by the Italian National Association of Buffalo Breeders. VCs and EBVs were estimated for each trait fitting a single-trait animal model and using the official DNA-verified pedigree. Successively, EBVs were re-estimated using modified pedigrees with two different proportion of missing genealogies (30 or 60% of buffalo with records), and two different grouping strategies, year of birth (Y30/Y60) or genetic clustering (GC30, GC60). The different set of VCs, estimated EBVs and their standard errors were compared with the results obtained using the original pedigree. Results were also compared in terms of efficiency of selection. Differences among VCs varied according to the trait and the scenario considered. The largest effect was observed for two traits, udder teat and body depth in the GC60 genetic cluster, whose heritability decreased by −0.07 and increased by +0.04, respectively. Considering buffalo cows with record, the average correlation across traits between official EBVs and EBVs from different scenarios was 0.91, 0.88, 0.84, and 0.79 for Y30, CG30, Y60, and CG60, respectively. In bulls the correlations between EBVs ranged from 0.90 for fore udder attachment and udder depth to 0.96 for stature and body length in the GC30 scenario and from 0.75 for udder depth to 0.90 for stature in the GC60 scenario. When a variable proportion of missing pedigree is present using the appropriate strategy to define genetic groups and including them in VC and EBV is a worth-while and low-demanding solution.

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