Genetic heterogeneity of residual variance - estimation of variance components using double hierarchical generalized linear models

Genetic heterogeneity of within-family variance of body weight in Atlantic salmon (Salmo salar)

BACKGROUND

Canalization is defined as the stability of a genotype against minor variations in both environment and genetics. Genetic variation in degree of canalization causes heterogeneity of within-family variance. The aims of this study are twofold: (1) quantify genetic heterogeneity of (within-family) residual variance in Atlantic salmon and (2) test whether the observed heterogeneity of (within-family) residual variance can be explained by simple scaling effects.

RESULTS

Analysis of body weight in Atlantic salmon using a double hierarchical generalized linear model (DHGLM) revealed substantial heterogeneity of within-family variance. The 95% prediction interval for within-family variance ranged from ~0.4 to 1.2 kg2, implying that the within-family variance of the most extreme high families is expected to be approximately three times larger than the extreme low families. For cross-sectional data, DHGLM with an animal mean sub-model resulted in severe bias, while a corresponding sire-dam model was appropriate. Heterogeneity of variance was not sensitive to Box-Cox transformations of phenotypes, which implies that heterogeneity of variance exists beyond what would be expected from simple scaling effects.

CONCLUSIONS

Substantial heterogeneity of within-family variance was found for body weight in Atlantic salmon. A tendency towards higher variance with higher means (scaling effects) was observed, but heterogeneity of within-family variance existed beyond what could be explained by simple scaling effects. For cross-sectional data, using the animal mean sub-model in the DHGLM resulted in biased estimates of variance components, which differed substantially both from a standard linear mean animal model and a sire-dam DHGLM model. Although genetic differences in canalization were observed, selection for increased canalization is difficult, because there is limited individual information for the variance sub-model, especially when based on cross-sectional data. Furthermore, potential macro-environmental changes (diet, climatic region, etc.) may make genetic heterogeneity of variance a less stable trait over time and space.

Unraveling the genetic architecture of environmental variance of somatic cell score using high-density single nucleotide polymorphism and cow data from experimental farms

In recent years, it has been shown that not only is the phenotype under genetic control, but also the environmental variance. Very little, however, is known about the genetic architecture of environmental variance. The main objective of this study was to unravel the genetic architecture of the mean and environmental variance of somatic cell score (SCS) by identifying genome-wide associations for mean and environmental variance of SCS in dairy cows and by quantifying the accuracy of genome-wide breeding values. Somatic cell score was used because previous research has shown that the environmental variance of SCS is partly under genetic control and reduction of the variance of SCS by selection is desirable. In this study, we used 37,590 single nucleotide polymorphism (SNP) genotypes and 46,353 test-day records of 1,642 cows at experimental research farms in 4 countries in Europe. We used a genomic relationship matrix in a double hierarchical generalized linear model to estimate genome-wide breeding values and genetic parameters. The estimated mean and environmental variance per cow was used in a Bayesian multi-locus model to identify SNP associated with either the mean or the environmental variance of SCS. Based on the obtained accuracy of genome-wide breeding values, 985 and 541 independent chromosome segments affecting the mean and environmental variance of SCS, respectively, were identified. Using a genomic relationship matrix increased the accuracy of breeding values relative to using a pedigree relationship matrix. In total, 43 SNP were significantly associated with either the mean (22) or the environmental variance of SCS (21). The SNP with the highest Bayes factor was on chromosome 9 (Hapmap31053-BTA-111664) explaining approximately 3% of the genetic variance of the environmental variance of SCS. Other significant SNP explained less than 1% of the genetic variance. It can be concluded that fewer genomic regions affect the environmental variance of SCS than the mean of SCS, but genes with large effects seem to be absent for both traits.

Genetic variance in micro-environmental sensitivity for milk and milk quality in Walloon Holstein cattle

Animals that are robust to environmental changes are desirable in the current dairy industry. Genetic differences in micro-environmental sensitivity can be studied through heterogeneity of residual variance between animals. However, residual variance between animals is usually assumed to be homogeneous in traditional genetic evaluations. The aim of this study was to investigate genetic heterogeneity of residual variance by estimating variance components in residual variance for milk yield, somatic cell score, contents in milk (g/dL) of 2 groups of milk fatty acids (i.e., saturated and unsaturated fatty acids), and the content in milk of one individual fatty acid (i.e., oleic acid, C18:1 cis-9), for first-parity Holstein cows in the Walloon Region of Belgium. A total of 146,027 test-day records from 26,887 cows in 747 herds were available. All cows had at least 3 records and a known sire. These sires had at least 10 cows with records and each herd × test-day had at least 5 cows. The 5 traits were analyzed separately based on fixed lactation curve and random regression test-day models for the mean. Estimation of variance components was performed by running iteratively expectation maximization-REML algorithm by the implementation of double hierarchical generalized linear models. Based on fixed lactation curve test-day mean models, heritability for residual variances ranged between 1.01×10(-3) and 4.17×10(-3) for all traits. The genetic standard deviation in residual variance (i.e., approximately the genetic coefficient of variation of residual variance) ranged between 0.12 and 0.17. Therefore, some genetic variance in micro-environmental sensitivity existed in the Walloon Holstein dairy cattle for the 5 studied traits. The standard deviations due to herd × test-day and permanent environment in residual variance ranged between 0.36 and 0.45 for herd × test-day effect and between 0.55 and 0.97 for permanent environmental effect. Therefore, nongenetic effects also contributed substantially to micro-environmental sensitivity. Addition of random regressions to the mean model did not reduce heterogeneity in residual variance and that genetic heterogeneity of residual variance was not simply an effect of an incomplete mean model.

Estimation of genetic variance for macro- and micro-environmental sensitivity using double hierarchical generalized linear models

BACKGROUND

Genetic variation for environmental sensitivity indicates that animals are genetically different in their response to environmental factors. Environmental factors are either identifiable (e.g. temperature) and called macro-environmental or unknown and called micro-environmental. The objectives of this study were to develop a statistical method to estimate genetic parameters for macro- and micro-environmental sensitivities simultaneously, to investigate bias and precision of resulting estimates of genetic parameters and to develop and evaluate use of Akaike's information criterion using h-likelihood to select the best fitting model.

METHODS

We assumed that genetic variation in macro- and micro-environmental sensitivities is expressed as genetic variance in the slope of a linear reaction norm and environmental variance, respectively. A reaction norm model to estimate genetic variance for macro-environmental sensitivity was combined with a structural model for residual variance to estimate genetic variance for micro-environmental sensitivity using a double hierarchical generalized linear model in ASReml. Akaike's information criterion was constructed as model selection criterion using approximated h-likelihood. Populations of sires with large half-sib offspring groups were simulated to investigate bias and precision of estimated genetic parameters.

RESULTS

Designs with 100 sires, each with at least 100 offspring, are required to have standard deviations of estimated variances lower than 50% of the true value. When the number of offspring increased, standard deviations of estimates across replicates decreased substantially, especially for genetic variances of macro- and micro-environmental sensitivities. Standard deviations of estimated genetic correlations across replicates were quite large (between 0.1 and 0.4), especially when sires had few offspring. Practically, no bias was observed for estimates of any of the parameters. Using Akaike's information criterion the true genetic model was selected as the best statistical model in at least 90% of 100 replicates when the number of offspring per sire was 100. Application of the model to lactation milk yield in dairy cattle showed that genetic variance for micro- and macro-environmental sensitivities existed.

CONCLUSION

The algorithm and model selection criterion presented here can contribute to better understand genetic control of macro- and micro-environmental sensitivities. Designs or datasets should have at least 100 sires each with 100 offspring.

Weight, age and coefficients of variation in renal solute excretion

BACKGROUND

Homoscedasticity (constant variance over axes or among statistical factors) is an integral assumption of most statistical analyses. However, a number of empirical studies in model organisms and humans demonstrate significant differences in residual variance (that component of phenotype unexplained by known factors) or intra-individual variation among genotypes. Our work suggests that renal traits may be particularly susceptible to randomization by genetic and non-genetic factors, including endogenous variables like age and weight.

METHODS

We tested associations between age, weight and intra-individual variation in urinary calcium, citrate, chloride, creatinine, potassium, magnesium, sodium, ammonium, oxalate, phosphorus, sulfate, uric acid and urea nitrogen in 9,024 male and 6,758 female kidney stone patients. Coefficients of variation (CVs) were calculated for each individual for each solute from paired 24-hour urines. Analysis of CVs was corrected for inter-measurement collection variance in creatinine and urine volume. CVs for sodium and urea nitrogen were included to correct for dietary salt and protein.

RESULTS

Age was positively associated with individual CVs for calcium and negatively associated with CVs for potassium, ammonium and phosphorus (p(FDR) < 0.01). Weight was associated with CVs for creatinine, magnesium and uric acid, and negatively associated with CVs for calcium, potassium and oxalate (p(FDR) < 0.05).

CONCLUSION

Intra-individual variation changes over age and weight axes for numerous urinary solutes. Changing residual variance over age and weight could cause bias in the detection or estimation of genetic or environmental effects. New methodologies may need to account for such residual unpredictability, especially in diverse collections.

Variance component and breeding value estimation for genetic heterogeneity of residual variance in Swedish Holstein dairy cattle

Trait uniformity, or micro-environmental sensitivity, may be studied through individual differences in residual variance. These differences appear to be heritable, and the need exists, therefore, to fit models to predict breeding values explaining differences in residual variance. The aim of this paper is to estimate breeding values for micro-environmental sensitivity (vEBV) in milk yield and somatic cell score, and their associated variance components, on a large dairy cattle data set having more than 1.6 million records. Estimation of variance components, ordinary breeding values, and vEBV was performed using standard variance component estimation software (ASReml), applying the methodology for double hierarchical generalized linear models. Estimation using ASReml took less than 7 d on a Linux server. The genetic standard deviations for residual variance were 0.21 and 0.22 for somatic cell score and milk yield, respectively, which indicate moderate genetic variance for residual variance and imply that a standard deviation change in vEBV for one of these traits would alter the residual variance by 20%. This study shows that estimation of variance components, estimated breeding values and vEBV, is feasible for large dairy cattle data sets using standard variance component estimation software. The possibility to select for uniformity in Holstein dairy cattle based on these estimates is discussed.

Recent developments in statistical methods for detecting genetic loci affecting phenotypic variability

A number of recent works have introduced statistical methods for detecting genetic loci that affect phenotypic variability, which we refer to as variability-controlling quantitative trait loci (vQTL). These are genetic variants whose allelic state predicts how much phenotype values will vary about their expected means. Such loci are of great potential interest in both human and non-human genetic studies, one reason being that a detected vQTL could represent a previously undetected interaction with other genes or environmental factors. The simultaneous publication of these new methods in different journals has in many cases precluded opportunity for comparison. We survey some of these methods, the respective trade-offs they imply, and the connections between them. The methods fall into three main groups: classical non-parametric, fully parametric, and semi-parametric two-stage approximations. Choosing between alternatives involves balancing the need for robustness, flexibility, and speed. For each method, we identify important assumptions and limitations, including those of practical importance, such as their scope for including covariates and random effects. We show in simulations that both parametric methods and their semi-parametric approximations can give elevated false positive rates when they ignore mean-variance relationships intrinsic to the data generation process. We conclude that choice of method depends on the trait distribution, the need to include non-genetic covariates, and the population size and structure, coupled with a critical evaluation of how these fit with the assumptions of the statistical model.

Genetic and environmental heterogeneity of residual variance of weight traits in Nellore beef cattle

Background

Many studies have provided evidence of the existence of genetic heterogeneity of environmental variance, suggesting that it could be exploited to improve robustness and uniformity of livestock by selection. However, little is known about the perspectives of such a selection strategy in beef cattle.

Methods

A two-step approach was applied to study the genetic heterogeneity of residual variance of weight gain from birth to weaning and long-yearling weight in a Nellore beef cattle population. First, an animal model was fitted to the data and second, the influence of additive and environmental effects on the residual variance of these traits was investigated with different models, in which the log squared estimated residuals for each phenotypic record were analyzed using the restricted maximum likelihood method. Monte Carlo simulation was performed to assess the reliability of variance component estimates from the second step and the accuracy of estimated breeding values for residual variation.

Results

The results suggest that both genetic and environmental factors have an effect on the residual variance of weight gain from birth to weaning and long-yearling in Nellore beef cattle and that uniformity of these traits could be improved by selecting for lower residual variance, when considering a large amount of information to predict genetic merit for this criterion. Simulations suggested that using the two-step approach would lead to biased estimates of variance components, such that more adequate methods are needed to study the genetic heterogeneity of residual variance in beef cattle.

Genetic analysis of environmental variation

Environmental variation (VE) in a quantitative trait - variation in phenotype that cannot be explained by genetic variation or identifiable genetic differences - can be regarded as being under some degree of genetic control. Such variation may be either between repeated expressions of the same trait within individuals (e.g. for bilateral traits), in the phenotype of different individuals, where variation within families may differ, or in both components. We consider alternative models for defining the distribution of phenotypes to include a component due to heterogeneity of VE. We review evidence for the presence of genetic variation in VE and estimates of its magnitude. Typically the heritability of VE is under 10%, but its genetic coefficient of variation is typically 20% or more. We consider experimental designs appropriate for estimating genetic variance in VE and review alternative methods of estimation. We consider the effects of stabilizing and directional selection on VE and review both the forces that might be maintaining levels of VE and heritability found in populations. We also evaluate the opportunities for reducing VE in breeding programmes. Although empirical and theoretical studies have increased our understanding of genetic control of environmental variance, many issues remain unresolved.

Detecting major genetic loci controlling phenotypic variability in experimental crosses

Traditional methods for detecting genes that affect complex diseases in humans or animal models, milk production in livestock, or other traits of interest, have asked whether variation in genotype produces a change in that trait's average value. But focusing on differences in the mean ignores differences in variability about that mean. The robustness, or uniformity, of an individual's character is not only of great practical importance in medical genetics and food production but is also of scientific and evolutionary interest (e.g., blood pressure in animal models of heart disease, litter size in pigs, flowering time in plants). We describe a method for detecting major genes controlling the phenotypic variance, referring to these as vQTL. Our method uses a double generalized linear model with linear predictors based on probabilities of line origin. We evaluate our method on simulated F₂ and collaborative cross data, and on a real F₂ intercross, demonstrating its accuracy and robustness to the presence of ordinary mean-controlling QTL. We also illustrate the connection between vQTL and QTL involved in epistasis, explaining how these concepts overlap. Our method can be applied to a wide range of commonly used experimental crosses and may be extended to genetic association more generally.