Lars Rönnegård

Inheritance beyond plain heritability: variance-controlling genes in Arabidopsis thaliana.

The phenotypic effect of a gene is normally described by the mean-difference between alternative genotypes. A gene may, however, also influence the phenotype by causing a difference in variance between genotypes. Here, we reanalyze a publicly available Arabidopsis thaliana dataset [1] and show that genetic variance heterogeneity appears to be as common as normal additive effects on a genomewide scale. The study also develops theory to estimate the contributions of variance differences between genotypes to the phenotypic variance, and this is used to show that individual loci can explain more than 20% of the phenotypic variance. Two well-studied systems, cellular control of molybdenum level by the ion-transporter MOT1 and flowering-time regulation by the FRI-FLC expression network, and a novel association for Leaf serration are used to illustrate the contribution of major individual loci, expression pathways, and gene-by-environment interactions to the genetic variance heterogeneity.

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.

Evaluation of four methods used to estimate population density of moose Alces alces

Abstract Various survey methods are used to monitor and manage ungulate populations. The choice of optimal method depends on estimation accuracy, management objective and financial constraints. Here we compare estimates produced by four different methods for estimating population size, i.e. aerial counts, hunter observations, pellet group counts and cohort analysis. A Swedish moose Alces alces population was studied during 1973–2005 in the Grimsö Wildlife Research Area (135 km2). The highest correlation was found between cohort analysis and aerial counts (r=0.69, P<0.05), and the hunter observations and the aerial counts (r=0.76, P<0.10). The different methods produced relatively consistent trends in population estimates over years. Pellet group counts prior to 1997 were not significantly correlated with the other methods, probably due to unrepresentative spatial sampling. A comparison of the aerial and pellet group counts in 2002 and 2006, showed that the average defecation rate was estimated at approximately 14 pellet groups per day per moose. Our results show the importance of having representative spatial sampling in pellet group surveys and indicate that hunter observations can be a useful tool for estimating long-term population trends even in moderately sized areas.

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

BackgroundThe sensitivity to microenvironmental changes varies among animals and may be under genetic control. It is essential to take this element into account when aiming at breeding robust farm animals. Here, linear mixed models with genetic effects in the residual variance part of the model can be used. Such models have previously been fitted using EM and MCMC algorithms.ResultsWe propose the use of double hierarchical generalized linear models (DHGLM), where the squared residuals are assumed to be gamma distributed and the residual variance is fitted using a generalized linear model. The algorithm iterates between two sets of mixed model equations, one on the level of observations and one on the level of variances. The method was validated using simulations and also by re-analyzing a data set on pig litter size that was previously analyzed using a Bayesian approach. The pig litter size data contained 10,060 records from 4,149 sows. The DHGLM was implemented using the ASReml software and the algorithm converged within three minutes on a Linux server. The estimates were similar to those previously obtained using Bayesian methodology, especially the variance components in the residual variance part of the model.ConclusionsWe have shown that variance components in the residual variance part of a linear mixed model can be estimated using a DHGLM approach. The method enables analyses of animal models with large numbers of observations. An important future development of the DHGLM methodology is to include the genetic correlation between the random effects in the mean and residual variance parts of the model as a parameter of the DHGLM.

A Novel Generalized Ridge Regression Method for Quantitative Genetics

As the molecular marker density grows, there is a strong need in both genome-wide association studies and genomic selection to fit models with a large number of parameters. Here we present a computationally efficient generalized ridge regression (RR) algorithm for situations in which the number of parameters largely exceeds the number of observations. The computationally demanding parts of the method depend mainly on the number of observations and not the number of parameters. The algorithm was implemented in the R package bigRR based on the previously developed package hglm. Using such an approach, a heteroscedastic effects model (HEM) was also developed, implemented, and tested. The efficiency for different data sizes were evaluated via simulation. The method was tested for a bacteria-hypersensitive trait in a publicly available Arabidopsis data set including 84 inbred lines and 216,130 SNPs. The computation of all the SNP effects required <10 sec using a single 2.7-GHz core. The advantage in run time makes permutation test feasible for such a whole-genome model, so that a genome-wide significance threshold can be obtained. HEM was found to be more robust than ordinary RR (a.k.a. SNP-best linear unbiased prediction) in terms of QTL mapping, because SNP-specific shrinkage was applied instead of a common shrinkage. The proposed algorithm was also assessed for genomic evaluation and was shown to give better predictions than ordinary RR.

Separation of base allele and sampling term effects gives new insights in variance component QTL analysis

BackgroundVariance component (VC) models are commonly used for Quantitative Trait Loci (QTL) mapping in outbred populations. Here, the QTL effect is given as a random effect and a critical part of the model is the relationship between the phenotypic values and the random effect. In the traditional VC model, each individual has a unique QTL effect and the relationship between these random effects is given as a covariance structure (known as the identity-by-descent (IBD) matrix).ResultsWe present an alternative notation of the variance component model, where the elements of the random effect are independent base generation allele effects and sampling term effects. The relationship between the phenotypic vales and the random effect is given by an incidence matrix, which results in a novel, but statistically equivalent, version of the traditional VC model. A general algorithm to estimate this incidence matrix is presented. Since the model is given in terms of base generation allele effects and sampling term effects, these effects can be estimated separately using best linear unbiased prediction (BLUP). From simulated data, we showed that biallelic QTL effects could be accurately clustered using the BLUP obtained from our model notation when markers are fully informative, and that the accuracy increased with the size of the QTL effect. We also developed a measure indicating whether a base generation marker homozygote is a QTL heterozygote or not, by comparing the variances of the sampling term BLUP and the base generation allele BLUP. A ratio greater than one gives strong support for a QTL heterozygote.ConclusionWe developed a simple presentation of the VC QTL model for identification of base generation allele effects in QTL linkage analysis. The base generation allele effects and sampling term effects were separated in our model notation. This clarifies the assumptions of the model and should also enhance the development of genome scan methods.

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

AbstractA 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.

Fine mapping and replication of QTL in outbred chicken advanced intercross lines

BackgroundLinkage mapping is used to identify genomic regions affecting the expression of complex traits. However, when experimental crosses such as F2 populations or backcrosses are used to map regions containing a Quantitative Trait Locus (QTL), the size of the regions identified remains quite large, i.e. 10 or more Mb. Thus, other experimental strategies are needed to refine the QTL locations. Advanced Intercross Lines (AIL) are produced by repeated intercrossing of F2 animals and successive generations, which decrease linkage disequilibrium in a controlled manner. Although this approach is seen as promising, both to replicate QTL analyses and fine-map QTL, only a few AIL datasets, all originating from inbred founders, have been reported in the literature.MethodsWe have produced a nine-generation AIL pedigree (n = 1529) from two outbred chicken lines divergently selected for body weight at eight weeks of age. All animals were weighed at eight weeks of age and genotyped for SNP located in nine genomic regions where significant or suggestive QTL had previously been detected in the F2 population. In parallel, we have developed a novel strategy to analyse the data that uses both genotype and pedigree information of all AIL individuals to replicate the detection of and fine-map QTL affecting juvenile body weight.ResultsFive of the nine QTL detected with the original F2 population were confirmed and fine-mapped with the AIL, while for the remaining four, only suggestive evidence of their existence was obtained. All original QTL were confirmed as a single locus, except for one, which split into two linked QTL.ConclusionsOur results indicate that many of the QTL, which are genome-wide significant or suggestive in the analyses of large intercross populations, are true effects that can be replicated and fine-mapped using AIL. Key factors for success are the use of large populations and powerful statistical tools. Moreover, we believe that the statistical methods we have developed to efficiently study outbred AIL populations will increase the number of organisms for which in-depth complex traits can be analyzed.

Estimation of breeding values for mean and dispersion, their variance and correlation using double hierarchical generalized linear models

The possibility of breeding for uniform individuals by selecting animals expressing a small response to environment has been studied extensively in animal breeding. Bayesian methods for fitting models with genetic components in the residual variance have been developed for this purpose, but have limitations due to the computational demands. We use the hierarchical (h)-likelihood from the theory of double hierarchical generalized linear models (DHGLM) to derive an estimation algorithm that is computationally feasible for large datasets. Random effects for both the mean and residual variance parts of the model are estimated together with their variance/covariance components. An important feature of the algorithm is that it can fit a correlation between the random effects for mean and variance. An h-likelihood estimator is implemented in the R software and an iterative reweighted least square (IRWLS) approximation of the h-likelihood is implemented using ASReml. The difference in variance component estimates between the two implementations is investigated, as well as the potential bias of the methods, using simulations. IRWLS gives the same results as h-likelihood in simple cases with no severe indication of bias. For more complex cases, only IRWLS could be used, and bias did appear. The IRWLS is applied on the pig litter size data previously analysed by Sorensen & Waagepetersen (2003) using Bayesian methodology. The estimates we obtained by using IRWLS are similar to theirs, with the estimated correlation between the random genetic effects being -0·52 for IRWLS and -0·62 in Sorensen & Waagepetersen (2003).

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

BackgroundGenetic 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.MethodsWe 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.ResultsDesigns 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.ConclusionThe 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.