Search

Phenotypic variability of a genotype is relevant both in natural and domestic populations. In the past two decades, variability has been studied as a heritable quantitative genetic trait in its own right, often referred to as inherited variability or environmental canalization. So far, studies on inherited variability have only considered genetic effects of the focal individual, that is, direct genetic effects on inherited variability. Observations from aquaculture populations and some plants, however, suggest that an additional source of genetic variation in inherited variability may be generated through competition. Social interactions, such as competition, are often a source of Indirect Genetic Effects (IGE). An IGE is a heritable effect of an individual on the trait value of another individual. IGEs may substantially affect heritable variation underlying the trait, and the direction and magnitude of response to selection. To understand the contribution of IGEs to evolution of environmental canalization in natural populations, and to exploit such inherited variability in animal and plant breeding, we need statistical models to capture this effect. To our knowledge, it is unknown to what extent the current statistical models commonly used for IGE and inherited variability capture the effect of competition on inherited variability. Here, we investigate the potential of current statistical models for inherited variability and trait values, to capture the direct and indirect genetic effects of competition on variability. Our results show that a direct model of inherited variability almost entirely captures the genetic sensitivity of individuals to competition, whereas an indirect model of inherited variability captures the cooperative genetic effects of individuals on their partners. Models for trait levels, however, capture only a small part of the genetic effects of competition. The estimation of direct and indirect genetic effects of competition, therefore, is possible with models for inherited variability but may require a two-step analysis., Competing Interests: The authors declare that they have no competing interests., (© 2022 The Authors. Evolutionary Applications published by John Wiley & Sons Ltd.)

The cerebellum has a highly conserved neural structure across species but varies widely in size. The wide variation in cerebellar size (both absolute and in proportion to the rest of the brain) among species and populations suggests that functional specialization is linked to its size. There is increasing recognition that the cerebellum contributes to cognitive processing and emotional control in addition to its role in motor coordination. However, to what extent cerebellum size reflects variation in these behavioral processes within species remains largely unknown. By using a unique intercross chicken population based on parental lines with high divergence in cerebellum size, we compared the behavior of individuals repeatedly exposed to the same fear test (emergence test) early in life and after sexual maturity (eight trials per age group) with proportional cerebellum size and cerebellum neural density. While proportional cerebellum size did not predict the initial fear response of the individuals (trial 1), it did increasingly predict adult individuals response as the trials progressed. Our results suggest that proportional cerebellum size does not necessarily predict an individual's fear response, but rather the habituation process to a fearful stimulus. Cerebellum neuronal density did not predict fear behavior in the individuals which suggests that these effects do not result from changes in neuronal density but due to other variables linked to proportional cerebellum size which might underlie fear habituation., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2022 Stingo-Hirmas, Cunha, Cardoso, Carra, Rönnegård, Wright and Henriksen.)

Introduction: Although breast and prostate cancers arise in different organs and are more frequent in the opposite sex, multiple studies have reported an association between their family history. Analysis of single nucleotide polymorphism data, based on distant relatives, has revealed a small positive genetic correlation between these cancers explained by common variants. The estimate of genetic correlation based on close relatives reveals the extent to which shared genetic risks are explained by both common and rare variants. This estimate is unknown for breast and prostate cancer., Method: We estimated the relative risks, heritability, and genetic correlation of breast cancer and prostate cancer, based on the Minnesota Breast and Prostate Cancer Study, a family study of 141 families ascertained for breast cancer., Results: Heritability of breast cancer was 0.34 (95% credible interval: 0.23-0.49) and 0.65 (95% credible interval: 0.36-0.97) for prostate cancer, and the genetic correlation was 0.23. In terms of odds ratios, these values correspond to a 1.3 times higher odds of breast cancer among probands, given that the brother has prostate cancer., Conclusion: This study shows the inherent relation between prostate cancer and breast cancer; an incident of one in a family increases the risk of developing the other. The large difference between estimates of genetic correlation from distant and close relatives, if replicated, suggests that rare variants contribute to the shared genetic risk of breast and prostate cancer. However, the difference could steam from genotype-by-family effects shared between the two types of cancers., (The Author(s). Published by S. Karger AG, Basel.)

We develop a Bayesian model (BayesRR-RC) that provides robust SNP-heritability estimation, an alternative to marker discovery, and accurate genomic prediction, taking 22 seconds per iteration to estimate 8.4 million SNP-effects and 78 SNP-heritability parameters in the UK Biobank. We find that only ≤10% of the genetic variation captured for height, body mass index, cardiovascular disease, and type 2 diabetes is attributable to proximal regulatory regions within 10kb upstream of genes, while 12-25% is attributed to coding regions, 32-44% to introns, and 22-28% to distal 10-500kb upstream regions. Up to 24% of all cis and coding regions of each chromosome are associated with each trait, with over 3,100 independent exonic and intronic regions and over 5,400 independent regulatory regions having ≥95% probability of contributing ≥0.001% to the genetic variance of these four traits. Our open-source software (GMRM) provides a scalable alternative to current approaches for biobank data., (© 2021. The Author(s).)

Real-time indoor positioning using ultra-wideband devices provides an opportunity for modern dairy farms to monitor the behavior of individual cows; however, missing data from these devices hinders reliable continuous monitoring and analysis of animal movement and social behavior. The objective of this study was to examine the data quality, in terms of missing data, in one commercially available ultra-wideband-based real-time location system for dairy cows. The focus was on detecting major obstacles, or sections, inside open freestall barns that resulted in increased levels of missing data. The study was conducted on 2 dairy farms with an existing commercial real-time location system. Position data were recorded for 6 full days from 69 cows on farm 1 and from 59 cows on farm 2. These data were used in subsequent analyses to determine the locations within the dairy barns where position data were missing for individual cows. The proportions of missing data were found to be evenly distributed within the 2 barns after fitting a linear mixed model with spatial smoothing to logit-transformed proportions (mean = 18% vs. 4% missing data for farm 1 and farm 2, respectively), with the exception of larger proportions of missing data along one of the walls on both farms. On farm 1, the variation between individual tags was large (range: 9-49%) compared with farm 2 (range: 12-38%). This greater individual variation of proportions of missing data indicates a potential problem with the individual tag, such as a battery malfunction or tag placement issue. Further research is needed to guide researchers in identifying problems relating to data capture problems in real-time monitoring systems on dairy farms. This is especially important when undertaking detailed analyses of animal movement and social interactions between animals., (© 2021.)

One of the most common and reliable ways of monitoring udder health and milk quality in dairy herds is by monthly cow composite somatic cell counts (CMSCC). However, such sampling can be time consuming, and more automated sampling tools entail extra costs. Machine learning methods for prediction have been widely investigated in mastitis detection research, and CMSCC is normally used as a predictor or gold standard in such models. Predicted CMSCC between samplings could supply important information and be used as an input for udder health decision-support tools. To our knowledge, methods to predict CMSCC are lacking. Our aim was to find a method to predict CMSCC by using regularly recorded quarter milk data such as milk flow or conductivity. The milk data were collected at the quarter level for 8 wk when milking 372 Holstein-Friesian cows, resulting in a data set of 30,734 records with information on 87 variables. The cows were milked in an automatic milking rotary and sampled once weekly to obtain CMSCC values. The machine learning methods chosen for evaluation were the generalized additive model (GAM), random forest, and multilayer perceptron (MLP). For each method, 4 models with different predictor variable setups were evaluated: models based on 7-d lagged or 3-d lagged records before the CMSCC sampling and additionally for each setup but removing cow number as a predictor variable (which captures indirect information regarding cows' overall level of CMSCC based on previous samplings). The methods were evaluated by a 5-fold cross validation and predictions on future data using models with the 4 different variable setups. The results indicated that GAM was the superior model, although MLP was equally good when fewer data were used. Information regarding the cows' level of previous CMSCC was shown to be important for prediction, lowering prediction error in both GAM and MLP. We conclude that the use of GAM or MLP for CMSCC prediction is promising., (The Authors. Published by Elsevier Inc. and Fass Inc. on behalf of the American Dairy Science Association®. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).)

Background and Objectives: Levodopa concentration in patients with Parkinson's disease is frequently modelled with ordinary differential equations (ODEs). Here, we investigate a pharmacokinetic model of plasma levodopa concentration in patients with Parkinson's disease by introducing stochasticity to separate the intra-individual variability into measurement and system noise, and to account for auto-correlated errors. We also investigate whether the induced stochasticity provides a better fit than the ODE approach., Methods: In this study, a system noise variable is added to the pharmacokinetic model for duodenal levodopa/carbidopa gel (LCIG) infusion described by three ODEs through a standard Wiener process, leading to a stochastic differential equations (SDE) model. The R package population stochastic modelling (PSM) was used for model fitting with data from previous studies for modelling plasma levodopa concentration and parameter estimation. First, the diffusion scale parameter (σ w ), measurement noise variance, and bioavailability are estimated with the SDE model. Second, σ w is fixed to certain values from 0 to 1 and bioavailability is estimated. Cross-validation was performed to compare the average root mean square errors (RMSE) of predicted plasma levodopa concentration., Results: Both the ODE and the SDE models estimated bioavailability to be approximately 75%. The SDE model converged at different values of σ w that were significantly different from zero. The average RMSE for the ODE model was 0.313, and the lowest average RMSE for the SDE model was 0.297 when σ w was fixed to 0.9, and these two values are significantly different., Conclusions: The SDE model provided a better fit for LCIG plasma levodopa concentration by approximately 5.5% in terms of mean percentage change of RMSE.

The increasing amount of available biological information on the markers can be used to inform the models applied for genomic selection to improve predictions. The objective of this study was to propose a general model for genomic selection using a link function approach within the hierarchical generalized linear model framework (hglm) that can include external information on the markers. These models can be fitted using the well-established hglm package in R. We also present an R package (CodataGS) to fit these models, which is significantly faster than the hglm package. Simulated data were used to validate the proposed model. We tested categorical, continuous and combination models where the external information on the markers was related to 1) the location of the QTL on the genome with varying degree of uncertainty, 2) the relationship of the markers with the QTL calculated as the LD between them, and 3) a combination of both. The proposed models showed improved accuracies from 3.8% up to 23.2% compared to the SNP-BLUP method in a simulated population derived from a base population with 100 individuals. Moreover, the proposed categorical model was tested on a dairy cattle dataset for two traits (Milk Yield and Fat Percentage). These results also showed improved accuracy compared to SNP-BLUP, especially for the Fat% trait. The performance of the proposed models depended on the genetic architecture of the trait, as traits that deviate from the infinitesimal model benefited more from the external information. Also, the gain in accuracy depended on the degree of uncertainty of the external information provided to the model. The usefulness of these type of models is expected to increase with time as more accurate information on the markers becomes available., (Copyright © 2019 Mouresan et al.)

When individuals interact, their phenotypes may be affected not only by their own genes but also by genes in their social partners. This phenomenon is known as Indirect Genetic Effects (IGEs). In aquaculture species and some plants, however, competition not only affects trait levels of individuals, but also inflates variability of trait values among individuals. In the field of quantitative genetics, the variability of trait values has been studied as a quantitative trait in itself, and is often referred to as inherited variability. Such studies, however, consider only the genetic effect of the focal individual on trait variability and do not make a connection to competition. Although the observed phenotypic relationship between competition and variability suggests an underlying genetic relationship, the current quantitative genetic models of IGE and inherited variability do not allow for such a relationship. The lack of quantitative genetic models that connect IGEs to inherited variability limits our understanding of the potential of variability to respond to selection, both in nature and agriculture. Models of trait levels, for example, show that IGEs may considerably change heritable variation in trait values. Currently, we lack the tools to investigate whether this result extends to variability of trait values. Here we present a model that integrates IGEs and inherited variability. In this model, the target phenotype, say growth rate, is a function of the genetic and environmental effects of the focal individual and of the difference in trait value between the social partner and the focal individual, multiplied by a regression coefficient. The regression coefficient is a genetic trait, which is a measure of cooperation; a negative value indicates competition, a positive value cooperation, and an increasing value due to selection indicates the evolution of cooperation. In contrast to the existing quantitative genetic models, our model allows for co-evolution of IGEs and variability, as the regression coefficient can respond to selection. Our simulations show that the model results in increased variability of body weight with increasing competition. When competition decreases, i.e., cooperation evolves, variability becomes significantly smaller. Hence, our model facilitates quantitative genetic studies on the relationship between IGEs and inherited variability. Moreover, our findings suggest that we may have been overlooking an entire level of genetic variation in variability, the one due to IGEs.

The ability of a population to adapt to changes in their living conditions, whether in nature or captivity, often depends on polymorphisms in multiple genes across the genome. In-depth studies of such polygenic adaptations are difficult in natural populations, but can be approached using the resources provided by artificial selection experiments. Here, we dissect the genetic mechanisms involved in long-term selection responses of the Virginia chicken lines, populations that after 40 generations of divergent selection for 56-day body weight display a 9-fold difference in the selected trait. In the F15 generation of an intercross between the divergent lines, 20 loci explained >60% of the additive genetic variance for the selected trait. We focused particularly on fine-mapping seven major QTL that replicated in this population and found that only two fine-mapped to single, bi-allelic loci; the other five contained linked loci, multiple alleles or were epistatic. This detailed dissection of the polygenic adaptations in the Virginia lines provides a deeper understanding of the range of different genome-wide mechanisms that have been involved in these long-term selection responses. The results illustrate that the genetic architecture of a highly polygenic trait can involve a broad range of genetic mechanisms, and that this can be the case even in a small population bred from founders with limited genetic diversity., (© The Author 2017. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

Individuals involved in a social interaction exhibit different behavioral traits that, in combination, form the individual's behavioral responses. Selectively bred strains of silver foxes (Vulpes vulpes) demonstrate markedly different behaviors in their response to humans. To identify the genetic basis of these behavioral differences we constructed a large F 2 population including 537 individuals by cross-breeding tame and aggressive fox strains. 98 fox behavioral traits were recorded during social interaction with a human experimenter in a standard four-step test. Patterns of fox behaviors during the test were evaluated using principal component (PC) analysis. Genetic mapping identified eight unique significant and suggestive QTL. Mapping results for the PC phenotypes from different test steps showed little overlap suggesting that different QTL are involved in regulation of behaviors exhibited in different behavioral contexts. Many individual behavioral traits mapped to the same genomic regions as PC phenotypes. This provides additional information about specific behaviors regulated by these loci. Further, three pairs of epistatic loci were also identified for PC phenotypes suggesting more complex genetic architecture of the behavioral differences between the two strains than what has previously been observed.

We analyze a real data set pertaining to reindeer fecal pellet-group counts obtained from a survey conducted in a forest area in northern Sweden. In the data set, over 70% of counts are zeros, and there is high spatial correlation. We use conditionally autoregressive random effects for modeling of spatial correlation in a Poisson generalized linear mixed model (GLMM), quasi-Poisson hierarchical generalized linear model (HGLM), zero-inflated Poisson (ZIP), and hurdle models. The quasi-Poisson HGLM allows for both under- and overdispersion with excessive zeros, while the ZIP and hurdle models allow only for overdispersion. In analyzing the real data set, we see that the quasi-Poisson HGLMs can perform better than the other commonly used models, for example, ordinary Poisson HGLMs, spatial ZIP, and spatial hurdle models, and that the underdispersed Poisson HGLMs with spatial correlation fit the reindeer data best. We develop R codes for fitting these models using a unified algorithm for the HGLMs. Spatial count response with an extremely high proportion of zeros, and underdispersion can be successfully modeled using the quasi-Poisson HGLM with spatial random effects.

Genomewide association studies (GWAS) enable detailed dissections of the genetic basis for organisms' ability to adapt to a changing environment. In long-term studies of natural populations, individuals are often marked at one point in their life and then repeatedly recaptured. It is therefore essential that a method for GWAS includes the process of repeated sampling. In a GWAS, the effects of thousands of single-nucleotide polymorphisms (SNPs) need to be fitted and any model development is constrained by the computational requirements. A method is therefore required that can fit a highly hierarchical model and at the same time is computationally fast enough to be useful.Our method fits fixed SNP effects in a linear mixed model that can include both random polygenic effects and permanent environmental effects. In this way, the model can correct for population structure and model repeated measures. The covariance structure of the linear mixed model is first estimated and subsequently used in a generalized least squares setting to fit the SNP effects. The method was evaluated in a simulation study based on observed genotypes from a long-term study of collared flycatchers in Sweden.The method we present here was successful in estimating permanent environmental effects from simulated repeated measures data. Additionally, we found that especially for variable phenotypes having large variation between years, the repeated measurements model has a substantial increase in power compared to a model using average phenotypes as a response.The method is available in the r package RepeatABEL. It increases the power in GWAS having repeated measures, especially for long-term studies of natural populations, and the R implementation is expected to facilitate modelling of longitudinal data for studies of both animal and human populations.

Understanding the genetic basis of traits involved in adaptation is a major challenge in evolutionary biology but remains poorly understood. Here, we use genome-wide association mapping using a custom 50 k single nucleotide polymorphism (SNP) array in a natural population of collared flycatchers to examine the genetic basis of clutch size, an important life-history trait in many animal species. We found evidence for an association on chromosome 18 where one SNP significant at the genome-wide level explained 3.9% of the phenotypic variance. We also detected two suggestive quantitative trait loci (QTLs) on chromosomes 9 and 26. Fitness differences among genotypes were generally weak and not significant, although there was some indication of a sex-by-genotype interaction for lifetime reproductive success at the suggestive QTL on chromosome 26. This implies that sexual antagonism may play a role in maintaining genetic variation at this QTL. Our findings provide candidate regions for a classic avian life-history trait that will be useful for future studies examining the molecular and cellular function of, as well as evolutionary mechanisms operating at, these loci.

Reindeer herding in Sweden is a form of pastoralism practised by the indigenous Sámi population. The economy is mainly based on meat production. Herd size is generally regulated by harvest in order not to overuse grazing ranges and keep a productive herd. Nonetheless, herd growth and room for harvest is currently small in many areas. Negative herd growth and low harvest rate were observed in one of two herds in a reindeer herding community in Central Sweden. The herds (A and B) used the same ranges from April until the autumn gathering in October-December, but were separated on different ranges over winter. Analyses of capture-recapture for 723 adult female reindeer over five years (2007-2012) revealed high annual losses (7.1% and 18.4%, for herd A and B respectively). A continuing decline in the total reindeer number in herd B demonstrated an inability to maintain the herd size in spite of a very small harvest. An estimated breakpoint for when herd size cannot be kept stable confirmed that the observed female mortality rate in herd B represented a state of herd collapse. Lower calving success in herd B compared to A indicated differences in winter foraging conditions. However, we found only minor differences in animal body condition between the herds in autumn. We found no evidence that a lower autumn body mass generally increased the risk for a female of dying from one autumn to the next. We conclude that the prime driver of the on-going collapse of herd B is not high animal density or poor body condition. Accidents or disease seem unlikely as major causes of mortality. Predation, primarily by lynx and wolverine, appears to be the most plausible reason for the high female mortality and state of collapse in the studied reindeer herding community.

MAPfastR is a software package developed to analyze quantitative trait loci data from inbred and outbred line-crosses. The package includes a number of modules for fast and accurate quantitative trait loci analyses. It has been developed in the R language for fast and comprehensive analyses of large datasets. MAPfastR is freely available at: http://www.computationalgenetics.se/?page_id=7.

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.

The purpose of this correspondence is to discuss and clarify a few points about data transformation used in genome-wide association studies, especially for phenotypic variability. By commenting on the recent publication by Sun et al. in the American Journal of Human Genetics, we emphasize the importance of statistical power in detecting functional loci and the real meaning of the scale of the phenotype in practice.

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.

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.

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.

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., Competing Interests: The authors have declared that no competing interests exist.

We introduce this communication with a brief outline of the historical landmarks in genetic modeling, especially concerning epistasis. Then, we present methods for the use of genetic modeling in QTL analyses. In particular, we summarize the essential expressions of the natural and orthogonal interactions (NOIA) model of genetic effects. Our motivation for reviewing that theory here is twofold. First, this review presents a digest of the expressions for the application of the NOIA model, which are often mixed with intermediate and additional formulae in the original articles. Second, we make the required theory handy for the reader to relate the genetic concepts to the particular mathematical expressions underlying them. We illustrate those relations by providing graphical interpretations and a diagram summarizing the key features for applying genetic modeling with epistasis in comprehensive QTL analyses. Finally, we briefly review some examples of the application of NOIA to real data and the way it improves the interpretability of the results.

Dealing with genotype uncertainty is an ongoing issue in genetic analyses of complex traits. Here we consider genotype uncertainty in quantitative trait loci (QTL) analyses for large crosses in variance component models, where the genetic information is included in identity-by-descent (IBD) matrices. An IBD matrix is one realization from a distribution of potential IBD matrices given available marker information. In QTL analyses, its expectation is normally used resulting in potentially reduced accuracy and loss of power. Previously, IBD distributions have been included in models for small human full-sib families. We develop an Expectation-Maximization (EM) algorithm for estimating a full model based on Monte Carlo imputation for applications in large animal pedigrees. Our simulations show that the bias of variance component estimates using traditional expected IBD matrix can be adjusted by accounting for the distribution and that the calculations are computationally feasible for large pedigrees.

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.

Background: Genome-wide dense markers have been used to detect genes and estimate relative genetic values. Among many methods, Bayesian techniques have been widely used and shown to be powerful in genome-wide breeding value estimation and association studies. However, computation is known to be intensive under the Bayesian framework, and specifying a prior distribution for each parameter is always required for Bayesian computation. We propose the use of hierarchical likelihood to solve such problems., Results: Using double hierarchical generalized linear models, we analyzed the simulated dataset provided by the QTLMAS 2010 workshop. Marker-specific variances estimated by double hierarchical generalized linear models identified the QTL with large effects for both the quantitative and binary traits. The QTL positions were detected with very high accuracy. For young individuals without phenotypic records, the true and estimated breeding values had Pearson correlation of 0.60 for the quantitative trait and 0.72 for the binary trait, where the quantitative trait had a more complicated genetic architecture involving imprinting and epistatic QTL., Conclusions: Hierarchical likelihood enables estimation of marker-specific variances under the likelihoodist framework. Double hierarchical generalized linear models are powerful in localizing major QTL and computationally fast.

Background: Linkage mapping is used to identify genomic regions affecting the expression of complex traits. However, when experimental crosses such as F(2) 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 F(2) 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., Methods: We 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 F(2) 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., Results: Five of the nine QTL detected with the original F(2) 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., Conclusions: Our 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.

Background: The 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., Results: We 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., Conclusions: We 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.

Development of variance component algorithms in genetics has previously mainly focused on animal breeding models or problems in human genetics with a simple data structure. We study alternative methods for constrained likelihood maximization in quantitative trait loci (QTL) analysis for large complex pedigrees. We apply a forward selection scheme to include several QTL and interaction effects, as well as polygenic effects, with up to five variance components in the model. We show that the implemented active set and primal-dual schemes result in accurate solutions and that they are robust. In terms of computational speed, a comparison of two approaches for approximating the Hessian of the log-likelihood shows that the method using an average information matrix is the method of choice for the five-dimensional problem. The active set method, with the average information method for Hessian computation, exhibits the fastest convergence with an average of 20 iterations per tested position, where the change in variance components <0.0001 was used as convergence criterion., (Copyright 2010 Elsevier Ltd. All rights reserved.)

Background: The aim of this paper is to develop a flexible model for analysis of quantitative trait loci (QTL) in outbred line crosses, which includes both additive and dominance effects. Our flexible intercross analysis (FIA) model accounts for QTL that are not fixed within founder lines and is based on the variance component framework. Genome scans with FIA are performed using a score statistic, which does not require variance component estimation., Results: Simulations of a pedigree with 800 F2 individuals showed that the power of FIA including both additive and dominance effects was almost 50% for a QTL with equal allele frequencies in both lines with complete dominance and a moderate effect, whereas the power of a traditional regression model was equal to the chosen significance value of 5%. The power of FIA without dominance effects included in the model was close to those obtained for FIA with dominance for all simulated cases except for QTL with overdominant effects. A genome-wide linkage analysis of experimental data from an F2 intercross between Red Jungle Fowl and White Leghorn was performed with both additive and dominance effects included in FIA. The score values for chicken body weight at 200 days of age were similar to those obtained in FIA analysis without dominance., Conclusion: We have extended FIA to include QTL dominance effects. The power of FIA was superior, or similar, to standard regression methods for QTL effects with dominance. The difference in power for FIA with or without dominance is expected to be small as long as the QTL effects are not overdominant. We suggest that FIA with only additive effects should be the standard model to be used, especially since it is more computationally efficient.

Variance component models are commonly used to detect quantitative trait loci (QTL) in general pedigrees. The variance-covariance structure of the random QTL effect is given by the identity by descent (IBD) between genotypes. Epistatic effects have previously been modeled, both for unlinked and linked loci, as a random effect with a variance-covariance structure given by the Hadamard product between the IBD matrices of the direct QTL effects. In the original papers, the model was given but not derived. Here, we identify the underlying assumptions of this previously proposed model. It assumes that either an unlinked QTL or a fully informative marker (i.e., all marker alleles are unique in the base generation) is located between the loci. We discuss the need of developing a general algorithm to estimate the variance-covariance structure of the random epistatic effect for linked loci.

We present a new flexible, simple, and powerful genome-scan method (flexible intercross analysis, FIA) for detecting quantitative trait loci (QTL) in experimental line crosses. The method is based on a pure random-effects model that simultaneously models between- and within-line QTL variation for single as well as epistatic QTL. It utilizes the score statistic and thereby facilitates computationally efficient significance testing based on empirical significance thresholds obtained by means of permutations. The properties of the method are explored using simulations and analyses of experimental data. The simulations showed that the power of FIA was as good as, or better than, Haley-Knott regression and that FIA was rather insensitive to the level of allelic fixation in the founders, especially for pedigrees with few founders. A chromosome scan was conducted for a meat quality trait in an F(2) intercross in pigs where a mutation in the halothane (Ryanodine receptor, RYR1) gene with a large effect on meat quality was known to segregate in one founder line. FIA obtained significant support for the halothane-associated QTL and identified the base generation allele with the mutated allele. A genome scan was also performed in a previously analyzed chicken F(2) intercross. In the chicken intercross analysis, four previously detected QTL were confirmed at a 5% genomewide significance level, and FIA gave strong evidence (P < 0.01) for two of these QTL to be segregating within the founder lines. FIA was also extended to account for epistasis and using simulations we show that the method provides good estimates of epistatic QTL variance even for segregating QTL. Extensions of FIA and its applications on other intercross populations including backcrosses, advanced intercross lines, and heterogeneous stocks are also discussed.

Recent technological development in genetics has made large-scale marker genotyping fast and practicable, facilitating studies for detection of QTL in large general pedigrees. We developed a method that speeds up restricted maximum-likelihood (REML) algorithms for QTL analysis by simplifying the inversion of the variance-covariance matrix of the trait vector. The method was tested in an experimental chicken pedigree including 767 phenotyped individuals and 14 genotyped markers on chicken chromosome 1. The computation time in a chromosome scan covering 475 cM was reduced by 43% when the analysis was based on linkage only and by 72% when linkage disequilibrium information was included. The relative advantage of using our method increases with pedigree size, marker density, and linkage disequilibrium, indicating even greater improvements in the future.

Background: Variance 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)., Results: We 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., Conclusion: We 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.

In order to decrease environmental impacts in waste management the choice of treatment method must be based on the characteristics of the waste. Present sampling procedures do not provide statistically representative samples of solid waste and this provides difficulties in characterization. The objective of this study was to develop a procedure for waste component analysis and sampling of waste after collection and at plant level. A further objective was to characterize the waste delivered to an incineration plant for physical and chemical properties and to determine the amounts of delivered waste that could be classified as biofuels and fossil fuels. The proportions of recyclables and hazardous waste were also examined. Samples were taken randomly from waste trucks and divided by square implementation. Statistical analysis of the results showed that the number of sub-samples could be decreased with only a moderate increase in the confidence interval. This means that future waste composition analyses could be made more efficient and thereby less expensive. The analysis of the waste delivered to the Lidköping incineration plant (Central Sweden) showed that 66.4% of the household waste was composed of biofuels and 21.3% of non-renewable combustibles, of which 40.3% were recyclables. In addition, 11.6% of the household waste was non-combustible and 0.6% hazardous waste. The heat value for the biofuels was 18.0-19.7 MJ kg(-1) dry mass (DM) and for the fossil fuels 28.2-33.9 MJ kg(-1) DM. The industrial waste consisted of 35.9% biofuels, 62.0% fossil fuels, 1.6% non-combustible and 0.5% hazardous waste. The heat value was 19.5 MJ kg(-1) DM for the biofuels and 31.4 MJ kg(-1) DM for the fossil fuels.