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.     

The consequences of including non-additive effects on the genetic evaluation of harvest body weight in Coho salmon (Oncorhynchus kisutch)

Background

In this study, we used different animal models to estimate genetic and environmental variance components on harvest weight in two populations of Oncorhynchus kisutch, forming two classes i.e. odd- and even-year spawners.

Methods

The models used were: additive, with and without inbreeding as a covariable (A + F and A respectively); additive plus common environmental due to full-sib families and inbreeding (A + C + F); additive plus parental dominance and inbreeding (A + D + F); and a full model (A + C + D + F). Genetic parameters and breeding values obtained by different models were compared to evaluate the consequences of including non-additive effects on genetic evaluation.

Results

Including inbreeding as a covariable did not affect the estimation of genetic parameters, but heritability was reduced when dominance or common environmental effects were included. A high heritability for harvest weight was estimated in both populations (even = 0.46 and odd = 0.50) when simple additive models (A + F and A) were used. Heritabilities decreased to 0.21 (even) and 0.37 (odd) when the full model was used (A + C + D + F). In this full model, the magnitude of the dominance variance was 0.19 (even) and 0.06 (odd), while the magnitude of the common environmental effect was lower than 0.01 in both populations. The correlation between breeding values estimated with different models was very high in all cases (i.e. higher than 0.98). However, ranking of the 30 best males and the 100 best females per generation changed when a high dominance variance was estimated, as was the case in one of the two populations (even).

Conclusions

Dominance and common environmental variance may be important components of variance in harvest weight in O. kisutch, thus not including them may produce an overestimation of the predicted response; furthermore, genetic evaluation was seen to be partially affected, since the ranking of selected animals changed with the inclusion of non-additive effects in the animal model.     

A simulation study for the analysis of uncertain binary responses: Application to first insemination success in beef cattle

A simulation was carried out to investigate the methods of analyzing uncertain binary responses for success or failure at first insemination. A linear mixed model that included, herd, year, and month of mating as fixed effects; and unrelated service sire, sire and residual as random effects was used to generate binary data. Binary responses were assigned using the difference between days to calving and average gestation length. Females deviating from average gestation length lead to uncertain binary responses. Thus, the methods investigated were the following: (1) a threshold model fitted to certain (no uncertainty) binary data (M1); (2) a threshold model fitted to uncertain binary data ignoring uncertainty (M2); and (3) analysis of uncertain binary data, accounting for uncertainty from day 16 to 26 (M3) or from day 14 to 28 (M4) after introduction of the bull, using a threshold model with fuzzy logic classification. There was virtually no difference between point estimates obtained from M1, M3, and M4 with true values. When uncertain binary data were analyzed ignoring uncertainty (M2), sire variance and heritability were underestimated by 22 and 24%, respectively. Thus, for noisy binary data, a threshold model contemplating uncertainty is needed to avoid bias when estimating genetic parameters.     

Quantitative Trait Evolution and Environmental Change

Background

Given the recent changes in climate, there is an urgent need to understand the evolutionary ability of populations to respond to these changes.

Methodology/Principal Findings

We performed individual-based simulations with different shapes of the fitness curve, different heritabilities, different levels of density compensation, and different autocorrelation of environmental noise imposed on an environmental trend to study the ability of a population to adapt to changing conditions. The main finding is that when there is a positive autocorrelation of environmental noise, the outcome of the evolutionary process is much more unpredictable compared to when the noise has no autocorrelation. In addition, we found that strong selection resulted in a higher load, and more extinctions, and that this was most pronounced when heritability was low. The level of density-compensation was important in determining the variance in load when there was strong selection, and when genetic variance was lower when the level of density-compensation was low.

Conclusions

The strong effect of the details of the environmental fluctuations makes predictions concerning the evolutionary future of populations very hard to make. In addition, to be able to make good predictions we need information on heritability, fitness functions and levels of density compensation. The results strongly suggest that patterns of environmental noise must be incorporated in future models of environmental change, such as global warming.     

Enlarging a training set for genomic selection by imputation of un-genotyped animals in populations of varying genetic architecture

Background

The most common application of imputation is to infer genotypes of a high-density panel of markers on animals that are genotyped for a low-density panel. However, the increase in accuracy of genomic predictions resulting from an increase in the number of markers tends to reach a plateau beyond a certain density. Another application of imputation is to increase the size of the training set with un-genotyped animals. This strategy can be particularly successful when a set of closely related individuals are genotyped.

Methods

Imputation on completely un-genotyped dams was performed using known genotypes from the sire of each dam, one offspring and the offspring’s sire. Two methods were applied based on either allele or haplotype frequencies to infer genotypes at ambiguous loci. Results of these methods and of two available software packages were compared. Quality of imputation under different population structures was assessed. The impact of using imputed dams to enlarge training sets on the accuracy of genomic predictions was evaluated for different populations, heritabilities and sizes of training sets.

Results

Imputation accuracy ranged from 0.52 to 0.93 depending on the population structure and the method used. The method that used allele frequencies performed better than the method based on haplotype frequencies. Accuracy of imputation was higher for populations with higher levels of linkage disequilibrium and with larger proportions of markers with more extreme allele frequencies. Inclusion of imputed dams in the training set increased the accuracy of genomic predictions. Gains in accuracy ranged from close to zero to 37.14%, depending on the simulated scenario. Generally, the larger the accuracy already obtained with the genotyped training set, the lower the increase in accuracy achieved by adding imputed dams.

Conclusions

Whenever a reference population resembling the family configuration considered here is available, imputation can be used to achieve an extra increase in accuracy of genomic predictions by enlarging the training set with completely un-genotyped dams. This strategy was shown to be particularly useful for populations with lower levels of linkage disequilibrium, for genomic selection on traits with low heritability, and for species or breeds for which the size of the reference population is limited.     

Rapid screening for phenotype-genotype associations by linear transformations of genomic evaluations

Background

Currently, association studies are analysed using statistical mixed models, with marker effects estimated by a linear transformation of genomic breeding values. The variances of marker effects are needed when performing the tests of association. However, approaches used to estimate the parameters rely on a prior variance or on a constant estimate of the additive variance. Alternatively, we propose a standardized test of association using the variance of each marker effect, which generally differ among each other. Random breeding values from a mixed model including fixed effects and a genomic covariance matrix are linearly transformed to estimate the marker effects.

Results

The standardized test was neither conservative nor liberal with respect to type I error rate (false-positives), compared to a similar test using Predictor Error Variance, a method that was too conservative. Furthermore, genomic predictions are solved efficiently by the procedure, and the p-values are virtually identical to those calculated from tests for one marker effect at a time. Moreover, the standardized test reduces computing time and memory requirements.The following steps are used to locate genome segments displaying strong association. The marker with the highest − log(p-value) in each chromosome is selected, and the segment is expanded one Mb upstream and one Mb downstream of the marker. A genomic matrix is calculated using the information from those markers only, which is used as the variance-covariance of the segment effects in a model that also includes fixed effects and random genomic breeding values. The likelihood ratio is then calculated to test for the effect in every chromosome against a reduced model with fixed effects and genomic breeding values. In a case study with pigs, a significant segment from chromosome 6 explained 11% of total genetic variance.

Conclusions

The standardized test of marker effects using their own variance helps in detecting specific genomic regions involved in the additive variance, and in reducing false positives. Moreover, genome scanning of candidate segments can be used in meta-analyses of genome-wide association studies, as it enables the detection of specific genome regions that affect an economically relevant trait when using multiple populations.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2105-15-246) contains supplementary material, which is available to authorized users.     

Modelling and estimation of genotype by environment interactions for production traits in French dairy cattle

Background

Genotype by environment interactions are currently ignored in national genetic evaluations of dairy cattle. However, this is often questioned, especially when environment or herd management is wide-ranging. The aim of this study was to assess genotype by environment interactions for production traits (milk, protein, fat yields and fat and protein contents) in French dairy cattle using an original approach to characterize the environments.

Methods

Genetic parameters of production traits were estimated for three breeds (Holstein, Normande and Montbéliarde) using multiple-trait and reaction norm models. Variables derived from Herd Test Day profiles obtained after a test day model evaluation were used to define herd environment.

Results

Multiple-trait and reaction norm models gave similar results. Genetic correlations were very close to unity for all traits, except between some extreme environments. However, a relatively wide range of heritabilities by trait and breed was found across environments. This was more the case for milk, protein and fat yields than for protein and fat contents.

Conclusions

No real reranking of animals was observed across environments. However, a significant scale effect exists: the more intensive the herd management for milk yield, the larger the heritability.     

Inheritance of fertility in broiler chickens

Background

The fertility of a chicken''s egg is a trait which depends on both the hen that lays the egg and on her mate. It is also known that fertility of an individual changes over the laying period.

Methods

Longitudinal models including both random genetic and permanent environmental effects of both the female and her male mate were used to model the proportion of fertile eggs in a pedigree broiler population over the ages 29-54 weeks.

Results

Both the male and the female contribute to variation in fertility. Estimates of heritability of weekly records were typically 7% for female and 10% for male contributions to fertility. Repeatability estimates ranged from 24 to 33%, respectively. The estimated genetic variance remained almost constant for both sexes over the laying period and the genetic correlations between different ages were close to 1.0. The permanent environment components increased substantially towards the end of the analyzed period, and correlations between permanent environment effects at different ages declined with increasing age difference The heritability of mean fertility over the whole laying period was estimated at 13% for females and 17% for males. A small positive correlation between genetic effects for male and female fertility was found.

Conclusion

Opportunities to improve fertility in broiler stocks by selection on both sexes exist and should have an impact throughout the laying period.     

Breeding experience and the heritability of female mate choice in collared flycatchers

Background

Heritability in mate preferences is assumed by models of sexual selection, and preference evolution may contribute to adaptation to changing environments. However, mate preference is difficult to measure in natural populations as detailed data on mate availability and mate sampling are usually missing. Often the only available information is the ornamentation of the actual mate. The single long-term quantitative genetic study of a wild population found low heritability in female mate ornamentation in Swedish collared flycatchers. One potentially important cause of low heritability in mate ornamentation at the population level is reduced mate preference expression among inexperienced individuals.

Methodology/Principal Findings

Applying animal model analyses to 21 years of data from a Hungarian collared flycatcher population, we found that additive genetic variance was 50 percent and significant for ornament expression in males, but less than 5 percent and non-significant for mate ornamentation treated as a female trait. Female breeding experience predicted breeding date and clutch size, but mate ornamentation and its variance components were unrelated to experience. Although we detected significant area and year effects on mate ornamentation, more than 85 percent of variance in this trait remained unexplained. Moreover, the effects of area and year on mate ornamentation were also highly positively correlated between inexperienced and experienced females, thereby acting to remove difference between the two groups.

Conclusions/Significance

The low heritability of mate ornamentation was apparently not explained by the presence of inexperienced individuals. Our results further indicate that the expression of mate ornamentation is dominated by temporal and spatial constraints and unmeasured background factors. Future studies should reduce unexplained variance or use alternative measures of mate preference. The heritability of mate preference in the wild remains a principal but unresolved question in evolutionary ecology.     

Statistical distributions of test statistics used for quantitative trait association mapping in structured populations

Background

Spurious associations between single nucleotide polymorphisms and phenotypes are a major issue in genome-wide association studies and have led to underestimation of type 1 error rate and overestimation of the number of quantitative trait loci found. Many authors have investigated the influence of population structure on the robustness of methods by simulation. This paper is aimed at developing further the algebraic formalization of power and type 1 error rate for some of the classical statistical methods used: simple regression, two approximate methods of mixed models involving the effect of a single nucleotide polymorphism (SNP) and a random polygenic effect (GRAMMAR and FASTA) and the transmission/disequilibrium test for quantitative traits and nuclear families. Analytical formulae were derived using matrix algebra for the first and second moments of the statistical tests, assuming a true mixed model with a polygenic effect and SNP effects.

Results

The expectation and variance of the test statistics and their marginal expectations and variances according to the distribution of genotypes and estimators of variance components are given as a function of the relationship matrix and of the heritability of the polygenic effect. These formulae were used to compute type 1 error rate and power for any kind of relationship matrix between phenotyped and genotyped individuals for any level of heritability. For the regression method, type 1 error rate increased with the variability of relationships and with heritability, but decreased with the GRAMMAR method and was not affected with the FASTA and quantitative transmission/disequilibrium test methods.

Conclusions

The formulae can be easily used to provide the correct threshold of type 1 error rate and to calculate the power when designing experiments or data collection protocols. The results concerning the efficacy of each method agree with simulation results in the literature but were generalized in this work. The power of the GRAMMAR method was equal to the power of the FASTA method at the same type 1 error rate. The power of the quantitative transmission/disequilibrium test was low. In conclusion, the FASTA method, which is very close to the full mixed model, is recommended in association mapping studies.     

Predicting heterosis for egg production traits in crossbred offspring of individual White Leghorn sires using genome-wide SNP data

Background

The development of a reliable method to predict heterosis would greatly improve the efficiency of commercial crossbreeding schemes. Extending heterosis prediction from the line level to the individual sire level would take advantage of variation between sires from the same pure line, and further increase the use of heterosis in crossbreeding schemes. We aimed at deriving the theoretical expectation for heterosis due to dominance in the crossbred offspring of individual sires, and investigating how much extra variance in heterosis can be explained by predicting heterosis at the individual sire level rather than at the line level. We used 53 421 SNP (single nucleotide polymorphism) genotypes of 3427 White Leghorn sires, allele frequencies of six White Leghorn dam-lines and cage-based records on egg number and egg weight of ~210 000 crossbred hens.

Results

We derived the expected heterosis for the offspring of individual sires as the between- and within-line genome-wide heterozygosity excess in the offspring of a sire relative to the mean heterozygosity of the pure lines. Next, we predicted heterosis by regressing offspring performance on the heterozygosity excess. Predicted heterosis ranged from 7.6 to 16.7 for egg number, and from 1.1 to 2.3 grams for egg weight. Between-line differences accounted for 99.0% of the total variance in predicted heterosis, while within-line differences among sires accounted for 0.7%.

Conclusions

We show that it is possible to predict heterosis at the sire level, thus to distinguish between sires within the same pure line with offspring that show different levels of heterosis. However, based on our data, variation in genome-wide predicted heterosis between sires from the same pure line was small; most differences were observed between lines. We hypothesise that this method may work better if predictions are based on SNPs with identified dominance effects.     

A Bayesian generalized random regression model for estimating heritability using overdispersed count data

Background

Faecal egg counts are a common indicator of nematode infection and since it is a heritable trait, it provides a marker for selective breeding. However, since resistance to disease changes as the adaptive immune system develops, quantifying temporal changes in heritability could help improve selective breeding programs. Faecal egg counts can be extremely skewed and difficult to handle statistically. Therefore, previous heritability analyses have log transformed faecal egg counts to estimate heritability on a latent scale. However, such transformations may not always be appropriate. In addition, analyses of faecal egg counts have typically used univariate rather than multivariate analyses such as random regression that are appropriate when traits are correlated. We present a method for estimating the heritability of untransformed faecal egg counts over the grazing season using random regression.

Results

Replicating standard univariate analyses, we showed the dependence of heritability estimates on choice of transformation. Then, using a multitrait model, we exposed temporal correlations, highlighting the need for a random regression approach. Since random regression can sometimes involve the estimation of more parameters than observations or result in computationally intractable problems, we chose to investigate reduced rank random regression. Using standard software (WOMBAT), we discuss the estimation of variance components for log transformed data using both full and reduced rank analyses. Then, we modelled the untransformed data assuming it to be negative binomially distributed and used Metropolis Hastings to fit a generalized reduced rank random regression model with an additive genetic, permanent environmental and maternal effect. These three variance components explained more than 80 % of the total phenotypic variation, whereas the variance components for the log transformed data accounted for considerably less. The heritability, on a link scale, increased from around 0.25 at the beginning of the grazing season to around 0.4 at the end.

Conclusions

Random regressions are a useful tool for quantifying sources of variation across time. Our MCMC (Markov chain Monte Carlo) algorithm provides a flexible approach to fitting random regression models to non-normal data. Here we applied the algorithm to negative binomially distributed faecal egg count data, but this method is readily applicable to other types of overdispersed data.     

Quantifying Spatial Disparities in Neonatal Mortality Using a Structured Additive Regression Model

Background

Neonatal mortality contributes a large proportion towards early childhood mortality in developing countries, with considerable geographical variation at small areas within countries.

Methods

A geo-additive logistic regression model is proposed for quantifying small-scale geographical variation in neonatal mortality, and to estimate risk factors of neonatal mortality. Random effects are introduced to capture spatial correlation and heterogeneity. The spatial correlation can be modelled using the Markov random fields (MRF) when data is aggregated, while the two dimensional P-splines apply when exact locations are available, whereas the unstructured spatial effects are assigned an independent Gaussian prior. Socio-economic and bio-demographic factors which may affect the risk of neonatal mortality are simultaneously estimated as fixed effects and as nonlinear effects for continuous covariates. The smooth effects of continuous covariates are modelled by second-order random walk priors. Modelling and inference use the empirical Bayesian approach via penalized likelihood technique. The methodology is applied to analyse the likelihood of neonatal deaths, using data from the 2000 Malawi demographic and health survey. The spatial effects are quantified through MRF and two dimensional P-splines priors.

Results

Findings indicate that both fixed and spatial effects are associated with neonatal mortality.

Conclusions

Our study, therefore, suggests that the challenge to reduce neonatal mortality goes beyond addressing individual factors, but also require to understanding unmeasured covariates for potential effective interventions.     

Evaluating alternate models to estimate genetic parameters of calving traits in United Kingdom Holstein-Friesian dairy cattle

Background

The focus in dairy cattle breeding is gradually shifting from production to functional traits and genetic parameters of calving traits are estimated more frequently. However, across countries, various statistical models are used to estimate these parameters. This study evaluates different models for calving ease and stillbirth in United Kingdom Holstein-Friesian cattle.

Methods

Data from first and later parity records were used. Genetic parameters for calving ease, stillbirth and gestation length were estimated using the restricted maximum likelihood method, considering different models i.e. sire (−maternal grandsire), animal, univariate and bivariate models. Gestation length was fitted as a correlated indicator trait and, for all three traits, genetic correlations between first and later parities were estimated. Potential bias in estimates was avoided by acknowledging a possible environmental direct-maternal covariance. The total heritable variance was estimated for each trait to discuss its theoretical importance and practical value. Prediction error variances and accuracies were calculated to compare the models.

Results and discussion

On average, direct and maternal heritabilities for calving traits were low, except for direct gestation length. Calving ease in first parity had a significant and negative direct-maternal genetic correlation. Gestation length was maternally correlated to stillbirth in first parity and directly correlated to calving ease in later parities. Multi-trait models had a slightly greater predictive ability than univariate models, especially for the lowly heritable traits. The computation time needed for sire (−maternal grandsire) models was much smaller than for animal models with only small differences in accuracy. The sire (−maternal grandsire) model was robust when additional genetic components were estimated, while the equivalent animal model had difficulties reaching convergence.

Conclusions

For the evaluation of calving traits, multi-trait models show a slight advantage over univariate models. Extended sire models (−maternal grandsire) are more practical and robust than animal models. Estimated genetic parameters for calving traits of UK Holstein cattle are consistent with literature. Calculating an aggregate estimated breeding value including direct and maternal values should encourage breeders to consider both direct and maternal effects in selection decisions.     

Identity-by-descent genomic selection using selective and sparse genotyping

Background

Genomic selection methods require dense and widespread genotyping data, posing a particular challenge if both sexes are subject to intense selection (e.g., aquaculture species). This study focuses on alternative low-cost genomic selection methods (IBD-GS) that use selective genotyping with sparse marker panels to estimate identity-by-descent relationships through linkage analysis. Our aim was to evaluate the potential of these methods in selection programs for continuous traits measured on sibs of selection candidates in a typical aquaculture breeding population.

Methods

Phenotypic and genomic data were generated by stochastic simulation, assuming low to moderate heritabilities (0.10 to 0.30) for a Gaussian trait measured on sibs of the selection candidates in a typical aquaculture breeding population that consisted of 100 families (100 training animals and 20 selection candidates per family). Low-density marker genotype data (~ 40 markers per Morgan) were used to trace genomic identity-by-descent relationships. Genotyping was restricted to selection candidates from 30 phenotypically top-ranking families and varying fractions of their phenotypically extreme training sibs. All phenotypes were included in the genetic analyses. Classical pedigree-based and IBD-GS models were compared based on realized genetic gain over one generation of selection.

Results

Genetic gain increased substantially (13 to 32%) with IBD-GS compared to classical selection and was greatest with higher heritability. Most of the extra gain from IBD-GS was obtained already by genotyping the 5% phenotypically most extreme sibs within the pre-selected families. Additional genotyping further increased genetic gains, but these were small when going from genotyping 20% of the extremes to all phenotyped sibs. The success of IBD-GS with sparse and selective genotyping can be explained by the fact that within-family haplotype blocks are accurately traced even with low-marker densities and that most of the within-family variance for normally distributed traits is captured by a small proportion of the phenotypically extreme sibs.

Conclusions

IBD-GS was substantially more effective than classical selection, even when based on very few markers and combined with selective genotyping of small fractions of the population. The study shows that low-cost GS programs can be successful by combining sparse and selective genotyping with pedigree and linkage information.     

Lagged Effect of Diurnal Temperature Range on Mortality in a Subtropical Megacity of China

Background

Many studies have found extreme temperature can increase the risk of mortality. However, it is not clear whether extreme diurnal temperature range (DTR) is associated with daily disease-specific mortality, and how season might modify any association.

Objectives

To better understand the acute effect of DTR on mortality and identify whether season is a modifier of the DTR effect.

Methods

The distributed lag nonlinear model (DLNM) was applied to assess the non-linear and delayed effects of DTR on deaths (non-accidental mortality (NAD), cardiovascular disease (CVD), respiratory disease (RD) and cerebrovascular disease (CBD)) in the full year, the cold season and the warm season.

Results

A non-linear relationship was consistently found between extreme DTR and mortality. Immediate effects of extreme low DTR on all types of mortality were stronger than those of extreme high DTR in the full year. The cumulative effects of extreme DTRs increased with the increment of lag days for all types of mortality in cold season, and they were greater for extreme high DTRs than those of extreme low DTRs. In hot season, the cumulative effects for extreme low DTRs increased with the increment of lag days, but for extreme high DTR they reached maxima at a lag of 13 days for all types of mortality except for CBD(at lag6 days), and then decreased.

Conclusions

Our findings suggest that extreme DTR is an independent risk factor of daily mortality, and season is a modifier of the association of DTR with daily mortality.     

QTL fine mapping with Bayes C(π): a simulation study

Background

Accurate QTL mapping is a prerequisite in the search for causative mutations. Bayesian genomic selection models that analyse many markers simultaneously should provide more accurate QTL detection results than single-marker models. Our objectives were to (a) evaluate by simulation the influence of heritability, number of QTL and number of records on the accuracy of QTL mapping with Bayes Cπ and Bayes C; (b) estimate the QTL status (homozygous vs. heterozygous) of the individuals analysed. This study focussed on the ten largest detected QTL, assuming they are candidates for further characterization.

Methods

Our simulations were based on a true dairy cattle population genotyped for 38 277 phased markers. Some of these markers were considered biallelic QTL and used to generate corresponding phenotypes. Different numbers of records (4387 and 1500), heritability values (0.1, 0.4 and 0.7) and numbers of QTL (10, 100 and 1000) were studied. QTL detection was based on the posterior inclusion probability for individual markers, or on the sum of the posterior inclusion probabilities for consecutive markers, estimated using Bayes C or Bayes Cπ. The QTL status of the individuals was derived from the contrast between the sums of the SNP allelic effects of their chromosomal segments.

Results

The proportion of markers with null effect (π) frequently did not reach convergence, leading to poor results for Bayes Cπ in QTL detection. Fixing π led to better results. Detection of the largest QTL was most accurate for medium to high heritability, for low to moderate numbers of QTL, and with a large number of records. The QTL status was accurately inferred when the distribution of the contrast between chromosomal segment effects was bimodal.

Conclusions

QTL detection is feasible with Bayes C. For QTL detection, it is recommended to use a large dataset and to focus on highly heritable traits and on the largest QTL. QTL statuses were inferred based on the distribution of the contrast between chromosomal segment effects.     

A GWAS assessment of the contribution of genomic imprinting to the variation of body mass index in mice

Background

Genomic imprinting is an epigenetic mechanism that can lead to differential gene expression depending on the parent-of-origin of a received allele. While most studies on imprinting address its underlying molecular mechanisms or attempt at discovering genomic regions that might be subject to imprinting, few have focused on the amount of phenotypic variation contributed by such epigenetic process. In this report, we give a brief review of a one-locus imprinting model in a quantitative genetics framework, and provide a decomposition of the genetic variance according to this model. Analytical deductions from the proposed imprinting model indicated a non-negligible contribution of imprinting to genetic variation of complex traits. Also, we performed a whole-genome scan analysis on mouse body mass index (BMI) aiming at revealing potential consequences when existing imprinting effects are ignored in genetic analysis.

Results

10,021 SNP markers were used to perform a whole-genome single marker regression on mouse BMI using an additive and an imprinting model. Markers significant for imprinting indicated that BMI is subject to imprinting. Marked variance changed from 1.218 ×10⁻⁴ to 1.842 ×10⁻⁴ when imprinting was considered in the analysis, implying that one third of marked variance would be lost if existing imprinting effects were not accounted for. When both marker and pedigree information were used, estimated heritability increased from 0.176 to 0.195 when imprinting was considered.

Conclusions

When a complex trait is subject to imprinting, using an additive model that ignores this phenomenon may result in an underestimate of additive variability, potentially leading to wrong inferences about the underlying genetic architecture of that trait. This could be a possible factor explaining part of the missing heritability commonly observed in genome-wide association studies (GWAS).     

Connectedness among herds of beef cattle bred under natural service

Background

A procedure to measure connectedness among herds was applied to a beef cattle population bred by natural service. It consists of two steps: (a) computing coefficients of determination (CDs) of comparisons among herds; and (b) building sets of connected herds.

Methods

The CDs of comparisons among herds were calculated using a sampling-based method that estimates empirical variances of true and predicted breeding values from a simulated n-sample. Once the CD matrix was estimated, a clustering method that can handle a large number of comparisons was applied to build compact clusters of connected herds of the Bruna dels Pirineus beef cattle. Since in this breed, natural service is predominant and there are almost no links with reference sires, to estimate CDs, an animal model was used taking into consideration all pedigree information and, especially, the connections with dams. A sensitivity analysis was performed to contrast single-trait sire and animal model evaluations with different heritabilities, multiple-trait animal model evaluations with different degrees of genetic correlations and models with maternal effects.

Results

Using a sire model, the percentage of connected herds was very low even for highly heritable traits whereas with an animal model, most of the herds of the breed were well connected and high CD values were obtained among them, especially for highly heritable traits (the mean of average CD per herd was 0.535 for a simulated heritability of 0.40). For the lowly heritable traits, the average CD increased from 0.310 in the single-trait evaluation to 0.319 and 0.354 in the multi-trait evaluation with moderate and high genetic correlations, respectively. In models with maternal effects, the average CD per herd for the direct effects was similar to that from single-trait evaluations. For the maternal effects, the average CD per herd increased if the maternal effects had a high genetic correlation with the direct effects, but the percentage of connected herds for maternal effects was very low, less than 12%.

Conclusions

The degree of connectedness in a bovine population bred by natural service mating, such as Bruna del Pirineus beef cattle, measured as the CD of comparisons among herds, is high. It is possible to define a pool of animals for which estimated breeding values can be compared after an across-herds genetic evaluation, especially for highly heritable traits.     

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.