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

Macro- and micro-genetic environmental sensitivity of yearling weight in Angus beef cattle

Australian beef cattle experience variable conditions, which may give rise to genotype-by-environment interactions depending on the genotypes' macro- and/or micro-genetic environmental sensitivity (GES). Macro-GES gives rise to genotype-by-environment interactions across definable and shared environments, while micro-GES causes heritable variation of phenotypes, e.g., the performance of progeny from one sire may be more variable than other sires. Yearling weight (YW) is a key trait in Australian Angus cattle that may be impacted by both macro- and micro-GES. Current models for genetic evaluation of YW attempt to account for macro-GES by fitting sire-by-herd interactions (S × H). Variation in micro-GES had not yet been estimated for YW in Australian Angus. The aim of this study was to estimate genetic variation due to macro- and micro-GES in YW of Australian Angus cattle. A reaction norm with contemporary group effects as the environmental covariate was fitted either as an alternative to or in combination with a random S × H effect to account for macro-GES. Double hierarchical generalised linear models (DHGLM), fitted as sire models, were used to estimate the genetic variance of the dispersion as a measure of micro-GES. Variation due to both macro- and micro-GES were found in YW. The variance of the slope of the reaction norm was 0.02-0.03 (SEs 0.00), while the S × H variance accounted for 7% of the phenotypic variance in all models. Results showed that both a random S × H effect and a reaction norm should be included to account for both macro-GES and the additional variation captured by an S × H effect. The heritability of the dispersion on the measurement scale ranged from 0.06 to 0.10 (SEs 0.00) depending on which model was used. It should therefore be possible to alter both macro- and micro-GES of YW in Australian Angus through selection. However, care should be taken to ensure an appropriate data structure when including sire-by-herd interactions in the mean part of a DHGLM; otherwise, it can cause biased estimates of micro-GES.

Micro-genetic environmental sensitivity across macro-environments of chickens reared in Burkina Faso and France

BACKGROUND

Commercial poultry production systems follow a pyramidal structure with a nucleus of purebred animals under controlled conditions at the top and crossbred animals under commercial production conditions at the bottom. Genetic correlations between the same phenotypes on nucleus and production animals can therefore be influenced by differences both in purebred-crossbred genotypes and in genotype-by-environment interactions across the two environments, known as macro-genetic environmental sensitivity (GES). Within each environment, genotype-by-environment interactions can also occur due to so-called micro-GES. Micro-GES causes heritable variation in phenotypes and decreases uniformity. In this study, genetic variances of body weight (BW) and of micro-GES of BW and the impacts of purebred-crossbred differences and macro-environmental differences on micro-GES of BW were estimated. The dataset contained three subpopulations of slow-growing broiler chickens: purebred chickens (PB) reared in France, and crossbred chickens reared in France (FR) under the same conditions as PB or reared in Burkina Faso (BF) under local conditions. The crossbred chickens were offspring of the same dam line and had PB as their sire line.

RESULTS

Estimates of heritability of BW and micro-GES of BW were 0.54 (SE of 0.02) and 0.06 (0.01), 0.67 (0.03) and 0.03 (0.01), and 0.68 (0.04) and 0.02 (0.01) for the BF, FR, and PB subpopulations, respectively. Estimates of the genetic correlations for BW between the three subpopulations were moderately positive (0.37 to 0.53) and those for micro-GES were weakly to moderately positive (0.01 to 0.44).

CONCLUSIONS

The results show that the heritability of the micro-GES of BW varies with macro-environment, which indicates that responses to selection are expected to differ between macro-environments. The weak to moderate positive genetic correlations between subpopulations indicate that both macro-environmental differences and purebred-crossbred differences can cause re-ranking of sires based on their estimated breeding values for micro-GES of BW. Thus, the sire that produces the most variable progeny in one macro-environment may not be the one that produces the most variable offspring in another. Similarly, the sire that produces the most variable purebred progeny may not produce the most variable crossbred progeny. The results highlight the need for investigating micro-GES for all subpopulations included in the selection scheme, to ensure optimal genetic gain in all subpopulations.

Disentangling the dynamics of energy allocation to develop a proxy for robustness of fattening pigs

BACKGROUND

There is a growing need to improve robustness of fattening pigs, but this trait is difficult to phenotype. Our first objective was to develop a proxy for robustness of fattening pigs by modelling the longitudinal energy allocation coefficient to growth, with the resulting environmental variance of this allocation coefficient considered as a proxy for robustness. The second objective was to estimate its genetic parameters and correlations with traits under selection and with phenotypes that are routinely collected. In total, 5848 pigs from a Pietrain NN paternal line were tested at the AXIOM boar testing station (Azay-sur-Indre, France) from 2015 to 2022. This farm is equipped with an automatic feeding system that records individual weight and feed intake at each visit. We used a dynamic linear regression model to characterize the evolution of the allocation coefficient between the available cumulative net energy, which was estimated from feed intake, and cumulative weight gain during the fattening period. Longitudinal energy allocation coefficients were analysed using a two-step approach to estimate both the genetic variance of the coefficients and the genetic variance in their residual variance, which will be referred to as the log-transformed squared residual (LSR).

RESULTS

The LSR trait, which could be interpreted as an indicator of the response of the animal to perturbations/stress, showed a low heritability (0.05 ± 0.01), a high favourable genetic correlation with average daily growth (- 0.71 ± 0.06), and unfavourable genetic correlations with feed conversion ratio (- 0.76 ± 0.06) and residual feed intake (- 0.83 ± 0.06). Segmentation of the population in four classes using estimated breeding values for LSR showed that animals with the lowest estimated breeding values were those with the worst values for phenotypic proxies of robustness, which were assessed using records routinely collected on farm.

CONCLUSIONS

Results of this study show that selection for robustness, based on estimated breeding values for environmental variance of the allocation coefficients to growth, can be considered in breeding programs for fattening pigs.

Genomic prediction for grain yield and micro-environmental sensitivity in winter wheat

Individuals within a common environment experience variations due to unique and non-identifiable micro-environmental factors. Genetic sensitivity to micro-environmental variation (i.e. micro-environmental sensitivity) can be identified in residuals, and genotypes with lower micro-environmental sensitivity can show greater resilience towards environmental perturbations. Micro-environmental sensitivity has been studied in animals; however, research on this topic is limited in plants and lacking in wheat. In this article, we aimed to (i) quantify the influence of genetic variation on residual dispersion and the genetic correlation between genetic effects on (expressed) phenotypes and residual dispersion for wheat grain yield using a double hierarchical generalized linear model (DHGLM); and (ii) evaluate the predictive performance of the proposed DHGLM for prediction of additive genetic effects on (expressed) phenotypes and its residual dispersion. Analyses were based on 2,456 advanced breeding lines tested in replicated trials within and across different environments in Denmark and genotyped with a 15K SNP-Illumina-BeadChip. We found that micro-environmental sensitivity for grain yield is heritable, and there is potential for its reduction. The genetic correlation between additive effects on (expressed) phenotypes and dispersion was investigated, and we observed an intermediate correlation. From these results, we concluded that breeding for reduced micro-environmental sensitivity is possible and can be included within breeding objectives without compromising selection for increased yield. The predictive ability and variance inflation for predictions of the DHGLM and a linear mixed model allowing heteroscedasticity of residual variance in different environments (LMM-HET) were evaluated using leave-one-line-out cross-validation. The LMM-HET and DHGLM showed good and similar performance for predicting additive effects on (expressed) phenotypes. In addition, the accuracy of predicting genetic effects on residual dispersion was sufficient to allow genetic selection for resilience. Such findings suggests that DHGLM may be a good choice to increase grain yield and reduce its micro-environmental sensitivity.

Education interacts with genetic variants near GJD2, RBFOX1, LAMA2, KCNQ5 and LRRC4C to confer susceptibility to myopia

Myopia most often develops during school age, with the highest incidence in countries with intensive education systems. Interactions between genetic variants and educational exposure are hypothesized to confer susceptibility to myopia, but few such interactions have been identified. Here, we aimed to identify genetic variants that interact with education level to confer susceptibility to myopia. Two groups of unrelated participants of European ancestry from UK Biobank were studied. A 'Stage-I' sample of 88,334 participants whose refractive error (avMSE) was measured by autorefraction and a 'Stage-II' sample of 252,838 participants who self-reported their age-of-onset of spectacle wear (AOSW) but who did not undergo autorefraction. Genetic variants were prioritized via a 2-step screening process in the Stage-I sample: Step 1 was a genome-wide association study for avMSE; Step 2 was a variance heterogeneity analysis for avMSE. Genotype-by-education interaction tests were performed in the Stage-II sample, with University education coded as a binary exposure. On average, participants were 58 years-old and left full-time education when they were 18 years-old; 35% reported University level education. The 2-step screening strategy in the Stage-I sample prioritized 25 genetic variants (GWAS P < 1e-04; variance heterogeneity P < 5e-05). In the Stage-II sample, 19 of the 25 (76%) genetic variants demonstrated evidence of variance heterogeneity, suggesting the majority were true positives. Five genetic variants located near GJD2, RBFOX1, LAMA2, KCNQ5 and LRRC4C had evidence of a genotype-by-education interaction in the Stage-II sample (P < 0.002) and consistent evidence of a genotype-by-education interaction in the Stage-I sample. For all 5 variants, University-level education was associated with an increased effect of the risk allele. In this cohort, additional years of education were associated with an enhanced effect of genetic variants that have roles including axon guidance and the development of neuronal synapses and neural circuits.

A quantile integral linear model to quantify genetic effects on phenotypic variability

Detecting genetic variants associated with the variance of complex traits, that is, variance quantitative trait loci (vQTLs), can provide crucial insights into the interplay between genes and environments and how they jointly shape human phenotypes in the population. We propose a quantile integral linear model (QUAIL) to estimate genetic effects on trait variability. Through extensive simulations and analyses of real data, we demonstrate that QUAIL provides computationally efficient and statistically powerful vQTL mapping that is robust to non-Gaussian phenotypes and confounding effects on phenotypic variability. Applied to UK Biobank (n = 375,791), QUAIL identified 11 vQTLs for body mass index (BMI) that have not been previously reported. Top vQTL findings showed substantial enrichment for interactions with physical activities and sedentary behavior. Furthermore, variance polygenic scores (vPGSs) based on QUAIL effect estimates showed superior predictive performance on both population-level and within-individual BMI variability compared to existing approaches. Overall, QUAIL is a unified framework to quantify genetic effects on the phenotypic variability at both single-variant and vPGS levels. It addresses critical limitations in existing approaches and may have broad applications in future gene-environment interaction studies.

Genome-wide variance quantitative trait locus analysis suggests small interaction effects in blood pressure traits

Genome-wide variance quantitative trait loci (vQTL) analysis complements genome-wide association study (GWAS) and has the potential to identify novel variants associated with the trait, explain additional trait variance and lead to the identification of factors that modulate the genetic effects. I conducted genome-wide analysis of the UK Biobank data and identified 27 vQTLs associated with systolic blood pressure (SBP), diastolic blood pressure (DBP) and pulse pressure (PP). The top single-nucleotide polymorphisms (SNPs) are enriched for expression QTLs (eQTLs) or splicing QTLs (sQTLs) annotated by GTEx, suggesting their regulatory roles in mediating the associations with blood pressure (BP). Of the 27 vQTLs, 14 are known BP-associated QTLs discovered by GWASs. The heteroscedasticity effects of the 13 novel vQTLs are larger than their genetic main effects, which were not detected by existing GWASs. The total R-squared of the 27 top SNPs due to variance heteroscedasticity is 0.28%, compared with 0.50% owing to their main effects. The overall effect size of the variance heteroscedasticity is small in GWAS SNPs compared with their main effects. For the 411, 384 and 285 GWAS SNPs associated with SBP, DBP and PP, respectively, their heteroscedasticity effects were 0.52%, 0.43%, and 0.16%, and their main effects were 5.13%, 5.61%, and 3.75%, respectively. The number and effects of the vQTLs are small, which suggests that the effects of gene-environment and gene-gene interactions are small. The main effects of the SNPs remain the major source of genetic variance for BP, which would probably be true for other complex traits as well.

Assessment of two statistical approaches for variance genome-wide association studies in plants

Genomic loci that control the variance of agronomically important traits are increasingly important due to the profusion of unpredictable environments arising from climate change. The ability to identify such variance-controlling loci in association studies will be critical for future breeding efforts. Two statistical approaches that have already been used in the variance genome-wide association study (vGWAS) paradigm are the Brown-Forsythe test (BFT) and the double generalized linear model (DGLM). To ensure that these approaches are deployed as effectively as possible, it is critical to study the factors that influence their ability to identify variance-controlling loci. We used genome-wide marker data in maize (Zea mays L.) and Arabidopsis thaliana to simulate traits controlled by epistasis, genotype by environment (GxE) interactions, and variance quantitative trait nucleotides (vQTNs). We then quantified true and false positive detection rates of the BFT and DGLM across all simulated traits. We also conducted a vGWAS using both the BFT and DGLM on plant height in a maize diversity panel. The observed true positive detection rates at the maximum sample size considered (N = 2815) suggest that both of these vGWAS approaches are capable of identifying epistasis and GxE for sufficiently large sample sizes. We also noted that the DGLM decisively outperformed the BFT for simulated traits controlled by vQTNs at sample sizes of N = 500. Although we conclude that there are still certain aspects of vGWAS approaches that need further refinement, this study suggests that the BFT and DGLM are capable of identifying variance-controlling loci in current state-of-the-art plant or agronomic data sets.

Genetic Modeling and Genomic Analyses of Yearling Temperament in American Angus Cattle and Its Relationship With Productive Efficiency and Resilience Traits

Cattle temperament has been considered by farmers as a key breeding goal due to its relevance for cattlemen's safety, animal welfare, resilience, and longevity and its association with many economically important traits (e.g., production and meat quality). The definition of proper statistical models, accurate variance component estimates, and knowledge on the genetic background of the indicator trait evaluated are of great importance for accurately predicting the genetic merit of breeding animals. Therefore, 266,029 American Angus cattle with yearling temperament records (1-6 score) were used to evaluate statistical models and estimate variance components; investigate the association of sex and farm management with temperament; assess the weighted correlation of estimated breeding values for temperament and productive, reproductive efficiency and resilience traits; and perform a weighted single-step genome-wide association analysis using 69,559 animals genotyped for 54,609 single-nucleotide polymorphisms. Sex and extrinsic factors were significantly associated with temperament, including conception type, age of dam, birth season, and additional animal-human interactions. Similar results were observed among models including only the direct additive genetic effect and when adding other maternal effects. Estimated heritability of temperament was equal to 0.39 on the liability scale. Favorable genetic correlations were observed between temperament and other relevant traits, including growth, feed efficiency, meat quality, and reproductive traits. The highest approximated genetic correlations were observed between temperament and growth traits (weaning weight, 0.28; yearling weight, 0.28). Altogether, we identified 11 genomic regions, located across nine chromosomes including BTAX, explaining 3.33% of the total additive genetic variance. The candidate genes identified were enriched in pathways related to vision, which could be associated with reception of stimulus and/or cognitive abilities. This study encompasses large and diverse phenotypic, genomic, and pedigree datasets of US Angus cattle. Yearling temperament is a highly heritable and polygenic trait that can be improved through genetic selection. Direct selection for temperament is not expected to result in unfavorable responses on other relevant traits due to the favorable or low genetic correlations observed. In summary, this study contributes to a better understanding of the impact of maternal effects, extrinsic factors, and various genomic regions associated with yearling temperament in North American Angus cattle.

Capturing indirect genetic effects on phenotypic variability: Competition meets canalization

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.

Evaluation of the phenotypic and genomic background of variability based on litter size of Large White pigs

BACKGROUND

The genetic background of trait variability has captured the interest of ecologists and animal breeders because the genes that control it could be involved in buffering various environmental effects. Phenotypic variability of a given trait can be assessed by studying the heterogeneity of the residual variance, and the quantitative trait loci (QTL) that are involved in the control of this variability are described as variance QTL (vQTL). This study focuses on litter size (total number born, TNB) and its variability in a Large White pig population. The variability of TNB was evaluated either using a simple method, i.e. analysis of the log-transformed variance of residuals (LnVar), or the more complex double hierarchical generalized linear model (DHGLM). We also performed a single-SNP (single nucleotide polymorphism) genome-wide association study (GWAS). To our knowledge, this is only the second study that reports vQTL for litter size in pigs and the first one that shows GWAS results when using two methods to evaluate variability of TNB: LnVar and DHGLM.

RESULTS

Based on LnVar, three candidate vQTL regions were detected, on Sus scrofa chromosomes (SSC) 1, 7, and 18, which comprised 18 SNPs. Based on the DHGLM, three candidate vQTL regions were detected, i.e. two on SSC7 and one on SSC11, which comprised 32 SNPs. Only one candidate vQTL region overlapped between the two methods, on SSC7, which also contained the most significant SNP. Within this vQTL region, two candidate genes were identified, ADGRF1, which is involved in neurodevelopment of the brain, and ADGRF5, which is involved in the function of the respiratory system and in vascularization. The correlation between estimated breeding values based on the two methods was 0.86. Three-fold cross-validation indicated that DHGLM yielded EBV that were much more accurate and had better prediction of missing observations than LnVar.

CONCLUSIONS

The results indicated that the LnVar and DHGLM methods resulted in genetically different traits. Based on their validation, we recommend the use of DHGLM over the simpler method of log-transformed variance of residuals. These conclusions can be useful for future studies on the evaluation of the variability of any trait in any species.

Estimation of macro- and micro-genetic environmental sensitivity in unbalanced datasets

Genotype-by-environment interaction is caused by variation in genetic environmental sensitivity (GES), which can be subdivided into macro- and micro-GES. Macro-GES is genetic sensitivity to macro-environments (definable environments often shared by groups of animals), while micro-GES is genetic sensitivity to micro-environments (individual environments). A combined reaction norm and double hierarchical generalised linear model (RN-DHGLM) allows for simultaneous estimation of base genetic, macro- and micro-GES effects. The accuracy of variance components estimated using a RN-DHGLM has been explicitly studied for balanced data and recommendation of a data size with a minimum of 100 sires with at least 100 offspring each have been made. In the current study, the data size (numbers of sires and progeny) and structure requirements of the RN-DHGLM were investigated for two types of unbalanced datasets. Both datasets had a variable number of offspring per sire, but one dataset also had a variable number of offspring within macro-environments. The accuracy and bias of the estimated macro- and micro-GES effects and the estimated breeding values (EBVs) obtained using the RN-DHGLM depended on the data size. Reasonably accurate and unbiased estimates were obtained with data containing 500 sires with 20 offspring or 100 sires with 50 offspring, regardless of the data structure. Variable progeny group sizes, alone or in combination with an unequal number of offspring within macro-environments, had little impact on the dispersion of the EBVs or the bias and accuracy of variance component estimation, but resulted in lower accuracies of the EBVs. Compared to genetic correlations of zero, a genetic correlation of 0.5 between base genetic, macro- and micro-GES components resulted in a slight decrease in the percentage of replicates that converged out of 100 replicates, but had no effect on the dispersion and accuracy of variance component estimation or the dispersion of the EBVs. The results show that it is possible to apply the RN-DHGLM to unbalanced datasets to obtain estimates of variance due to macro- and micro-GES. Furthermore, the levels of accuracy and bias of variance estimates when analysing macro- and micro-GES simultaneously are determined by average family size, with limited impact from variability in family size and/or cohort size. This creates opportunities for the use of field data from populations with unbalanced data structures when estimating macro- and micro-GES.

The impact of late-career job loss and genetic risk on body mass index: Evidence from variance polygenic scores

Unemployment shocks from the COVID-19 pandemic have reignited concerns over the long-term effects of job loss on population health. Past research has highlighted the corrosive effects of unemployment on health and health behaviors. This study examines whether the effects of job loss on changes in body mass index (BMI) are moderated by genetic predisposition using data from the U.S. Health and Retirement Study (HRS). To improve detection of gene-by-environment (G × E) interplay, we interacted layoffs from business closures-a plausibly exogenous environmental exposure-with whole-genome polygenic scores (PGSs) that capture genetic contributions to both the population mean (mPGS) and variance (vPGS) of BMI. Results show evidence of genetic moderation using a vPGS (as opposed to an mPGS) and indicate genome-wide summary measures of phenotypic plasticity may further our understanding of how environmental stimuli modify the distribution of complex traits in a population.

Genetic parameters for uniformity of harvest weight in Pacific white shrimp (Litopenaeus vannamei)

Background

Uniformity of body weight is a trait of great economic importance in the production of white shrimp (Litopenaeus vannamei). A necessary condition to improve this trait through selective breeding is the existence of genetic variability for the environmental variance of body weight. Although several studies have reported such variability in other aquaculture species, to our knowledge, no estimates are available for shrimp. Our aim in this study was to estimate the genetic variance for weight uniformity in a farmed population of shrimp to determine the potential of including this trait in the selection program. We also estimated the genetic correlation of weight uniformity between two environments (selection nucleus and commercial population).

Methods

The database contained phenotypic records for body weight on 51,346 individuals from the selection nucleus and 38,297 individuals from the commercial population. A double hierarchical generalized linear model was used to analyse weight uniformity in the two environments. Fixed effects included sex and year for the nucleus data and sex and year-pond combination for the commercial data. Environmental and additive genetic effects were included as random effects.

Results

The estimated genetic variance for weight uniformity was greater than 0 (0.06 ± 0.01) in both the nucleus and commercial populations and the genetic coefficient of variation for the residual variance was 0.25 ± 0.01. The genetic correlation between weight and weight uniformity was close to zero in both environments. The estimate of the genetic correlation of weight uniformity between the two environments (selection nucleus and commercial population) was 0.64 ± 0.06.

Conclusions

The existence of genetic variance for weight uniformity suggests that genetic improvement of this trait is possible. Selection for weight uniformity should not decrease weight, given the near zero genetic correlation between these two traits. The strong genetic correlation of weight uniformity between the two environments indicates that response to selection for uniformity in the nucleus will be at least partially transmitted to the commercial population if this trait is included in the breeding goal.

Variance heterogeneity genome-wide mapping for cadmium in bread wheat reveals novel genomic loci and epistatic interactions

Genome-wide association mapping identifies quantitative trait loci (QTL) that influence the mean differences between the marker genotypes for a given trait. While most loci influence the mean value of a trait, certain loci, known as variance heterogeneity QTL (vQTL) determine the variability of the trait instead of the mean trait value (mQTL). In the present study, we performed a variance heterogeneity genome-wide association study (vGWAS) for grain cadmium (Cd) concentration in bread wheat. We used double generalized linear model and hierarchical generalized linear model to identify vQTL associated with grain Cd. We identified novel vQTL regions on chromosomes 2A and 2B that contribute to the Cd variation and loci that affect both mean and variance heterogeneity (mvQTL) on chromosome 5A. In addition, our results demonstrated the presence of epistatic interactions between vQTL and mvQTL, which could explain variance heterogeneity. Overall, we provide novel insights into the genetic architecture of grain Cd concentration and report the first application of vGWAS in wheat. Moreover, our findings indicated that epistasis is an important mechanism underlying natural variation for grain Cd concentration.

Genetic variance for behavioural 'predictability' of stress response

Genetic factors underpinning phenotypic variation are required if natural selection is to result in adaptive evolution. However, evolutionary and behavioural ecologists typically focus on variation among individuals in their average trait values and seek to characterize genetic contributions to this. As a result, less attention has been paid to if and how genes could contribute towards within-individual variance or trait 'predictability'. In fact, phenotypic 'predictability' can vary among individuals, and emerging evidence from livestock genetics suggests this can be due to genetic factors. Here, we test this empirically using repeated measures of a behavioural stress response trait in a pedigreed population of wild-type guppies. We ask (a) whether individuals differ in behavioural predictability and (b) whether this variation is heritable and so evolvable under selection. Using statistical methodology from the field of quantitative genetics, we find support for both hypotheses and also show evidence of a genetic correlation structure between the behavioural trait mean and individual predictability. We show that investigating sources of variability in trait predictability is statistically tractable and can yield useful biological interpretation. We conclude that, if widespread, genetic variance for 'predictability' will have major implications for the evolutionary causes and consequences of phenotypic variation.

Estimation of genetic parameters for micro-environmental sensitivities of production traits in Holstein cows using two-step method

Context The request for more uniform animal products, which is motivated chiefly by economic reasons, has enhanced the interest in decreasing variability of characters via selection. In the present dairy operation, breeding dairy cows which have strong resistance against environmental changes for main traits is very important. Aims The aim of this study was to estimate genetic parameters for heterogeneity of residual variance in milk yield and composition of Iranian Holstein cows. Methods The dataset included 305-day production records of cows which were provided by the Animal Breeding Center and Promotion of Animal Products of Iran between 1983 and 2014. In two-step method, univariate analyses were conducted to estimate variance components for 305-day production traits. Then, genetic variability of residual variances was estimated. Key results Estimates of heritability for micro-environmental sensitivities of milk, fat and protein yields in the first three lactations of Holstein cows were low and equal to 0.043, 0.028 and 0.039; 0.031, 0.019 and 0.024; 0.027, 0.016 and 0.019 respectively. Considerable genetic coefficient of variations of residual variance for above mentioned traits (0.261, 0.247 and 0.218; 0.221, 0.204 and 0.194; 0.219, 0.199 and 0.178 respectively) indicated significant additive genetic variation for micro-environmental sensitivities. Conclusions The results of this study indicate that micro-environmental sensitivities were present for milk production traits of Iranian Holsteins. High genetic coefficient of variation for micro-environmental sensitivities indicated the possibility of reducing environmental variation and increase in uniformity via selection. Implications Reduction of environmental sensitivities would increase the predicted performance of animals and decreased corresponding threats for dairy farmers.

Body Weight Deviations as Indicator for Resilience in Layer Chickens

Resilience is the capacity of an animal to be minimally affected by disturbances or to rapidly return to the state pertained before exposure to a disturbance. Less resilient animals are expected to be more susceptible to environmental perturbations, such as diseases, and will consequently show more and/or greater fluctuations in production than more resilient animals. Natural antibodies (NAb) are antibodies recognizing antigens without previous exposure to these, and are hypothesized to be an indication of general disease resistance. The objective of this research was to investigate genetic parameters of resilience indicators based on standardized body weight (BW) deviations and to investigate its relation with immunity (i.e. NAb) and disease resistance. Keyhole limpet hemocyanin-binding NAb were measured in layer chickens, which were selectively bred for high and low keyhole limpet hemocyanin-binding NAb levels during six generations. In addition, BW data of these layers were collected on a four-weekly interval from 4 weeks of age until 32 weeks of age. Standardized deviations of BW from an individual were compared to lines’ average BW (i.e. across individuals), and these were used to calculate resilience indicators: natural logarithm-transformed variance [ln(variance)], skewness, and lag-one autocorrelation of deviations (i.e. all within an individual). Heritabilities of resilience indicators were between 0.09 and 0.11. Genetic correlations between the three resilience indicators were between -0.20 and 0.40 (with high SE), which might suggest that the resilience indicators capture different aspects of resilience. Genetic correlations between resilience indicators and NAb were close to zero, which suggests that the resilience indicators and NAb capture different aspects of immunity. This might indicate that, in this dataset, environmental perturbations are only to a small extent affected by disease incidence, possibly due to a lack of disease occurrence. However, a lower estimated breeding value for ln(variance) was predictive for lower lesion scores after an avian pathogenic Escherichia coli inoculation and vice versa. In conclusion, this study shows that there is genetic variation in resilience indicators based on BW deviations in layer chickens, which opens up possibilities to improve resilience by means of selective breeding.

Quantifying individual variation in reaction norms: Mind the residual

Phenotypic plasticity is a central topic in ecology and evolution. Individuals may differ in the degree of plasticity (individual-by-environment interaction (I × E)), which has implications for the capacity of populations to respond to selection. Random regression models (RRMs) are a popular tool to study I × E in behavioural or life-history traits, yet evidence for I × E is mixed, differing between species, populations, and even between studies on the same population. One important source of discrepancies between studies is the treatment of heterogeneity in residual variance (heteroscedasticity). To date, there seems to be no collective awareness among ecologists of its influence on the estimation of I × E or a consensus on how to best model it. We performed RRMs with differing residual variance structures on simulated data with varying degrees of heteroscedasticity and plasticity, sample size and environmental variability to test how RRMs would perform under each scenario. The residual structure in the RRMs affected the precision of estimates of simulated I × E as well as statistical power, with substantial lack of precision and high false-positive rates when sample size, environmental variability and plasticity were small. We show that model comparison using information criteria can be used to choose among residual structures and reinforce this point by analysis of real data of two study populations of great tits (Parus major). We provide guidelines that can be used by biologists studying I × E that, ultimately, should lead to a reduction in bias in the literature concerning the statistical evidence and the reported magnitude of variation in plasticity.

Genetics and genomics of uniformity and resilience in livestock and aquaculture species: A review

Genetic control of residual variance offers opportunities to increase uniformity and resilience of livestock and aquaculture species. Improving uniformity and resilience of animals will improve health and welfare of animals and lead to more homogenous products. Our aims in this review were to summarize the current models and methods to study genetic control of residual variance, genetic parameters and genomic results for residual variance and discuss future research directions. Typically, the genetic coefficient of variation is high (median = 0.27; range 0-0.86) and the heritability of residual variance is low (median = 0.01; range 0-0.10). Higher heritabilities can be achieved when increasing the number of records per animal. Divergent selection experiments have supported the feasibility of selecting for high or low residual variance. Genomic studies have revealed associations in regions related to stress, including those from the heat shock protein family. Although the number of studies is growing, genetic control of residual variance is still poorly understood, but big data and genomics offer great opportunities.

Genomic Prediction Including SNP-Specific Variance Predictors

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.

Bayesian factor analytic model: An approach in multiple environment trials

One of the main challenges in plant breeding programs is the efficient quantification of the genotype-by-environment interaction (GEI). The presence of significant GEI may create difficulties for breeders in the selection and recommendation of superior genotypes for a wide environmental network. Among the diverse statistical procedures developed for this purpose, we highlight those based on mixed models and factor analysis that are called factor analytic (FA) models. However, some inferential issues are related to the factor analytic model, such as Heywood cases that make the model non-identifiable. Moreover, the representation of the loads and factors in the conventional biplot does not involve any measurement of uncertainty. In this work, we propose dealing with the FA model using the Bayesian framework with direct sampling of factor loadings via spectral decomposition; this guarantees identifiability in the estimation process and eliminates the need for the rotationality of factor loadings or imposition of any ad hoc constraints. We used simulated and real data to illustrate the method's application in multi-environment trials (MET) and to compare it with traditional FA mixed models on controlled unbalancing. In general, the Bayesian FA model was robust under different simulated unbalanced levels, presenting the superior predictive ability of missing data when compared to competing models, such as those based on FA mixed models. In addition, for some scenarios, the classical FA mixed model failed in estimating the full FA model, illustrating the parametric problems of convergence in these models. Our results suggest that Bayesian factorial models might be successfully used in plant breeding for MET analysis.

Genotype-by-environment interactions inferred from genetic effects on phenotypic variability in the UK Biobank

Genotype-by-environment interaction (GEI) is a fundamental component in understanding complex trait variation. However, it remains challenging to identify genetic variants with GEI effects in humans largely because of the small effect sizes and the difficulty of monitoring environmental fluctuations. Here, we demonstrate that GEI can be inferred from genetic variants associated with phenotypic variability in a large sample without the need of measuring environmental factors. We performed a genome-wide variance quantitative trait locus (vQTL) analysis of ~5.6 million variants on 348,501 unrelated individuals of European ancestry for 13 quantitative traits in the UK Biobank and identified 75 significant vQTLs with P < 2.0 × 10-9 for 9 traits, especially for those related to obesity. Direct GEI analysis with five environmental factors showed that the vQTLs were strongly enriched with GEI effects. Our results indicate pervasive GEI effects for obesity-related traits and demonstrate the detection of GEI without environmental data.

Estimation of genetic variation for macro- and micro-environmental sensitivities of milk yield and composition in Holstein cows using double hierarchical generalized linear models

The aim of this study was to estimate genetic parameters for environmental sensitivities in milk yield and composition of Iranian Holstein cows using the double hierarchical generalized linear model (DHGLM) method. Data set included test-day productive records of cows which were provided by the Animal Breeding Center and Promotion of Animal Products of Iran during 1983 to 2014. In the DHGLM method, a random regression model was fitted which included two parts of mean and residual variance. A random regression model (mean model) and a residual variance model were used to study the genetic variation of micro-environmental sensitivities. In order to consider macro-environmental sensitivities, DHGLM was extended using a reaction norm model, and a sire model was applied. Based on the mean model, additive genetic variances for the mean were 38.25 for milk yield, 0.23 for fat yield and 0.03 for protein yield in the first lactation, respectively. Based on the residual variance model, additive genetic variances for residual variance were 0.039 for milk yield, 0.030 for fat yield and 0.020 for protein yield in the first lactation, respectively. Estimates of genetic correlation between milk yield and macro- and micro-environmental sensitivities were 0.660 and 0.597 in the first lactation, respectively. The results of this study indicated that macro- and micro-environmental sensitivities were present for milk production traits of Iranian Holsteins. High genetic coefficient of variation for micro-environmental sensitivities indicated the possibility of reducing environmental variation and increase in uniformity via selection.

Genetic Effects on Dispersion in Urinary Albumin and Creatinine in Three House Mouse (Mus musculus) Cohorts

Conventionally, quantitative genetics concerns the heredity of trait means, but there is growing evidence for the existence of architectures in which certain alleles cause random variance in phenotype, termed ‘phenotypic dispersion’ (PD) or ‘variance QTL’ (vQTL), including in physiological traits like disease signs. However, the structure of this phenomenon is still poorly known. PD for urinary albumin (PD_UAlb) and creatinine (PD_UCrea) was mapped using curated data from two nearly genetically identical F₂ mouse (Mus musculus) cohorts (383 male F₂ C57BL/6J×A/J (97 SNP) and 207 male F₂ C57BL/6J×A/J ApoE knockout mice (144 SNP)) and a related mapping cohort (340 male F₂ DBA/2J×C57BL/6J (83 SNP, 8 microsatellites)). PD_UAlb was associated with markers in regions of Chr 1 (5-64 megabases (MB); 141-158 MB), 3 (∼113 MB), 8 (37-68 MB), 14 (92-117 MB) and 17 (14-24 MB) with several positions and quantitative architectures in common between the two C57BL/6J×A/J cohorts, most of which had a negative dominant construction. One locus for PD_UCrea was detected on Chr 19 (57 MB) in the C57BL/6J×A/J ApoE^−/− cohort. The large number of negative dominant loci for albuminuria dispersion relative to conventional quantitative trait loci suggests that the development of albuminuria may be largely genetically dynamic and that randomization in this development is detrimental.

Identifying loci affecting trait variability and detecting interactions in genome-wide association studies

Identification of genetic variants with effects on trait variability can provide insights into the biological mechanisms that control variation and can identify potential interactions. We propose a two-degree-of-freedom test for jointly testing mean and variance effects to identify such variants. We implement the test in a linear mixed model, for which we provide an efficient algorithm and software. To focus on biologically interesting settings, we develop a test for dispersion effects, that is, variance effects not driven solely by mean effects when the trait distribution is non-normal. We apply our approach to body mass index in the subsample of the UK Biobank population with British ancestry (n ~408,000) and show that our approach can increase the power to detect associated loci. We identify and replicate novel associations with significant variance effects that cannot be explained by the non-normality of body mass index, and we provide suggestive evidence for a connection between leptin levels and body mass index variability.

Genomic regions underlying uniformity of yearling weight in Nellore cattle evaluated under different response variables

BACKGROUND

In livestock, residual variance has been studied because of the interest to improve uniformity of production. Several studies have provided evidence that residual variance is partially under genetic control; however, few investigations have elucidated genes that control it. The aim of this study was to identify genomic regions associated with within-family residual variance of yearling weight (YW; N = 423) in Nellore bulls with high density SNP data, using different response variables. For this, solutions from double hierarchical generalized linear models (DHGLM) were used to provide the response variables, as follows: a DGHLM assuming non-null genetic correlation between mean and residual variance (rmv ≠ 0) to obtain deregressed EBV for mean (dEBVm) and residual variance (dEBVv); and a DHGLM assuming rmv = 0 to obtain two alternative response variables for residual variance, dEBVv_r0 and log-transformed variance of estimated residuals (ln_[Formula: see text]).

RESULTS

The dEBVm and dEBVv were highly correlated, resulting in common regions associated with mean and residual variance of YW. However, higher effects on variance than the mean showed that these regions had effects on the variance beyond scale effects. More independent association results between mean and residual variance were obtained when null rmv was assumed. While 13 and 4 single nucleotide polymorphisms (SNPs) showed a strong association (Bayes Factor > 20) with dEBVv and ln_[Formula: see text], respectively, only suggestive signals were found for dEBVv_r0. All overlapping 1-Mb windows among top 20 between dEBVm and dEBVv were previously associated with growth traits. The potential candidate genes for uniformity are involved in metabolism, stress, inflammatory and immune responses, mineralization, neuronal activity and bone formation.

CONCLUSIONS

It is necessary to use a strategy like assuming null rmv to obtain genomic regions associated with uniformity that are not associated with the mean. Genes involved not only in metabolism, but also stress, inflammatory and immune responses, mineralization, neuronal activity and bone formation were the most promising biological candidates for uniformity of YW. Although no clear evidence of using a specific response variable was found, we recommend consider different response variables to study uniformity to increase evidence on candidate regions and biological mechanisms behind it.

Modelling the co-evolution of indirect genetic effects and inherited variability

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.

Heritable Micro-environmental Variance Covaries with Fitness in an Outbred Population of Drosophila serrata

The genetic basis of stochastic variation within a defined environment, and the consequences of such micro-environmental variance for fitness are poorly understood . Using a multigenerational breeding design in Drosophila serrata, we demonstrated that the micro-environmental variance in a set of morphological wing traits in a randomly mating population had significant additive genetic variance in most single wing traits. Although heritability was generally low (<1%), coefficients of additive genetic variance were of a magnitude typical of other morphological traits, indicating that the micro-environmental variance is an evolvable trait. Multivariate analyses demonstrated that the micro-environmental variance in wings was genetically correlated among single traits, indicating that common mechanisms of environmental buffering exist for this functionally related set of traits. In addition, through the dominance genetic covariance between the major axes of micro-environmental variance and fitness, we demonstrated that micro-environmental variance shares a genetic basis with fitness, and that the pattern of selection is suggestive of variance-reducing selection acting on micro-environmental variance.

Selection for environmental variance of litter size in rabbits

Background

In recent years, there has been an increasing interest in the genetic determination of environmental variance. In the case of litter size, environmental variance can be related to the capacity of animals to adapt to new environmental conditions, which can improve animal welfare.

Results

We developed a ten-generation divergent selection experiment on environmental variance. We selected one line of rabbits for litter size homogeneity and one line for litter size heterogeneity by measuring intra-doe phenotypic variance. We proved that environmental variance of litter size is genetically determined and can be modified by selection. Response to selection was 4.5% of the original environmental variance per generation. Litter size was consistently higher in the Low line than in the High line during the entire experiment.

Conclusions

We conclude that environmental variance of litter size is genetically determined based on the results of our divergent selection experiment. This has implications for animal welfare, since animals that cope better with their environment have better welfare than more sensitive animals. We also conclude that selection for reduced environmental variance of litter size does not depress litter size.

Genetic control of residual variance of yearling weight in Nellore beef cattle

There is evidence for genetic variability in residual variance of livestock traits, which offers the potential for selection for increased uniformity of production. Different statistical approaches have been employed to study this topic; however, little is known about the concordance between them. The aim of our study was to investigate the genetic heterogeneity of residual variance on yearling weight (YW; 291.15 ± 46.67) in a Nellore beef cattle population; to compare the results of the statistical approaches, the two-step approach and the double hierarchical generalized linear model (DHGLM); and to evaluate the effectiveness of power transformation to accommodate scale differences. The comparison was based on genetic parameters, accuracy of EBV for residual variance, and cross-validation to assess predictive performance of both approaches. A total of 194,628 yearling weight records from 625 sires were used in the analysis. The results supported the hypothesis of genetic heterogeneity of residual variance on YW in Nellore beef cattle and the opportunity of selection, measured through the genetic coefficient of variation of residual variance (0.10 to 0.12 for the two-step approach and 0.17 for DHGLM, using an untransformed data set). However, low estimates of genetic variance associated with positive genetic correlations between mean and residual variance (about 0.20 for two-step and 0.76 for DHGLM for an untransformed data set) limit the genetic response to selection for uniformity of production while simultaneously increasing YW itself. Moreover, large sire families are needed to obtain accurate estimates of genetic merit for residual variance, as indicated by the low heritability estimates (<0.007). Box-Cox transformation was able to decrease the dependence of the variance on the mean and decreased the estimates of genetic parameters for residual variance. The transformation reduced but did not eliminate all the genetic heterogeneity of residual variance, highlighting its presence beyond the scale effect. The DHGLM showed higher predictive ability of EBV for residual variance and therefore should be preferred over the two-step approach.

Genetic basis of between-individual and within-individual variance of docility

Between-individual variation in phenotypes within a population is the basis of evolution. However, evolutionary and behavioural ecologists have mainly focused on estimating between-individual variance in mean trait and neglected variation in within-individual variance, or predictability of a trait. In fact, an important assumption of mixed-effects models used to estimate between-individual variance in mean traits is that within-individual residual variance (predictability) is identical across individuals. Individual heterogeneity in the predictability of behaviours is a potentially important effect but rarely estimated and accounted for. We used 11 389 measures of docility behaviour from 1576 yellow-bellied marmots (Marmota flaviventris) to estimate between-individual variation in both mean docility and its predictability. We then implemented a double hierarchical animal model to decompose the variances of both mean trait and predictability into their environmental and genetic components. We found that individuals differed both in their docility and in their predictability of docility with a negative phenotypic covariance. We also found significant genetic variance for both mean docility and its predictability but no genetic covariance between the two. This analysis is one of the first to estimate the genetic basis of both mean trait and within-individual variance in a wild population. Our results indicate that equal within-individual variance should not be assumed. We demonstrate the evolutionary importance of the variation in the predictability of docility and illustrate potential bias in models ignoring variation in predictability. We conclude that the variability in the predictability of a trait should not be ignored, and present a coherent approach for its quantification.

Estimation of breeding values for uniformity of growth in Atlantic salmon (Salmo salar) using pedigree relationships or single-step genomic evaluation

Background

In farmed Atlantic salmon, heritability for uniformity of body weight is low, indicating that the accuracy of estimated breeding values (EBV) may be low. The use of genomic information could be one way to increase accuracy and, hence, obtain greater response to selection. Genomic information can be merged with pedigree information to construct a combined relationship matrix (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{H}}$$\end{document}H matrix) for a single-step genomic evaluation (ssGBLUP), allowing realized relationships of the genotyped animals to be exploited, in addition to numerator pedigree relationships (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{A}}$$\end{document}A matrix). We compared the predictive ability of EBV for uniformity of body weight in Atlantic salmon, when implementing either the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{A}}$$\end{document}A or \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{H}}$$\end{document}H matrix in the genetic evaluation. We used double hierarchical generalized linear models (DHGLM) based either on a sire-dam (sire-dam DHGLM) or an animal model (animal DHGLM) for both body weight and its uniformity.

Results

With the animal DHGLM, the use of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{H}}$$\end{document}H instead of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{A}}$$\end{document}A significantly increased the correlation between the predicted EBV and adjusted phenotypes, which is a measure of predictive ability, for both body weight and its uniformity (41.1 to 78.1%). When log-transformed body weights were used to account for a scale effect, the use of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{H}}$$\end{document}H instead of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{A}}$$\end{document}A produced a small and non-significant increase (1.3 to 13.9%) in predictive ability. The sire-dam DHGLM had lower predictive ability for uniformity compared to the animal DHGLM.

Conclusions

Use of the combined numerator and genomic relationship matrix (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{H}}$$\end{document}H) significantly increased the predictive ability of EBV for uniformity when using the animal DHGLM for untransformed body weight. The increase was only minor when using log-transformed body weights, which may be due to the lower heritability of scaled uniformity, the lower genetic correlation of transformed body weight with its uniformity compared to the untransformed traits, and the small number of genotyped animals in the reference population. This study shows that ssGBLUP increases the accuracy of EBV for uniformity of body weight and is expected to increase response to selection in uniformity.

Electronic supplementary material

The online version of this article (doi:10.1186/s12711-017-0308-3) contains supplementary material, which is available to authorized users.

Joint estimation of (co) variance components and breeding values for mean and dispersion of days from calving to first service in Holstein cow

The present study explored the possibility of selection for uniformity of days from calving to first service (DFS) in dairy cattle. A double hierarchical generalised linear model with an iterative reweighted least-squares algorithm was used to estimate covariance components for the mean and dispersion of DFS. Data included the records of 27 113 Iranian Holstein cows (parity, 1–6) in 15 herds from 1981 to 2007. The estimated additive genetic variance for the mean and dispersion were 32.25 and 0.0139; both of these values had low standard errors. The genetic standard deviation for dispersion of DFS was 0.117, indicating that decreasing the estimated breeding value of dispersion by one genetic standard deviation can increase the uniformity by 12%. A strong positive genetic correlation (0.689) was obtained between the mean and dispersion of DFS. This genetic correlation is favourable since one of the aims of breeding is to simultaneously decrease the mean and increase the uniformity of DFS. The Spearman rank correlations between estimated breeding values in the mean and dispersion for sires with a different number of daughter observations were 0.907. In the studied population, the genetic trend in the mean of DFS was significant and favourable (–0.063 days/year), but the genetic trend in the dispersion of DFS was not significantly different from zero. The results obtained in the present study indicated that the mean and uniformity of DFS can simultaneously be improved in dairy cows.

Genetic parameters for uniformity of harvest weight and body size traits in the GIFT strain of Nile tilapia

Background

Animal breeding programs have been very successful in improving the mean levels of traits through selection. However, in recent decades, reducing the variability of trait levels between individuals has become a highly desirable objective. Reaching this objective through genetic selection requires that there is genetic variation in the variability of trait levels, a phenomenon known as genetic heterogeneity of environmental (residual) variance. The aim of our study was to investigate the potential for genetic improvement of uniformity of harvest weight and body size traits (length, depth, and width) in the genetically improved farmed tilapia (GIFT) strain. In order to quantify the genetic variation in uniformity of traits and estimate the genetic correlations between level and variance of the traits, double hierarchical generalized linear models were applied to individual trait values.

Results

Our results showed substantial genetic variation in uniformity of all analyzed traits, with genetic coefficients of variation for residual variance ranging from 39 to 58 %. Genetic correlation between trait level and variance was strongly positive for harvest weight (0.60 ± 0.09), moderate and positive for body depth (0.37 ± 0.13), but not significantly different from 0 for body length and width.

Conclusions

Our results on the genetic variation in uniformity of harvest weight and body size traits show good prospects for the genetic improvement of uniformity in the GIFT strain. A high and positive genetic correlation was estimated between level and variance of harvest weight, which suggests that selection for heavier fish will also result in more variation in harvest weight. Simultaneous improvement of harvest weight and its uniformity will thus require index selection.

Electronic supplementary material

The online version of this article (doi:10.1186/s12711-016-0218-9) contains supplementary material, which is available to authorized users.

Estimating the purebred-crossbred genetic correlation for uniformity of eggshell color in laying hens

Background

Uniformity of eggs is an important aspect for retailers because consumers prefer homogeneous products. One of these characteristics is the color of the eggshell, especially for brown eggs. Existence of a genetic component in environmental variance would enable selection for uniformity of eggshell color. Therefore, the objective of this study was to quantify the genetic variance in environmental variance of eggshell color in purebred and crossbred laying hens, to estimate the genetic correlation between environmental variance of eggshell color in purebred and crossbred laying hens and to estimate genetic correlations between environmental variance at different times of the laying period.

Methods

We analyzed 167,651 and 79,345 eggshell color records of purebred and crossbred laying hens, respectively. The purebred and crossbred laying hens originated mostly from the same sires. Since eggshell color records of crossbred laying hens were collected per cage, these records could be related only to cage and sire family. A double hierarchical generalized linear sire model was used to estimate the genetic variance of the mean of eggshell color and its environmental variance. Approximate standard errors for heritability and the genetic coefficient of variation for environmental variance were derived.

Results

The genetic variance in environmental variance at the log scale was equal to 0.077 and 0.067, for purebred and crossbred laying hens, respectively. The genetic coefficient of variation for environmental variance was equal to 0.28 and 0.26, for purebred and crossbred laying hens, respectively. A genetic correlation of 0.70 was found between purebred and crossbred environmental variance of eggshell color, which indicates that there is some reranking of sires for environmental variance of eggshell color in purebred and crossbred laying hens. Genetic correlations between environmental variance of eggshell color in different laying periods were generally higher than 0.85, except between early laying and mid or late laying periods.

Conclusions

Our results indicate that genetic selection can be efficient to improve uniformity of eggshell color in purebreds and crossbreds, ideally by applying combined crossbred and purebred selection. This methodology can be used to estimate genetic correlations between purebred and crossbred lines for uniformity of other traits and species.

Electronic supplementary material

The online version of this article (doi:10.1186/s12711-016-0212-2) contains supplementary material, which is available to authorized users.

Genetic heteroscedastic models for ordinal traits: application to sheep litter size

BACKGROUND

Classical genetic canalization models, which accommodate the mean and variance of a trait separately, provide a flexible approach to take heteroscedasticity for continuous traits into account. However, this model is not appropriate for discrete traits. The aim of this work was to propose heteroscedastic threshold models suitable for the genetic analysis of ordinal data.

METHODS

In order to first fit the mean and variance of ordinal traits separately, we extended the classical threshold model (TM) for discrete data by introducing non-genetic and genetic factors of heterogeneity on the variance of its underlying variable, which leads to a homothetic threshold model HTM and its alternative parameterization HTM' in which the thresholds of different individuals are linked by a homothetic-translation. Relaxing the constraint between the thresholds led us to propose an independent threshold model ITM that was more flexible than HTM' but required the estimation of more parameters. TM, HTM and ITM models were applied to study 19,671 records on litter size in Romane sheep.

RESULTS

Both HTM and ITM were able to disentangle the link between the mean and variance that holds in the classical homoscedastic threshold model. The results obtained for the litter size of Romane ewes showed that the data was best fitted with HTM compared to ITM and TM. The correlations between the observed and predicted variances were equal to 0.6 and 0.2 for HTM and TM, respectively. These analyses showed the existence of a genetic component for the heterogeneity of litter size in sheep that was taken into account in HTM.

CONCLUSIONS

HTM is the most suitable model to study the variability of litter size in sheep. It accommodates both the mean and variance separately while requiring the estimation of only a few parameters.

Genetic analysis of within-litter variation in piglets' birth weight using genomic or pedigree relationship matrices

The objective of this study was to estimate the genetic variance for within-litter variation of birth weight (BW0) using genomic (GRM) or pedigree relationship matrices (PRM) and to compare the accuracy of estimated breeding values (EBV) for within-litter variation of BW0 using GRM and PRM. The BW0 and residual variance of BW0 were modeled by the double hierarchical generalized linear model using GRM or PRM. Data came from 2 dam lines: Landrace and Large White. After editing, the data set in Landrace consisted of 748 sows with 1,938 litters and 29,430 piglets and in Large White of 989 sows with 3,320 litters and 51,818 piglets. To construct GRM, 46,466 (Landrace) and 44,826 (Large White) single nucleotide polymorphisms were used, whereas to construct PRM, 5 generations of pedigree were used. The accuracy of EBV with GRM was estimated with 8-fold cross-validation and compared to PRM. Estimated variance components were highly similar for GRM and PRM. The maternal genetic variance in residual variance of BW0 in Landrace was 0.05 with GRM and 0.06 with PRM. In Large White these were 0.04 with GRM and 0.05 with PRM. The genetic coefficient of variation (GCV SDe) was about 0.10 in both dam lines. This indicates a change of 10% in residual SD of BW0 when achieving a genetic response of 1 genetic standard deviation. The genetic correlation between birth weight and its residual variance was about 0.6 in both dam lines. The accuracies of selection for within-litter variation of birth weight were 0.35 with GRM and 0.23 with PRM in Landrace and 0.29 with GRM and 0.34 with PRM in Large White. In this case, using GRM did not significantly increase accuracies of selection. Results, however, show good opportunities to select for reduced within-litter variation of BW0. Genomic selection can increase accuracy of selection when reference populations contain at least 2,000 sows.

Genome-wide association study reveals novel loci for litter size and its variability in a Large White pig population

Background

In many traits, not only individual trait levels are under genetic control, but also the variation around that level. In other words, genotypes do not only differ in mean, but also in (residual) variation around the genotypic mean. New statistical methods facilitate gaining knowledge on the genetic architecture of complex traits such as phenotypic variability. Here we study litter size (total number born) and its variation in a Large White pig population using a Double Hierarchical Generalized Linear model, and perform a genome-wide association study using a Bayesian method.

Results

In total, 10 significant single nucleotide polymorphisms (SNPs) were detected for total number born (TNB) and 9 SNPs for variability of TNB (varTNB). Those SNPs explained 0.83 % of genetic variance in TNB and 1.44 % in varTNB. The most significant SNP for TNB was detected on Sus scrofa chromosome (SSC) 11. A possible candidate gene for TNB is ENOX1, which is involved in cell growth and survival. On SSC7, two possible candidate genes for varTNB are located. The first gene is coding a swine heat shock protein 90 (HSPCB = Hsp90), which is a well-studied gene stabilizing morphological traits in Drosophila and Arabidopsis. The second gene is VEGFA, which is activated in angiogenesis and vasculogenesis in the fetus. Furthermore, the genetic correlation between additive genetic effects on TNB and on its variation was 0.49. This indicates that the current selection to increase TNB will also increase the varTNB.

Conclusions

To the best of our knowledge, this is the first study reporting SNPs associated with variation of a trait in pigs. Detected genomic regions associated with varTNB can be used in genomic selection to decrease varTNB, which is highly desirable to avoid very small or very large litters in pigs. However, the percentage of variance explained by those regions was small. The SNPs detected in this study can be used as indication for regions in the Sus scrofa genome involved in maintaining low variability of litter size, but further studies are needed to identify the causative loci.

Genetic selection for increased mean and reduced variance of twinning rate in Belclare ewes

It is sometimes possible to breed for more uniform individuals by selecting animals with a greater tendency to be less variable, that is, those with a smaller environmental variance. This approach has been applied to reproduction traits in various animal species. We have evaluated fecundity in the Irish Belclare sheep breed by analyses of flocks with differing average litter size (number of lambs per ewe per year, NLB) and have estimated the genetic variance in environmental variance of lambing traits using double hierarchical generalized linear models (DHGLM). The data set comprised of 9470 litter size records from 4407 ewes collected in 56 flocks. The percentage of pedigreed lambing ewes with singles, twins and triplets was 30, 54 and 14%, respectively, in 2013 and has been relatively constant for the last 15 years. The variance of NLB increases with the mean in this data; the correlation of mean and standard deviation across sires is 0.50. The breeding goal is to increase the mean NLB without unduly increasing the incidence of triplets and higher litter sizes. The heritability estimates for lambing traits were NLB, 0.09; triplet occurrence (TRI) 0.07; and twin occurrence (TWN), 0.02. The highest and lowest twinning flocks differed by 23% (75% versus 52%) in the proportion of ewes lambing twins. Fitting bivariate sire models to NLB and the residual from the NLB model using a double hierarchical generalized linear model (DHGLM) model found a strong genetic correlation (0.88 ± 0.07) between the sire effect for the magnitude of the residual (VE ) and sire effects for NLB, confirming the general observation that increased average litter size is associated with increased variability in litter size. We propose a threshold model that may help breeders with low litter size increase the percentage of twin bearers without unduly increasing the percentage of ewes bearing triplets in Belclare sheep.

Behavioral idiosyncrasy reveals genetic control of phenotypic variability

Quantitative genetics has primarily focused on describing genetic effects on trait means and largely ignored the effect of alternative alleles on trait variability, potentially missing an important axis of genetic variation contributing to phenotypic differences among individuals. To study the genetic effects on individual-to-individual phenotypic variability (or intragenotypic variability), we used Drosophila inbred lines and measured the spontaneous locomotor behavior of flies walking individually in Y-shaped mazes, focusing on variability in locomotor handedness, an assay optimized to measure variability. We discovered that some lines had consistently high levels of intragenotypic variability among individuals, whereas lines with low variability behaved as although they tossed a coin at each left/right turn decision. We demonstrate that the degree of variability is itself heritable. Using a genome-wide association study (GWAS) for the degree of intragenotypic variability as the phenotype across lines, we identified several genes expressed in the brain that affect variability in handedness without affecting the mean. One of these genes, Ten-a, implicates a neuropil in the central complex of the fly brain as influencing the magnitude of behavioral variability, a brain region involved in sensory integration and locomotor coordination. We validated these results using genetic deficiencies, null alleles, and inducible RNAi transgenes. Our study reveals the constellation of phenotypes that can arise from a single genotype and shows that different genetic backgrounds differ dramatically in their propensity for phenotypic variabililty. Because traditional mean-focused GWASs ignore the contribution of variability to overall phenotypic variation, current methods may miss important links between genotype and phenotype.

Genetic (co)variance of rainbow trout (Oncorhynchus mykiss) body weight and its uniformity across production environments

Background

When rainbow trout from a single breeding program are introduced into various production environments, genotype-by-environment (GxE) interaction may occur. Although growth and its uniformity are two of the most important traits for trout producers worldwide, GxE interaction on uniformity of growth has not been studied. Our objectives were to quantify the genetic variance in body weight (BW) and its uniformity and the genetic correlation (r_g) between these traits, and to investigate the degree of GxE interaction on uniformity of BW in breeding (BE) and production (PE) environments using double hierarchical generalized linear models. Log-transformed data were also used to investigate whether the genetic variance in uniformity of BW, GxE interaction on uniformity of BW, and r_g between BW and its uniformity were influenced by a scale effect.

Results

Although heritability estimates for uniformity of BW were low and of similar magnitude in BE (0.014) and PE (0.012), the corresponding coefficients of genetic variation reached 19 and 21%, which indicated a high potential for response to selection. The genetic re-ranking for uniformity of BW (r_g = 0.56) between BE and PE was moderate but greater after log-transformation, as expressed by the low r_g (-0.08) between uniformity in BE and PE, which indicated independent genetic rankings for uniformity in the two environments when the scale effect was accounted for. The r_g between BW and its uniformity were 0.30 for BE and 0.79 for PE but with log-transformed BW, these values switched to -0.83 and -0.62, respectively.

Conclusions

Genetic variance exists for uniformity of BW in both environments but its low heritability implies that a large number of relatives are needed to reach even moderate accuracy of selection. GxE interaction on uniformity is present for both environments and sib-testing in PE is recommended when the aim is to improve uniformity across environments. Positive and negative r_g between BW and its uniformity estimated with original and log-transformed BW data, respectively, indicate that increased BW is genetically associated with increased variance in BW but with a decrease in the coefficient of variation. Thus, the scale effect substantially influences the genetic parameters of uniformity, especially the sign and magnitude of its r_g.

Heritable environmental variance causes nonlinear relationships between traits: application to birth weight and stillbirth of pigs

There is recent evidence from laboratory experiments and analysis of livestock populations that not only the phenotype itself, but also its environmental variance, is under genetic control. Little is known about the relationships between the environmental variance of one trait and mean levels of other traits, however. A genetic covariance between these is expected to lead to nonlinearity between them, for example between birth weight and survival of piglets, where animals of extreme weights have lower survival. The objectives were to derive this nonlinear relationship analytically using multiple regression and apply it to data on piglet birth weight and survival. This study provides a framework to study such nonlinear relationships caused by genetic covariance of environmental variance of one trait and the mean of the other. It is shown that positions of phenotypic and genetic optima may differ and that genetic relationships are likely to be more curvilinear than phenotypic relationships, dependent mainly on the environmental correlation between these traits. Genetic correlations may change if the population means change relative to the optimal phenotypes. Data of piglet birth weight and survival show that the presence of nonlinearity can be partly explained by the genetic covariance between environmental variance of birth weight and survival. The framework developed can be used to assess effects of artificial and natural selection on means and variances of traits and the statistical method presented can be used to estimate trade-offs between environmental variance of one trait and mean levels of others.

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

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