Bayesian analysis of the linear reaction norm model with unknown covariates

Influence of different environmental challenges on the expression of productive traits in Holstein cattle in the southern region of Brazil

The genotype-environment interaction (GEI) can lead to variations in gene expression related to traits, affecting the breeding value of animals. Assess the effects of GEI on milk yield (MY), fat yield (FY), and protein yield (PY) at 305 days in milk in first-, second and third-parity cows, employing the reaction norms model for Holstein cattle in Paraná state. The study utilized data from the milk testing service provided by the Paraná Association of Holstein Cattle Breeders (APCBRH) in Curitiba, PR, Brazil. This encompassed records from 378,000 records across one to three lactations from 2012 to 2022, originating from 513 herds in 72 cities within the state of Paraná. The environmental gradient was established by standardizing the contemporary group solutions derived from the animal model, disregarding GEI. Reaction norms were calculated using a Random Regression Model, and genotype classification correlations were determined by Spearman's correlation, comparing the breeding values estimated for the analyzed traits in each environmental gradient. Heritability for MY during the first lactation was moderate (0.28) in the least challenging environmental gradient, but of low magnitude (0.18) in the most challenging one. FY heritability estimates varied from low (0.09) to moderate (0.28) across environmental gradients, whereas PY heritability remained low regardless of lactation number and environmental challenge. The study did not identify the occurrence of GEI effects on fat yield, irrespective of parity. No GEI effect was observed on MY or PY in the first and second lactations. However, in the third lactation, GEI affected significantly the MY and PY in Holstein cattle in the state of Paraná, particularly under extreme environmental gradients. The selection for MY, PY, and FY during the first lactation may be the best strategy to promote genetic progress in these traits, because of the smaller effect of GEI at this stage.

Influence of different environmental challenges on the expression of reproductive traits in Holstein cattle in Southern Brazil

The aim of this study was to assess the impact of genotype-environment interaction (GEI) on the manifestation of traits such as age at first calving (AFC), age at first service (AFS), and calving interval (CI) through the application of the reaction norm model in Holstein cattle raised in Paraná state, Brazil. Utilizing data from the milk testing service of the Paraná Association of Holstein Cattle Breeders (APCBRH), this study analyzed records from 179,492 animals undergoing their first, second, and third lactations from the years 2012 to 2022. These animals were part of 513 herds spread across 72 municipalities in Paraná. The environmental gradient was established by normalizing contemporary group solutions, derived from the animal model, with the 305-day-corrected milk yield serving as the dependent variable. Subsequently, reaction norms were determined utilizing a Random Regression Model. Spearman's correlation was then applied to compare the estimates of breeding values across different environmental gradients for the studied traits. The highest EG (+ 4) indicates the least challenging environments, where animals experience better environmental conditions. Conversely, lower EG (-4) values represent the most challenging environments, where animals endure worse conditions. The only trait that exhibited a moderate heritability magnitude was AFC (0.23) in the least challenging environmental condition. The other traits were classified as having low heritability magnitudes regardless of the evaluated environmental gradient. While minimal evidence was found for the influence of GEI on CI, a clear GEI effect was observed for AFC and AFS across all environmental gradients examined. A reversal in genotype ranking occurred under extreme environmental conditions. The findings suggest that the best-performing genotype under one environmental gradient may not necessarily excel under another.

Genome-Wide Gene-Environment Interaction Analysis Identifies Novel Candidate Variants for Growth Traits in Beef Cattle

Complex traits are widely considered to be the result of a compound regulation of genes, environmental factors, and genotype-by-environment interaction (G × E). The inclusion of G × E in genome-wide association analyses is essential to understand animal environmental adaptations and improve the efficiency of breeding decisions. Here, we systematically investigated the G × E of growth traits (including weaning weight, yearling weight, 18-month body weight, and 24-month body weight) with environmental factors (farm and temperature) using genome-wide genotype-by-environment interaction association studies (GWEIS) with a dataset of 1350 cattle. We validated the robust estimator's effectiveness in GWEIS and detected 29 independent interacting SNPs with a significance threshold of 1.67 × 10-6, indicating that these SNPs, which do not show main effects in traditional genome-wide association studies (GWAS), may have non-additive effects across genotypes but are obliterated by environmental means. The gene-based analysis using MAGMA identified three genes that overlapped with the GEWIS results exhibiting G × E, namely SMAD2, PALMD, and MECOM. Further, the results of functional exploration in gene-set analysis revealed the bio-mechanisms of how cattle growth responds to environmental changes, such as mitotic or cytokinesis, fatty acid β-oxidation, neurotransmitter activity, gap junction, and keratan sulfate degradation. This study not only reveals novel genetic loci and underlying mechanisms influencing growth traits but also transforms our understanding of environmental adaptation in beef cattle, thereby paving the way for more targeted and efficient breeding strategies.

Genetic interrogation of phenotypic plasticity informs genome-enabled breeding in cotton

Phenotypic plasticity, or the ability to adapt to and thrive in changing climates and variable environments, is essential for developmental programs in plants. Despite its importance, the genetic underpinnings of phenotypic plasticity for key agronomic traits remain poorly understood in many crops. In this study, we aim to fill this gap by using genome-wide association studies to identify genetic variations associated with phenotypic plasticity in upland cotton (Gossypium hirsutum L.). We identified 73 additive quantitative trait loci (QTLs), 32 dominant QTLs, and 6799 epistatic QTLs associated with 20 traits. We also identified 117 additive QTLs, 28 dominant QTLs, and 4691 epistatic QTLs associated with phenotypic plasticity in 19 traits. Our findings reveal new genetic factors, including additive, dominant, and epistatic QTLs, that are linked to phenotypic plasticity and agronomic traits. Meanwhile, we find that the genetic factors controlling the mean phenotype and phenotypic plasticity are largely independent in upland cotton, indicating the potential for simultaneous improvement. Additionally, we envision a genomic design strategy by utilizing the identified QTLs to facilitate cotton breeding. Taken together, our study provides new insights into the genetic basis of phenotypic plasticity in cotton, which should be valuable for future breeding.

Heteroscedastic Reaction Norm Models Improve the Assessment of Genotype by Environment Interaction for Growth, Reproductive, and Visual Score Traits in Nellore Cattle

The assessment of the presence of genotype by environment interaction (GxE) in beef cattle is very important in tropical countries with diverse climatic conditions and production systems. The present study aimed to assess the presence of GxE by using different reaction norm models for eleven traits related to growth, reproduction, and visual score in Nellore cattle. We studied five reaction norm models (RNM), fitting a linear model considering homoscedastic residual variance (RNM_homo), and four models considering heteroskedasticity, being linear (RNM_hete), quadratic (RNM_quad), linear spline (RNM_l-l), and quadratic spline (RNM_q-q). There was the presence of GxE for age at first calving (AFC), scrotal circumference (SC), weaning to yearling weight gain (WYG), and yearling weight (YW). The best models were RNM_l-l for YW and RNM_q-q for AFC, SC, and WYG. The heritability estimates for RNM_l-l ranged from 0.07 to 0.20, 0.42 to 0.61, 0.24 to 0.42, and 0.47 to 0.63 for AFC, SC, WYG, and YW, respectively. The heteroskedasticity in reaction norm models improves the assessment of the presence of GxE for YW, WYG, AFC, and SC. Additionally, the trajectories of reaction norms for these traits seem to be affected by a non-linear component, and selecting robust animals for these traits is an alternative to increase production and reduce environmental sensitivity.

Integrating a growth degree-days based reaction norm methodology and multi-trait modeling for genomic prediction in wheat

Multi-trait and multi-environment analyses can improve genomic prediction by exploiting between-trait correlations and genotype-by-environment interactions. In the context of reaction norm models, genotype-by-environment interactions can be described as functions of high-dimensional sets of markers and environmental covariates. However, comprehensive multi-trait reaction norm models accounting for marker × environmental covariates interactions are lacking. In this article, we propose to extend a reaction norm model incorporating genotype-by-environment interactions through (co)variance structures of markers and environmental covariates to a multi-trait reaction norm case. To do that, we propose a novel methodology for characterizing the environment at different growth stages based on growth degree-days (GDD). The proposed models were evaluated by variance components estimation and predictive performance for winter wheat grain yield and protein content in a set of 2,015 F6-lines. Cross-validation analyses were performed using leave-one-year-location-out (CV1) and leave-one-breeding-cycle-out (CV2) strategies. The modeling of genomic [SNPs] × environmental covariates interactions significantly improved predictive ability and reduced the variance inflation of predicted genetic values for grain yield and protein content in both cross-validation schemes. Trait-assisted genomic prediction was carried out for multi-trait models, and it significantly enhanced predictive ability and reduced variance inflation in all scenarios. The genotype by environment interaction modeling via genomic [SNPs] × environmental covariates interactions, combined with trait-assisted genomic prediction, boosted the benefits in predictive performance. The proposed multi-trait reaction norm methodology is a comprehensive approach that allows capitalizing on the benefits of multi-trait models accounting for between-trait correlations and reaction norm models exploiting high-dimensional genomic and environmental information.

Weak genotype x environment interaction suggests that measuring scrotal circumference at 12 and 18 months of age is helpful to select precocious Brahman cattle

The aim of this study was to evaluate the genotype x environment interaction (GxE) for scrotal circumference (SC) measured at different ages using pedigree-based (A -1) and pedigree and genomic-based (H -1) relationship matrices. Data from 1,515 Brahman bulls, from the Cooperative Research Centre for Beef Genetic Technologies (Beef CRC) experimental dataset were used in this study. SC was adjusted to age and body weight measured at 6 months (SC6), 12 months (SC12), 18 months (SC18) and 24 months of age (SC24). Body weight (BW) measured at 6 months (BW6), 12 months (BW12), 18 months (BW18) and 24 months of age (BW24) were used as criteria to describe the environment for SC in each age. All the animals measured were genotyped using medium-density SNP chips ("50k" or "70k" SNP) and their genotype were imputed using a reference panel with 729,068 SNP. The environment gradient (EG) was obtained by standardizing the solutions of the contemporary groups obtained by Animal Model with BW as the dependent variable. Then, the reaction norms (RN) were determined through a Random Regression Model. The breeding values (EBV) were estimated using either A -1 or H -1. The rank correlation was obtained using Spearman's correlation among the EBV estimated for the traits in analysis. For SC6 and SC24, higher estimates of heritability (h²) were obtained using A -1, when compared to those observed with H -1. In those ages, the improvement of the environment decreases the h² coefficient. On the other hand, the h² for SC12 and SC18 increased as the environment became more favorable, regardless of the matrix used. The RN for SC6 and SC24 estimated using A -1 and H -1 showed a decrease of variance from the worst to the best environment, an indication of existence of GxE. On the other hand, for SC12 and SC18, there were no significant differences between the EBV estimated in the lower and in the higher environments, regardless of the kinship matrix used, suggesting absence of GxE on those ages. Spearman's correlation among EBV estimated using A -1 and H -1 in different EG were practically equal to unity for all traits evaluated. In our study, there was weak evidence of GxE effect on SC in ages suitable for selection for sexual precocity. So, the absence of GxE at 12 and 18 months means these ages are advantageous for measuring SC to selection for sexual precocity. The advantage is that no changes in classification were observed when the sires were evaluated in different environments.

Trend, population structure, and trait mapping from 15 years of national varietal trials of UK winter wheat

There are now a rich variety of genomic and genotypic resources available to wheat researchers and breeders. However, the generation of high-quality and field-relevant phenotyping data which is required to capture the complexities of gene × environment interactions remains a major bottleneck. Historical datasets from national variety performance trials (NVPT) provide sufficient dimensions, in terms of numbers of years and locations, to examine phenotypic trends and study gene × environment interactions. Using NVPT for winter wheat varieties grown in the United Kingdom between 2002 and 2017, we examined temporal trends for eight traits related to yield, adaptation, and grain quality performance. We show a non-stationary linear trend for yield, grain protein content, Hagberg Falling Number (HFN), and days to ripening. Our data also show high environmental stability for yield, grain protein content, and specific weight in UK winter wheat varieties and high environmental sensitivity for HFN. We also show that UK varieties released within this period cluster into four main population groups. Using the historical NVPT data in a genome-wide association analysis, we uncovered a significant marker-trait association peak on wheat chromosome 6A spanning the NAM-A1 gene that have been previously associated with early senescence. Together, our results show the value of utilizing the data routinely collected during national variety evaluation process for examining breeding progress and the genetic architecture of important traits.

Multiple trait breeding programs with genotype-by-environment interactions based on reaction norms, with application to genetic improvement of disease resilience

Background

Genotype-by-environment interactions for a trait can be modeled using multiple-trait, i.e. character-state, models, that consider the phenotype as a different trait in each environment, or using reaction norm models based on a functional relationship, usually linear, between phenotype and a quantitative measure of the quality of the environment. The equivalence between character-state and reaction norm models has been demonstrated for a single trait. The objectives of this study were to extend the equivalence of the reaction norm and character-state models to a multiple-trait setting and to both genetic and environmental effects, and to illustrate the application of this equivalence to the design and optimization of breeding programs for disease resilience.

Methods

Equivalencies between reaction norm and character-state models for multiple-trait phenotypes were derived at the genetic and environmental levels, which demonstrates how multiple-trait reaction norm parameters can be derived from multiple-trait character state parameters. Methods were applied to optimize selection for a multiple-trait breeding goal in a target environment based on phenotypes collected in a healthy and disease-challenged environment, and to optimize the environment in which disease-challenge phenotypes should be collected.

Results and conclusions

The equivalence between multiple-trait reaction norm and multiple-trait character-state parameters allow genetic improvement for a multiple-trait breeding goal in a target environment to be optimized without recording phenotypes and estimating parameters for the target environment.

The theory on and software simulating large-scale genomic data for genotype-by-environment interactions

Background

With the emphasis on analysing genotype-by-environment interactions within the framework of genomic selection and genome-wide association analysis, there is an increasing demand for reliable tools that can be used to simulate large-scale genomic data in order to assess related approaches.

Results

We proposed a theory to simulate large-scale genomic data on genotype-by-environment interactions and added this new function to our developed tool GPOPSIM. Additionally, a simulated threshold trait with large-scale genomic data was also added. The validation of the simulated data indicated that GPOSPIM2.0 is an efficient tool for mimicking the phenotypic data of quantitative traits, threshold traits, and genetically correlated traits with large-scale genomic data while taking genotype-by-environment interactions into account.

Conclusions

This tool is useful for assessing genotype-by-environment interactions and threshold traits methods.

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.

Genotype by environment interactions for body weight in Mediterranean buffaloes using reaction norm models

Background: Buffalo breeding has significantly increased in Brazil over recent years. However, few genetic evaluations have been conducted. Objective: To assess Genotype x Environment Interactions in the Mediterranean Water Buffalo in Brazil, for weight at 205 days of age, using reaction norm models via random regression. Methods: Data for buffaloes born between 1990 and 2014 were collected from five farms ascribed to the Brazilian Buffaloe Improvement Program, located in the North (1), Northeast (1), South (2) and Southeast (1) regions of Brazil. The initial database consisted of 5,280 observations at 205 days of age (W205). We assessed fit using two hierarchical reaction norm models: a two-step (HRNM2s) and a one-step (HRNM1s). Model fit was estimated using the Deviance Information Criterion, Deviance Based on Bayes Factors and Deviance based on Conditional Predictive Ordinate. The environmental descriptors were created to group individuals into common production environments based on year, season, herd and sex. Results: The best fit was obtained for the hierarchical reaction norm model with one-step (HRNM1s). Direct heritability estimates for this model ranged from 0.17 to 0.67 and the maternal heritability from 0.02 to 0.11 with increasing environmental gradient. Lower correlations among the sire classifications were obtained in comparison with HRNM1s in environments with low and high management, confirming the presence of genotype x environment interactions. Conclusion: We recommend a wider application of genetic evaluation in buffalo aimed at identifying optimal genotypes within specific environments.

Genotype-by-environment interaction in Holstein heifer fertility traits using single-step genomic reaction norm models

Background

The effect of heat stress on livestock production is a worldwide issue. Animal performance is influenced by exposure to harsh environmental conditions potentially causing genotype-by-environment interactions (G × E), especially in highproducing animals. In this context, the main objectives of this study were to (1) detect the time periods in which heifer fertility traits are more sensitive to the exposure to high environmental temperature and/or humidity, (2) investigate G × E due to heat stress in heifer fertility traits, and, (3) identify genomic regions associated with heifer fertility and heat tolerance in Holstein cattle.

Results

Phenotypic records for three heifer fertility traits (i.e., age at first calving, interval from first to last service, and conception rate at the first service) were collected, from 2005 to 2018, for 56,998 Holstein heifers raised in 15 herds in the Beijing area (China). By integrating environmental data, including hourly air temperature and relative humidity, the critical periods in which the heifers are more sensitive to heat stress were located in more than 30 days before the first service for age at first calving and interval from first to last service, or 10 days before and less than 60 days after the first service for conception rate. Using reaction norm models, significant G × E was detected for all three traits regarding both environmental gradients, proportion of days exceeding heat threshold, and minimum temperature-humidity index. Through single-step genome-wide association studies, PLAG1, AMHR2, SP1, KRT8, KRT18, MLH1, and EOMES were suggested as candidate genes for heifer fertility. The genes HCRTR1, AGRP, PC, and GUCY1B1 are strong candidates for association with heat tolerance.

Conclusions

The critical periods in which the reproductive performance of heifers is more sensitive to heat stress are trait-dependent. Thus, detailed analysis should be conducted to determine this particular period for other fertility traits. The considerable magnitude of G × E and sire re-ranking indicates the necessity to consider G × E in dairy cattle breeding schemes. This will enable selection of more heat-tolerant animals with high reproductive efficiency under harsh climatic conditions. Lastly, the candidate genes identified to be linked with response to heat stress provide a better understanding of the underlying biological mechanisms of heat tolerance in dairy cattle.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12864-021-07496-3.

Why breed disease-resilient livestock, and how?

BACKGROUND

Fighting and controlling epidemic and endemic diseases represents a considerable cost to livestock production. Much research is dedicated to breeding disease resilient livestock, but this is not yet a common objective in practical breeding programs. In this paper, we investigate how future breeding programs may benefit from recent research on disease resilience.

MAIN BODY

We define disease resilience in terms of its component traits resistance (R: the ability of a host animal to limit within-host pathogen load (PL)) and tolerance (T: the ability of an infected host to limit the damage caused by a given PL), and model the host's production performance as a reaction norm on PL, depending on R and T. Based on this, we derive equations for the economic values of resilience and its component traits. A case study on porcine respiratory and reproductive syndrome (PRRS) in pigs illustrates that the economic value of increasing production in infectious conditions through selection for R and T can be more than three times higher than by selection for production in disease-free conditions. Although this reaction norm model of resilience is helpful for quantifying its relationship to its component traits, its parameters are difficult and expensive to quantify. We consider the consequences of ignoring R and T in breeding programs that measure resilience as production in infectious conditions with unknown PL-particularly, the risk that the genetic correlation between R and T is unfavourable (antagonistic) and that a trade-off between them neutralizes the resilience improvement. We describe four approaches to avoid such antagonisms: (1) by producing sufficient PL records to estimate this correlation and check for antagonisms-if found, continue routine PL recording, and if not found, shift to cheaper proxies for PL; (2) by selection on quantitative trait loci (QTL) known to influence both R and T in favourable ways; (3) by rapidly modifying towards near-complete resistance or tolerance, (4) by re-defining resilience as the animal's capacity to resist (or recover from) the perturbation caused by an infection, measured as temporal deviations of production traits in within-host longitudinal data series.

CONCLUSIONS

All four alternatives offer promising options for genetic improvement of disease resilience, and most rely on technological and methodological developments and innovation in automated data generation.

The superiority of multi-trait models with genotype-by-environment interactions in a limited number of environments for genomic prediction in pigs

Background

Different production systems and climates could lead to genotype-by-environment (G × E) interactions between populations, and the inclusion of G × E interactions is becoming essential in breeding decisions. The objective of this study was to investigate the performance of multi-trait models in genomic prediction in a limited number of environments with G × E interactions.

Results

In total, 2,688 and 1,384 individuals with growth and reproduction phenotypes, respectively, from two Yorkshire pig populations with similar genetic backgrounds were genotyped with the PorcineSNP80 panel. Single- and multi-trait models with genomic best linear unbiased prediction (GBLUP) and BayesC π were implemented to investigate their genomic prediction abilities with 20 replicates of five-fold cross-validation. Our results regarding between-environment genetic correlations of growth and reproductive traits (ranging from 0.618 to 0.723) indicated the existence of G × E interactions between these two Yorkshire pig populations. For single-trait models, genomic prediction with GBLUP was only 1.1% more accurate on average in the combined population than in single populations, and no significant improvements were obtained by BayesC π for most traits. In addition, single-trait models with either GBLUP or BayesC π produced greater bias for the combined population than for single populations. However, multi-trait models with GBLUP and BayesC π better accommodated G × E interactions, yielding 2.2% – 3.8% and 1.0% – 2.5% higher prediction accuracies for growth and reproductive traits, respectively, compared to those for single-trait models of single populations and the combined population. The multi-trait models also yielded lower bias and larger gains in the case of a small reference population. The smaller improvement in prediction accuracy and larger bias obtained by the single-trait models in the combined population was mainly due to the low consistency of linkage disequilibrium between the two populations, which also caused the BayesC π method to always produce the largest standard error in marker effect estimation for the combined population.

Conclusions

In conclusion, our findings confirmed that directly combining populations to enlarge the reference population is not efficient in improving the accuracy of genomic prediction in the presence of G × E interactions, while multi-trait models perform better in a limited number of environments with G × E interactions.

Genomic prediction of growth traits for pigs in the presence of genotype by environment interactions using single-step genomic reaction norm model

Economically important traits are usually complex traits influenced by genes, environment and genotype-by-environment (G × E) interactions. Ignoring G × E interaction could lead to bias in the estimation of breeding values and selection decisions. A total of 1,778 pigs were genotyped using the PorcineSNP80 BeadChip. The existence of G × E interactions was investigated using a single-step reaction norm model for growth traits of days to 100 kg (AGE) and backfat thickness adjusted to 100 kg (BFT), based on a pedigree-based relationship matrix (A) or a genomic-pedigree joint relationship matrix (H). In the reaction norm model, the herd-year-season effect was measured as the environmental variable (EV). Our results showed no G × E interactions for AGE, but for BFT. For both AGE and BFT, the genomic reaction norm model (H) produced more accurate predictions than the conventional reaction norm model (A). For BFT, the accuracies were greater based on the reaction norm model than those based on the reduced model without exploiting G × E interaction, with EV ranging from 0.5 to 1, and accuracy increasing by 3.9% and 4.6% in the reaction norm model based on A and H matrices, respectively, while reaction norm model yielded approximately 8.4% and 7.9% lower accuracy for EVs ranging from 0 to 0.4, based on A and H matrices, respectively. In addition, for BFT, the highest accuracy was obtained in the BJLM6 farm for realizing directional selection. This study will help to apply G × E interactions to practical genomic selection.

Genotype-environment interaction for age at first calving in Holstein cows in Brazil

Dairy cattle production is distributed throughout the Brazilian regions. However, Brazilian producing regions are different in air temperature and humidity, diet, birth season, and other factors that may alter the reproductive performances of cows. The age of the cow at first calving (AFC) is a good indicator of sexual precocity since it shows the beginning of the female reproductive life and has a great influence on cow replacement costs. Researches on genotype-environment interaction (GEI) show the importance of using specific bulls for the different production systems in Brazil since most semen used in the country is imported. The objective of this work was to evaluate GEI for AFC in Holstein cows in Brazil, using reaction norms. The statistical models used were the standard animal model, which disregards the GEI, and hierarchical reaction norm models with homoscedastic (HRNMHO) and heteroscedastic (HRNMHE) residual variance, and one (HRNMHO1S and HRNMHE1S) and two (HRNMHO2S and HRNMHE2S) steps. HRNMHO1S presented better fit to the data, with lower heritability for environments with lower AFC, and higher heritability for environments with higher AFC. The GEI found was complex, with a reclassification of bulls, denoting the importance of considering GEI for evaluation and selection of bulls for different production levels. The reduction of AFC is possible when using breeding bulls adapted to the tropical and subtropical conditions of Brazil.

Genotype-environment interaction for productive traits of Holstein cows in Brazil described by reaction norms

Brazil is the world's fourth largest milk producer; this activity extends throughout the national territory, with productions of approximate 34 billion liters of milk per year. The objective of this work was to evaluate the genotype-environment interaction (GEI) in purebred Holstein cows for milk (M), protein (P), and fat (F) yields. The statistical models used were the standard animal model (AM), which disregards the GEI, and hierarchical reaction norm models with homoscedastic (HRNMHO) and heteroscedastic (HRNMHE) residual variance, and one (HRNMHO1S and HRNMHE1S) and two (HRNMHO2S and HRNMHE2S) steps. HRNMHO1S presented a better fit of the data for all traits, with higher heritability for the best environments. Most bulls presented robust phenotypes; however, GEI was found with a reclassification of the bulls in the environmental gradient. Although few, and less used, bulls with plastic phenotypes were found for all traits, and the use of them can optimize genetic gains in specific environments.

Genomic reaction norm models exploiting genotype × environment interaction on sexual precocity indicator traits in Nellore cattle

Brazilian beef cattle are raised predominantly on pasture in a wide range of environments. In this scenario, genotype by environment (G×E) interaction is an important source of phenotypic variation in the reproductive traits. Hence, the evaluation of G×E interactions for heifer's early pregnancy (HP) and scrotal circumference (SC) traits in Nellore cattle, belonging to three breeding programs, was carried out to determine the animal's sensitivity to the environmental conditions (EC). The dataset consisted of 85 874 records for HP and 151 553 records for SC, from which 1800 heifers and 3343 young bulls were genotyped with the BovineHD BeadChip. Genotypic information for 826 sires was also used in the analyses. EC levels were based on the contemporary group solutions for yearling body weight. Linear reaction norm models (RNM), using pedigree information (RNM_A) or pedigree and genomic information (RNM_H), were used to infer G×E interactions. Two validation schemes were used to assess the predictive ability, with the following training populations: (a) forward scheme-dataset was split based on year of birth from 2008 for HP and from 2011 for SC; and (b) environment-specific scheme-low EC (-3.0 and -1.5) and high EC (1.5 and 3.0). The inclusion of the H matrix in RNM increased the genetic variance of the intercept and slope by 18.55 and 23.00% on average respectively, and provided genetic parameter estimates that were more accurate than those considering pedigree only. The same trend was observed for heritability estimates, which were 0.28-0.56 for SC and 0.26-0.49 for HP, using RNM_H, and 0.26-0.52 for SC and 0.22-0.45 for HP, using RNM_A. The lowest correlation observed between unfavorable (-3.0) and favorable (3.0) EC levels were 0.30 for HP and -0.12 for SC, indicating the presence of G×E interaction. The G×E interaction effect implied differences in animals' genetic merit and re-ranking of animals on different environmental conditions. SNP marker-environment interaction was detected for Nellore sexual precocity indicator traits with changes in effect and variance across EC levels. The RNM_H captured G×E interaction effects better than RNM_A and improved the predictive ability by around 14.04% for SC and 21.31% for HP. Using the forward scheme increased the overall predictive ability for SC (20.55%) and HP (11.06%) compared with the environment-specific scheme. The results suggest that the inclusion of genomic information combined with the pedigree to assess the G×E interaction leads to more accurate variance components and genetic parameter estimates.

Genetic architecture of phenotypic means and plasticities of kernel size and weight in maize

Genetic relationships between the phenotypic means and plasticities of kernel size and weight revealed the common genetic control of these traits in maize. Kernel size and weight are crucial components of grain yield in maize, and phenotypic plasticity in these traits facilitates adaptations to changing environments. Elucidating the genetic architecture of the mean phenotypic values and plasticities of kernel size and weight may be essential for breeding climate-robust maize varieties. Here, a maize nested association mapping (CN-NAM) population and association panel were grown in different environments. A joint linkage analysis and genome-wide association mapping were performed for five kernel size and weight phenotypic traits and two phenotypic plasticity measures. The mean phenotypes and plasticities were significantly correlated. The overall results of quantitative trait locus (QTL) and candidate gene analyses indicated moderate and high levels of common genetic control for the two traits. Furthermore, the mean phenotypes or plasticities of the hundred-kernel weight and volume were commonly regulated to a high degree. One pleiotropic locus on chromosome 10 simultaneously controlled the mean phenotypic values and plasticities of kernel size and weight. Therefore, the plasticity of kernel size and weight might be indirectly selected during maize breeding; however, selecting for high or low plasticity in combination with high or low mean phenotypic values of kernel size and weight traits may be difficult.

Unraveling genetic sensitivity of beef cattle to environmental variation under tropical conditions

BACKGROUND

Selection of cattle that are less sensitive to environmental variation in unfavorable environments and more adapted to harsh conditions is of primary importance for tropical beef cattle production systems. Understanding the genetic background of sensitivity to environmental variation is necessary for developing strategies and tools to increase efficiency and sustainability of beef production. We evaluated the degree of sensitivity of beef cattle performance to environmental variation, at the animal and molecular marker levels (412 K single nucleotide polymorphisms), by fitting and comparing the results of different reaction norm models (RNM), using a comprehensive dataset of Nellore cattle raised under diverse environmental conditions.

RESULTS

Heteroscedastic RNM (with different residual variances for environmental level) provided better fit than homoscedastic RNM. In addition, spline and quadratic RNM outperformed linear RNM, which suggests the existence of a nonlinear genetic component affecting the performance of Nellore cattle. This nonlinearity indicates that within-animal sensitivity depends on the environmental gradient (EG) level and that animals may present different patterns of sensitivity according to the range of environmental variations. The spline RNM showed that sensitivity to environmental variation from harsh to average EG is lowly correlated with sensitivity from average to good EG, at both the animal and molecular marker levels. Although the genomic regions that affect sensitivity in harsher environments were not the same as those associated with less challenging environments, the candidate genes within those regions participate in common biological processes such as those related to inflammatory and immune response. Some plausible candidate genes were identified.

CONCLUSIONS

Sensitivity of tropical beef cattle to environmental variation is not continuous along the environmental gradient, which implies that animals that are less sensitive to harsher conditions are not necessarily less responsive to variations in better environmental conditions, and vice versa. The same pattern was observed at the molecular marker level, i.e. genomic regions and, consequently, candidate genes associated with sensitivity to harsh conditions were not the same as those associated with sensitivity to less challenging conditions.

Genotype by environment interaction for female fertility traits under conventional and organic production systems in Danish Holsteins

Conventional and organic production systems mainly differ in feeding strategies, outdoor and pasture access, and the use of antibiotic treatments. These environmental differences could lead to a genotype by environment interaction (G × E) and a requirement for including G × E in breeding decisions. The objectives of this study were to estimate variance components and heritabilities for conventional and organic production systems and investigate G × E under these 2 production systems for female fertility traits in Danish Holsteins. The analyzed traits included the interval from calving to first insemination (ICF), the interval from first to last insemination, number of inseminations per conception (NINS), and non-return rate within 56 d after the first insemination. Records of female fertility in heifers and the first 3 lactations in cows as well as grass ratio of feed at herd level were collected during the period from 2011 to 2016. The performances of a trait in heifers and cows (lactation 1 to 3) were considered as different traits. The (co)variance components and the resulting heritabilities and genetic correlations were estimated using 2 models. One was a bivariate model treating performances of a trait under organic and conventional production systems as 2 different traits using a reduced data set, and the other was a reaction norm model with random regression on the production system and the grass ratio of feed using a full data set. The full data set comprised records of 37,836 females from 112 organic herds and 513,599 females from 1,224 conventional herds, whereas the reduced data set comprised records from all these 112 organic herds and 92,696 females from 185 convention herds extracted from the full data set with grass ratio of feed lower than 0.20. All female fertility performances of the organic production system were superior to those of the conventional production system. Besides, heterogeneities in additive genetic variances and heritabilities were observed between conventional and organic production systems for all traits. Furthermore, genetic correlations between these 2 production systems ranged from 0.607 to 1.000 estimated from bivariate models and from 0.848 to 0.999 estimated from reaction norm models. Statistically significant G × E were observed for NINS in heifers, non-return rate within 56 d after the first insemination in heifers, and ICF from the bivariate model, and for ICF and NINS in cows from the reaction norm model.

Reaction norm analysis of pig growth using environmental descriptors based on alternative traits

Contemporary group (CG) estimates of different phenotypes have not been widely explored for pigs. The objective of this study was to extend the traits used to derive environmental descriptors of the growing pig, to include CG estimates of early growth between birth and start of feed intake test (EADG), growth during feed intake test (TADG), lifetime growth (ADG), daily feed intake (DFI), backfat (BF) and muscle depth (MD). Pedigree and performance records (n = 7,746) from a commercial Australian piggery were used to derive environmental descriptors based on CG estimates of these six traits. The CG estimates of growth traits described different aspects of the environment from the CG estimates of carcass traits (r < 0.10). These definitions of the environment then were used in reaction norm analysis of growth, to evaluate sire-by-environment interaction (Sire × E) for growth. The most appropriate reaction norm model to evaluate Sire × E for growth was dependent on the environmental descriptor used. If the trait used to derive an environmental descriptor was distinctly different from growth (e.g., BF and MD), CG as an additional random effect was required in the model. If not included, inflated common litter effect and sire intercept variance suggest there was unaccounted environmental variability. There was no significant Sire × E using any of the definitions of the environment, with estimated variance in sire slopes largest when environments were defined by BF ( σ ^ bi 2  = 97 ± 83 (g/day)² ), followed by environments defined by DFI ( σ ^ bi 2  = 39 ± 101 (g/day)² ). While there appears to be differences in ability to detect Sire × E, improved data structure is required to better assess these environmental descriptors based on alternative traits. The ideal trait, or combination of traits, used to derive environmental descriptors may be unique for individual herds. Therefore, multiple phenotypes should be further explored for the evaluation of Sire × E for growth in the pig.

Genotype-by-environment interaction of fertility traits in Danish Holstein cattle using a single-step genomic reaction norm model

Genotype-by-environment (G × E) interactions could play an important role in cattle populations, and it should be considered in breeding programmes to select the best sires for different environments. The objectives of this study were to study G × E interactions for female fertility traits in the Danish Holstein dairy cattle population using a reaction norm model (RNM), and to detect the particular genomic regions contributing to the performance of these traits and the G × E interactions. In total 4534 bulls were genotyped by an Illumina BovineSNP50 BeadChip. An RNM with a pedigree-based relationship matrix and a pedigree-genomic combined relationship matrix was used to explore the existence of G × E interactions. In the RNM, the environmental gradient (EG) was defined as herd effect. Further, the genomic regions affecting interval from calving to first insemination (ICF) and interval from first to last insemination (IFL) were detected using single-step genome-wide association study (ssGWAS). The genetic correlations between extreme EGs indicated that G × E interactions were sizable for ICF and IFL. The genomic RNM (pedigree-genomic combined relationship matrix) had higher prediction accuracy than the conventional RNM (pedigree-based relationship matrix). The top genomic regions affecting the slope of the reaction norm included immunity-related genes (IL17, IL17F and LIF), and growth-related genes (MC4R and LEP), while the top regions influencing the intercept of the reaction norm included fertility-related genes such as EREG, AREG and SMAD4. In conclusion, our findings validated the G × E interactions for fertility traits across different herds and were helpful in understanding the genetic background of G × E interactions for these traits.

Crop genome-wide association study: a harvest of biological relevance

With the advent of rapid genotyping and next-generation sequencing technologies, genome-wide association study (GWAS) has become a routine strategy for decoding genotype-phenotype associations in many species. More than 1000 such studies over the last decade have revealed substantial genotype-phenotype associations in crops and provided unparalleled opportunities to probe functional genomics. Beyond the many 'hits' obtained, this review summarizes recent efforts to increase our understanding of the genetic architecture of complex traits by focusing on non-main effects including epistasis, pleiotropy, and phenotypic plasticity. We also discuss how these achievements and the remaining gaps in our knowledge will guide future studies. Synthetic association is highlighted as leading to false causality, which is prevalent but largely underestimated. Furthermore, validation evidence is appealing for future GWAS, especially in the context of emerging genome-editing technologies.

Macro-environmental sensitivity for growth rate in Danish Duroc pigs is under genetic control

The aim of this study was to examine (i) the genetic variation in macro-environmental sensitivity (macro-ES) for ADG in Danish Duroc pigs, (ii) the genetic heterogeneity among sexes, and (iii) residual variance heterogeneity among herds. Record of ADG for 32,297 boars (19 herds) and 42,724 gilts (16 herds) was used for analysis. The data were provided by the National Danish Pig Research Centre. The analysis was performed by fitting univariate reaction norm models with the herd-year-month on test (HYM) effect as environmental covariates and herd-specific residual variance for boars and gilts separately under a Bayesian setting. The environmental covariate was inferred simultaneously with other parameters of the model. Gibbs sampling was used to sample model dispersion and location parameters. The posterior means and highest posterior density intervals of the additive genetic variance, genetic correlations for ADG, and heritability were calculated over the continuous environmental range of -3σh to +3σh (SD of the HYM effect). The coheritability of ADG at the average environmental level and ADG in the environments along the -3σh to +3σh environmental gradient were also calculated. The analysis showed significant variation in macro-ES, revealing genotype by environment interactions (G × E) for ADG. The presence of G × E resulted in changes in additive genetic variance and heritability across the -3σh to +3σh range. The genetic correlations were high and positive between ADG in environments differing by 1σh units or less and decreased to moderately positive between ADG in the extreme environments in both sexes. The coheritability of ADG in the environment at the average level and the -3σh environment for boars were greater than the heritability in the environment at the average level, while it was less for gilts. The coheritability of ADG in the environment at the average level and the +3σh environment for boars was less than heritability in the environment at the average level, while it was either the same or greater for gilts, depending on the residual variance. Boars had larger additive genetic and residual variances than gilts. Heterogeneity of residual variances across herds was shown for both sexes. In conclusion, this study shows the presence of macro-ES, genetic variance heterogeneity among sexes for ADG in pigs, and residual variance heterogeneity across herds.

Sensitivity of breeding values of meat quail as a result of tryptophan: lysine ratios in the diet

SUMMARY We aimed to evaluate the random regression models that promote the best fit of residual variance predicting the breeding values of quail body weights and the sensitivity of its breeding values to the variations of different tryptophan:lysine ratios in the diets via reaction norms. A total of 1112 meat quails from LF1 and LF2 lines with 35 days of age were evaluated. During the period of 1 to 21 days of age, birds were fed with different tryptophan:lysine ratios (0.17, 0.20, 0.23, 0.26 and 0.29%) containing 2900 kcal ME/kg and 26.10% crude protein, followed by basal diet provided up to 35 days. The best model fit for residual variance was evaluated comparing heterogeneity (2, 3 and 4 classes) and homogeneity (1 class), including sex as fixed effect and the additive genetic effect as random. The second order Legendre polynomial was used to analyze the genotype x environment interaction using reaction norms. The model considering two classes of residual variance was the one that promoted the best fit of the data, being adopted to predict the breeding values. Thus, we observed changes in the sensitivity of the breeding values, characterized by the rearrangement of the breeding values, according to the different ratios of amino acids, suggesting the genotype x environment interaction.

Genotype by environment interaction for yearling weight in Nellore cattle applying reaction norms models

In the present study, a possible existence of genotype × environment interaction was verified for yearling weight in Nellore cattle, utilising a reaction norms model. Therefore, possible changes in the breeding value were evaluated for 46 032 animals, from three distinct herds, according to the environmental gradient variation of the different contemporary groups. Under a Bayesian approach, analyses were carried out utilising INTERGEN software resulting in solutions of contemporary groups dispersed in the environmental gradient from –90 to +100 kg. The estimates of heritability coefficients ranged from 0.19 to 0.63 through the environmental gradient and the genetic correlation between intercept and slope of the reaction norms was 0.76. The genetic correlation considering all animals of the herds in the environmental gradient ranged from 0.83 to 1.0, and the correlation between breeding values of bulls in different environments ranged from 0.79 to 1.0. The results showed no effect of genotype × environment interaction on yearling weight in the herds of this study. However, it is important to verify a possible influence of the genotype × environment in the genetic evaluation of beef cattle, as different environments might cause interference in gene expression and consequently difference in phenotypic response.

Distinct genetic architectures for phenotype means and plasticities in Zea mays

Phenotypic plasticity describes the phenotypic variation of a trait when a genotype is exposed to different environments. Understanding the genetic control of phenotypic plasticity in crops such as maize is of paramount importance for maintaining and increasing yields in a world experiencing climate change. Here, we report the results of genome-wide association analyses of multiple phenotypes and two measures of phenotypic plasticity in a maize nested association mapping (US-NAM) population grown in multiple environments and genotyped with ~2.5 million single-nucleotide polymorphisms. We show that across all traits the candidate genes for mean phenotype values and plasticity measures form structurally and functionally distinct groups. Such independent genetic control suggests that breeders will be able to select semi-independently for mean phenotype values and plasticity, thereby generating varieties with both high mean phenotype values and levels of plasticity that are appropriate for the target performance environments.

Estimação de valores genéticos para codornas europeias em função dos níveis da relação treonina: lisina da dieta: do nascimento aos 21 dias de idade

RESUMO O presente trabalho foi realizado com o objetivo de avaliar a sensibilidade dos valores genéticos dos pesos corporais e as características de carcaças de codornas europeias às mudanças do gradiente ambiental (níveis da relação treonina com a lisina das dietas), do nascimento aos 21 dias de idade, por meio de modelos de regressão aleatória com diferentes classes de variância residual. Os dados utilizados neste estudo são provenientes de 915 codornas de corte da linhagem LF1 e 839 da linhagem LF2, pertencentes ao Programa de Melhoramento Genético da Universidade Federal dos Vales do Jequitinhonha e Mucuri. Foram avaliados os pesos corporais e os rendimentos da carcaça das aves. As sensibilidades dos valores genéticos às mudanças nos níveis da relação treonina:lisina (interação genótipo x ambiente) foram obtidas por modelos de regressão aleatória (utilizando normas de reação) por meio do programa Wombat, que utiliza o princípio da máxima verossimilhança restrita (REML). O modelo de regressão aleatória que considerou duas classes de variância residual foi o mais indicado para a maioria das análises realizadas. Verificaram-se alterações na classificação dos valores genéticos para as duas linhagens de codornas de corte estudadas. Esse comportamento indica sensibilidade de valores genéticos aditivos às mudanças nutricionais, o que caracteriza a existência de interação genótipo x ambiente. A predição dos valores genéticos deve ser feita com o mesmo nível da relação treonina:lisina da dieta com a qual as codornas serão alimentadas no sistema de produção.

Sensitivity of breeding values for carcass traits of meat-type quail to changes in dietary (methionine + cystine):lysine ratio using reaction norm models

Our objective was to evaluate changes in breeding values for carcass traits of two meat-type quail (Coturnix coturnix) strains (LF1 and LF2) to changes in the dietary (methionine + cystine):lysine ([Met + Cys]:Lys) ratio due to genotype by environment (G × E) interaction via reaction norm. A total of 7000 records of carcass weight and yield were used for analyses. During the initial phase (from hatching to day 21), five diets with increasing (Met + Cys):Lys ratios (0.61, 0.66, 0.71, 0.76 and 0.81), containing 26.1% crude protein and 2900 kcal ME/kg, were evaluated. Analyses were performed using random regression models that included linear functions of sex (fixed effect) and breeding value (random effect) for carcass weight and yield, without and with heterogeneous residual variance adjustment. Both fixed and random effects were modelled using Legendre polynomials of second order. Genetic variance and heritability estimates were affected by both (Met + Cys):Lys ratio and strain. We observed that a G × E interaction was present, with changes in the breeding value ranking. Therefore, genetic evaluation for carcass traits should be performed under the same (Met + Cys):Lys ratio in which quails are raised.

Increased Proportion of Variance Explained and Prediction Accuracy of Survival of Breast Cancer Patients with Use of Whole-Genome Multiomic Profiles

Whole-genome multiomic profiles hold valuable information for the analysis and prediction of disease risk and progression. However, integrating high-dimensional multilayer omic data into risk-assessment models is statistically and computationally challenging. We describe a statistical framework, the Bayesian generalized additive model ((BGAM), and present software for integrating multilayer high-dimensional inputs into risk-assessment models. We used BGAM and data from The Cancer Genome Atlas for the analysis and prediction of survival after diagnosis of breast cancer. We developed a sequence of studies to (1) compare predictions based on single omics with those based on clinical covariates commonly used for the assessment of breast cancer patients (COV), (2) evaluate the benefits of combining COV and omics, (3) compare models based on (a) COV and gene expression profiles from oncogenes with (b) COV and whole-genome gene expression (WGGE) profiles, and (4) evaluate the impacts of combining multiple omics and their interactions. We report that (1) WGGE profiles and whole-genome methylation (METH) profiles offer more predictive power than any of the COV commonly used in clinical practice (e.g., subtype and stage), (2) adding WGGE or METH profiles to COV increases prediction accuracy, (3) the predictive power of WGGE profiles is considerably higher than that based on expression from large-effect oncogenes, and (4) the gain in prediction accuracy when combining multiple omics is consistent. Our results show the feasibility of omic integration and highlight the importance of WGGE and METH profiles in breast cancer, achieving gains of up to 7 points area under the curve (AUC) over the COV in some cases.

Estimation of genetic parameters and breeding values across challenged environments to select for robust pigs

Robustness is an important issue in the pig production industry. Since pigs from international breeding organizations have to withstand a variety of environmental challenges, selection of pigs with the inherent ability to sustain their productivity in diverse environments may be an economically feasible approach in the livestock industry. The objective of this study was to estimate genetic parameters and breeding values across different levels of environmental challenge load. The challenge load (CL) was estimated as the reduction in reproductive performance during different weeks of a year using 925,711 farrowing records from farms distributed worldwide. A wide range of levels of challenge, from favorable to unfavorable environments, was observed among farms with high CL values being associated with confirmed situations of unfavorable environment. Genetic parameters and breeding values were estimated in high- and low-challenge environments using a bivariate analysis, as well as across increasing levels of challenge with a random regression model using Legendre polynomials. Although heritability estimates of number of pigs born alive were slightly higher in environments with extreme CL than in those with intermediate levels of CL, the heritabilities of number of piglet losses increased progressively as CL increased. Genetic correlations among environments with different levels of CL suggest that selection in environments with extremes of low or high CL would result in low response to selection. Therefore, selection programs of breeding organizations that are commonly conducted under favorable environments could have low response to selection in commercial farms that have unfavorable environmental conditions. Sows that had experienced high levels of challenge at least once during their productive life were ranked according to their EBV. The selection of pigs using EBV ignoring environmental challenges or on the basis of records from only favorable environments resulted in a sharp decline in productivity as the level of challenge increased. In contrast, selection using the random regression approach resulted in limited change in productivity with increasing levels of challenge. Hence, we demonstrate that the use of a quantitative measure of environmental CL and a random regression approach can be comprehensively combined for genetic selection of pigs with enhanced ability to maintain high productivity in harsh environments.

Genotype by environment interaction for tick resistance of Hereford and Braford beef cattle using reaction norm models

Background

The cattle tick is a parasite that adversely affects livestock performance in tropical areas. Although countries such as Australia and Brazil have developed genetic evaluations for tick resistance, these evaluations have not considered genotype by environment (G*E) interactions. Genetic gains could be adversely affected, since breedstock comparisons are environmentally dependent on the presence of G*E interactions, particularly if residual variability is also heterogeneous across environments. The objective of this study was to infer upon the existence of G*E interactions for tick resistance of cattle based on various models with different assumptions of genetic and residual variability.

Methods

Data were collected by the Delta G Connection Improvement program and included 10,673 records of tick counts on 4363 animals. Twelve models, including three traditional animal models (AM) and nine different hierarchical Bayesian reaction norm models (HBRNM), were investigated. One-step models that jointly estimate environmental covariates and reaction norms and two-step models based on previously estimated environmental covariates were used to infer upon G*E interactions. Model choice was based on the deviance criterion information.

Results

The best-fitting model specified heterogeneous residual variances across 10 subclasses that were bounded by every decile of the contemporary group (CG) estimates of tick count effects. One-step models generally had the highest estimated genetic variances. Heritability estimates were normally higher for HBRNM than for AM. One-step models based on heterogeneous residual variances also usually led to higher heritability estimates. Estimates of repeatability varied along the environmental gradient (ranging from 0.18 to 0.45), which implies that the relative importance of additive and permanent environmental effects for tick resistance is influenced by the environment. Estimated genetic correlations decreased as the tick infestation level increased, with negative correlations between extreme environmental levels, i.e., between more favorable (low infestation) and harsh environments (high infestation).

Conclusions

HBRNM can be used to describe the presence of G*E interactions for tick resistance in Hereford and Braford beef cattle. The preferred model for the genetic evaluation of this population for tick counts in Brazilian climates was a one-step model that considered heteroscedastic residual variance. Reaction norm models are a powerful tool to identify and quantify G*E interactions and represent a promising alternative for genetic evaluation of tick resistance, since they are expected to lead to greater selection efficiency and genetic progress.

FW: An R Package for Finlay-Wilkinson Regression that Incorporates Genomic/Pedigree Information and Covariance Structures Between Environments

The Finlay–Wilkinson regression (FW) is a popular method among plant breeders to describe genotype by environment interaction. The standard implementation is a two-step procedure that uses environment (sample) means as covariates in a within-line ordinary least squares (OLS) regression. This procedure can be suboptimal for at least four reasons: (1) in the first step environmental means are typically estimated without considering genetic-by-environment interactions, (2) in the second step uncertainty about the environmental means is ignored, (3) estimation is performed regarding lines and environment as fixed effects, and (4) the procedure does not incorporate genetic (either pedigree-derived or marker-derived) relationships. Su et al. proposed to address these problems using a Bayesian method that allows simultaneous estimation of environmental and genotype parameters, and allows incorporation of pedigree information. In this article we: (1) extend the model presented by Su et al. to allow integration of genomic information [e.g., single nucleotide polymorphism (SNP)] and covariance between environments, (2) present an R package (FW) that implements these methods, and (3) illustrate the use of the package using examples based on real data. The FW R package implements both the two-step OLS method and a full Bayesian approach for Finlay–Wilkinson regression with a very simple interface. Using a real wheat data set we demonstrate that the prediction accuracy of the Bayesian approach is consistently higher than the one achieved by the two-step OLS method.

Genotype by environment interaction and breeding for robustness in livestock

The increasing size of the human population is projected to result in an increase in meat consumption. However, at the same time, the dominant position of meat as the center of meals is on the decline. Modern objections to the consumption of meat include public concerns with animal welfare in livestock production systems. Animal breeding practices have become part of the debate since it became recognized that animals in a population that have been selected for high production efficiency are more at risk for behavioral, physiological and immunological problems. As a solution, animal breeding practices need to include selection for robustness traits, which can be implemented through the use of reaction norms analysis, or though the direct inclusion of robustness traits in the breeding objective and in the selection index. This review gives an overview of genotype × environment interactions (the influence of the environment, reaction norms, phenotypic plasticity, canalization, and genetic homeostasis), reaction norms analysis in livestock production, options for selection for increased levels of production and against environmental sensitivity, and direct inclusion of robustness traits in the selection index. Ethical considerations of breeding for improved animal welfare are discussed. The discussion on animal breeding practices has been initiated and is very alive today. This positive trend is part of the sustainable food production movement that aims at feeding 9.15 billion people not just in the near future but also beyond.

Modelos de norma de reação para estudo das características de qualidade da carne de codornas de corte em função das razões (metionina + cistina): lisina da dieta

RESUMOObjetivou-se avaliar a sensibilidade dos valores genéticos para características de qualidade da carne em codornas de corte alimentadas com dietas contendo diferentes relações de (metionina + cistina): lisina, do nascimento aos 21 dias de idade, por meio de modelos de normas de reação. Utilizaram-se 9011 informações de qualidade de carne referentes a 1400 progênies de 80 reprodutores e 160 matrizes de duas linhas (LF1 e LF2). Para o ajuste dos modelos de regressão aleatória, foi usado o programa WOMBAT, considerando-se nas análises homogeneidade de variância residual. As codornas foram alimentadas do nascimento aos 21 dias de idade com dietas contendo as relações 0,61; 0,66; 0,71; 0,76 e 0,81 de (metionina + cistina): lisina, mantendo os níveis de proteína bruta de 26,12% e de energia em 2900 kcal EM/kg da dieta. Dos 22 aos 35 dias de idade, todas as codornas foram alimentadas com dieta contendo 22% de proteína bruta e 3050 kcal EM/kg da dieta. As estimativas da variância genética e da herdabilidade foram influenciadas pelo gradiente ambiental e pela linha, com mudanças nessas estimativas com o aumento do gradiente ambiental. Os valores genéticos das características de qualidade de carne referentes a cada uma das linhas se alteraram com o aumento das relações de aminoácidos das dietas em razão das mudanças no ordenamento dos valores genéticos, evidenciando a existência da interação genótipo x nível de relação dos aminoácidos da dieta para características de qualidade de carne. Predições de valores genéticos de características de qualidade de carne com base em determinada relação de (metionina + cistina): lisina da dieta não são válidas para outras relações desses aminoácidos.

A comparison of alternative random regression and reaction norm models for whole genome predictions

Whole genome prediction (WGP) based on high density SNP marker panels is known to improve the accuracy of breeding value (BV) prediction in livestock. However, these accuracies can be compromised when genotype by environment interaction (G×E) exists but is not accounted for. Reaction norm (RN) and random regression (RR) models have proven to be useful in accounting for G×E in pre-WGP evaluations by modeling BV as linear or higher order functions of environmental or temporal covariates. We extend these RR/RN models based on several alternative specifications for SNP-specific intercepts and linear slopes on environmental covariates. One specification is based on bivariate normality (BVN) of SNP-specific intercepts and slopes, whereas 2 others, IW-BayesA and based on inverted Wishart (IW) extensions IW-BayesB, are, respectively, bivariate Student t extensions of currently popular models without (BayesA) or with (BayesB) variable selection. We highlight alternative specifications based on the square root free Cholesky decomposition (CD) of SNP-specific variance-covariance (VCV) matrices in an attempt to better differentially model environmentally sensitive from environmentally robust QTL. Two CD specifications were considered with (CD-BayesB) or without (CD-BayesA) any variable selection on intercept and slope effects. We compared each of the 5 models based on an RN simulation study. Six scenarios were considered based on differences in overall genetic correlations between SNP-specific intercept and slope effects as well as on heritabilities and numbers of environmentally robust versus sensitive QTL. In most scenarios, IW-BayesA had the greatest accuracy, whereas CD-BayesB exhibited the greatest accuracy in low complexity architectures (i.e., low number of QTL). In an RR application of a Duroc × Pietrain resource population at Michigan State University, 5,271 SNP markers and 928 F2 animals with known pedigree were analyzed for backfat thickness at wk 10, 13, 16, 19, and 22. SNP-based RR methods had a 2.5% greater (P < 0.0001) cross-validation accuracy for predicting phenotypes than the SNP-based conventional BayesA/BayesB and/or pedigree based RR BLUP; however, none of the proposed RR models had performances that were different from each other.

Expected responses to different strategies of selection to increase heat tolerance assessed by changes in litter size in rabbit

Response on litter size (LS) to selection based on EBV of the own trait and several indexes including EBV of 1 or more parameters of a reaction norm model (RNM) was evaluated by simulation. The RNM described animal's performance under different environmental temperatures assuming that this has an animal-specific effect on LS beyond an animal-specific temperature threshold (i.e., it had 3 parameters: intercept [Int], slope [Slp], and threshold [Thr]). Litter size data were generated assuming this model under 2 environmental conditions (comfort [CC] and comfort-to-heat [CtHC]). Variance components for Int, Slp, Thr, and LS were taken from literature. The initial base population consisted of 125 females and 25 males. Ten generations of selection were conducted keeping constant the population size. Eight different selection criteria were considered, depending on both the evaluation model and the index combining EBV for 1 or more parameters of the RNM. In 1 case selection was based on EBV of the own trait predicted by using a repeatability animal model. In the other 7 cases the genetic evaluation was conducted using the same model as that used in the simulation. For each scenario 25 replicates were conducted and response to selection was assessed within replicate as the difference between generations in the average of trait. Results indicate that, under the studied conditions and for the used genetic parameters, selection based on the observed trait seems to have the same effect as selection based on some index, including EBV of the RNM parameters. In addition, response to selection could be greater under CtHC rather than CC. Animals selected exclusively for EBV of the Slp and Thr are not expected to have good performance under CC. Under CtHC, selection for LS has a major response on those parameters, whereas response on Int was very small. Under CC, response to selection on LS is mainly determined by a change in Int, whereas Slp does not change and Thr slightly increases. Selection based on EBV of Slp, Thr, or on an index including both seems to have the same effect on the trait and it was doubly effective in modifying the shape of the RNM under CtHC than under CC. Selection based on EBV of Thr and Slp does not seem to lead to any response in LS. Selection based on EBV of Int seems to have no effect on the trait or on animal's tolerance to heat under CtHC, but it would lead to a positive response in LS under CC.

Short communication: Heterosis by environment and genotype by environment interactions for protein yield in Danish Jerseys

Crossing of lines or strains within and between breeds has been demonstrated to be beneficial for dairy cattle performance. However, even within breed, differences between strains may also give rise to heterosis. A key question is whether an interaction exists between heterosis and environment (H × E) that is independent of genotype by environment (G × E) interactions. In this study, H × E and G × E interactions were estimated in a population of approximately 300,000 Danish Jersey cows. The cows were a mixture of pure Danish Jerseys and crosses of US and Danish Jerseys. The phenotype studied was protein yield. A reaction norm model where the unknown environmental covariates are inferred simultaneously with the other parameters in the model was used to analyze the data. When H × E, but not G × E, was included in the model, heterosis was estimated to be 3.8% for the intermediate environmental level. However, when both H × E and G × E were included in the model, heterosis was estimated to be 4.1% for the intermediate environmental level. Furthermore, when only H × E was included in the model, the regression on the unknown environmental covariate was estimated to be 0.15, interpreted as meaning that an increase of average herd-year protein yield by 1 kg of protein led to an increase in heterosis of 0.15 kg above the average heterosis for a first-cross cow. When both H × E and G × E were included in the model, the regression on the unknown environmental covariate was not significantly different from zero, meaning that heterosis was similar in all environments investigated. The genetic correlation of protein yields for different environmental levels ranged from 0.72 to 0.93, which was significantly different from unity, indicating that G × E exist for protein yield.

A reaction norm model for genomic selection using high-dimensional genomic and environmental data

New methods that incorporate the main and interaction effects of high-dimensional markers and of high-dimensional environmental covariates gave increased prediction accuracy of grain yield in wheat across and within environments. In most agricultural crops the effects of genes on traits are modulated by environmental conditions, leading to genetic by environmental interaction (G × E). Modern genotyping technologies allow characterizing genomes in great detail and modern information systems can generate large volumes of environmental data. In principle, G × E can be accounted for using interactions between markers and environmental covariates (ECs). However, when genotypic and environmental information is high dimensional, modeling all possible interactions explicitly becomes infeasible. In this article we show how to model interactions between high-dimensional sets of markers and ECs using covariance functions. The model presented here consists of (random) reaction norm where the genetic and environmental gradients are described as linear functions of markers and of ECs, respectively. We assessed the proposed method using data from Arvalis, consisting of 139 wheat lines genotyped with 2,395 SNPs and evaluated for grain yield over 8 years and various locations within northern France. A total of 68 ECs, defined based on five phases of the phenology of the crop, were used in the analysis. Interaction terms accounted for a sizable proportion (16 %) of the within-environment yield variance, and the prediction accuracy of models including interaction terms was substantially higher (17-34 %) than that of models based on main effects only. Breeding for target environmental conditions has become a central priority of most breeding programs. Methods, like the one presented here, that can capitalize upon the wealth of genomic and environmental information available, will become increasingly important.