Because single genetic variants may have pleiotropic effects, one trait can be a confounder in a genome-wide association study (GWAS) that aims to identify loci associated with another trait. A typical approach to address this issue is to perform an additional analysis adjusting for the confounder. However, obtaining conditional results can be time-consuming. We propose an approximate conditional phenotype analysis based on GWAS summary statistics, the covariance between outcome and confounder, and the variant minor allele frequency (MAF). GWAS summary statistics and MAF are taken from GWAS meta-analysis results while the traits covariance may be estimated by two strategies: (i) estimates from a subset of the phenotypic data; or (ii) estimates from published studies. We compare our two strategies with estimates using individual level data from the full GWAS sample (gold standard). A simulation study for both binary and continuous traits demonstrates that our approximate approach is accurate. We apply our method to the Framingham Heart Study (FHS) GWAS and to large-scale cardiometabolic GWAS results. We observed a high consistency of genetic effect size estimates between our method and individual level data analysis. Our approach leads to an efficient way to perform approximate conditional analysis using large-scale GWAS summary statistics. GCKR, IGF1) associated with FI1. Manning et al. 2012 also conducted a GWAS meta-analysis of FI and additionally identified 6 previously unreported loci  after adjusting for BMI2. Conducting a sensitivity analysis for GWAS by additionally adjusting for one or more traits may lead to new findings. However, in analyses in which many studies contribute to the final results, as is often the case in consortia-based meta-analyses, asking each study to rerun a genome-wide is time-consuming and potentially prohibitive. Moreover, using GWAS summary statistics has the advantage of protecting personal identifiable information and making data sharing possible without violating the participants’ privacy.Genome-wide association studies (GWAS) have been successful in identifying the associations between genetic variants and complex traits. Because genetic variants may have pleiotropic effects, one trait can be a confounder in a GWAS to identify loci associated with another trait. A typical approach to address the confounding issue is to test the association between the trait and a genetic variant adjusting for the confounders. Association results may vary due to confounding, so further adjustment for potential confounders in GWAS is crucial. Moreover, adjusting for traits that explain a large proportion of the variance may increase power to detect genetic associations by reducing the variance of the adjusted traits. For example, Dupuis et al. 2010 conducted a GWAS of fasting insulin (FI) without adjustment for body mass index (BMI) and identified two loci , in 2017 Deng and Pan proposed an approach to perform approximate conditional analysis to adjust for continuous confounders4. However, their method can only be applied to quantitative traits. Zhu et al. 2018 proposed a method to estimate the genetic effects of genetic variants on disease adjusting for other risk factors by integrating Mendelian randomization of summary GWAS statistics and LD-score regressions to approximate the covariance between the trait of interest and the risk factors5. This method is applicable to both continuous and binary traits. In addition, Wolf et al. 2020 proposed an approach for continuous outcomes using summary statistics of outcomes and covariates derived from the same study6.An approximate conditional analysis approach has been proposed earlier by Yang et al. 2012 to evaluate the association between a trait and a single nucleotide polymorphism (SNP) adjusting for other SNPs using summary statistics from GWAS and linkage disequilibrium (LD) estimates between SNPsOur proposed approach differs from the above-mentioned methods that use genotype data to estimate the covariance between phenotypic traits. We propose estimating the covariance directly from the phenotype data. For example, in order to estimate the covariance between FI and BMI, the best approach would be to use all the available phenotypic data for FI and BMI. However, gathering the full phenotype data in a large consortium is challenging, and confidentiality restrictions often prohibit sharing individual level data. Alternative approaches to estimate the covariance include: (1) evaluating covariance in a subset of the full samples (e.g. estimating the covariance between traits from one cohort in a multi-cohort study); and (2) using a covariance estimate from published articles.We evaluate our approximate conditional analysis approach and compare the results to the gold standard  using a simulation study. To illustrate results of the approach, we apply our method to cardiometabolic traits studied in one cohort, the Framingham Heart Study (FHS), and in meta-analysis results from several large-scale cardiometabolic GWAS consortia. We selected traits and outcomes that are substantially influenced by one or more secondary traits. In FHS we evaluated anthropometric traits including waist circumference adjusted for BMI, or BMI adjusted for ever-smoking, and cardiac traits including atrial fibrillation adjusted for height or adjusted for both heart failure and myocardial infarction. In large-scale cardiometabolic GWAS consortia meta-analyses, we compared our method with existing approaches using results from multiple traits, including fasting insulin adjusted for BMI, BMI adjusted for ever-smoking, and atrial fibrillation adjusted for BMI or adjusted for coronary artery disease.The rest of this article is organized as follows. We present simulation results comparing our approach to the gold standard. We then follow with applications to real data sets from FHS and consortium GWAS meta-analyses. In the Method section, we present the formulation details of our new approximate conditional phenotype analysis for the following four scenarios: 1) two continuous traits; (2) continuous outcome adjusted for a binary trait; (3) binary outcome adjusted for a continuous trait; and (4) two binary traits. Our investigation framework is presented in Fig.  two contWe compare our proposed method to the gold standard , and quantile–quantile plots for the FHS GWAS results are displayed in Fig. 9. When the outcome is binary (AF), our approximate approach does not perfectly match estimates from individual level data (the correlation coefficient between the approximation and gold standard for the effect estimates (betas) ranges from 0.87 to 0.92, while correlation coefficient for –log10  ranges from 0.64 to 0.75 Fig. A–E. TherWe compared our method with Wolf et al.’s proposed approximation in FHS using WC GWAS adjusted for BMI  and the adjustment covariate is BMI, the correlation between the gold standard effect estimates and the estimates obtained from our method, with relationship between traits estimated from a subset of individuals, is r = 0.88, very similar to the correlation coefficient obtained from GCTA_mtCOJO Fig. . The effThe correlation coefficients of − log10  between the gold standard  and our method using a subset of the data to evaluate the relationship between outcome and adjustment covariate (r = 0.61) is similar to the correlation coefficient obtained for the − log10  from gold standard versus GCTA_mtCOJO (r = 0.62).COBLL1, ANKS1A, and TAF11) which have not been identified by GCTA_mtCOJO or marginal GWAS but have been validated by gold standard results , our method and GCTA_mtCOJO yields very similar results in effect estimates and p-values. Results from these analyses are presented in Supplemental Fig. In our investigation, we notice that most GWAS studies require data transformation  for continuous traits, especially when the continuous trait is the outcome. In order to see the effect of the data transformation, we apply an inverse-normal transformation to the WC residuals in FHS and use the full phenotype data to estimate the relationship between outcome and covariate. Despite high correlation coefficients for effect estimates (r = 0.95), the approximate effect sizes are two times smaller than the individual level data estimates. We also find biased estimates when we use mtCOJO by GCTA from consortium data (r for effect estimates = 0.69) when the trait of interest has been transformed.Another issue when applying our method to existing GWAS results relates to allele frequency differences between GWAS datasets. This issue is observed when we analyzed FI adjusted for BMI; one variant has a very different allele frequency in the meta-analysis for BMI (MAF = 11.68%) compared to meta-analysis results for FI (MAF = 0.83%). This variant, rs11672564, also has a great discrepancy between the approximate method and gold standard, which can be explained by the effect allele frequency difference between the two datasets. To address this issue, we use the mean allele frequencies or the minimum allele frequency in the two consortia. However, the results do not improve substantially  because our method is more efficient in data processing and data storage. When analyzing all GWAS variants, results obtained from our method and existing approaches  for continuous or binary outcomes are similar. However, we recommend our method over GCTA_mtCOJO in situations where there are very few or no genome-wide significant associations from the GWAS for the covariates because of the difficulty in estimating the genetic correlation between outcome and covariate from GWAS summary statistics.12. Because the real causal relationships among genetic variants, the covariate, and the outcome are unknown, we suggest reporting the GWAS results with and without the covariate adjustment. Our approximation method can provide covariate adjusted results without requiring additional individual-level data analysis based on the summary statistics. With the adjusted and unadjusted information at hand, we can potentially estimate the bias of including the covariate and interpret the GWAS results more cautiously12. For continuous outcomes, Wang et al13 provided corrections to filter potentially spurious associations  using GWAS summary statistics. We utilized their approach when applying our proposed method and removed more than 100 variants which might be false positives in the WC GWAS adjusted for BMI in the FHS  in order to perform a statistical test of the hypothesis H0:m×1 is a vector of test statistics (beta/SE(beta)) from the unadjusted models testing the association of genome-wide SNPs other than SNP 4.Because entclass1pt{minimaWhen the adjustment trait is binary, M2 becomes a logistic model. However, other models  remain OLS models. Note that Eqs.  will not2 is binary, our proposed approximation requires knowledge of the number of cases   7) to ev1 is binary and Y2 is continuous, M1, M3, and M4 are logistic models, while M2 remains an OLS model. In order to estimate the genetic effect size after adjusting for When YIn Eq. , the onlWhen both mentclass2pt{minimrom Eqs.  and 9)..\documenrom Eqs.  to estimfrom Eq.  in Sect.Y2), the method is easily extended to multiple confounders  the latent variable exceeds the genotype specific thresholds of 0.1 (X = 0), 0.2 (X = 1) and 0.4 (X = 2); and 2) Y2 exceeds the 20th percentile of the Y2 distribution.When When If We updated In our simulation, we estimate In addition, we compute the type I error and power of our proposed approaches and compare them to the gold standard. For the type I error, we consider the following two scenarios: (1) genetic variant We assess power assuming 16. Details of the genotype and phenotype data collection for FHS can be found elsewhere17. A subset of FHS participants with available genotypes for approximately 550,000 SNPs was selected for analysis. The phenotypes were measured at the time closest to the DNA collection. Our method was applied to the FHS under four scenarios: (1) the outcome is waist circumference (WC) and the adjustment covariate is BMI; (2) the outcome is BMI and the adjustment covariate is ever-smoking; (3) the outcome is atrial fibrillation (AF) and the adjustment covariate is height; and (4) the outcome is AF and the two adjustment covariates are history of myocardial infarction (MI) and history of heart failure (HF). Age, sex, and the first ten principle components, to account for possible population stratification, are included as covariates in the models.The Framingham Heart Study (FHS) is an observational community-based longitudinal study, launched in 1948 to assess risk factors for cardiovascular diseases7 reporting on the relationship between WC and BMI, the reports from Plurphanswat et al8 and Dare et al9, describing the relationship between BMI and ever smoking, the report from Alonso et al10 on the relationship between AF and height, or the article from Schnabel et al11 describing the relationship between AF and MI or HF.The gold standard for our method is the GWAS analysis conducted on individual level data. We compare the effect sizes and significance of each SNPs with the approximate estimates using our proposed approach based on GWAS summary statistics. When applying our proposed method, the phenotypes relationships are estimated under the following three scenarios: (1) using the full phenotypes data; (2) using a randomly selected sample of 1,000 individuals from the full phenotypes data; and (3) using published study estimates. Such published reports include the study of Bozeman et al2, Genetic Investigation of Anthropometric Traits (GIANT) for BMI18, Tobacco and Genetics (TAG) for ever-smoking19, Atrial Fibrillation Consortium (AFGen)20, and Coronary Artery Disease Genome wide Replication and Meta-analysis plus The Coronary Artery Disease (C4D) Genetics consortium (CARDIoGRAMplusC4D) for CAD21. Because some summary statistics are based on Genome Build 36, we use the web provided tool to convert the genome coordinates to Genome Build 37 (https://genome.ucsc.edu/cgi-bin/hgLiftOver) to get the same coordinates for the different assemblies.We download GWAS summary statistics of fasting insulin (FI), BMI, ever-smoking, AF, and coronary artery diseases (CAD) from several consortia: Meta-analysis of Glucose and Insulin-related traits (MAGIC) for FIWe then use the summary statistics and the estimates of relationship between the outcome and the covariate based on FHS phenotypes data, a participating cohort in these consortia, to approximately estimate the GWAS effect after adjustment for one additional covariate: (1) FI adjusted for BMI; (2) BMI adjusted for ever-smoking; (3) AF adjusted for BMI; and (4) AF adjusted for CAD. Among those four applications, we only have the gold standard  from MAGIC for FI adjusted for BMI. For the other analyses, GWAS results adjusted for the additional trait are not available for comparison purpose. We also compare our method with the multi-trait-based conditional and joint analysis (mtCOJO) implemented in GCTA 1.9 which leverages GWAS summary statistics to estimate the relationships for both continuous and binary traits. When conducting the analysis by GCTA_mtCOJO, we use unrelated individuals from FHS as the LD reference panel. We compare the effect sizes and − log10  obtained from our method, the gold standard, and GCTA_mtCOJO.The difference between our method and GCTA_mtCOJO results from the way the relationship between the outcome and the covariates is estimated: we directly estimate the relationship based on phenotype data , while GCTA_mtCOJO uses a causal variants set and heritability of the outcome to estimate the phenotypes relationship. Details regarding estimation of the relationship between the two traits for both methods are in Table http://sites.bu.edu/fhspl/publications/approximate-conditional-analysis/.All our analyses  were run using R/3.6.0. For details, see Supplementary Information.


Further, h2SNP for maths and science remained after removing shared variance between subjects or IQ (N = 3197–5895). One genome-wide significant single nucleotide polymorphism  and four gene-level associations with science attainment  were identified. Rs952964 remained significant after removing the variance shared between academic subjects. The findings highlight the benefits of using environmentally homogeneous samples for genetic analyses and indicate that finer-grained phenotyping will help build more specific biological models of variance in learning processes and abilities.How well one does at school is predictive of a wide range of important cognitive, socioeconomic, and health outcomes. The last few years have shown marked advancement in our understanding of the genetic contributions to, and correlations with, academic attainment. However, there exists a gap in our understanding of the specificity of genetic associations with performance in academic subjects during adolescence, a critical developmental period. To address this, the Avon Longitudinal Study of Parents and Children was used to conduct genome-wide association studies of standardised national English (N = 5983), maths (N = 6017) and science (N = 6089) tests. High SNP-based heritabilities (h As a consequence, identifying the contributions of specific genetic  factors to individual differences in AA and understanding the aetiology of these observed relationships could be informative for a range of societal issues.Academic attainment  consistently and reliably associates with a diverse array of emotional, cognitive and health outcomes3. The first genome-wide association studies (GWAS) of learning abilities using modest (< 2500) sample sizes demonstrated that they are highly polygenic with thousands of common DNA variants contributing to heritability6. Furthermore, both twin and DNA-based studies suggest that the same genetic variants influence variability in cognitive functions across domains—dubbed ‘generalists genes’7. As a consequence, there has been a shift away from examining finer-grained measures of cognitive processes towards performing population-scale GWAS of broad measures of academic attainment, primarily how long one spends in education (EduYrs). The first EduYrs GWAS  was a meta-analysis of 42 cohorts performed by the Social Science Genetic Association Consortium . Three independent genome-wide significant single nucleotide polymorphisms (SNPs) were identified, each accounting for around 0.02% of the variance in EduYrs. Functional interrogation revealed that the signals were located in (or close to) genes previously associated with health and cognition, and demonstrated the utility of taking a broad phenotype to maximise discovery of common genetic variants of very small effect9. The subsequent SSGAC GWAS  identified a further 74 SNP associations that were mostly located in regions involved in the regulation of gene expression during foetal brain development10. The most recent SSGAC GWAS comprised over 1 million people (EduYrs3) and reported 1271 significantly associated loci and an enrichment of genes involved in neurophysiological brain functions. These included genes involved in neurotransmitter secretion, the activation of ion channels, synaptic plasticity, as well as those expressed in neural tissue both pre- and postnatally11. Construction of an EduYrs genome-wide polygenic score  was predictive of 7–10% of the variance in general cognitive ability and 11–13% in educational attainment, making it one of the most predictive polygenic scores currently available in the behavioural sciences11. The EduYrs GPS associates with many phenotypes, which is perhaps not surprising: such a broad-brush measure taken in adulthood (many levels removed from cell structure and brain function) will necessarily capture a wide range of variables influencing the length of time people stay in formal education. For example, beyond cognitive ability the EduYrs GPS predicts traits such as child behavioural problems, negative symptoms of affect related to depression, callous and unemotional traits, and Attention Deficit Hyperactivity Disorder (ADHD)13. If these polygenic scores are to have practical applications, we need a much better understanding of the specificity and generality of genetic causes of variance in educational performance across development.A large body of twin and DNA-based research robustly demonstrates that AA and learning abilities are heritable, with a recent meta-analysis of 61 twin studies reporting a heritability estimate of 66% for AA14. Consistent with these findings, bivariate twin estimates of English, maths and science attainment at ages 7–16 years suggest that just over half to two thirds of the heritability is shared between subjects after controlling for IQ , leaving a considerable proportion of the heritability not shared across subjects and independent of general cognitive function15. Similarly, in a study of 13,262 12-year-old twins, maths retained a heritability of 0.44 when controlling for both general intelligence and reading ability16.Whilst studies are limited, there is evidence of specificity in the genetic profiles of individual academic subjects and cognitive abilities. Donati, Meaburn and Dumontheil demonstrated that a structural equation model that divides AA into separate academic subjects fits standardised national test score data better than a common AA model, and that there is cognitive specificity to attainment in different subjects17. An exception is a recent GWAS of Han Chinese samples (combined N = 1597) that reported four independent SNPs associated with maths ability18, although these have yet to be independently replicated. The largest maths GWAS to date used adult self-report retrospective measures of maths ability  and highest maths class completed , and found genetic correlations of 0.51 and 0.81 respectively with EduYrs311. A multivariate twin and DNA-based analysis of reading and maths ability at age 12 in a UK twin cohort failed to identify any genome-wide significant loci but reported a SNP-based genetic correlation of 0.74 16. We are not aware of published GWAS that examine English or science as discrete academic subjects, but note that a large GWAS of latent cognitive domains captured by school grades in Danish, English and maths is in preprint19. GWAS of reading ability and receptive language (both components of English performance) have been reported20.Taken together, these findings highlight the need to maintain specificity when investigating genetic predictors of academic attainment, and to consider the temporality of associations across childhood and adolescence. However, adequately powered molecular genetic studies focused on characterising genetic contributions to performance in individual academic subjects and their cognitive and non-cognitive genetic correlates are sparse. For instance, published GWAS of maths ability using general population samples have been limited in size  and thus far have failed to identify robustly associated variants21. Furthermore, a diverse range of cognitive and non-cognitive traits including well-being, personality and behavioural problems have been shown to contribute to the heritability of adolescent academic performance22.Untangling the generality, specificity and developmental timing of genetic causes of variance in discrete educational outcomes is necessary for understanding causal paths and will have far-reaching implications for the development of polygenic predictors and intervention strategies aimed at improving learning outcomes. To date, there have been no published GWAS for standardized attainment scores in English and maths during adolescence, and no GWAS at all for science. Adolescence is a crucial developmental period during which individuals’ executive function continues to mature and they are able to learn increasingly abstract and complex conceptsThis study aimed to assess whether there exist academic subject-specific molecular genetic contributions to English, maths and science—signal over and above that found for generalist genetic effects. This was approached in three ways: Firstly we performed three univariate GWA analyses of English, maths and science attainment to identify SNP-AA associations and estimate SNP-based heritability. Secondly to further explore the genetic contributions to subject-specific variance, we performed two further GWAS for each subject, one with the shared variance with the other subjects removed, and one with the shared variance with IQ removed. These GWAS were performed separately to assess whether subjects shared genetic variance over and above that shared with IQ. Thirdly, we used publicly available GWAS summary statistics from independent studies to estimate pairwise genetic correlations between academic attainment and 13 cognitive and non-cognitive traits and disorders in order to explore the magnitude and specificity of genetic correlations between individual academic subjects and related cognitive, mental health and personality traits. We predicted that (1) we would find both differences and commonalities in the outcomes of the three GWAS, (2) that there would exist some residual subject-specific SNP-based heritability after removing effects of generalist genes, and (3) that genetic correlations between the three academic subjects and the 13 related traits would vary in magnitude.–8)  with science, 38 for maths and 16 for English  at 11 and 14 years of age, designed to assess performance in the academic subjects of English, maths and science. In the current study academic attainment scores for English (N = 5983), maths (N = 6017) and science (N = 6089) were calculated by summing age- and sex-regressed SAT scores from these two time points for each academic subject see “”. Genome–8) Fig. , but non–8) Fig. –C. A fur23 (“–6) gene-based associations with science were identified: MEF2C , BRINP1 , S100A1  and S100A13 . No significant gene-based associations were found for maths or English. We further examined gene expression patterns for the four genes using the Genotype-Tissue Expression (GTEx) portal  and gene-level associations for science attainment in this independent longitudinal cohort, although the smaller sample and different phenotype complicates interpretation 2SNP) for science, maths, and English: LD-score regression (LDSC26) and Genome-Based Restricted Maximum Likelihood (GREML) analysis27. LDSC regression h2SNP estimates using GWAS summary statistics were moderate and significant for all three academic subjects , with the highest estimate obtained for science  to 0.53 (science)  Table .Table 3Sg) between academic subjects estimated by LDSC regression performed in Unix were high (rg = 0.62–0.75) but significantly less than 1, illustrating a degree of genetic specificity , maths  and science , or regressing out attainment in the other two subjects (N = 5895)   to 0.21 (IQreg-maths)  see “”. Univar95) see “. LDSC-baS100A1: z = 1.9, p = 0.03; S100A13: z = 1.3, p = 0.10; MEF2C: z = 2.3, p = 0.01; BRINP1: z = 2.2, p = 0.01; IQreg science S100A1: z = 1.3, p = 0.10; S100A13, z = 0.8, p = 0.19; MEF2C: z = 1.7, p = 0.05, BRINP1: z = 1.8, p = 0.03).Finally, in order to check the specificity of the SNP association identified with science, we performed a hypothesis-driven lookup in the AAreg and IQreg GWAS results Table  using a Using a z-test we were able to show that rs9529641 is significantly more associated with science than English  but not maths . It was significantly more associated with AAreg science than both AAreg English  and AAreg maths , and it was also significantly more associated with IQreg science than IQreg English , but not IQreg maths .http://ldsc.broadinstitute.org/ldhub/). Table g = 0.89 to 1.26). Genetic correlations with personality and psychiatric traits were lower, with some variation across subjects, although not statistically different after correction , which must be supported by a degree of genetic specificity. To understand these mechanisms better, analyses of more specific phenotypes are needed.This study reports the first GWAS of science attainment and the largest published GWAS of maths and English attainment using national standardised tests. The current dominant framework for assessing the genetic contributions to variance in academic attainment and its relationship to other outcomes uses a broad measure of attainmentNBEA is largely expressed in the brain, and de novo variants in NBEA have been reported in neurodevelopmental cohorts28. Rs9529641 was also nominally associated with maths (p = 0.0001), but not English (p = 0.011) leaving open the possibility that the difference in p-values between the subjects is due to chance and the slightly different sample sizes, however the significant differences in effect sizes suggests otherwise. Rs9529641 also reaches p ≤ 0.001 in both the EduYrs311 and Intelligence25 large GWAS meta-analyses. Furthermore, after regressing out variance explained by performance in the other two academic subjects, this association remained significant and specific to science. What predicts variance in science academic achievement is an understudied topic compared to maths and English. Research to-date suggests a pattern similar to the genetic results found here, with considerable similarities but also some subtle differences in the patterns of association with executive function skills, vocabulary and IQ29. There is some evidence that science achievement may be more dependent than mathematics or English on central executive working memory processes and more complex aspects of EF, such as planning30. When regressing out IQ, the science association with rs9529641 was not significant after correction for multiple testing, however the effect size remained the same. Although the SNP association with science failed to replicate in the independent Twins Early Development Study sample, we note the relatively small sample available and that the TEDS attainment measures were based on teacher ratings and not standardised across participants.The three GWAS of maths, science and English found one genome-wide significant SNP (rs9529641) associated with science attainment. Rs9529641 is not an expression quantitative trait loci, i.e. it does not influence gene expression, but the nearby gene MEF2C gene, which also shows strong evidence of association in the EduYrs3 and Intelligence GWAS studies. Notably, studies looking at general cognitive ability have sought MEF2C associations in hypothesis driven tests31 and more recently it has been associated with a large meta-analysis of intelligence and years in education32 and the largest depression GWAS to date33. MEF2C, located on chromosome 5, has been linked to synaptic plasticity, memory and learning34. It is primarily expressed in the brain and haploinsufficiency of MEF2C is associated with severe cognitive impairment, stereotypic movements, epilepsy and cerebral malformation35. Evidence from animal models also suggests that it is involved in the development of memory and the consolidation of information34. Over-expression of MEF2C has also been implicated in poor developmental and cognitive outcomes37 and it has been associated with Alzheimer’s disease38. Given its apparently more general role in cognition, and the lower but not trivial associations with maths (p = 5.12 × 10–6) and English (p = 9.76 × 10–5), we are not suggesting MEF2C is a science specific gene. Rather, we suggest there may be evidence for a ‘dosage effect’, where the brain mechanisms that are built through the MEFC2 gene may explain more variance in science than in English and maths. A similar effect may be at play with the rs9529641, where the mechanism linked to this SNP leads to greater individual differences in science than in English and maths.Gene-based association analyses identified four genes associated with attainment in science, but none for maths or English. The strongest signal came from the BRINP1, which is also primarily expressed in the brain, and is involved in protein binding. BRINP1 has been involved in a wide range of processes related to cognition and behaviour40. The final two associated genes were S100A1 and S100A13, both of which are members of the S100 protein family that encode calcium binding proteins and are involved in the regulation of a wide range of intra- and extracellular processes. These include cell cycle progression, differentiation and possibly stimulation of Ca2+ release42. After correction for multiple testing, none of the four genes were significantly associated with science after regressing out variance explained by maths and English or IQ.The second most strongly associated gene was 2SNP = 47%) and 54% for science (h2SNP = 54%)15 than is often the case with DNA-based estimates (e.g. maths ability h2SNP = 0.1611). This is unusual because twin estimates capture all additive genetic effects that contribute to a phenotype, whereas GWAS estimates include only additive effects of common SNPs. These high estimates might be driven by the homogenous nature of the sample, both environmentally and ancestrally, as well as the use of a standardised assessment of academic ability. Moreover, they suggest that the majority of the genetic variance contributing to individual differences in academic attainment in adolescence comes from the additive effects of common, rather than rare, genetic variation.SNP-based heritability estimates were moderate for all three subjects, and substantially closer to the twin-based heritability estimates of 65% for maths (hg = 0.62–0.75). The degree of specificity estimated by looking at genetic correlations using LDscore indicate a moderate to small but potentially informative degree of specificity. In order to confirm this, we performed further GWA analyses of each subject with the variance of the other two subjects removed and controlling for IQ. Maths and science maintained heritability significantly higher than 0 in both instances. Interestingly the IQ regressed measures retained more heritability than the AA regressed measures suggesting that the subject attainment measures shared more heritable variance with each other than with IQ.We found a significant overlap of common genetic variants influencing variability in the three academic subjects, indicated by the large, but significantly smaller than 1, genetic correlations  and between mathematics and ‘g’ (rgTWIN = 0.67), but noted that approximately a third of the genetic variance in mathematics was independent of both of these factors, suggesting some degree of genetic specificity7. A subsequent study controlling for performance in maths, English and ‘g’ investigated the extent to which there was genetic specificity in science attainment in childhood48. The authors report a h2twin of 49% for science and genetic effects beyond the other factors, which were therefore specific to science.Broadly, the results suggest that although there are underlying cognitive features which contribute to variance across all three academic subjects, there are other (both genetic and non-genetic) factors which contribute to subject-specific variance. These results reflect the conclusions of multivariate twin studies that examine genetic covariance between cognitive ability and subject attainment in a large UK twin cohort. For example, Kovas et al. (2005) investigated the genetic overlap between mathematics performance, reading and general intelligence in childhood. They reported considerable genetic correlations between mathematics and reading  risks inducing collider bias and distorting towards or away from true associations. However, we note that the focus of the AAreg and IQreg analyses were on exploring the specificity of science attainment associations, rather than identification of novel associations50.Whilst this study represents the largest GWAS to-date for science and English attainment, it is still underpowered to detect common variants of very small effect. Recently developed multivariate GWAS approaches such as genomic-structural equation modellingMEFC2 and BRINP1 were significantly and robustly associated with science attainment. We also found differences in SNP-based heritability estimates and genetic correlations with other cognitive traits indicating, as with the phenotypic data, a degree of overlap and specificity between academic subjects. These findings suggest that understanding the sources of individual differences in academic attainment may facilitate a better understanding of the causal paths to later educational outcomes and mental health disorders. Future studies should examine these genetic relationships within a multivariate framework to allow the separation of general versus specific effects at the level of individual DNA sequence variants.In this study, we performed a series of univariate GWAS of English, maths and science standardised national attainment scores, estimated SNP-based heritability and assessed shared genetic architecture with educational, cognitive, behavioural and psychiatric phenotypes. We found that rs9529641, http://www.bristol.ac.uk/alspac/) is an on-going population-based study investigating factors influencing development and health. The study website contains details of all the data that is available through a fully searchable data dictionary . Initial recruitment included 14,541 mothers with 13,988 children alive at age one. A second round of recruitment at around age 7 yielded a total sample size for data collected after this age of 15,247. See Supplementary Note 52. The sample for this study is comprised of children for whom data were available at both age 11 and 14 for English, maths or science attainment, along with genome-wide SNP genotyping data. Ethical approval for the study was obtained from the ALSPAC Ethics and Law Committee, and Birkbeck’s Department of Psychological Sciences Research Ethics committee. All research was performed in accordance with ALSPAC’s and Birkbeck’s Departmental relevant guidelines/regulations. Parents and/or legal guardians gave informed consent, and the authors had no access to any participant identifying information.The Avon Longitudinal Study of Parents and Children (ALSPAC)  and age 14 (end of Key Stage 3), national exams—known as the SATs—were obligatory in schools across the UK when these data were collected. Pupils sat the tests under exam conditions and scripts were externally marked, standardised, and given a curriculum level 1–9 (low to high).At ages 11 and 14 the English SATs assess reading, grammar, punctuation and spelling, in addition to comprehension and interpretation of a studied text. Maths is assessed at both ages by written SATs that cover all areas of mathematics including conceptual understanding, mathematical reasoning and problem solving. At age 11, the maths SAT also includes a ‘mental maths’ component in which the students are asked questions orally and, under timed conditions, must record their answers having performed the computations in their head. The science SAT at ages 11 and 14 assesses the development of scientific thinking and knowledge, experimental skills and strategies, analysis and evaluation, scientific vocabulary, units, symbols and nomenclature.To get the most reliable score of attainment only individuals with data at both 11 and 14 years (r = 0.67 to 0.81) were included. To remove variance associated with sex and age at testing, each academic subject score was first regressed on age and sex (at each time point) and the residuals from the linear regression were summed together to create a final score for each subject. This resulted in sample sizes of 5983 for English, 6017 for maths and 6089 for science.53 at age 15. In the Vocabulary subtest participants were asked the meaning of a list of gradually more complex words. The Matrix reasoning subtest consisted of a multiple-choice visual puzzle in which the participants were presented with a series of pictures and had to choose the missing image.To assess subject-specific genetics effects, AA regressed scores were created by removing the variance shared with the other two subjects from each of the final scores. This resulted in a sample of 5,895 individuals for each subject. Finally, in order to assess genetic effects independent of general cognitive ability, IQ regressed scores were created by removing the variance shared with IQ from each of the individual subject scores, leaving a smaller sample due to the lower availability of IQ scores than academic attainment measures  and the Laboratory Corporation of America . The raw genotype data were subjected to standard quality control procedures to identify individuals and SNPs for exclusion. Samples that passed quality control stages were phased and imputed using the Haplotype Reference Consortium panel of ~ 31,000 phased whole genomes and Impute V355. Scores were regressed on the first 10 ancestry principal components to control for population structure and then quantile normalized in SNPtest56. In total nine GWA analyses were performed using (1) individual subject scores for attainment in English, maths and science, (2) AA regressed scores for attainment in English, maths and science (3), and IQ regressed scores for in English, maths and science. Each univariate GWA analysis was performed in SNPTest v.2 using an additive linear model and imputation probability calls57. Independent SNP association signals were identified by LD clumping in PLINKv1.9, with a genome-wide significance threshold for index SNPs and 0.2 threshold for LD clumping58.All data preparation was performed using R 3.459. Significantly associated genes were identified as those surviving Bonferroni correction for multiple testing . Competitive gene-set analyses were also carried out in MAGMA using 10,673 gene sets  obtained from MsigDB v5.2. Functional interrogation of gene-based associations was conducted using the GTEx portal .Gene-based association analyses, which test for association between aggregated SNP effects across each gene, were performed using MAGMA within the FUMA programme, using the summary statistics from each GWAS2SNP), was estimated using two methods that have differing modelling assumptions of the underlying genetic architecture60, with the view to gain consensus estimates of SNP heritability for academic attainment. GREML was implemented in the GCTA software package in Unix to provide h2SNP estimates using individual level genetic data27. LD-score regression (LDSC26) in Unix was used to estimate h2SNP using the GWAS summary statistics. Genetic correlations were estimated between cognitive, educational, psychiatric and personality traits available in—and using—LD hub (http://ldsc.broadinstitute.org). See Supplementary Note 2 intercept was constrained to 1. We note that this will result in lower standard errors26 and also report unconstrained estimates. The AA-regressed and IQ-regressed attainment scores were excluded from this LDSC analysis due to the low SNP heritability estimates (and large standard errors) obtained leading to low heritability z-score (z < 4). Finally, z-tests were used to assess whether heritability results were significantly larger than 0, whether correlations were significantly smaller than 1 and whether correlations were significantly different from each other (p < 0.05).The proportion of variance in science, maths or English accounted for by all the SNPs on the array passing QC, i.e. SNP heritability (hwww.teds.ac.uk)24. TEDS participants completed various web and telephone-based tests and questionnaires at regular intervals over childhood and adolescence designed to assess various aspects of cognition, language and behaviour, which are described in detail elsewhere61. The available sample consisted of 2352 individuals (one member of each twin pair) for whom academic attainment data at age 14 and genome-wide SNP genotyping data were available , regressed on the first 10 ancestry principal components and were quantile normalized in SNPtest57. Platform-specific results were then meta-analysed using METAL62. Gene-level replication was performed using MAGMA59.Replication of independent significantly associated SNPs and genes was performed using data from the Twins Early Development Study. TEDS is a longitudinal study investigating the cognitive and behavioural development of twins born in England and Wales between January 1994 and December 1996 (Supplementary Information 1.Supplementary Information 2.


A comprehensive study was conducted to study the effects of partition of variance on accuracy of genetic parameters and genetic trends of economic traits in Vanaraja male line/project directorate-1 (PD-1) chicken.Variance component analysis utilizing restricted maximum likelihood animal model was carried out with five generations data to delineate the population status, direct additive, maternal genetic, permanent environmental effects, besides genetic trends and performance of economic traits in PD-1 chickens. Genetic trend was estimated by regression of the estimated average breeding values (BV) on generations.The body weight (BW) and shank length (SL) varied significantly (p≤0.01) among the generations, hatches and sexes. The least squares mean of SL at six weeks, the primary trait was 77.44±0.05 mm. All the production traits, viz., BWs, age at sexual maturity, egg production (EP) and egg weight were significantly influenced by generation. Model four with additive, maternal permanent environmental and residual effects was the best model for juvenile growth traits, except for zero-day BW. The heritability estimates for BW and SL at six weeks (SL6) were 0.20±0.03 and 0.17±0.03, respectively. The BV of SL6 in the population increased linearly from 0.03 to 3.62 mm due to selection. Genetic trend was significant (p≤0.05) for SL6, BW6, and production traits. The average genetic gain of EP40 for each generation was significant (p≤0.05) with an average increase of 0.38 eggs per generation. The average inbreeding coefficient was 0.02 in PD-1 line.The population was in ideal condition with negligible inbreeding and the selection was quite effective with significant genetic gains in each generation for primary trait of selection. The animal model minimized the over-estimation of genetic parameters and improved the accuracy of the BV, thus enabling the breeder to select the suitable breeding strategy for genetic improvement. Diversity in the populations exists due to the variability in genetics, environment and their interaction effects which form the basis for any genetic improvement program. Selection experiments continue to be powerful tools to generate information on quantitative traits in terms of their underlying genetic variability, the relationships between traits and their effects on performance . GeneticPrecise estimation of genetic parameters (heritability and correlation) plays a major role in determining the realized response in the economic traits. For precise estimates, the variance needs to be partitioned and attributed to maximum possible sources and to their interaction effects that lead to reduced error variance and minimized over weightage to some components. Animal model is a powerful tool for the geneticist to accommodate additional components of variance, which makes the estimates less biased by confounding environmental variation and explicit modeling of environmental (co) variance .Determining the breeding value (BV) with the objective to select the parents for next generation is very important for the success of any breeding program. The precise estimation of BV depends on the effects considered in the statistical model in most of the cases. Additive genetic variance primarily determines the heritability of the trait, although non-genetic components are also important factors in determining the variability of the traits. Maternal effects play a significant role in development and expression of the economic traits due to genetic or environmental differences between dams or by the combination of genetic or environmental differences ,5. The iAnalysis of vast data from more number of generations using robust algorithm like restricted maximum likelihood (REML) will delineate the status and structure of the population with respect to genetic variability, genetic trends, inbreeding etc. Therefore, the present study was carried out with an aim to delineate the population status and direct additive, maternal genetic and permanent environmental effects, besides genetic trends and performance with respect to growth and production traits in Vanaraja male line/project directorate -1 (PD-1) chicken.The study was carried out at the experimental poultry farm of Indian Council of Agriculture Research (ICAR)-Directorate of Poultry Research, Hyderabad, India. Hyderabad is located in Deccan plateau in southern part of India positioned between 17°23’ N and 78°28’ E at height of 500 m from sea level. The region experiences tropical environment with hot summer (33°C to 45°C) and pleasant winter (16°C to 20°C) conditions. The poultry houses were covered with paddy straw with sprinklers to reduce the shed temperature in hot summer (March to June). The experiment was approved by the Institutional Animal Ethics Committee vide approval No. IAEC/DPR/17/4.Vanaraja, a popular dual purpose rural chicken variety developed by ICAR-Directorate of Poultry Research.Vanaraja male line (PD-1) was derived from a low performing Red Cornish population which has been under selection for higher 6 week shank length (SL6) since last eight generations from 2010–11. Higher SL is one of the major selection criterion in rural poultry lines as it enable the birds to move faster in free range conditions and reduces the predation. PD-1 is the male parent line for production of ad-libitum up to six weeks of age. The chicks were vaccinated against Marek’s disease (MD), Newcastle disease (ND), infectious bursal disease (IBD) and fowl pox on zero, 5th, 14th, and 21st day, respectively. Body weight (BW) data were recorded at zero day, two, four, and six weeks of age, while SL was measured at six weeks of age. At the end of the six weeks, 450 females and 200 males were selected in each generation based on higher SL6, the primary trait of selection. The birds were kept on feed restriction schedule from seventh week onwards to maintain the target BW at laying. The birds were fed with broiler grower  ration till 16 weeks of age and broiler breeder  ration from 17 weeks to end of the production cycle (72 weeks). The adult birds were vaccinated against ND and IBD at 22 weeks of age and Infectious Bronchitis at 25 weeks of age.Chicks were hatched in 3 to 4 hatches in each generation in a pedigreed mating with 50 sires and 250 dams, each sire mated to five dams (1:5). In each generation, about 3,000 healthy chicks were produced; wing banded and reared on deep litter in an open sided poultry house. Standard brooding, feeding and management practices were followed. The chicks were fed broiler starter ration with 2,900 kcal metabolisable energy (ME) and 22.0% crude protein (CP) The data on growth and production performance of PD-1 line chickens collected over five generations (S7 to S11) from 2013–14 to 2018–19 were utilized in the present study, which were numbered serially from 1 to 5. In each generation, juvenile BW at zero day (BW0), two (BW2), four (BW4), and six (BW6) weeks; SL6; adult BWs at 20 (BW20) and 40 (BW40) weeks of age were measured. The BWs were measured to 0.1 g accuracy using digital balance while SL was measured to the nearest of 0.01 mm accuracy using digital Vernier calipers. Age at sexual maturity (ASM), part period egg production (EP) up to 40 weeks of age (EP40) and egg weight (EW) at 40 weeks (EW40) were recorded. The weight of eggs was recorded using a digital balance to an accuracy of 0.01 g. The detailed characteristics of data are presented in −8. To ensure that a global maximum is reached, analyses were restarted and continued till convergence. Univariate animal models were fitted to estimate (co)variance components for all the traits. Different models which account for the direct and maternal effects were constructed as follows:Variance and covariance components were estimated by REML fitting an animal model . Data wey is the vector of records; β, a, m, pe, and ɛ are vectors of fixed, direct additive genetic, maternal additive genetic and permanent environmental effects of the dam, and residual effects, respectively; with association matrices X, Za, Zm, and Zpe; A is the numerator relationship matrix between animals; and σam is the covariance between additive direct and maternal genetic effects. Assumptions for variance (V) and covariance (Cov) matrices involving random effects wereWhere 2a, σ2m, σ2c, and σ2e, are additive direct, additive maternal, maternal permanent environmental and residual variances, respectively. The total heritability (h2t), was calculated using the formula h2t = (h2+ 0.5 m2+1.5mramh) [Where, I is an identity matrix and σ .5mramh) . The bes.5mramh) .A = 0 is specified [C = 0. Significance of residual and phenotypic correlations was tested by hypothesis test to decide whether the value of the correlation coefficient is significantly different from zero [For the bivariate analysis, the best models from the single trait analyses were combined with appropriate covariance between random effects in the model. The best model identified as per likelihood ratio test for specific trait was only used for the bivariate analysis with starting values derived from single trait analysis. Estimates of genetic parameters like genetic, phenotypic and environmental correlations between different economic traits were obtained by average information restricted maximum likelihood (AIREML) fitting an animal model WOMBAT . To formpecified . Signifirom zero .Genetic trend was estimated by regression of the estimated BV averages on generation for trait under selection (SL6) and other economically important BW and production traits under study . The BVsThe least squares means (LSMs) over the generations for juvenile BWs up to six weeks of age and SL6 are presented in Production traits i.e., BW20, BW40, ASM, EP40, and EW40 of five generations were analyzed and the overall LSMs were presented in The estimates of (co) variance components and genetic parameters estimated using best model for BW0, BW2, BW4, BW6, and SL6 are presented in 2 of 0.09. For other production traits; BW20, BW40, EP40, and EW40, the model one was the best with additive direct and residual effects  negative association with EP40 for direct additive, residual and phenotypic correlation which was in desirable direction. The magnitude of association was very low between ASM and EW40. The association between ASM and BWs was negative with less magnitude for all the components . The corThe genetic trend of the primary trait and correlated traits are presented in Among the production traits, ASM reduced linearly with an annual reduction of 0.56 days in each generation. The BV of EP at 40 weeks of age increased linearly. The average genetic gain for each generation was significant (p≤0.05) over the five generations with an average increase of 0.38 eggs per generation. The EW 40 also showed the linear trend with an average genetic gain of 0.12 g per generation. The average inbreeding coefficient of the population was 0.02 and that of inbred birds was 0.04 in the population.The importance of partitioning and attributing the variance to various non genetic factors like maternal permanent environment, residual and phenotypic effects in addition to the direct additive effects for a quantitative trait was discussed in this article. The traits which had significant effect of generation, hatch and sex were further utilized in the model for the estimation of the variance components and genetic parameters.The LSMs for BWs significantly varied in different generations, hatches and sex in the population . Many auThe LSMs for ASM significantly and gradually reduced over the generations in desired direction, which may be due to the correlated response to the selection for SL6. The SL is positively correlated to BW and higher BW at ASM ultimately leads to reduction in ASM though direct selection was not practiced for the trait . CurrentModel four with additive, maternal permanent environ mental, residual and phenotypic effects was the best model for juvenile BW and SL, except for BW0. For BW0, the Model five was the best model, which has maternal genetic effects in addition to effects of model 4. Maternal effects are proportional to the contribution of maternal additive, dominant gene effects and the differences in allele frequencies between favorable and unfavorable alleles . MaternaModel 1 with direct additive effects was the best model for all the production traits , except for ASM, which showed the maternal effect  of lesser magnitude. As the age advanced, the maternal effects gradually reduced and only the direct additive genetic effects prevailed. This may be the reason that all the production traits have only direct additive genetic effects in the present study. The direct additive effects model without or negligible maternal effects were suitable for EP, which was true in the present study also ,27. Howe2 estimated using REML animal model was more precise as it reduced the overestimation of the genetic parameters by partitioning the variance and covariance in to maximum possible components. Similar findings of less magnitude for h2 were reported by many authors using REML [2 [2 from 0.17 (model four) to 0.28 (model one) for SL 6, the primary trait of selection. Similar results were observed for other traits also.The heritability estimates of BWs and SL length estimated using REML were lesser as compared to the traditional Henderson variance component (full sib) analysis and the model one (direct additive) of WOMBAT animal model. The hing REML ,5,6,26.  REML [2 ,29. The  REML [2 . In the Positive genetic correlation indicates that selection for one trait can improve the performance in other traits and the negative correlation reduces the performance ,9. The cThe genetic trend showed that the selection was operating with an average genetic gain of 0.89 mm in SL, which was the primary trait of selection. The average BV of the population increased significantly in a linear direction indicating the effectiveness of selection . SimilarThe BV of ASM gradually reduced over the generations which were in desired direction. The EP 40 BV showed a linear positive trend with an average genetic gain of 0.38 eggs per generation. Similar trend was observed in EW also. The response observed in all the production traits is due to the correlated response as the traits were not included in the selection program.The rate of inbreeding in the population was very low, which may be because of adoption of proper and effective breeding plan where care was taken that close relatives of two generations were not allowed to mate. The status of the population at the end of the 5th generation is ideal with 0.032 inbreeding coefficient. The inbreeding was negligible till this generation, however, may increase in further generations due to the selection.The study concluded that the population is in ideal condition without any deleterious effects of inbreeding and the selection is quite effective with significant genetic gains in each generation for primary trait of selection and other associated traits. The fact that precise estimation of genetic parameters, heritability and correlation with REML model further improve accuracy of the BV estimates, thus enabling the breeder’s decision making related to the selection and breeding strategy more accurate and ultimately aiding in genetic improvement of the populations.


The prediction accuracy of GS models (GBLUP) for AAs was high (PAAC: 0.63–0.67) and comparable or slightly higher than pedigree‐based (ABLUP) or BayesCπ models. We show that AA traits can be improved and that GS speeds up the selection of improved trees for insect resistance and for growth and wood quality traits. Various selection strategies were tested to optimize multitrait gains.With climate change, the pressure on tree breeding to provide varieties with improved resilience to biotic and abiotic stress is increasing. As such, pest resistance is of high priority but has been neglected in most tree breeding programs, given the complexity of phenotyping for these traits and delays to assess mature trees. In addition, the existing genetic variation of resistance and its relationship with productivity should be better understood for their consideration in multitrait breeding. In this study, we evaluated the prospects for genetic improvement of the levels of acetophenone aglycones (AAs) in white spruce needles, which have been shown to be tightly linked to resistance to spruce budworm. Furthermore, we estimated the accuracy of genomic selection (GS) for these traits, allowing selection at a very early stage to accelerate breeding. A total of 1,516 progeny trees established on five sites and belonging to 136 full‐sib families from a mature breeding population in New Brunswick were measured for height growth and genotyped for 4,148 high‐quality SNPs belonging to as many genes along the white spruce genome. In addition, 598 trees were assessed for levels of AAs piceol and pungenol in needles, and 578 for wood stiffness. GS models were developed with the phenotyped trees and then applied to predict the trait values of unphenotyped trees. AAs were under moderate‐to‐high genetic control ( It occurs on a variety of soils and under a wide range of climatic conditions Farrar, . It is aChoristoneura fumiferana (Clem), SBW) is a native insect prevalent in North Eastern America and a defoliator that periodically attacks spruce forests in eastern Canada  Mill.) and on spruces such as white spruce (Picea glauca (Moench) Voss) and to a lesser extent on black spruce (Picea mariana (Mill.) BSP). Molecular mechanisms of resistance of white spruce to SBW and its genetic control have recently been reported , piceol and pungenol  estimate the genetic control of AA concentrations related to SBW resistance in white spruce and better understand their genetic relationships with growth and wood quality traits; (b) evaluate the performance of genomic selection models for each of these traits; and (c) estimate the expected genetic gains for AAs alone and in conjunction with the other traits in various multitrait selection schemes.22.1Data were collected in white spruce selection plantations established in New Brunswick, Canada, and managed by the New Brunswick Tree Improvement Council (NBTIC). These plantations regrouped full‐sib families that were produced by controlled pollinations between 212 elite parents . Families were evaluated in 22 tests established on five sites in as many different localities (Table S1). For the present study, we sampled 1,310 progeny trees from 136 full‐sib families  measured at standing trees , were 86%, 95%, and 93% for picein, piceol, and pungenol, respectively.Quantitative liquid chromatography–mass spectrometry (LC‐MS) analysis of acetophenones piceol, pungenol, and picein was conducted from needle samples for the subset of 598 progeny trees. In addition to determining the concentrations of the two acetophenone aglycones piceol and pungenol found in needles and known to be the active compounds related to spruce budworm resistance, concentrations of the constitutive glycosylated acetophenone picein were also determined as a positive control to monitor for the efficiency of acetophenone extraction from spruce needles. This glycoside appears to be inactive against the spruce budworm in white spruce  formic acid; solvent B was acetonitrile with 0.2% (v/v) formic acid. The following gradient was used: start at 5% solvent B and hold for 0.2 min; increase to 10% solvent B and hold from 0.2 to 0.5 min; increase to 15% solvent B and hold from 0.5 to 4.0 min; increase to 90% solvent B and hold from 4.0 to 7.0 min; hold at 90% solvent B from 7.0 to 8.0 min; decrease to 5% solvent B and hold from 8.0 to 8.1 min; and hold at 5% solvent B from 8.1 to 12 min. Injections of 5 µl per sample were performed with a column flow rate of 0.65 ml/min and a column temperature of 70°C. The mass spectrometer was run under electrospray ionization in negative mode, with the nebulizer pressure at 60 psi, dry gas flow rate of 12 L/min, and dry temperature of 350°C. The mass scan range was 50–400. Acetophenone peaks were extracted using the following mass ions: 343 , 135 , and 151 . Authentic standards of picein, piceol, and pungenol were used to prepare standard curves for quantitation and verify peak identities in needle extracts .2.2Previous to this study, a large registry of gene SNP markers  was first computed based on the registered pedigree information using the function “ainverse” of the R package ASReml‐R v.4.1  was computed with the “A.mat” function of the R package rrBLUP  or the genomic‐based (GBLUP) individual‐tree mixed models in ASReml‐R v.4.1:y is the phenotype; β represents vectors of fixed effects including the overall mean, the site, the test within site, and the age of the trees fitted as a covariate; a is the random additive genetic effect, with a∼N0,σa2A; and e is the residual term, with e ~ N, where R is a block diagonal matrix specifying a heterogeneous error variance structure for the five sites. For the ABLUP method, the matrix A is the pedigree‐based relationship matrix, which was replaced by the realized genomic relationship matrix G for the GBLUP method . The matrices X and Z1 are incidence matrices of their corresponding effects. The interaction of site with additive genetic effects, or genotype‐by‐environment interactions, could not be accurately estimated because the majority of families were present in only one or two sites.where The dominance effect was evaluated using the following additive–dominance model:y, β, a, and e are as defined in Equation d is the random dominance genetic effect estimated using the family source of variation (σf2) for the ABLUP model, with d∼N0,σf2I, or using the realized dominance relationship matrix (GDom) calculated following Vitezica, Varona, and Legarra , we performed a likelihood‐ratio test between the full model , broad‐sense heritability (H^ind2), and the portion of individual phenotypic variation due to dominance (d^ind2) were estimated as:Individual narrow‐sense heritability . For each trait, estimated breeding values (EBVs from ABLUP model) or genomic estimated breeding values (GEBVs from GBLUP model) for the 1,516 trees were obtained from model [a). Estimated genetic values (EGVs from ABLUP model) or genomic estimated genetic values (GEGVs from GBLUP model) of individual trees were obtained from model [a) to the BLUPs of the dominance effect (d).where 2.5To estimate phenotypic and genetic correlations between traits, bivariate models were run for all pairs of traits in ASReml‐R. The following additive‐only model was fitted:y1 and y2 are the stacked vectors of phenotypic observations for trait 1 and trait 2 respectively; β is the vector of fixed effects, including an overall mean for each trait, the site within trait, the test within site and within trait, and the age of the trees within trait; a(t) is the random additive effect within trait, with a(t)∼N; and e is the residual error, with e∼N. The matrix A (ABLUP) was replaced by the realized genomic relationship matrix (G) for the GBLUP method. The total genetic correlations (additive and dominance effects) were estimated using the following model:where y1, y2, β, a(t), and e are as defined in Equation d(t)is the random dominance genetic effect within trait estimated using the family source of variation for the ABLUP model, with d(t)∼N, or using the realized dominance relationship matrix (GDom) for the GBLUP model, with d(t)∼N. The matrices AV, DV, and RV in Equations ar, dr, and er, respectively) and unique variances for each trait . To facilitate convergence, we provided starting values for the variance components in AV, DV, and RV matrices that were taken from the results of the single‐trait models , but this parameter was allowed to vary in the model. The additive genetic correlation between traits was directly given by the estimated parameter r^a from model [where σ^a12 and σ^d12 are the estimated additive and dominance variance (family variance in the case of ABLUP) of trait 1 (same for trait 2), respectively. The phenotypic correlations were calculated as:where σ^a12, σ^a22, σ^d12, and σ^d22 are defined as above, and σ^e12 and σ^e22 are the residual variance of trait 1 and 2, respectively. The significance of the genetic correlations was tested by performing a likelihood‐ratio test between the full model in Equation ar = 0 and dr = 0 . The significance of the phenotypic correlations was tested by performing a likelihood‐ratio test between the full model in Equation ar = 0, dr = 0, and er = 0).where 2.6The prediction accuracy of conventional pedigree‐based (ABLUP) and genomic selection (GBLUP) models was estimated using the following procedure. For growth traits, the full set of 1,310 phenotyped individual trees was randomly split into 10 folds, each containing ~1/10th of the trees from each family. For each round of CV, nine folds  were used in model training, which was used to predict the breeding or genetic values, depending on the model used, for the remaining fold . This 10‐fold cross‐validation was repeated 10 times, for a total of 100 models for each trait. For acetophenone aglycones and acoustic velocity, respectively 598 and 578 progeny trees were successfully phenotyped, and thus, each fold used for model training contained respectively 540 and 520 trees, with the remaining phenotyped trees for these traits set aside for model validation.PA) of the models was evaluated as the Pearson correlation coefficient between the predicted breeding or genetic values of the validation trees and the adjusted phenotypes (y*). Adjusted phenotypes were obtained by taking the residuals (y* = e) of a model that included an overall mean, the site, the test within site, and the age fixed effects as described in Equation PACC) was estimated in three different ways: (a) first prediction accuracy was estimated from PA as PACC=PA/h^ind2 for the model in Equation PACC=PA/H^ind2 for the model in Equation PACC of both ABLUP and GBLUP models, we used the h^ind2 estimated from the additive effects GBLUP model . The incidence matrix Z2 ij for the dominance effects d denotes genotypes for individual i at marker j coded as 0 for homozygous and 1 for heterozygous genotypes  of marker effects are shrunk toward zero. This is modeled by assigning a prior for marker effects (a and d) that is a mixture of a point of mass at zero and a Gaussian slab  implemented in the R package coda  and PACC=PA/H^ind2 (additive–dominance model), we used the GBLUP heritability estimates so that PACC for ABLUP, GBLUP, and BayesCπ can be compared on equal grounds.The GBLUP method, which considers that a quantitative trait is under the control of a large (infinite) number of loci with small genetic effects, may not be ideally suited if acetophenone aglycone traits such as piceol and pungenol are controlled by a few genes with large effects. To consider this possibility, we also tested the BayesCπ genomic selection model, which should perform better in cases of oligogenic inheritance. In the BayesCπ method, marker effects are estimated and used to predict breeding values based on tree genotypes. We fitted the same models as in Equation [33.1h^ind2) were significantly different from zero for all traits under both ABLUP and GBLUP models  (Table S2). The additive genetic correlations between the acetophenone aglycones and growth traits were also low, negative, and generally not significant, except for a significant correlation between height and piceol under the GBLUP model (r^a = −0.38 ± 0.15) (Table r^a = 0.60 ± 0.09), whereas picein and pungenol concentrations were negatively correlated (r^a = −0.65 ± 0.07)  Equation  were useH^ind2) were higher for acoustic velocity, picein, piceol, and pungenol than for the other traits, with values varying between 0.57 and 0.85 with ABLUP, and between 0.45 and 0.64 with GBLUP. The total genetic correlations  varied from about 0.40 to 0.48 for aglycones and acoustic velocity, and from about 0.11 to 0.26 for growth traits. Higher PA values for aglycones and acoustic velocity were anticipated given the higher heritability estimates for these traits. PA was of the same order of magnitude between the ABLUP and the GBLUP models, but it was slightly larger for three of the six traits  under the GBLUP models. The first prediction accuracy (PACC) estimates were obtained from standardizing PA by the square root of the GBLUP narrow‐sense heritability estimates. Even after this standardization, PACC estimates were much higher for acetophenone aglycones and acoustic velocity (0.61–0.70) than for growth traits (0.31–0.52). The differences in PACC between ABLUP and GBLUP models were only due to differences in PA since we used the same heritability estimates for both types of models. Similar to PA values, the PACC estimates increased by 0.02–0.07 for three traits  under the GBLUP models, as compared to ABLUP. PACC was slightly larger under ABLUP only for piceol (+0.02). The other PACC estimates were based on the assumptions that the true breeding values (TBVs) were obtained either from ABLUP or from GBLUP models with 100% phenotypes, and were higher than those obtained with the first method (PA/h^ind2). The highest values were observed for both types of models when considering that the TBVs were obtained with the same models. Hence, depending on the trait, they varied from 0.70 to 0.82 for the ABLUP model with the TBVs obtained from ABLUP and from 0.81 to 0.86 for the GBLUP model with the TBVs obtained from GBLUP. Thus, we found slightly higher PACC for all traits with the GBLUP models using this approach to estimate PACC. We also tested the BayesCπ additive‐only models and found similar PA and PACC values than with GBLUP for growth traits, but slightly lower PA and PACC values for acoustic velocity, piceol, and pungenol  estimates obtained with the AD effects models were slightly lower than those obtained with the additive‐only effects models, even for the traits that showed significant dominance effects  under the BayesCπ model as compared to the GBLUP model. However, when the TGVs were assumed to be obtained from the GBLUP model, we surprisingly found a higher accuracy of the BayesCπ model as compared to GBLUP. These discrepancies and the lower accuracy found for GBLUP (predicted GBLUP versus TGVs GBLUP) might potentially be caused by inaccurate estimates of the dominance effects under GBLUP or that this method of estimating accuracy using TGVs is not accurate. It is likely that using the first method (PA/H^ind2) instead of TBVs and TGVs provided more robust estimates of predictive accuracy since the TBVs and TGVs are unknown. Finally, with the BayesCπ AD model, the estimated proportion of marker having an additive effect for pungenol and piceol  or dominance effect  was in the same range as for growth traits , indicating a similar gene control implicating a large number of genes for all traits.Regarding the BayesCπ additive and dominance effects models, the trends found Table  were sim3.5w = 0.5) to both aglycones would be 32% and 41% for piceol and pungenol concentration, respectively, and the selected trees would represent 26 full‐sib families. However, following such a selection index scheme, no progress would be made for height or wood stiffness (loss of 0.03% in height and loss of 0.5% in wood acoustic velocity).We estimated the genetic gains that could be expected from the selection of the top 5% trees for acetophenone aglycones based on either their GEBVs for the establishment of seed orchards, or GEGVs in the context of multiclonal/multivarietal forestry  affected close to 85 million hectares, killing about half of the host trees and leading to a commercial volume loss of 3–68 m4.1h^i2 = 0.50 ± 0.07 for piceol concentration in needles, and h^i2 = 0.55 ± 0.07 for pungenol concentration. For picein concentration, a constitutive glycosylated acetophenone used herein as a control, Méndez‐Espinoza et al. (h^i2 = 0.60 ± 0.06). In the present study, we found higher narrow‐sense heritability estimates for piceol, pungenol, and picein using ABLUP, but comparable and more realistic estimates using GBLUP. These results confirm that the genetic control of piceol and pungenol is moderate to strong in white spruce and that higher levels of accumulation of these compounds in needles could be achieved through breeding and selection.The narrow‐sense heritability estimates obtained using the additive‐only effects models for acetophenone aglycones in the current study are in line with those reported by Méndez‐Espinoza et al.  for 9‐yea et al.  reportedh^i2 = 0.25), whereas estimates obtained for 15‐year‐old full‐sib progeny trees were slightly higher (h^i2 = 0.33)  using a clonal trial made of 951 individuals belonging to 61 full‐sib families. These authors showed that, compared with using pedigree information, use of the realized genomic relationships in GBLUP models resulted in a substantially more precise separation of additive and nonadditive components of genetic variance. The experimental design available in the present study was not designed to obtain accurate estimates of dominance variance since each family was present in only one test (one family plot) per site in our sampled dataset, and some tests contained a small number of families. Thus, it is likely that the dominance effects of specific crosses were in part confounded with the test effects and the within‐test microenvironment differences between family plot effects.It appears that the ABLUP and GBLUP models did not succeed to separate well the additive and the dominance genetic effects, which was especially apparent for the ABLUP AD models. Hence, under the ABLUP AD models, the portion of phenotypic variation due to additive genetic effects  dropped to near zero and all of the genetic variance was assigned to dominance for growth traits, indicating that additive and dominance effects were confounded. Using ABLUP, dominance was only significant for height and the standard errors of dominance estimates were large for all traits. In contrast, with GBLUP significant dominance was found for the three growth traits and acoustic velocity, with much smaller standard errors, which is in line with results reported by Muñoz et al.  for treeH^i2 = 0.66 ± 0.07; pungenol, H^i2 = 0.60 ± 0.08; picein, H^i2 = 0.77 ± 0.05). However, for older ramets in New Brunswick, their estimates were much lower , but nevertheless showing a moderate genotypic control for these traits. Unfortunately, these authors did not estimate dominance effects. Thus, further studies will be required to verify whether the low dominance effects observed in the present study are only typical of the breeding population analyzed herein. However, we consider that the results of the present study and those of previous studies support the idea that the genetic control of the acetophenone aglycones in white spruce is moderate to high and that substantial genetic gains can be expected from the selection of superior genotypes and their vegetative propagation through somatic embryogenesis or cuttings or a combination of both , by Méndez‐Espinoza et al.  observed from previous studies, at the phenotypic level by Lamara et al.  and at b4.1.2Because the true breeding values of the tested material are unknown, one preferred method to estimate predictive accuracy is to calculate the Pearson correlation coefficient between the predicted breeding values and the adjusted phenotypes, and then standardize by the square root of heritability  obtained from the models with 100% of phenotypes were also estimated Table  because The genetic control of plant defense sometimes conforms to an oligogenic model, especially in the case of resistance to pathogens Walters, . To testPinus taeda L.). Indeed, de Almeida Filho et al. (d2 > 0.2). Bouvet, Makouanzi, Cros, and Vigneron  in a structured breeding population of loblolly pine , were detected for growth traits and acoustic velocity under the GBLUP model. However, dominance effects were not important in white spruce for aglycones related to resistance to spruce budworm, similar to what was found for resistance to fusiform rust in loblolly pine  again did not support a hypothesis of oligogenic control of these traits .Overall, we conclude that the additive GBLUP model was sufficient to obtain highly accurate predictions of the concentrations of piceol and pungenol in needles using only a small subset  of the breeding population. These very encouraging results should allow for significant cost savings by reducing phenotyping costs for such metabolites implicated in pest resistance, which are cumbersome and expensive to assess.4.2From this dataset, important genetic gains of more than 35 and 45% for piceol and pungenol concentrations in needles, respectively, were expected when low‐intensity selection (top 5%) was based on the respective traits. Besides genetic control, those high percentages are related to the skewed trait distribution of needle concentrations of piceol and pungenol in the population and the fact that less than a fifth of individuals carried meaningful concentrations of those molecules Figure . The effIn multitrait selection scenarios, loss of needle concentrations in one or both of piceol and pungenol should be avoided in order to keep trees with adequate levels of acetophenone aglycones leading to meaningful resistance in the breeding population. In this study, we were able to identify correlation breakers, that is, progeny trees that combined good growth and high levels of acetophenone aglycones leading to genetic gain for both categories of traits. Overall, a balanced gain in concentrations of both acetophenone aglycones piceol and pungenol, as well as moderate gain in growth, should be the ideal compromise scenario to look for when breeding for improved SBW resistance in white spruce. Additional field testing would be advisable to help determine the appropriate weights that should be given to each trait and to evaluate the effective gains obtained from selecting more resistant white spruce trees to SBW attacks in terms of reduced defoliation and higher growth in plantation site conditions.5We have argued that with climate change and its potential effects on pest distributions and host–pest relationships, pest resistance should be of high priority in tree breeding programs and that the existing genetic variation for resistance traits and relationships with productivity traits should be better understood for their consideration in multitrait breeding. In this study, we evaluated the prospects for genetic improvement of the levels of acetophenone aglycones in white spruce needles, which have been shown to be tightly linked to resistance to spruce budworm. We showed that aglycones were under moderate‐to‐strong genetic control with null or marginally negative genetic correlations with other traits. The prediction accuracy of GS models for these metabolites was also high and comparable with that of pedigree‐based models. These are very encouraging result for their genetic improvement with regard to enhancing white spruce resistance to spruce budworm at a very early stage and without the need to test and phenotype all candidates. GS can thus be deployed early to conduct such selection or to infer breeding and genetic values of unphenotyped material, thus saving time and costs. Finally, we showed that various selection strategies involving GS can be used to simultaneously improve productivity and adaptation traits such as pest resistance, which are essential to face climate change pressures and help maintain health and productivity of forest plantations.None declared.Appendix S1Click here for additional data file.Appendix S2Click here for additional data file.Appendix S3Click here for additional data file.Supplementary MaterialClick here for additional data file.


Horses produce only one foal from an eleven-month gestation period, making the maintenance of high reproductive rates essential. Genetic bottlenecks and inbreeding can increase the frequency of deleterious variants, resulting in reduced reproductive levels in a population. In this study we examined the influence of inbreeding levels on foaling rate, gestation length and secondary sex ratio in Australian Thoroughbred mares. We also investigated the genetic change in these traits throughout the history of the breed. Phenotypic data were obtained from 27,262 breeding records of Thoroughbred mares provided by three Australian stud farms. Inbreeding was estimated using the pedigree of each individual dating back to the foundation of the breed in the eighteenth century.While both gestation length and foaling rate were heritable, no measurable effect of inbreeding on either trait was found. However, we did find that the genetic value for both traits had decreased within recent generations. A number of environmental factors also had significant effects on foaling rate and gestation length. Secondary sex ratio had only an extremely small paternal heritable effect and was not susceptible to environmental influences.In contrast to racing performance, inbreeding had no measurable effect on foaling rate or gestation length in Australian Thoroughbred horses. This could be because the level of inbreeding in the population examined is not high enough to show a discernible effect on reproductive traits. Populations that experience higher levels of inbreeding due to use of artificial reproductive technologies or extremely small population sizes may show a more pronounced reduction in natural foaling rate or gestation length. It is also possible that the intensive management techniques used in the Thoroughbred population masks any negative effects of inbreeding. The decrease in the genetic value of foaling rate is likely to be because horses with unfavourable genetic potential have not yet been selected out of the population. The change in genetic value of gestation length may be due to selective breeding favouring horses with shorter pregnancies. We also found that prioritising the mating of older mares, and avoiding out of season mating could lead to an increased breeding success. Horses have an 11 month gestation period, both conceiving and giving birth in the spring and summer , 3.Deleterious genetic variants have accumulated in the genomes of modern horses as a result of population bottlenecks during domestication and breed foundation events , 5. In tThe effects of inbreeding on reproductive traits vary between studies. Increased inbreeding levels were associated with reduced fertility in some domestic and wild horse populations , 3, 10. As well as affecting fertility, there is some evidence that increased inbreeding can skew secondary sex ratios (the sex ratio at birth) in animal populations . VariatiMaintaining high reproductive rates is particularly important for the Thoroughbred horse breed. The Thoroughbred population has been closed since the eighteenth century, resulting in reduced levels of genetic diversity in current individuals –24. AlthDespite many generations of selective breeding for athletic ability, increased inbreeding is associated with reduced racing performance in Thoroughbred horses . In thisData were available for 27,296 coverings of 12,922 mares bred to 131 stallions between 2000 and 2017. The pedigree of these individuals dating back to the founders of the population consisted of 92,852 individuals. The conceptuses, mares and stallions in the dataset had an average pedigree depth of 29 generations and a mean level of inbreeding of 0.156 ± 0.012 (mean ± SD).P < 0.001)  .The overall proportion of mares with a positive 15 day scan each season was 81.65% . Based on the estimated variances from the mixed models, the maternal heritability of foaling rate was 0.058 (± 0.015), and 0.00 (± 0.00) for paternal heritability. Estimated breeding values for all individuals in the pedigree based on the foaling rate of their modern descendants showed a decrease in recent generations from a mean of − 0.002 (± 0.092) in 1990 to − 0.133 (± 0.138) by 2017 . Environmental variables of mare age and month of birth also had no significant relationship with sex ratio .The sex of 7578 live foal births were recorded in the dataset, 3785 of which were colts (49.95%) and 3793 were fillies (50.05%). Secondary sex ratio did not have an estimated heritable component for maternal genetic estimates (0.005 (± 0.026)), but had a small paternal heritability estimate of 0.011 (± 0.005). The sex ratio was not influenced by the sire, dam or foal inbreeding level (P < 0.001) , going from a mean of 342 days at 2 years old to a mean of over 354 days by 24 years old . Gestation length had no significant association with the sire (P = 0.087), dam (P = 0.419) or foal (P = 0.062) inbreeding level.Gestation length data were available for 764 foals from 152 mares covered by 89 stallions. Gestation length was normally distributed, with a mean of 341 days (± 8.633), a minimum of 311 and a maximum of 376. Based on the estimated variances from the mixed model, the maternal heritability of gestation length was found to be 0.562 (± 0.042) and the paternal heritability was 0.004 (± 0.001). The average estimated breeding value in the pedigree remained at a mean of 0.03 (± 0.241) and showed little variation between − 4.695 and 3.959 from the foundation of the population until 1990  . UnexpecIn contrast to gestation length and covering success, we found that secondary sex ratio had a negligible maternal heritable component (0.005) with a high standard error, indicating that genetic variation in the mare has no influence on the sex of the foal. However, paternal heritability estimates revealed an extremely small but nonetheless significant effect of sire genetic variation on foal sex ratios (0.011). Other studies in mammals have also found evidence of male-driven sex ratio bias , 34. HowIn this study there was found to be little improvement in the estimated breeding value  for reproductive traits in Thoroughbred horses from the eighteenth century until present day. The horses for which these values are obtained only include the direct ancestors to the horses with reproductive trait records in our study. Some individuals in previous generations may have had greater variation in genetic value but do not appear in the pedigree of modern Thoroughbreds. We found no change in the mean genetic value for foaling rate until the most recent three generations Fig. . SelectiIn the past 30 years (approximately three generations), the average genetic value for foaling rate has decreased, and variation has increased. The decreasing mean may be because horses with a lower genetic value have not yet been selected out of the current Thoroughbred population. These horses may not appear in the pedigree of future Thoroughbreds, such that the values from their generation will show minimal variation. The decreasing average genetic value conflicts with an increased foaling rate reported in recent years . It is lSimilarly to foaling rate, the genetic value for gestation length has shown little variation since the foundation of the breed Fig. . HoweverIn contrast to foaling rate and gestation length, the genetic values for racing performance in the Thoroughbred population have increased in recent generations . This maWe also found that a number of environmental effects have significant influences on both gestation length and foaling rate. Our results showed that mares foaling down later in the season had significantly shorter gestation lengths Fig. . Our finWe also found that mares who produced male foals had significantly longer gestation lengths than those who produced female foals, possibly because of differences in maternal-foetal hormonal interactions , 32, 38.In contrast to foaling rate and gestation length, secondary sex ratio was not significantly influenced by any environmental effects included in these models. Mares in a poor nutritional condition at conception have been reported to have an increased chance of successfully carrying a female foetus, with reports of female foal ratios up to 80% , 40. In In this study we found that inbreeding had no measureable effect on reproductive traits in Australian Thoroughbred horses. Although this contrasts with previous findings in racing performance traits, we postulate that inbreeding levels are not yet high enough to have a measurable effect on the Thoroughbred reproduction traits examined in the current study. The effects of artificial reproductive technologies on natural fertility rates in other horse populations should be examined to ensure that such practices do not result in long-term reductions in natural fertility levels. Genomic scans for reproduction traits in Thoroughbred and other breeds may assist in understanding genetic variation that influences fertility. We also found that unlike racing performance, there has been little increase in the breeding value of reproductive traits in Thoroughbred horses. Breeding values of foaling rates have decreased in recent generations, possibly because these traits are primarily governed by negative rather than positive selection. Further monitoring of these traits in future generations would assist in understanding the selective forces influencing these traits.n = 7578) was also transformed into a binary trait . Additionally, more detailed reproductive trait data were available for 152 mares mated to 89 stallions over multiple seasons , including the date of the foal birth. The gestation length of each live foal birth was calculated from these data.Reproductive trait data were provided by three large Australian Thoroughbred stud farms that provide a representative sample of the population as a whole. These data included the mating records of 12,922 mares bred to 131 stallions between 2000 and 2017. The scan status of each mare covering (negative or positive at the first scan 15 days after covering) was transformed into a binary trait. The sex of each live foal recorded in the dataset  to reorder the pedigree to ensure that each individual was listed after their parents and to estimate Wright’s inbreeding coefficient for all individuals . We alsoThe genetic and environmental influences on the foaling rate, gestation length and sex ratio were estimated in ASReml-R , using aThe heritability of each outcome variable was estimated using the variance component estimates of the fitted models. Significance of model terms was evaluated through Wald statistics and the estimated value of each fixed effect tabulated. Estimated breeding values  for foaling rate and gestation length were calculated as best linear unbiased predictions for each individual in the pedigree using the models fitted in ASReml-R. This method uses the available phenotypic data and the associated pedigree structure in the models to provide genetic value estimates for all animals in the pedigree.