Lobelia inflata (Campanulaceae L.) strongly implies balancing selection. Lobelia inflata thus offers an exceptional opportunity for an empirical test of genotype-environment interaction (G × E) as a variance-maintaining mechanism under fluctuating selection: L. inflata is monocarpic and reproduces only by seed, facilitating assessment of lifetime fitness; genome-wide homozygosity precludes some mechanisms of balancing selection, and microsatellites are, in effect, genotypic lineage markers. Here, we find support for the temporal G × E hypothesis using a manipulated space-for-time approach across four environments: a field environment, an outdoor experimental plot and two differing growth-chamber environments. High genetic variance was confirmed: 83 field-collected individuals consisted of 45 distinct microsatellite lineages with, on average, 4.5 alleles per locus. Rank-order fitness, measured as lifetime fruit production in 16 replicated multilocus genotypes, changed significantly across environments. Phenotypic differences among microsatellite lineages were detected. Results thus support the G × E hypothesis in principle. However, the evaluation of the effect size of this mechanism and fitness effects of life-history traits will require a long-term study of fluctuating selection on labelled genotypes in the field.High levels of genetic variation are often observed in natural populations, suggesting the action of processes such as frequency-dependent selection, heterozygote advantage and variable selection. However, the maintenance of genetic variation in fitness-related traits remains incompletely explained. The extent of genetic variation in obligately self-fertilizing populations of  First, a high level of multilocus microsatellite  variation was observed in two natural populations of L. inflata: on average, over two of every five field-collected individuals showed unique genotypic signatures at three or more SSR loci )The sample size for analyses is dependent on the replication of microsatellite genotypes within the field environment (which was unknown at the time of collection), and on successful propagation and bolting within each of the three experimental environments. This results not only in imbalance but the variable overlap of nominal genotypes among treatments. We therefore take a hierarchical approach to analysis of fitness across environments, moving from analyses using the highest number of environments , with few replicated genotypes in common (six genotypes), to combinations of fewer environments that include sequentially more genotypes in common . Among the 83 field-collected individuals, there were 45 distinct microsatellite genotypes and, of these, 16 were represented by at least two individuals common to at least two environments—including the field environment—used in this study . Because it is the trade-off between the number of environments and the number of genotypes included that provides the rationale for performing multiple analyses, we do not include combinations of fewer environments if this does not increase the genotypic sample size. Strict application of this hierarchical approach results in four main analyses: six genotypes with replicated individuals occurred in all four environments, 11 replicated genotypes were in common among the long, short and field environments, eight were in common between short, long and garden environments and 16 were in common between the short and long chamber environments, with no other combinations of two environments resulting in an increase in common genotypes. Because we perform multiple tests, we use false discovery rate (FDR) to control for the number of inappropriately rejected null hypotheses  for eachFruit number is assumed here to be a relevant fitness measure (see §1); however, other measures are often used as fitness proxies, and we thus present analyses of the relationships among fruit count and plant height, stem diameter and extent of branching. To confirm the general assumption that variation in microsatellite genotype is associated with variation in phenotype, we analyse sources of variance in flower colour, shown to be consistently associated with genetic lineage in the previous work . In addi3.L. inflata from previous work ), the genotype-environment interaction (G[Pop] × E) as well as the Pop × E interaction. Although power is reduced (using the dataset with maximum sample size), results confirm a significant effect of the genotype-environment interaction, G[Pop] × E , genotypic effects may have been inflated by parental effects; however, we assess genetic effects across multiple environments rather than within a single environment and, crucially, we are interested in G × E effects rather than main genotype effects. Inflation of G × E effects would not only require that parental effects occur, but that variation in parental effects across environments is genotype-dependent. This is an interesting possibility that, to our knowledge, has not been explored.Inferences about underlying phenotypic causes of the observed fitness G × E remain hypothetical and are beyond the scope of the present study. However, analyses point to candidate life-history traits underlying environment-specific fitness deserving of future study. The evidence of invariant, ‘specialist’ traits for particular environment types would include those that show strong genotypic main effects and no rank order change in the trait across environments. Such traits that are optimized for performance in a single environment would thus be candidates for causing fitness variation across environments . By contF = 0.011; p = 0.92) than the interaction . However, in a model that also includes genotype, besides the main effect of environment, G × E is the only significant  predictor of fitness. Thus, the environment-dependent effects of traits on fitness may be complex in that combinations of traits studied may be favoured in particular environments; effects may also be mitigated by traits not included in this study, such as biennial behaviour and variable seed dormancy [Although direct assessment of differing fitness effects of underlying life-history traits cannot be made here, an exploratory analysis on the most plausible candidate—height at first flower—indicates its potential as an underlying but indirect influence on fitness variance. In a two-factor model predicting fitness (fruit number) that includes environment, height at flowering and their interaction, height appears to have a weaker effect  do not themselves moderate the generality of findings; they serve to isolate the potential effects of G × E. Strong effects were observed here using environmental variation that was at least in part artificially generated. We note that the potential importance of G × E is supported in principle by the present results derived from manipulated environments; however, because it is the particular qualities and frequencies of sequential environments that will determine the maintenance of genetic variation in nature, quantitative inferences about the importance of temporal fluctuations in maintaining genetic variation cannot be drawn from the present study. Thus, future study to track fitness of labelled genotypes in the field over the longer term will be required to provide insight into the relative importance of G × E in maintaining genetic variation in natural populations.The characteristics of


Our findings implicate more than 5% of all protein-coding genes and provide evidence for gene sets involved in neuron development and differentiation.Regional brain morphology has a complex genetic architecture, consisting of many common polymorphisms with small individual effects. This has proven challenging for genome-wide association studies (GWAS). Due to the distributed nature of genetic signal across brain regions, multivariate analysis of regional measures may enhance discovery of genetic variants. Current multivariate approaches to GWAS are ill-suited for complex, large-scale data of this kind. Here, we introduce the Multivariate Omnibus Statistical Test (MOSTest), with an efficient computational design enabling rapid and reliable inference, and apply it to 171 regional brain morphology measures from 26,502 UK Biobank participants. At the conventional genome-wide significance threshold of α = 5 × 10 Regional brain morphology has a complex genetic architecture. Here the authors present MOSTest, a multivariate statistical framework, apply it to UK Biobank data, and discover hundreds of loci associated with regional brain morphology. The predominant strategy for identifying genomic loci associated with complex traits is through genome-wide association studies (GWAS), a mass-univariate approach whereby the association between a single outcome measure and each of millions of genetic variants, in isolation, is tested. This is accompanied by a stringent multiple comparison correction to control the family-wise error rate, necessitating very large sample sizes to identify even relatively strong effects. To date, the largest GWAS of regional brain morphological features, based on brain scans obtained from up to 50,000 individuals, identified almost 200 genetic variants1, which together explained only a fraction of the reported narrow-sense heritability. These studies primarily investigate each region of interest individually, compounding the multiple-comparisons correction problem.Regional surface area and thickness of the cerebral cortex, and volume of subcortical structures, are highly heritable brain morphological features with complex genetic architectures, involving many common genetic variants with small effect sizes3. Thus, genetic variants probably have distributed effects across regions and morphological measures. We have shown that cortical thickness and surface area have extensive genetic overlap4, despite reports that they are phenotypically and genetically only weakly correlated to each other5, due to mixed directions of effects of the underlying genetic variants6. The discovery of these variants may be boosted through joint analysis of these traits in a multivariate framework. This avoids the family-wise error rate penalty for studying multiple outcome measures, or the use of strategies that reduce phenotypic information to a single composite score, which can cause considerable loss of statistical power7. Importantly, a multivariate approach is much more consistent with the notion of the brain being an integrated unit, with highly interconnected and biologically similar brain regions, compared to univariate approaches that ignore the information shared across these component measures.In addition to small effect sizes across many variants, the genetic architectures of sets of regional brain features are likely to strongly overlap. Gene expression studies of the human brain have shown widespread gradients across the cortex9. In this context, multivariate association at a given single-nucleotide polymorphism (SNP) means that at least one of multiple traits being considered is associated with the genotype vector of that SNP9. To test for multivariate association, MQFAM 10 and MultiPhen11 both perform a multiple regression whereby the genotype vector is used as an outcome variable, while each phenotype is turned into an explanatory variable; the p-value is then calculated from an F-test, which tests for an association between the genotype vector and the most predictive linear combination of phenotypes at each SNP. The advantage of MultiPhen is that it uses ordinal regression, whereas MQFAM is based on canonical correlation analysis, which in theory is less appropriate for prediction of a categorical variable such as 0-1-2 coded genotype vector. The statistical power of both methods is known to be similar to MANOVA8. MultiABEL is another multivariate GWAS approach, which implements Pillai’s trace MANOVA12 to calculate multivariate p-value from summary statistics; its authors further advocate the importance of rank-based inverse-normal transformation. Most recently, aMAT13 was introduced. This test, based on a chi-square test statistic, explores regularization  of the correlation matrix R as a way to further boost statistical power in multivariate methods. Distinct from these multivariate tests of association is the multi-trait analysis of GWAS (MTAG) method14, which boosts discovery in a primary trait by conditioning on one or more secondary traits and therefore does not test the multivariate null hypothesis that none of the traits are associated with a given SNP. Although all multivariate methods listed above have been shown to substantially increase gene discovery compared to univariate approaches8, they have not been widely adopted by large-scale international consortia. This may be due to that fact that the results can be less straightforward to interpret, in addition to high computational costs, lack of user friendliness, lack of method validation, and/or model assumptions not fitting with the real data.Several multivariate approaches to GWAS have been proposed to datez-values across univariate GWAS summary statistics, to integrate effects across the measures into a multivariate test statistic; and (4) employing the gamma cumulative density function to fit an analytic form for the null distribution, enabling extrapolation to and beyond the 5 × 10−8 significance threshold. The “Methods” section contains a detailed description of these steps. We further provide extensive simulations of MOSTest performance under a wide range of conditions to validate its assumptions and compare it to other multivariate approaches.Here we introduce the Multivariate Omnibus Statistical Test (MOSTest), designed to boost the statistical power of imaging genetics by capitalizing on the distributed nature of genetic influences across brain regions and pleiotropy across imaging modalities. MOSTest is efficient and capable of combining large-scale genome-wide analyses of dozens of measures for tens of thousands of individuals within hours while achieving enhanced statistical power. Key steps of the MOSTest analysis include: (1) applying a rank-based inverse-normal transformation to the input measures; (2) estimating the multivariate correlation structure from the GWAS on randomly permuted genotype data; (3) calculating the Mahalanobis norm, as the sum of squared de-correlated 1, referred to as the min-P approach; this approach takes the smallest p-value of each SNP across multiple univariate GWAS, and corrects this for the effective number of traits studied15, i.e., shared genetic architecture across traits does not contribute to statistical power. Min-P achieves its maximum power when the genetic effects across traits are independent; conversely, multivariate approaches have greater power when genetic effects are shared across traits8. We applied MOSTest to sets of regional brain morphology measures, hypothesizing that it will outperform the min-P approach due to the distributed nature of genetic effects and the presence of pleiotropy across modalities. We find that MOSTest improves locus discovery compared to min-P more than threefold, doubling the effective sample size, with significant loci having effects across regions and across feature subsets. Further, through simulations, we confirm that MOSTest maintains correct type-I error in a range of scenarios. We conclude that, due to the distributed nature of the genetic signal across brain regions, joint analysis of regional morphology measures in a multivariate statistical framework provides a way to enhance discovery of genetic variants with current sample sizes.We compare MOSTest with an established inferential methodology recently used by the Enhancing NeuroImaging Genetics through Meta-Analysis (ENIGMA) consortiumα = 5 × 10−8 across hundreds of independent loci, as shown in Fig. Through MOSTest, we identified thousands of independent SNPs reaching the genome-wide significance threshold of As can be seen in Fig. p-values by both min-P and MOSTest per discovered locus.We carried out replication analyses of the GWAS results in an additional 4884 UKB participants, whose neuroimaging data were released after we carried out our primary analyses. The loci discovered through MOSTest and min-P replicated at similar levels, with ~40% being significant in this smaller additional sample Table . Therefo16, we fitted a Gaussian mixture model of the null and non-null effects to the GWAS summary statistics, estimating for each feature set the number of SNPs involved, i.e., their combined polygenicity, and their effect size variance, or “discoverability”. Please see the “Methods” section for more details. The results are summarized in Fig. Using the MiXeR toolWe performed extensive validation of MOSTest methodology and implementation, checking its performance under a range of conditions through simulations with synthetic data, and comparing this with other multivariate approaches besides min-P, namely MultiABEL, MultiPhen, and MQFAM. We used a framework whereby effects are simulated on chromosome 21 to compute statistical power, while all other chromosomes are kept free of genetic signal to estimate type-I error under the null. Supplementary Tables p-values per M = 100 variants in the power analyses, for each one of 760 simulation runs. Therefore, it was impractical to run these tests for M = 7.3 million causal variants. See Supplementary Table Under a range of conditions, all methods showed similar statistical power, except for min-P with lower power. The methods all maintained correct type-I equally well under the null and following permutation, under these conditions, as summarized in Supplementary Figures The min-P approach outperformed the multivariate methods under one specific condition: when a small set of heritable features are analyzed together with a much larger set of non-heritable features ; all other maps are provided in the Supplementary Data. These maps revealed anterior-posterior gradients as well as hemisphere-specific effects of some of the lead SNPs, in line with previously reported genetic patterns of developmental regionalization in the brain19.Cortical maps, depicting the morphological associations of the lead SNPs identified with MOSTest on all features with regional surface area and thickness measures, made clear that these SNPs have distributed effects, often with mixed directions, across regions and feature sets. As an example, Fig. 21, indicated that 1034 out of all 18,775 protein-coding genes  were significant, with a p-value below a Bonferroni-corrected threshold of α = 0.05/18,775. Figure Gene-level analyses, using Multi-marker Analysis of GenoMic Annotation (MAGMA)2. Further, a direct comparison with the established min-P method in the same sample revealed a threefold increase in discovery. This improvement indicates the presence of extensive shared genetic architecture across brain regions and across morphological measures, attesting to the importance of estimating levels of polygenic overlap beyond those indicated by genetic correlations6, and arguing for techniques that boost discovery of genetic determinants leveraging shared signal between traits22. Indeed, overlapping genetic determinants are to be expected given the shared genetic control of neurodevelopment across brain regions23, and that similar molecular mechanisms operate across regional borders defined by gross morphological features. This is in accordance with the high levels of pleiotropy across many brain-related traits and disorders24. Therefore, our multivariate strategy is better tailored to the underlying neurobiological processes than conventional univariate approaches, as confirmed by our identification of highly significant links to gene sets of neuronal development and differentiation.Applying the MOSTest approach to structural brain imaging data, we discovered more loci associated with regional cortical and subcortical morphology than any previous GWAS of brain morphology, even those that had nearly double the sample sizeOur extensive validation of the MOSTest methodology and implementation show that the MOSTest is a valid statistical test with good statistical power to detect associations in a multivariate context, across a wide range of conditions, suitable for applications to large-scale data with many outcome measures. Key advantages of MOSTest include (1) an orders of magnitude shorter runtime as compared to MQFAM and MultiPhen, (2) a built-in genotype permutation scheme that allows detection of cases of invalid type-I error, (3) the ability to incorporate spectral regularization of the phenotype matrix, and (4) extensive validation in simulations.13, to select the best possible trade-off between univariate and current multivariate methods, to further improve power of the multivariate analysis. Further, due to practical limitations, we performed simulations of up to a hundred features, leaving validation of the MOSTest procedure when including more features as future work. Enabling the MOSTest procedure, and particularly its genotype permutation scheme, in a meta-analytical setting is a subject of future work.Our simulations showed that in some scenarios min-P outperforms the multivariate methods, specifically when genetic signal is sparse across phenotypes. As the level of sparsity will be different across SNPs, it is expected that min-P may discover a few additional SNPs that are missed by MOSTest, as also indicated in our comparison using real data. Further, these simulations made clear it is important to exclude traits with too low heritability to achieve best possible power. We are planning to develop an automated regularization strategy, in line with the aMAT methodp-value, but does not provide the effect direction, limiting the application of several post-GWAS tools. Second, currently, MOSTest requires the availability of raw genotype data. Third, while discrete phenotypes will turn into continuous scales after pre-residualization and inverse-normal transformation, we have not formally validated whether MOSTest is applicable to case/control traits. Removing these limitations is also a subject of future work.The MOSTest method has several limitations. First, as with several other multivariate methods, it only provides a 25, which we estimate will enable MOSTest to identify SNPs that explain about 40% of the additive genetic variance in regional brain morphology. MOSTest is well-suited as an exploratory tool, followed up by studies that investigate the relation between the set of discovered loci and individual features, with a much decreased multiple-comparisons burden. The MOSTest code is user friendly and publicly available, see the Supplementary Materials. In addition to brain structure, the MOSTest approach may also be of value in uncovering the genetic determinants of brain function and other complex human phenotypes consisting of correlated component measures, such as mental, cognitive, or cardiometabolic phenotypes, by taking advantage of the rich multivariate data sets now available.With the large gain of power and consequently lower required sample sizes of MOSTest, we predict that it will be possible to uncover the majority of SNPs influencing brain morphology in the upcoming years. The UKB initiative, for instance, is set to release neuroimaging data of a 100,000 individuals by 202226. For this study, we selected individuals that had undergone the neuroimaging protocol and had White European ancestry, as determined by a combination of self-identification as “White British” and similar genetic ancestry based on genetic principal components. For the primary analysis, making use of T1 MRI scan data released up to April 2019, we excluded 1094 individuals with a primary or secondary ICD10 diagnosis of a neurological or mental disorder, as well as 594 individuals with bad structural scan quality as indicated by an age and sex-adjusted Euler number27 more than three standard deviations lower than the scanner site mean. Our sample size for this analysis was n = 26,502, with a mean age of 55.51 years (SD = 7.42). 51.97% of the sample was female. For the replication analyses, we made use of an additional neuroimaging batch released in September 2019. After identical preprocessing steps as the primary sample, this sample consisted of 4884 individuals with a mean age of 55.47 years (SD = 7.37), 52.42% was female.We made use of data from participants of the UKB population cohort, obtained from the data repository under accession number 27412. The composition, set-up, and data gathering protocols of the UKB have been extensively described elsewhere1-weighted scans were collected from three scanning sites throughout the United Kingdom, all on identically configured Siemens Skyra 3T scanners, with 32-channel receive head coils. The UKB core neuroimaging team has published extensive information on the applied scanning protocols and procedures, which we refer to for more details25. The T1 scans were obtained from the UKB data repositories and stored locally at the secure computing cluster of the University of Oslo. We applied the standard “recon-all -all” processing pipeline of Freesurfer v5.3, performing automated surface-based morphometry and subcortical segmentation29. From the output, we extracted the sets of regional subcortical and cortical morphology measures, as well as estimated intracranial volume (eICV). Supplementary Table T30 to the residuals of each measure: : ri is the ordinary rank of the measure for ith individual, N gives the sample size, Φ−1 denotes the standard normal quantile, c = 0.5. This leads to normally distributed input into the univariate GWAS. See Supplementary Fig. We subsequently regressed out age, sex, scanner site, Euler number, and the first 20 genetic principal components from each measure. We further regressed out a global measure specific to each of the feature subsets: eICV for the subcortical volumes, mean thickness for the regional thickness measures, and total surface area for the regional surface area measures. This was done to ensure we are studying the genetic determinants of regional brain morphology rather than global effects. Following this, we applied rank-based inverse-normal transformationmentclasspt{minima31. After converting the BGEN format to PLINK binary format, we additionally carried out standard quality check procedures, including filtering out individuals with more than 10% missingness, SNPs with more than 5% missingness, and SNPs failing the Hardy–Weinberg equilibrium test at p = 1 × 10−9. We further set a minor allele frequency threshold of 0.005, leaving 7,428,630 SNPs.We made use of the UKB v3 imputed data, which has undergone extensive quality control procedures as described by the UKB genetics teamgj, and phenotype vector, y. Statistical significance was assessed from Pearson’s correlation coefficient rj = corr, as implemented in MATLAB’s corr function. This is equivalent to testing significance of the regression slope, rj are assumed to be t-distributed and have the same t-value: p-value, equal to Student’s t-cumulative distribution function (cdf) with N−2 degrees of freedom: N is the sample size16. Further, we validated that the above procedure produces the same results as the association test implemented in the commonly used PLINK’s additive model, option plink --assoc.The univariate GWAS on each of the 171 pre-residualized and normalized regional brain morphology measures were carried out using the standard additive model of linear association between genotype vector, 21. First, we select a subset of SNPs that pass genome-wide significance threshold 5 × 10−8 , and use PLINK to perform a clumping procedure at LD r2 = 0.6, to identify the list of independent significant SNPs. Second, we clump the list of independent significant SNPs at LD r2 = 0.1 threshold to identify lead SNPs. Third, we query the reference panel for all candidate SNPs in LD r2 of 0.1 or higher with any lead SNPs. Further, for each lead SNP, it’s corresponding genomic locus is defined as a contiguous region of the lead SNPs’ chromosome, containing all candidate SNPs in r2 = 0.1 or higher LD with the lead SNP. Finally, adjacent genomic loci are merged together if they are separated by <250 Kb. Allele LD correlations are computed from EUR population of the 1000 genomes Phase 3 data.Independent significant SNPs and genomic loci were identified in accordance with FUMA SNP2GENE definitionzij be the value of signed test statistic (z-score) calculated from the univariate association test between jth SNP and ith phenotype. Let zj =  be the vector of z-scores of jth SNP across K phenotypes. Let Z = {zij} be the matrix of z-scores, with rows corresponding to SNPs, and columns corresponding to phenotypes. Further, let z-scores, calculated from association tests on a randomly permuted genotype vector of each SNP. To preserve correlation structure among phenotypes, the permutation was performed only once for each SNP, and the resulting genotype vector was used in association test across all phenotypes.Let jth SNP is calculated as Mahalanobis norm zj is distributed as a multivariate normal random variable with zero mean and covariance p-value of the MOSTest test statistic, we calculated the tail probability that a Chi-square statistic exceeds 32. Instead of using theoretical values, we fit the two free parameters of the gamma distribution to the observed distribution of p-value of the MOSTest test statistic is then obtained from a cumulative distribution function of the gamma distribution, a, b) distribution is parametrized by shape (a) and scale (b), so that The MOSTest test statistic, S by replacing r smallest eigenvalues with the next smallest eigenvalue; r is an integer parameter that runs from 0 (no regularization) to K-1 (full regularization).In the simulation scenarios with regularization, the correlation matrix z-scores forming the input to MOSTest are normally distributed.Controlling for covariates, such as genetic principal components, is done via pre-residualization of all phenotype vectors, i.e., we replace them with the corresponding residual after multiple linear regression of the phenotype vector on the covariates. In addition, we perform a rank-based inverse-normal transformation of the residualized phenotypes, to ensure that https://github.com/precimed/mostest.MOSTest code is publicly available: 16 to estimate the percentage of variance explained by genome-wide significant SNPs as a function of sample size. For each SNP, i, MiXeR models its additive genetic effect of allele substitution, βi, as a point-normal mixture, π1 represents the proportion of non-null SNPs (polygenicity) and j, MiXeR incorporates LD information and allele frequencies for 9,997,231 SNPs extracted from 1000 Genomes Phase 3 data to estimate the expected probability distribution of the signed test statistic, N is sample size, Hi indicates heterozygosity of ith SNP, rij indicates allelic correlation between ith and jth SNPs, and zj, allowing us to calculate p-values, F−1 is the inverse function of the standard normal c.d.f., and pj is p-value from MOSTest. Finally, given the estimated parameters of the model, the power curve S(N) is then calculated from the posterior distribution p.We applied a causal mixture modelhttps://fuma.ctglab.nl/) to further process the output from MOSTest and min-P. Through FUMA, we carried out MAGMA-based gene analyses using default settings, which entail the application of a SNP-wide mean model and use of the 1000 Genomes Phase 3 EUR reference panel. Gene-set analyses were done in a similar manner, restricting the sets under investigation to those that are part of the Gene Ontology biological processes subset (n = 4436), as listed in the Molecular Signatures Database (MsigdB) v5.2.We made use of the Functional Mapping and Annotation of GWAS (FUMA) online platform  is an N by M genotype matrix, containing the number of reference alleles for the kth sample and jth variant. Here, βj is the causal effect size, and h2 = Var(Gβ)/Var(y). The computations were performed using publicly available tools (https://github.com/precimed/simu).In our simulations, we used the same panel of β, we randomly drew a certain number  of “causal” variants from chromosome 21 . The genetic effect sizes of all other variants were set to zero. Under the assumption of negligible linkage disequilibrium across chromosomes, this design allowed us to validate a uniform p-value distribution under null , thus confirming a correct type-I error. In addition, we validated the type-I error under the genotype permutation scheme employed by the MOSTest procedure. Across causal variants, the β values were drawn either from a normal distribution, or from a standard Cauchy distribution. The default settings, particularly nc = 100 and h2 = 0.004, were chosen to simulate a realistic magnitude of the genetic effects, with h2 = 29.1% heritability and nc = 7.3 K causal variants genome-wide, if all chromosomes would have been allowed to have genetic effects.To generate the vector of genetic effects, T = 25 features, we introduced covariance structure both in β and in T subcortical volumes, as defined in our main analysis. Further, for each causal genetic variant, we vary the number of non-zero effects across features, t, ranging from t = 1 (sparse effects scenario), to t = T (distributed effects scenario). In the sparse cases, t < T, we increased the total number of causal variants proportionally to the ratio of T/t, and ensured that each trait had exactly the pre-defined number of causal variants, while each causal variant, on average, contributed to t out of T traits.To simulate a realistic multivariate scenario with genetic and phenotypic correlation across up to f can be either identity, f(x) = x, or an exponent f(x) = ex. To simulate strict linear dependency between features , we replaced the set of T features, calculated as T(T − 1)/2 features, formed by all pairwise combinations. We then applied the link function f (identity or an exponent).We applied the link function to generate non-normally distributed phenotypes with heavy tails, yielding β and A detailed list of simulation parameters and scenarios is specified in Supplementary Tables https://github.com/precimed/mostestFinally, we executed MQFAM, MultiPhen and MultiABEL according to guidelines provided by the original software. A typical simulation result of a single run visualizes type-I error under null, type-I error under permutations, statistical power to detect non-null association at causal variants, and corresponding quantile–quantile plots . Full simulation scripts are available at Further information on research design is available in the Supplementary InformationPeer Review FileDescription of Additional Supplementary FilesSupplementary Data 1Supplementary Data 2Supplementary Data 3Supplementary Data 4Supplementary Data 5Supplementary Data 6Supplementary Data 7Supplementary Data 8Supplementary Data 9Supplementary Data 10Supplementary Data 11Supplementary Data 12Supplementary Data 13Supplementary Data 14Reporting Summary


Growth traits are important economic traits of pigs that are controlled by several major genes and multiple minor genes. To better understand the genetic architecture of growth traits, we performed a weighted single-step genome-wide association study (wssGWAS) to identify genomic regions and candidate genes that are associated with days to 100 kg (AGE), average daily gain (ADG), backfat thickness (BF) and lean meat percentage (LMP) in a Duroc pig population. In this study, 3945 individuals with phenotypic and genealogical information, of which 2084 pigs were genotyped with a 50 K single-nucleotide polymorphism (SNP) array, were used for association analyses. We found that the most significant regions explained 2.56–3.07% of genetic variance for four traits, and the detected significant regions (>1%) explained 17.07%, 18.59%, 23.87% and 21.94% for four traits. Finally, 21 genes that have been reported to be associated with metabolism, bone growth, and fat deposition were treated as candidate genes for growth traits in pigs. Moreover, gene ontology (GO) and Kyoto Encyclopedia of Genes and Genomes (KEGG) enrichment analyses implied that the identified genes took part in bone formation, the immune system, and digestion. In conclusion, such full use of phenotypic, genotypic, and genealogical information will accelerate the genetic improvement of growth traits in pigs. Pork is the primary source of protein for humans, with global pork consumption exceeding 110 metric kilotons per year . Furtherhttps://www.animalgenome.org/cgi-bin/QTLdb/SS/summary, release 27 August 2020). These findings have provided a certain number of molecular markers to porcine breeding for growth traits—for instance, Jiang et al. [Since the first genome-wide association study (GWAS) for age-related macular degeneration was published in 2005, GWAS has been widely used to identify quantitative trait loci (QTL) and to map candidate genes for complex traits in humans  and domeg et al.  performeg et al.  is prefeThe GWAS under the single-step genomic best linear unbiased prediction (ssGBLUP) framework is called ssGWAS, which intermixes genotypes, pedigree, and phenotypes data in a single analysis without creating pseudo-phenotypes . HoweverAll animals used in this study were used according to the guidelines for the care and use of experimental animals established by the Ministry of Agriculture and Rural Affairs of China. The ethics committee of South China Agricultural University  approved the entire study. No experimental animals were anesthetized or euthanized in this study.The animals used in this study were raised in two core farms of the Wens Foodstuff Group CO., Ltd.  with uniform standards. In brief, a total of 3945 Canadian Duroc pigs  born between 2015 and 2017 were used in this study. Among them, 2084 individuals had genotypes and four growth-trait phenotypes in the pedigree, while 1843 ungenotyped individuals in the pedigree had phenotypes of AGE and ADG, and 1825 ungenotyped individuals in the pedigree had phenotypes of BF and LMP. Furthermore, the complete pedigree could be traced back 3 generations, with 5204 pigs in the full pedigree .Days to 100 kg and ADG were measured from 30 to 115 kg and then adjusted to 100 kg. AGE was adjusted to 100 kg using the formula below :(1)AGE aADG was adjusted to 100 kg by following formula [ formula :(4)ADG ahttp://www.ccsi.ca/Reports/Reports_2007/Update_of_weight_adjustment_factors_for_fat_and_lean_depth.pdf):Adjusting LMP to 100 kg, phenotypes of BF and loin muscle depth (LMD) was measured between the last 3rd and 4th rib of Duroc pigs at the weight of 100 ± 5 kg by an Aloka 500 V SSD B ultrasound  . BF and LMD adjusted to 100 kg was calculated by the following equation [equation :(8)LMD aLMP was adjusted to 100 kg using the formula below [la below :(11)LMP Overall, 3927 individuals were used in wssGWAS for ADG and AGE; 3909 individuals were used in wssGWAS for BF and LMP.https://www.ensembl.org/biomart) in total. Quality control was performed by PLINK v1.09  [p-value was <10−6, minor allele frequency was <0.01, and SNPs were located in sex chromosomes and unmapped. After QC, a final set of 35,851 high-quality SNPs for 2084 Duroc pigs remained for subsequent analyses.DNA was extracted from ear tissue of 2084 Duroc pigs following the standard phenol/chloroform method, then quantified and diluted to 50 ng/μL. All DNA samples were genotyped by GeneSeek porcine 50 K SNP chip from Illumina , including 50,649 SNPs mapped to Sus scrofa11.1   in whichX was the incidence matrix of fix effect for relating phenotypes; b was the vector of fixed effect, including birth year, sex, and farm; Z was the incidence matrix of random effect; Variance components for AGE, ADG, BF, and LMP traits were estimated with two methods using the average information restricted maximum-likelihood (AIREML), including pedigree-based Best Linear Unbiased Prediction (BLUP) and ssGBLUP. The four traits were analyzed using the same single-trait animal model, as described below:G can be created as follows [Z was a centered matrix of SNP genotypes , D was a matrix of weights for SNP variances, n was the number of SNPs and Additionally, the GEBVs of all individuals were estimated via the same single-trait model as described previously using the ssGBLUP  approachmatrices . The invp matrix . The gen follows :(14)G=ZDi-th SNP .Initially, set Calculate Calculate GEBVs for whole data set by ssGBLUP method;Calculate SNPs effects: Calculate the weight of each SNP:Normalize SNP weights to keep total genetic variance constant viaSet The wssGWAS of SNP effects and weights were calculated following by Wang et al. :Initialli-th region consisting of The procedure was run for three iterations, as suggested by Wang et al. , which rThe procedures mentioned above were run with BLUPF90 software family programs  iterativhttps://www.ensembl.org/biomart) database within significant windows. To better understand the biological processes, GO and KEGG analyses were performed based on genes within significant regions using the database for annotation, visualization, and integrated discovery . A p-value of <0.05 was the threshold for significantly enriched GO terms and KEGG pathways.Genomic windows that explained higher than 1.0% of the total genetic variance were selected as candidate QTL regions associated with growth traits in this study, which was also used in previous studies ,13. SincDescriptive statistics of the phenotypes are presented in To better understand the genetic background of growth traits, we estimated the genetic variance . The expression of FAM135B promotes granulin (GRN) secretion, and GRN is a secreted growth factor with high expression in epithelial, immune, chondrocytes, and neuronal cells [FAM135B was reported as a candidate gene related to growth traits in beef cattle [Zinc Finger And AT-Hook Domain Containing (ZFAT) located in the region of 6.75–8.35 Mb on SSC4, and its mutation would lead to abnormal human body development and thyroid hormone secretion that played a key role in growth and metabolism [Among the significant windows of these two traits, the most important region (4.38–5.98 Mb on SSC4) harbored the f cattle  and reprf cattle . The ZinNuclear Factor, Interleukin 3 Regulated (NFIL3) and the Receptor Tyrosine Kinase-Like Orphan Receptor 2 (ROR2) were located in the regions of 1.63–3.23 Mb on SSC14. Wang et al. [NFIL3 affected the circadian lipid metabolism program, lipid–absorption, and export of intestinal epithelial through mouse experiments. The mice knocked out ROR2 resulted in shortened or deformed bones and neurodevelopmental dysplasia [The g et al.  reportedysplasia .Solute Carrier Family 27 Member 6 (SLC27A6) gene is located in the region of 130.75–132.35 Mb on SSC9. The SLC27A6 gene had high expression in fat and muscle tissue and worked on lipid metabolism in pigs [Adrenoceptor β 2 (ADRB2) gene, located in the region of 149.94–151.54 Mb on SSC2, encoded the β-adrenergic receptor that played an essential role in regulating metabolic level [ADRBs have a reduced metabolic rate and accelerated fat deposition. The members of the Tumor Necrosis Factor Receptor Superfamily (TNFS), among which TNFS11 was identified in the region of 24.24–25.04 Mb on SSC11, were responsible for bone growth in mice [TNFS11 led to the low level of serum insulin-like growth factor 1 (IGF1) influencing growth rate [The  in pigs . The Adric level . Furtheric level  found th in mice , and thewth rate .A total of 17 relevant QTL regions on SSC2, 3, 4, 6, 7, 10, 12, 13, 14, and 15 were identified for BF , where 9Death Domain Associated Protein (DAXX) was reported to affect fat deposition and fatty acid synthesis via regulating the transcriptional activity of the androgen receptor negatively [Inositol 1,4,5-Trisphosphate Receptor Type 3 (ITPR3), another gene located in the most important window, it was confirmed that mutations could cause taste disorders in mice [Inositol Hexakisphosphate Kinase 3 (IP6K3) gene was located in the same region. The mice without this gene resulted in a lower growth rate and metabolism and a shorter lifespan [Protein–Kinase C and Casein Kinase–Substrate In Neurons 1 (PACSIN1), a fourth gene located in the region of 29.34–30.94 Mb, was identified concerning the bodyweight [The most significant window was located in the region of 29.34–30.94 Mb on SSC7, where four genes were targeted and were related to BF. In previous studies, gatively ,47. For  in mice . Nonethelifespan . Proteindyweight  and loindyweight  in pigs.CYP7A1, a member of Cytochrome P450 Family 7 Subfamily A, was identified in the region of 74.12–74.92 Mb on SSC4. The CYP7A1 gene-encoded enzyme cholesterol 7α-hydroxylase mainly catalyzes the decomposition of cholesterol and synthesis of cholic acid [SECIS-Binding Protein 2 (SECISBP2) was located in the region of 0.43–1.22 Mb on SSC14, and its mutation brought about abnormal thyroid hormone metabolism in humans [lic acid . The SECn humans .N-α-Acetyltransferase 40 (NAA40) gene and Galectin 12 (LGALS12) gene were located in the region of 8.11–9.71 Mb on SSC2 with the highest percentage of total genetic variance. Liu et al. [NAA40 gene exhibited abnormal lipid metabolism and reduced fat mass. In addition, NAA40 was identified to be associated with the metabolism/transport of fatty acids or lipids in pigs [LGALS12, this gene was preferentially expressed in adipocytes, and mice lacking LGALS12 resulted in increased mitochondrial respiration, reduced adiposity and decreased insulin resistance/glucose tolerance [LGALS12 has been identified to be associated with intramuscular and subcutaneous fat in pigs [Altogether, 15 relevant regions on SSC2, 3, 4, 5, 6, 10, 11, 12, 17 and 18 were identified for LMP. These regions explained 1.00–2.68% of total genetic variance for LMP and 115 genes located in these genomic regions . The N-αu et al.  demonstr in pigs . For LGAolerance . Further in pigs .Corticotropin-Releasing Hormone Receptor 2 (CRHR2) gene, located in the region of 42.05–42.83 Mb on 18, was highly expressed in adipose tissue, which was involved in the regulation of energy homeostasis and the anorexia effect of fat levels in the corticotropin-releasing hormone (CRH) system [Peroxisomal Biogenesis Factor 16 (PEX16) and Cryptochrome Circadian Regulator 2 (CRY2) were associated with LMP. Hofer et al. [PEX6 affects adipocyte differentiation and increases peroxisomal fatty acid oxidation–reduction. For the CRY2 gene, Mármol-Sánchez et al. [CRY2 was significantly associated with stearic acid content in the longissimus dorsi muscle in Duroc pigs. The Acyl-CoA Thioesterase 8 (ACOT8) gene is located in the region of 47.67–48.83 Mb on SSC17. The protein encoded by this gene is an acyl-CoA thioesterase enzyme that influences the thyroid hormone to regulate lipid storage and utilization according to metabolic demands [The ) system . For ther et al.  found thz et al.  reported demands .In the present study, six genomic regions were found to be associated with both BF and LMP, including 41.40–42.12 Mb on SSC2,117.76–119.36 Mb on SSC3, 67.38–68.18 Mb, and 155.99–156.71 Mb on SSC6, and 38.67–40.27 Mb and 55.95–57.55 Mb on SSC10. Notably, BF and LMP were used as an important indicator of carcass fat content in production. Moreover, the genetic correlation of lipid deposition with growth rate and feed efficiency traits were positively high and negatively moderate, respectively . TherefoPotassium Inwardly Rectifying Channel Subfamily J Member 11 (KCNJ11), located in the region of 41.40–42.12 Mb on SSC2, was associated with type 2 diabetes in humans [Syndecan 1 (SDC1) gene was detected. The SDC1 gene has been proved to consume the intradermal fat layer, improve glucose tolerance, and significantly reduce body fat content in knockout mice [n humans . The regout mice . Two genNeuropilin 1 (NRP1) gene is located in the region of 55.95–57.55 Mb on SCC10, and several studies have exhibited its function in regulating fat cell–activity [MOB Kinase Activator 3B (MOB3B) gene was significantly associated with intramuscular fat and residual feed intake in cattle [Ras-Related Protein Rab-18 (RAB18), another gene located in the region of 38.67–40.27 Mb on SSC10, encoded a crucial Rab guanosine triphosphatase that controls the growth and maturation of lipid droplet, which lipid droplet was an intracellular organelle to stores triglycerides and cholesterol [Membrane Palmitoylated Protein 7 (MPP7) gene was detected, and Bhoj et al. [MPP7 gene expression affected glucose metabolism in the body.The activity  and reduactivity . For then cattle . Ras-Rellesterol . Still, j et al.  reportedIn the current study, gene set enrichment analyses revealed that several terms might be related to growth traits. Among them, seven biological processes, two cellular components, one molecular function, and four KEGG pathways were targeted significantly .The positive regulation of bone mineralization (GO:0030501) is a key biological process of bone formation, which promotes the deposition of inorganic minerals in the organic–matter of the bone. Bone mineralization affects the strength and density of bone, enabling it to bear the body weight. Shim et al.  found thThe positive regulation of lipophagy (GO:1904504) is an autophagic process that promotes cells to activate autophagy-related molecules to degrade lipids and regulate intracellular lipid content. Excessive fat deposition in pigs reduces feed conversion rate and affects growth rate, but also affects the quality of animal products . Hence, Potassium ion import (GO:0010107) mediates the transmembrane transport of ions and plays a key role in material exchange, energy transfer, and signal transduction. In particular, resting potassium currents make sour taste cells particularly sensitive to changes in intracellular pH, thereby affecting sour taste transduction . BesidesIn conclusion, we indicated 41 genomic regions to be associated with four growth traits  in a Canadian Duroc pig population using the wssGWAS method. The identified windows explained 1.00 to 3.07% of the genetic variance. Furthermore, 21 genes with related functional validation in previous studies were highlighted as candidate genes for growth traits in pigs. Moreover, GO, and KEGG enrichment analyses implied that the identified genes took part in bone formation, the immune system, and digestion, which were associated with growth traits. Such a full use of phenotypic and genotypic data and genealogical information will further advance our understanding of the genetic architecture and accelerate the genetic improvement of these economically important traits in pigs. In addition, the SNPs within identified regions may be useful for marker-assisted selection or genomic selection in future pig breeding.


The objective of this study was to quantify the benefit from the inclusion of genomic information in the estimation of breeding values for lactation yields of milk, fat, and protein or somatic cell score in a New Zealand dairy goat herd. The dataset included lactation yields of milk, fat, and protein and average somatic cell score of 839 does and genotypes from 388 does. A prototype single-step BayesC model was developed to predict genomic breeding values and demonstrated that including genomic information into the evaluation can increase the accuracy of predictions compared with the traditional best linear unbiased prediction methods based on pedigrees alone, which is currently implemented in the New Zealand dairy goat industry.Selection on genomic breeding values (GBVs) is now readily available for ranking candidates in improvement schemes. Our objective was to quantify benefits in terms of accuracy of prediction from including genomic information in the single-trait estimation of breeding values (BVs) for a New Zealand mixed breed dairy goat herd. The dataset comprised phenotypic and pedigree records of 839 does. The phenotypes comprised estimates of 305-day lactation yields of milk, fat, and protein and average somatic cell score from the 2016 production season. Only 388 of the goats were genotyped with a Caprine 50K SNP chip and 41,981 of the single nucleotide polymorphisms (SNPs) passed quality control. Pedigree-based best linear unbiased prediction (PBLUP) was used to obtain across-breed breeding values (EBVs), whereas a single-step BayesC model (ssBC) was used to estimate across-breed GBVs. The average prediction accuracies ranged from 0.20 to 0.22 for EBVs and 0.34 to 0.43 for GBVs. Accuracies of GBVs were up to 103% greater than EBVs. Breed effects were more reliably estimated in the ssBC model compared with the PBLUP model. The greatest benefit of genomic prediction was for individuals with no pedigree or phenotypic records. Including genomic information improved the prediction accuracy of BVs compared with the current pedigree-based BLUP method currently implemented in the New Zealand dairy goat population. The purpose of selection is to improve the performance of a population. Selection based on genomic breeding values (GBVs) can improve the rate of genetic gain compared with using only pedigree and performance records and has become a widely adopted method for ranking candidates for improvement schemes . The benUntil recently, the standard method of estimating breeding values was from a best linear unbiased prediction procedure that uses phenotypic records (PBLUP) of the individual and its relatives . That meLegarra et al.  suggesteFernando et al.  proposedEstimating GBVs conceptually involves a training population that has phenotypes and genotypes. In ssBR, the prediction model uses this “training data” to predict the influence of genetic markers by regression of the observed phenotypes on dosage covariates formed from marker genotypes. Then, the marker effects are summed across all loci to get the GBVs of individuals in a validation population that may not have observed phenotypic records.The Dairy Goat Cooperative (DGC) Ltd.  processes approximately 80% of goat milk in New Zealand. Farms that supply DGC and undertake herd testing participate in an annual genetic evaluation for lactation yields of milk (MY), fat (FY), and protein (PY) and for the average somatic cell score (SCS). Breeding values for these traits are estimated for each animal from an across-breed multi-trait repeatability animal model using the available pedigrees . CurrentThe aim of this study was to quantify the benefits from the inclusion of genomic information in the estimation of breeding values for a single New Zealand dairy goat herd.Phenotypic and pedigree records were provided for a single dairy goat herd by Dairy Goat Co-operative (NZ) Ltd.  from a herd test database maintained by Livestock Improvement Corporation (LIC) . The original dataset comprised lactation records from the 2016 season for 883 dairy goats. The phenotypic records were estimates of 305-day lactation yield records for MY, FY, PY, and SCS. The test interval method  was usedwww.goldenhelix.com). Individuals were discarded if they had a call rate < 95% or if they did not have phenotypic records. SNPs were discarded if they had a call rate < 90%, MAF < 1%, or deviated significantly from the Hardy-Weinberg equilibrium based on a threshold of p < 10−6. The majority of genotypes were from does in their second parity , while the remaining genotyped animals were in parity one , three , four , or beyond the fourth parity . The 388 genotyped animals were of Saanen (14) or ANTO (374) breed compositions.Skin samples were collected for SNP genotyping with the Illumina Caprine 50K BeadChip  in 2016. Of the 51,462 SNPs obtained, a total of 41,981 SNPs per animal remained after quality control. Quality control was performed using the SNP & Variation Suite v8 (SVS) software . A single-step BayesC model (ssBC) was used to estimate across-breed GBVs. Phenotypic and pedigree records from 839 animals were included in both models, and genotypes of the 388 animals were included in the ssBC model.y is the vector of phenotypes comprising at most one lactation record for MY, FY, PY, or SCS; b is the vector of fixed effects; d is the vector of effects of ANTO and unknown breeds; a is the vector of additive genetic effects ; e is the vector of random residual effects ; X and Z are design matrices relating the fixed and additive genetic effects, respectively; and D is a matrix with a row for each animal in the pedigree and columns for the proportion of ANTO and the proportion of unknown breeds (the regression coefficient for the Saanen breed effect was constrained to zero). Fixed effects included in b were the contemporary group and, as covariates, DMKD, DIM, and general heterosis. General heterosis was calculated as 1 − ∑fj = 1d2j, where dj is the proportion of each of the f = 3 breed groups  [Dd and variance Aσg2, where A is the numerator relationship matrix from the pedigree, and σg2 is the within-breed additive genetic variance. Residuals were assumed to have a normal distribution, with mean zero and variance Iσe2, where I is an identity matrix of size equal to the number of animals with a lactation record, and σe2 is the residual variance.The PBLUP was fitted using the ASReml 3.0 software package  with theunknown) . The addEstimated breeding values were calculated as:In this population, there is a known QTL with a large effect on milk traits ; therefoyn and yg are the vectors of the phenotypes; Xn and Xg are the incidence matrices for the fixed effects; and b is a vector of the fixed effects, including the contemporary group (does kidding in the same parity) and, as covariates, DMKD, DIM, and general heterosis. Dn and Dg are matrices with a row for each non-genotyped and genotyped animal in the pedigree and columns for the proportion of ANTO and the proportion of unknown breed, d is a vector of effects of the ANTO and unknown breeds, and Jn and Jg are matrices with a row for each non-genotyped and genotyped animal in the pedigree and columns for the J covariate for each breed group that were included as fixed effects to fit the difference between the genotyped founder and non-genotyped founder breeds. The matrix Jn is computed as AngAgg−1Jg, for breed f, where Ang and Agg−1 are submatrices of the numerator relationship matrix A, Jg is the matrix of the breed fractions identical to Dg, except that it includes the vector of breed fractions for Saanen, q is the vector containing the regression covariates for J, which account for the difference in breeding values between genotyped and non-genotyped animals of the same breed [Zn and Zg are incidence matrices that relate the breeding values of animals, Mg is the matrix of the centered marker covariates for the genotyped animals, Mn = AngAgg−1Mg is the matrix of the marker covariates for the non-genotyped animals that are imputed from the genotyped relatives, a is the vector of random marker effects, ε is the vector of genetic imputation error effects, Wn and Wg are incidence matrices that relate the residual polygenic effects, u is the vector of residual polygenic effects, and e is a vector of residuals.The model in matrix notation wasme breed , Zn and ak2, and the prior probability p that SNP k has zero effect and follows a two-component mixture prior:2ak ~ va,Sa2 X2va. A previous study in this population reported that the markers captured 12% of the genetic variance [Ann−AngAgg−1Agn)(1−w)sg2) [Ann, Ang, Agg, and Agn are submatrices of A; sg2 is the total genetic variance with  ~ vg,Sg2 Xvg2; w is the ratio of residual polygenic to total genetic variance (0.88); u ~ N that are not captured by markers; and e is ei|se2 ~ iidN, with  ~ ve Se2 Xve2.The fixed effects are assumed to have flat priors. The prior for the marker effects depends on the marker variance, svariance . To reco1−w)sg2) , where AJ covariates for each breed group, Genomic breeding values were calculated as:The BayesC mixture model requires that unknowns be estimated using MCMC techniques. Due to the limited number of observations in this evaluation (a single herd), variance components were estimated using the ssBC model and data from a larger dataset first . The posterior residual variance and heritability values previously estimated for this population  for eachPrediction accuracy for each model and trait were assessed using a validation process by splitting the herd into two subsets: the training set of the oldest 70% of the herd  and the validation set comprising the youngest 30% .The prediction accuracy was assessed and summarized based on the different levels of pedigree information available in the evaluation. Using predicted EBVs of animals in the validation set , the average prediction accuracies were calculated when the animal had: (A) both the sire and dam recorded , (B) the sire was recorded and had ≥5 progeny in the herd , (C) the dam was recorded and had ≥1 lactation record , or (D) neither the sire nor dam were recorded . To demonstrate the impact on prediction accuracy when both the sire and dam are unknown, the PBLUP evaluation was rerun an additional time but, by masking the pedigree records of animals that previously had records of both the sire and dam, resulted in 162 animals in the evaluations for scenario (D).Reliabilities of PBLUP EBVs were calculated as (1-(PEV/sg2)), where PEV is the predicted error variance calculated by inverting the coefficient matrix of the MME , and sg2The across-breed EBVs and GBVs were standardized to a consistent base for the independent PBLUP and ssBC evaluations by subtracting off each EBV the mean EBV of the base and similarly for GBV. The slope of standardized GBV against standardized EBV is used as a measure of genomic inflation. The expected value is one, indicating that the genomic predictions are on a similar scale as the EBVs, i.e., not inflated of deflated.The descriptive statistics are in The average accuracies of the GBVs obtained for MY, FY, PY, and SCS were greater than the average accuracies of EBVs . The greFor all scenarios and all traits, the GBVs had greater accuracies than the EBVs . When inThe breed and J covariate coefficients for each breed group obtained from the ssBC model are shown in The results of this study indicate that the ssBC model using genotypes, pedigrees, and phenotypic records can be used to obtain more accurate predictions of animal genetic merit compared with the PBLUP model currently used for the genetic evaluation of dairy goats in New Zealand. The increase in accuracy is particularly valuable, as these GBVs can be estimated for all individuals in the evaluation, even those without phenotypes or pedigree information. Whereas, with the PBLUP evaluation, those animals without phenotypic or pedigree records would have otherwise been excluded.The prediction accuracies obtained from the PBLUP model suggest the current pedigree records provide limited information to the genetic evaluation of animals in this herd. Whereas the genomic information provides a significant contribution to the evaluation, as shown by the increased prediction accuracies. Despite this increase, these accuracies are much lower than those reported in other dairy goat populations. Multiple studies using ssGBLUP approaches have published prediction accuracies for milk traits in dairy goats, including accuracies of 0.61 for MY in the UK ; 0.69 foThe accuracy of the GBVs of the FY and ASCS was slightly greater when the dam was recorded in the pedigree and had her own lactation record, compared with the animal having no pedigree records. However, the prediction accuracy was lower for the prediction of the MY and PY GBVs. These contradictory accuracies of GBVs could be due to the limited number of animals in the validation population that had dams with lactation records  and, therefore, was not an accurate representation of the true effect of having this additional information in the reference population. On the other hand, these differing accuracies between traits could suggest that the inclusion of the dam and her lactation records does not add much to the accuracy of the genomic predictions. The latter coincides with other genomic prediction studies, which also suggest that adding females to the reference population does not contribute a great deal to the accuracy of genomic predictions ,26.When the animals have a sire recorded in the pedigree that has at least five progeny records, the average prediction accuracy of both models was greater than the accuracies obtained when the dam was recorded in the pedigree and had her own lactation record. This difference in accuracy suggests that most of the information is captured by the males present in the reference population, rather than the females. Although actual sires were not included in the reference population, the link between the sires and their progeny provides greater benefits to the predictions compared with the information provided by the dams with lactation records.The prediction accuracies of EBVs and GBVs when animals have a sire recorded that has at least five progenies obtained the same prediction accuracies of EBVs and GBVs when both the sire and dam are known. This suggests that animals in the validation population that have recorded sires linked to the reference population provide as much information to the prediction of breeding values as the animals with both the sire and dam recorded.The accuracy of predictions is important in livestock genetic improvement programs, as this gives confidence of a reliable estimate of the individuals true breeding values. If the accuracy is low, there is greater risk that the EBVs and GBVs are not reliable, and there is more chance of selecting an animal with an inflated breeding value. The accuracy of genomic prediction largely depends on the size of the reference population , the relUnlike the dairy cattle industry that has high accuracies due to a well-established recording system and large reference populations , the daiThe prediction accuracies obtained in this study were lower than those obtained in other studies that used ssGBLUP approaches; however, this could be due to the limited information available in the current evaluation rather than the model used. The prediction accuracies are expected to increase as the size of the reference population increases.In this study, the regression coefficient of the GBV on the EBV for the MY was very close to one, indicating that the GBV and EBV for this trait were obtained in the same scale. The regression coefficients of the GBV on the EBV for the FY, PY, and SCS were less than one, indicating that the GBVs of these traits were slightly deflated or the EBVs were inflated. However, these regression coefficients give confidence that the standardized GBVs are similar to the EBVs and, given the improved accuracy of the GBVs, reiterates the potential of including genomic information in the genetic evaluation of these traits. Genomic relationships estimated from marker data provide more accurate estimates of the genetic covariance between relatives than the genetic relationships estimated from pedigree information . This, iThe breed effects included in the multibreed genetic evaluations can have a large influence on the accuracy of the EBVs and GBVs and will be important for the ranking of animals. Although this dataset is relatively small, the regression coefficients obtained for each breed group illustrate the importance of these breed effects. Likewise, the J coefficients obtained for the differences between the genotyped founder and non-genotyped founder breeds are included in the across-breed GBVs for each animal, where the values for the non-genotyped animals will vary widely, depending on how closely related they are to the genotyped animals and their breed proportions of each breed group. Previously, the GBVs were predicted based solely on their pedigrees and genotypes, which led to overestimation, as the genotyped animals were generally the most superior in the population. However, correcting for the differences between the genotyped and non-genotyped founder breeds enables the prediction of genetic merit in a population where selection is absent as the analysis is conditional on the data used for selection.A single-step approach that includes both genotyped and non-genotyped animals would be recommended for the genetic evaluation of the New Zealand dairy goat population, as the inclusion of genomic information improved the accuracy of prediction of the across-breed breeding values for all traits and for all scenarios. The accuracies obtained for the different scenarios demonstrated what farmers could expect with varying degrees of relationships to the reference animals. The results from this study suggest genomic prediction is possible in the New Zealand dairy goat population; however, this was based on a single herd and requires further investigation before implementing for the entire population.Including genomic information improved the prediction accuracy of breeding values compared with the pedigree-based BLUP method currently implemented in the New Zealand dairy goat industry. The prediction accuracies were slightly lower than other populations, but these accuracies are expected to increase as more animals enter the reference population. The use of a higher density SNP chip or whole-genome sequencing would increase the extent of the LD, which would improve accuracies of the across-breed genomic predictions. The inclusion of genomic information would enable the prediction of the GBVs for all animals, even those without known pedigree or phenotypic records, which would benefit the New Zealand dairy goat population.


Fragaria × ananassa) breeding program has implemented genomic prediction (GP) as a tool for choosing outstanding parents for crosses over the last five seasons. This has allowed the use of some parents 1 year earlier than with traditional methods, thus reducing the duration of the breeding cycle. However, as the number of breeding cycles increases over time, greater knowledge is needed on how multiple cycles can be used in the practical implementation of GP in strawberry breeding. Advanced selections and cultivars totaling 1,558 unique individuals were tested in field trials for yield and fruit quality traits over five consecutive years and genotyped for 9,908 SNP markers. Prediction of breeding values was carried out using Bayes B models. Independent validation was carried out using separate trials/years as training (TRN) and testing (TST) populations. Single-trial predictive abilities for five polygenic traits averaged 0.35, which was reduced to 0.24 when individuals common across trials were excluded, emphasizing the importance of relatedness among training and testing populations. Training populations including up to four previous breeding cycles increased predictive abilities, likely due to increases in both training population size and relatedness. Predictive ability was also strongly influenced by heritability, but less so by changes in linkage disequilibrium and effective population size. Genotype by year interactions were minimal. A strategy for practical implementation of GP in strawberry breeding is outlined that uses multiple cycles to predict parental performance and accounts for traits not included in GP models when constructing crosses. Given the importance of relatedness to the success of GP in strawberry, future work could focus on the optimization of relatedness in the design of TRN and TST populations to increase predictive ability in the short-term without compromising long-term genetic gains.The University of Florida strawberry ( The development of high throughput genotyping and new methods for analyzing genome-wide molecular data are revolutionizing crop improvement. In particular, genomic prediction (GP) is helping to increase genetic gains for genetically complex traits in animal , crop B, and treNe). If Ne decreases, it is expected that the individuals within the population will share larger chromosome segments, increasing prediction accuracy  is defined as the correlation between the observed phenotypic value and the BV: [r] . Differer] , or multr] , 2016. Hr] , and a gr] .Assessment of GP is not trivial. Some published studies have been based on a single population with the use of cross-validation techniques . Cross-vSome reports on independent validation and cross-validation across environments for multiple generations using a two-stage analysis have been published , 2017. IFragaria × ananassa) production area of Central Florida have indicated either very low or the absence of G × E interaction for the main strawberry commercial traits.For training populations tested across multiple environments, genotype-by-environment (G × E) interactions may be important. Several GP studies using real data under different scenarios of locations and/or environments have modeled the effects of G × E or marker × E interactions , 2017. PThe strawberry breeding program at the University of Florida (UF) conducts genetic trials at the Institute of Food and Agricultural Sciences, Gulf Coast Research and Education Center (GCREC) in Balm, FL, United States. Each year a clonally replicated field trial of advanced breeding selections is phenotyped for several polygenic traits and genotyped via single-nucleotide polymorphism (SNP) arrays. These advanced selections arose from previous marker-assisted seedling selection for simply inherited disease resistance and fruit quality traits  and subsNe on changes in predictive ability over time.The overall objective of the present study was to inform practical approaches for the use of GP in the breeding of horticultural crops by examining multiple cycles in the UF strawberry breeding program. Our specific objectives were to: (1) examine the effects on predictive ability of combining multiple cycles (or years) into TRN populations in the forward and backward directions; and (2) examine the effects of relatedness among the TRN and TST populations, LD and The elite population of the UF strawberry breeding program is treated as a single breeding pool from which the top-ranked parents of the previous year are used in a partial circular mating design to generate a large population of seedlings to be evaluated. This mating design is a modification of a partial diallel design with a reduced number of four to five crosses per parent, that fall along an off-diagonal matrix of parental crosses . The besReplicated seedling and advanced-selection trials were previously established at two sites, the Gulf Coast Research and Education Center (GCREC) in Balm, FL  and at the Florida Strawberry Growers Association in Dover, FL , during the 2013–2014 and 2014–2015 seasons. Very low genotype by location interactions were observed for yield and quality traits . ConsequThe populations included in the present study were established at the GCREC site during five consecutive seasons from 2013–2014 to 2017–2018. The strawberry breeding program uses an overlapping generation breeding strategy in which all the main breeding activities, crossing, testing, and selection, take place each year , therefoFive yield and fruit quality traits were assessed weekly from mid-November to mid-March in all five trials. At each harvest date, all ripe fruit per plant was removed. All marketable fruit (grams) by plant were considered as early marketable yield (EMY) if harvested before the first day of February. Total marketable yield (TMY) was calculated as the marketable fruit by plant collected until the first week of March. Average fruit weigh in grams, AWT, was estimated as the TMY divided by the number of marketable fruit. Total culls (TC), or unmarketable fruit, were counted and expressed as a proportion of the total number of fruits per plant (%). Soluble solids content (SSC) was measured five times during the season in each trial and was calculated as the mean of all measurements. One ripe fruit from each plant was squeezed by hand onto a handheld digital refractometer.® IStraw90  following one-stage analysis of tested phenotypes adjusted for the experimental factors in each trial. In most years, row and column location of each plant in the trial was recorded and the general linear mixed model was modified by adding spatial factors  and correlated residuals (autoregressive of order 1 for row and column), or independent residual units. Hence, multiple linear mixed models were tested for each trait and evaluated based on the Akaike and Bayesian information criteria  as well as their numbers of parameters .K) unknown factor loadings. When the factor analytic model is applied to the matrix of genotypic effects in each year (ug), the model can be written as: ug = (Γ⊗Im)f+δ,where Γ is the matrix of K vector loadings, f is a vector of genotypic scores; Im is the vector of genotypes in each year and δ is the vector of genetic regression residuals. The variance of the genotype effects by year takes the form: var(ug) = (Γ Ѓ + ψ)⊗Imwhere ψ is a diagonal matrix with ψi as the specific variance for the ith year, and the matrix across years is G = (Γ Ѓ + ψ).Genomic Best Linear Unbiased Prediction, GBLUP  allowed G was generated using all 9,908 markers and following the methodology described by G matrix and its inverse were performed with the software GenoMatrix  associated with the incidence matrix Z and e is the vector of residual effects. Bayes B is a variable selection and shrinkage method, which assumes that some SNP effects are non-zero with probability 1-π while others have zero effects with probability π, following a mixture of two different prior densities with a point of mass at zero and a slab with a scaled-t density  and predicting to other trials (or years), as testing sets . Therefore, when we used T2 as TRN population we made a prediction for all T4 to T10 trials, by employing a single matrix of marker effects. The genotypes in these trials are genetically related to various degrees, but they are statistically independent in the process of fitting and evaluating the genetic model. After the single predictions were performed, we increasingly averaged successive predictions from previous years to the latest cycle (T10) and evaluated their effect on predictive ability in both forward  and backward  directions. Each of these combinations was evaluated including or excluding common genotypes trialed across years. The Bayes B model was fitted in R  using thch trial , we did Ne. This set of markers was selected out of 14,332 markers in season 2015–2016 using the GenoMatrix software  and without relatedness (2vr), respectively  for T2 and T10 against genomic distances in Mb for T2 and T10  and LD corrected for relatedness (2vr) for T2 were slightly lower than our previous estimates of r2 = 0.26 and 2vr = 0.04 (r2) comes first from multiples copies of the same genotype and second from the progeny of full-sib families , but there were multiple full-sib families with different numbers of offspring in each cycle; therefore, the bias of the r2 estimate should only be due to this second factor. The presence of LD corrected for relatedness is the driving force for the long-term success of GP in the breeding population, as 2vr represents the prediction accuracy that will tend to persist over multiple cycles without the need for retraining  to T10 (Ne = 20). In the present study this apparent slight reduction in Ne and the corresponding increase in the extent of LD from T2 to T10 are likely contributing to increased predictive ability with the addition of later cycles. In the long-term it is important to recognize that intensive recurrent selection increases inbreeding. Therefore, to maintain long-term breeding progress, it will be important to continue to introgress diversity into the elite breeding population.The impact of  species . In longThe last 5 years of implementation of GP in the UF strawberry breeding program has allowed the use of some parents earlier in the breeding cycle and has increased the accuracy of estimation of breeding values. This study makes clear that the use of average predictions from multiple cycles in training GP models is very beneficial, at least up to four cycles when common individuals are included across trials. Based on these results, the following steps are currently used for the application of GP in the UF strawberry breeding program :(1)In the summer prior to each winter fruiting/crossing season, which in Florida extends roughly from mid-November through March, phenotypic and marker data from up to four previous cycles, including common individuals across trials, are used to train Bayes B models predicting the BVs of the most recent advanced selections. These selections were seedlings in the previous cycle and are genotyped over the summer but are not yet phenotyped for the five measured commercial traits AWT, EMY, SSC, TC, and TMY.(2)Breeding values for these five traits are combined in a selection index using economic weights for each trait to rank the advanced selections for their overall potential as parents.(3)In November and December, early-season field observations are made for these advanced selections for all visually evaluated traits, including: fruit shape, color, and flavor, disease resistance, plant architecture, etc.(4)Three to five advanced selections  that are noted for early-season field traits and ranked highly in the BV selection index are selected for use as parents in controlled crosses as males. These males are crossed to one or more elite females that have been field evaluated for multiple seasons and have complementary traits to the males chosen by GP. In this way, approximately 10% of crosses have a male parent chosen via GP methods that is being used in crossing at least 1 year earlier in the breeding cycle than normal.As this study suggests, increasing the size of the training population will increase prediction accuracy, but at some point, increasing size will not further improve GP models. This appears to have occurred for the UF strawberry breeding program at the fourth cycle. Given the demonstrated importance of relatedness in this study, future work on the optimal design of the relatedness within and among TRN and TST populations  could possibly increase predictive ability in the short term without compromising the potential of future genetic gains. It will also be important to monitor the performance of crosses chosen via GP versus those designed in the traditional manner to empirically test whether the implementation of GP in the breeding program is achieving the desired results.https://datadryad.org/stash/dataset/doi:10.5061/dryad.b5mkkwhc7.The datasets presented in this study can be found in Data Dryad via the following link: VW, SG, and LO conceived and designed the study. SV prepared the SNP data for the GP analyses and carried out the analyses of LD and Ne. SG and LO performed the GP analyses. LO wrote the initial draft and VW, SG, and SV corrected it and improved it. All authors read and approved the manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.