Gynandropsis gynandra (spider plant) is an African traditional leafy vegetable rich in minerals, vitamins and health-promoting compounds with potential for health promotion, micronutrients supplementation and income generation for stakeholders, including pharmaceutical companies. However, information on biomass productivity is limited and consequently constrains breeders’ ability to select high-yielding genotypes and end-users to make decisions on suitable cultivation and production systems. This study aimed to assess the phenotypic variability in biomass and related traits in a collection of G. gynandra advanced lines to select elite genotypes for improved cultivar development. Seventy-one advanced lines selected from accessions originating from Asia, West Africa, East Africa and Southern Africa were evaluated over two years with two replicates in a greenhouse using a 9 x 8 alpha lattice design. Significant statistical differences were observed among lines and genotype origins for all fourteen biomass and related traits. The results revealed three clusters, with each cluster dominated by lines derived from accessions from Asia (Cluster 1), West Africa (Cluster 2), and East/Southern Africa (Cluster 3). The West African and East/Southern African groups were comparable in biomass productivity and superior to the Asian group. Specifically, the West African group had a low number of long primary branches, high dry matter content and flowered early. The East/Southern African group was characterized by broad leaves, late flowering, a high number of short primary branches and medium dry matter content and was a candidate for cultivar release. The maintenance of lines’ membership to their group of origin strengthens the hypothesis of geographical signature in cleome diversity and genetic driver of the observed variation. High genetic variance, broad-sense heritability and genetic gains showed the potential to improve biomass yield and related traits. Significant and positive correlations among biomass per plant, plant height, stem diameter and leaf size showed the potential of simultaneous and direct selection for farmers’ desired traits. The present results provide insights into the diversity of spider plant genotypes for biomass productivity and represent key resources for further improvement in the species. Gynandropsis gynandra (L.) Briq. (Syn. Cleome gynandra L.), commonly known as spider plant, is an African leafy vegetable with great potential in addressing micronutrient deficiency  was the random effect of the lth incomplete block within the kth replicate at the jth year, Gi was the random effect of the ith line, GYij was the random effect of the interaction between the ith line and the jth year, and εijkl was the random residual. Heterogeneous variances were assumed for residual effects in different years. The likelihood ratio test [lrt implemented in the ASREML-R package. Standard broad-sense heritability across years [r is the number of replications, and n is the number of years.Variance components across years were estimated by fitting a linear mixed-effect model using the restricted maximum likelihood (REML) implemented in the ASReml-R package version 4.1.0.160  accordintio test  was usedss years  was calccorr from the R package “Hmisc” [“metan” R package [PCA function implemented in the R “FactoMineR” package [fviz_cluster and fviz_dendogram functions of the R package “factoextra” [ymi was the phenotypic observation of the ith line on the mth cluster, μ was the overall mean, Cm was the fixed effect of the mth cluster, and εmi was the random residual. In addition, the means of clusters were separated using Tukey’s honestly significant difference test (Tukey’s HSD post hoc test) at the 0.05 probability level using the R package “agricolae” [The phenotypic best linear unbiased predictors (BLUPs) were generated from model 2. BLUPs were used because they have good predictive accuracy over the best linear unbiased estimators (BLUEs) due to their high correlation with the true values and their ability to handle environmental effects and have been recommended for phenotypic selection in plant breeding –74. The  “Hmisc” . Genotyp “Hmisc” . Both ge package . A princ package  to assestoextra”  for factricolae” .GA = i × H2× σP, where σP was the phenotypic standard deviation, H2 was the broad-sense heritability, and i was the standardized selection differential at the selection intensity of 5% (i = 2.06) [GAM = (GA/μ) × 100, where μ was the overall mean and GA was the genetic advance of the trait. Genotypic, phenotypic and error coefficients of variation  were estimated according to Burton and DeVane [μ was the overall mean. R software version 4.1.1 [The genetic advance (GA) for each trait was computed as  = 2.06) . Geneticd DeVane  as folloon 4.1.1  was usedA highly significant variation (p < 0.001) was observed among genotypes for all agronomic traits each and across years Tables  and 3. B2 with an average of 53.22 ± 1.66 cm2. The dry matter content was 10.67 ± 0.09% on average, with a range of 7.60–15.42.The coefficient of variation evolved between 14.01% and 82.48%. Overall, lower values for dry matter content and higher values for primary branch length were observed. The average plant total fresh biomass and edible fresh biomass were 67.19 ± 2.67 g and 28.34 ± 1.08 g, respectively. As the second most variable trait, the plant total fresh biomass (CV = 63.59%) ranged from 2.10 g to 248.40 g, while the edible fresh biomass (CV = 61.08%) ranged between 1.20 g and 101.90 g per plant. The harvest index was 0.47 ± 0.01 on average with a range of 0.24–0.91. The spider plant genotypes flowered on average 60.14 ± 0.90 days after sowing, and days to 50% flowering ranged between 32 and 95 days after sowing. The plant height ranged from 13 cm to 117.5 cm, with an average of 70.6 ± 1.31 cm. The average number of primary branches was 10.7 ± 0.26 per plant and varied between 2.5 and 23.5. The single leaf area ranged from 5.64 to 147.76 cmThe distribution frequency of all agronomic traits according to the regions of origin of the lines is presented in Significant genotypic variances  . Genetic length) . Estimat length) .Significant phenotypic and genotypic correlation coefficients were observed among the fourteen agronomic traits . While tTo assess the relationship among genotypes, we first performed a principal component analysis. The results of the principal component analysis revealed that the first two components explained 72.43% of the total variation in the biomass and related traits and correlated with most traits . Traits Clustering pattern analysis using hierarchical clustering on principal components classified the lines into three clusters Figs  and 4. AGynandropsis gynandra for plant morphology [G. gynandra was found to be associated with the genetic makeup of the genotypes [Gynandropsis gynandra. Similar observations for morphological traits have also been reported for worldwide accessions [Genetic variation is the foundation of any plant breeding program. Significant and origin-driven variation has been reported in rphology ,55, secorphology , seed gerphology , leaf virphology , antioxirphology , and phorphology . Morpholrphology ,4,39,55.enotypes ,58. Whilenotypes  observedcessions , Ghana [cessions , and Burcessions . This siG. gynandra [On the other hand, the average and the highest total fresh biomass in the present study were higher than those reported by Omondi et al.  in East-gynandra –49. TherG. gynandra [The clustering analysis identified three groups, each dominated by lines derived from accessions originating from different geographical regions. Clusters 1, 2 and 3 were dominated by lines derived from Asian, West African, and East/Southern African accessions, respectively. The clustering results were supported by the significant differences observed among regions of origin for all fourteen investigated traits. These results align with previous reports on the association between the geographical origin and the morphology of the accessions of gynandra . Specifigynandra  reportedG. gynandra include high leaf yield and related traits (plant height and the number of leaves), broad leaves and late flowering [G. gynandra was reported earlier in the 1950s [G. gynandra might have occurred in South Africa. Using genome sequencing, Sogbohossou [Farmers’ preferred traits in lowering ,59–61. Wlowering ,85 and plowering ,22. In clowering . In Afrihe 1950s . The domhe 1950s . West Afhe 1950s  support bohossou  suggeste2) measures the proportion of the total phenotypic variation attributable to the variance of genetic values [G. gynandra for biomass yield and related traits [Heritability is important in breeding, as it helps in predicting the efficiency of the selection. Broad-sense heritability  and that 2000 μmol m-2 s-1, which is close to full sunlight, does not saturate photosynthesis in G. gynandra as it is a C4 plant. Similarly, Kocacinar [2 assimilation, and the species requires high temperature (30–40°C) to attain maximum photosynthesis, playing a key role in the species’ growth and biomass productivity. On the other hand, the year significantly affected some of these traits, implying that these traits might vary with year. In addition, the significant genotype × year interaction indicated that the genotypes’ performance was not consistent across environments, and selection should consider the interaction effect when selecting genotypes. However, evaluation in additional environments, particularly in field conditions, is required to better decipher the genotype by environment interaction in the species.Genotype × year interaction variances were significant for stem diameter, primary branch length, number of primary branches, leaf width and area, petiole length, harvest index and days to 50% flowering. This is showing that these traits were influenced not only by the genotype but also by the interaction between genotype and year. As agronomic practices were the same during the two years, the differential environmental conditions between 2020 and 2021 could play a significant role in the significance of genotype × year interaction. Potential environmental factors that might influence these traits could include the temperature, the relative humidity, the light intensity and the day length (photoperiod). Imbamba and Tieszen  found thocacinar  observedocacinar  observedocacinar  and the Understanding the association between traits offers an opportunity for efficient and simultaneous selection. Both phenotypic and genotypic correlations showed similar trends. In the present study, the correlation between total fresh biomass and edible fresh biomass was strong, positive and significant. In addition, these two traits were highly and positively correlated with plant height and stem diameter, suggesting that selection for vigorous and tall plants will lead to high-yielding cultivars. This might be accompanied by broad leaves resulting from the positive and moderate association between biomass and leaf-related traits . Previous findings corroborated these results as a positive and strong correlation of leaf biomass with plant height, stem diameter, leaf length and width and petiole length . SimilarThe number of primary branches was positively correlated with days to 50% flowering, suggesting that late flowering plants had more branches. In contrast, primary branch length had a negative and significant correlation with days to 50% flowering and number of branches, showing the existence of a trade-off between the number of primary branches, the primary branch length and days to 50% flowering in the species. After flowering, plants allocate resources for lateral branch growth, therefore, the plant can achieve higher biomass either by flowering early and developing long branches or delaying flowering to produce more branches. This might explain why West African genotypes had similar biomass yields to East/Southern genotypes, which are late flowering with a high number of short branches. This calls for an in-depth investigation to understand resource allocation in the species and genes involved in flowering time, branch development, and plant architecture. To this end, developing mapping populations using genotypes from all clusters will be insightful.In this study, the harvest index was negatively associated with plant biomass and most other agronomic traits, suggesting that selection for the harvest index might be difficult. However, using appropriate agronomic traits, such as early harvesting, could help improve the harvest index. Frequent harvesting  might increase biomass productivity and extend the harvesting period. This would strongly depend on the regrowth ability of the genotype. An evaluation of the germplasm under different agronomic practices, including harvesting techniques and frequency, is required, as suggested by Houdegbe et al. . AssessiDry matter content is associated with shelf life and determines the vegetable’s post-harvest behaviour –97. The Overall, considering farmers’ preferred traits, genotypes in cluster 3 and somewhat cluster 2 are good candidates for cultivar release and breeding programs. Superior genotypes from these clusters with multiple improved traits included SA10, SA12, SA17 , EA12, EA3 (fresh and edible biomasses and days to flowering), AS14, AS16, WA17, WA3 , EA7, SA2, and EA9 (days to 50% flowering time and number of primary branches). An intensive field evaluation of these genotypes through multi-environment trials within each region would help in understanding the genotype-by-environment interaction in the species and whether to breed for specific or broad adaptation. Furthermore, establishing the link between the phenotype and genotype is required to help implement marker-assisted selection in the species. Genome-wide association studies (GWAS) can be implemented to decipher genes associated with functional and farmers’ preferred traits and would serve in the validation of QTLs reported by Sogbohossou  on floweThe present study revealed that the biomass potential of advanced lines of spider plant was associated with their geographical origin, thus strengthening the hypothesis of geographical signature in cleome diversity. West and East/Southern African lines had higher biomass productivity than Asian lines, suggesting advanced selection and domestication in Africa than Asia for biomass. The significant genetic variation, high broad-sense heritability, genetic gain and positive correlation between plant biomass and related traits provides the opportunity for positive and simultaneous selection, especially for farmers’ preferred traits such as biomass yield, leaf size, flowering time and the number of branches. The genotypes SA10, SA12, SA17, EA12, EA3, AS14, AS16, WA17, WA3, EA7, SA2, EA9 are superior for multiple farmers’ desired traits and good candidates for breeding programs and cultivars release. Further studies should target multi-environment trials to determine genotype by environment interaction effect, determine the genotypes’ response to different agronomic practices such as cutting, fertilization considering the locally available resources, identify gene action and genes controlling farmers preferred traits and evaluate the germplasm tolerance to biotic and abiotic stress. Additionally, the association of plant biomass and related traits with key nutritional traits such as minerals is required to ensure the quality of the end products for users.S1 Table(CSV)Click here for additional data file.S2 Table(DOCX)Click here for additional data file.S3 Table(DOCX)Click here for additional data file.


We propose a simulation approach to compute response to genomic selection on a multi-environment framework to provide breeders the number of entries that need to be selected from the population to have a defined probability of selecting the truly best entry from the population and the probability of obtaining the truly best entries when some top-ranked entries are selected.The goal of any plant breeding program is to maximize genetic gain for traits of interest. In classical quantitative genetics, the genetic gain can be obtained from what is known as “Breeder’s equation”. In the past, only phenotypic data were used to compute the genetic gain. The advent of genomic prediction (GP) has opened the door to the utilization of dense markers for estimating genomic breeding values or GBV. The salient feature of GP is the possibility to carry out genomic selection with the assistance of the kinship matrix, hence improving the prediction accuracy and accelerating the breeding cycle. However, estimates of GBV as such do not provide the full information on the number of entries to be selected as in the classical response to selection. In this paper, we use simulation, based on a fitted mixed model for GP in a multi-environmental framework, to answer two typical questions of a plant breeder: (1) How many entries need to be selected to have a defined probability of selecting the truly best entry from the population; (2) what is the probability of obtaining the truly best entries when some top-ranked entries are selected.The online version contains supplementary material available at 10.1007/s00122-022-04157-1. Environmental effects and genotype × environment interactions play a role in masking the true genotype value. This is why a breeding program is never conducted in a single environment  allows breeders to estimate genomic-based breeding values via dense markers  using cross-validation. While this method is very useful in comparing alternative methods and designs, it does not usually give the plant breeder the full picture needed to decide on the number of breeding entries to be selected. Typical questions a plant breeder has in this regard may be exemplified as follows: (i) How many entries do I need to select to have a defined certainty (probability) of selecting the truly best entry from my population? (ii) If I select the Predictive accuracy, useful as it undoubtedly is, does not give direct answers to such crucial questions. These probabilities are hard to compute analytically for various reasons, including the imbalance of the data and the complexities of the mixed model used for analysis. The easiest and also the most tangible way to compute them is by simulation based on the fitted model. This idea was outlined and illustrated by examples in Piepho and Möhring , and it The phenotypic data are proprietary of a commercial hybrid rye breeding program by KWS LOCHOW established in central Europe. In the program, the seed and pollen gene pools are developed and tested independently. After crossing, a few generations of single plant selfing, selection and per se performance line selection, testcrosses are produced between inbred lines and two testers from the opposite heterotic pool.The testcrosses are submitted to field trials. In the first year of general combining ability (GCA) evaluation , entries (i.e. testcrosses) are planted in several locations. A subset of entries is selected and forwarded to a second year of field evaluations . The selected fraction from the GCA2 trials is evaluated on the field in a third year . The entries of the GCA3 trials are the testcrosses developed in the previous year. A sequence of GCA1 to GCA3 trials constitutes a selection cycle. All trials within a location are laid out as α-designs with two replicates. Alpha (α) designs are a class of generalized lattice designs generated based on alpha arrays , Cycle 2 (2017–2019), and Cycle 3 (2018–2020). For Cycle 4, the available dataset comprised only GCA1 (2019) and GCA2 (2020), and for Cycle 5, only GCA1 (2020) was available.All genotypes from the seed and pollen pools were genotyped with an Illumina INFINIUM chip with 9963 single-nucleotide polymorphisms (SNPs) . The SNP used across the years partially overlap the 600 k-SNP assay of Bauer et al.  and the The routine analysis we envision here is based on the current year’s dataset only, which in this study was taken to be the year 2020. This type of analysis is commonly done in many breeding programs, where the time between data acquisition from the current trials and selection decisions is limited. This approach also reflects the fact that selection decisions are made each year only for the entries tested in that year. We are focusing on GCA1 here, for which there are no data on the same entries from previous years.A key challenge is that a standard single-year analysis cannot dissect the GBV × year interaction effects from GBV main effects. In particular, response to selection based on such an analysis may be over-estimated because it is based on the sum of these two effects, whereas only the first component contributes to selection response in relation to future performance of the selected entries. However, if data from multiple years are available, variance components for these two effects can be estimated, and a key idea of this paper is to use such estimates for single-year analysis to dissect GBV and GBV × year effects.Estimation of the GBV × year variance from multi-year data can be done a priori and then plugged into the analysis for the data from the current year. In principle, we could also plug in the long-term estimate for the GBV variance estimate, but we prefer to use the current GBV variance to adjust for population structure in the current year. The major effect of the inclusion of a GBV × year interaction effect in a single-year analysis is an increased shrinkage of the genomic best linear unbiased predictions (GBLUPs) of the GBV main effects.Estimate Estimate the apparent GBV variance Multiply this estimate of Rerun the model for GCA1-2020 data by plugging in and fixing Moreover, the simulation based on this model will yield a smaller simulated response to selection. It is stressed here that this simulated response to selection is more realistic, as it properly reflects the fact that the apparent GBV main effect seen in a specific year based on the usual method of analysis is, in fact, the sum of the true GBV main effect and the GBV × year interaction effect for that year. In this study, the current-year (GCA1-2020) analysis uses estimates of the variances for GBV main effects and GBV × year interaction effects, which are obtained from the multi-year analysis based on the previous years. The steps for the multi-year analysis are, therefore, as follows:A key challenge with this approach is how ρ in the first step above can be estimated in the multi-year analysis. Here, we propose two alternative analyses for this purpose, i.e. a combined-cycles (CYC) and a multi-year analysis based on GCA1 data of the years 2016 to 2019 (MY). Figure Y is the vector of observed plot yields, 1 is a vector of ones, μ is the general mean, For the CYC and MY analyses, a two-stage approach was used. In the CYC analysis, the approach was applied for each cycle, while in the MY analysis, the approach was applied directly in the four-year dataset. In Stage 1, the entry means per year across locations were computed. Thus, the following linear mixed model was fitted per year for phenotypic analysis at the plot level:mentclasspt{minimamentclasspt{minimaj is a subscript for years, and jth year, as shown in Appendix  GBV variance mentclass2pt{minimAll terms are defined as for Eq. entclass1pt{minimaThe GCA2 trial is crucial since in this trial the entries will be selected for the final trial of a selection cycle, i.e. the GCA3. Thus, it is desirable to use the GCA1 and GCA2 datasets for the GCA2 analysis. However, there is a challenge in using the previous trials’ data, i.e. the GCA1. If all entries from GCA1 are also used, then an estimate of the genetic variance applying to GCA1 is obtained , location (l), entry × tester (gt), entry × location (gl), trial within location (ls), the replication (lsr), and the incomplete block (lsrb) effects were nested within years (y). Furthermore, the distributional assumption for each random effect, entclass1pt{miniman < N entries is to be performed. The random effects are assumed to be multivariate normal with zero mean and variance–covariance matrix The fitted linear mixed models have a random vector The key of the simulation approach is to simulate a large number We use a decomposition of the Ω matrix given by:This decomposition can be obtained by Cholesky decomposition, in case the matrix Ω is positive-definite, or using a singular value decomposition (SVD) in the case of the Ω is not positive-definite.We then simulate the values of For each of the Wickham, . AdditioIn the GCA1 assessment, the performance of the current-year model depends on the value of entclass1pt{minimaThe asymptotic correlations between the GBV and GBV × year variance estimates by the CYC and MY analyses for both pools given in Table The variance component estimates of Table The mean correlation coefficient between the true genetic values es Table .Table 7MN was only around 0.21, while with the MY analysis, the probability was around 0.80. In the pollen pool, both MY and CYC showed a similar trend. Both analyses implied that by selecting a small proportion of entries, i.e. 30%, the probability of obtaining truly ten best entries was around 0.76 and 0.62 for CYC and MY analyses, respectively. Moreover, Fig. The quantity of interest from the simulation is depicted as a plot of the probabilities of obtaining truly best entries for each selected proportion of the entries based on the GBLUPs, as presented in Fig. The variance estimates and standard errors for year In the seed pool, the year variance estimates in Cycle 3 to Cycle 4 were zero, while in the pollen pool, it was in the Cycle 1, Cycle 3, and Cycle 4. Furthermore, in the seed pool, the The asymptotic correlations between the GBV and GBV × year variance estimates of each cycle for both pools presented in Table Table Table The quantity of interest from the simulation for GCA2 assessment is depicted as a probability plot of obtaining truly best entries given the number of selected entries in Fig. m lines based on the proportion of the selected lines allows breeders to take decisions as to modifications of selection fractions in selection stages, trials, and years with increased error variances of mean estimates due to unfavourable environmental conditions (e.g. drought) to ensure that a certain portion of truly best genotypes are continued to the next selection stages. Likewise, in labour-intensive trait introgression (conversion) procedures with large numbers of entries in early selection stages, this probability allows optimizing the allocation of technical and personnel resources through an estimate of the risk of potential loss of superior lines in dependence of the number of the total number of converted entries.The response to selection has been widely used in plant breeding programs to measure genetic gain. Our proposed simulation approach allows breeders to obtain information on how well genomic selection can be made for the next stage. The response to selection can be measured in terms of the probability of selecting the truly best entry based on the number or proportion of selected entries. Knowing the probability of selecting the best per-se line selection stage for agronomic (non-yield) traits. In comparison with using only GCA1 from the years 2016 to 2019 as in the MY analysis, the CYC analysis benefits from using the entries in the selected fractions of GCA2 and GCA3 improving the connectivity across GCA trials. In the same vein, Smith et al.  that show a very particular change of ranking between years that leads to an over-estimation of GBV × year and an underestimation of We have also shown that the simulation for the GCA2 assessment is useful to measure the selection accuracy for the final trial in the GCA3. Thus, the simulation was only based on the selected entries that progressed to GCA2.In this study, the number of years was not large, i.e. only 4 years in the GCA1 assessment, and the simulations were conducted using the estimates produced by frequentist residual maximum likelihood method (REML). Furthermore, as demonstrated by our results, estimation of the variance components for GBV and GBV × year effects is the Achilles’ Heel of the whole approach. These variance components are expected to display year-to-year variation, which is why our approach prescribes re-estimation of each variance in a new year using a long-term estimate of An approach that can be beneficial is to continuously use a Bayesian framework to collect more information from the previous years and use it as a prior information to update the current-year analysis. This approach is known as Bayesian updating Supplementary file2 (R 1 kb)Supplementary file3 (R 2 kb)Supplementary file4 (R 1 kb)Supplementary file5 (R 15 kb)Supplementary file6 (PDF 224 kb)Supplementary file7 (HTML 1750 kb)Supplementary file8 (HTML 1750 kb)Supplementary file9 (PDF 226 kb)Supplementary file10 (PDF 226 kb)Supplementary file11 (PDF 226 kb)Supplementary file11 (PDF 144 kb)Below is the link to the electronic supplementary material.


K) to connect genotype to phenotype. Genomic relationship matrices share information among entries to estimate the observed entries’ genetic values and predict unobserved entries’ genetic values. One of the main parameters of such models is genomic variance , the value of the average diagonal element of K, and the assortment of alleles and heterozygosity (H) in the observed population. Using the average semivariance, we propose a new matrix, Many important traits in plants, animals, and microbes are polygenic and challenging to improve through traditional marker-assisted selection. Genomic prediction addresses this by incorporating all genetic data in a mixed model framework. The primary method for predicting breeding values is genomic best linear unbiased prediction, which uses the realized genomic relationship or kinship matrix ( Linear mixed model (LMM) analyses are routine in the prediction of breeding values in plants and animals (K), which measure the relatedness among entries  is K will impact Genomic variance , introduced by K by multiplying Arabidopsis thaliana (Triticum aestivium) breeding population (Mus musculus) population  breeding population (Sus scrofa) breeding population , i.e. The ASV estimator of the total variance  is half r(gi-gj) . Piepho In complex traits analyses, there is a crucial difference in the treatment of genotypes and effects in statistical models used for data analysis vs the quantitative genetics theory . In quany). y is the vector of phenotypic LSMs of for n entries, n is the number of entries, n-element vector of ones, μ is the population mean, n, g is an n-element vector of random effect values for entries with The analyses shown throughout this paper assume the dependent variables are least squared means (LSMs) or other adjusted means for entries (zed LMMs . The LMMG is the variance–covariance of the best linear unbiased predictors (BLUPs) of the genotypic values g, it can be inferred that the magnitude of The ASV definition of variance from LMM (3) isjp is the allele frequency of the jth SNP, which requires Hardy–Weinberg equilibrium (HWE) to hold  and the diagonals of the chosen GRM  for the jth SNP. This form assumes HWE and obtains jp from a historical reference population, not the observed population. When jp originates from the observed population, the centering by The form proposed by The normalized relationship matrix, This form is the most numerically similar to 2 is the coefficient of variation of the eigenvalues of S, S. Notably, at high marker densities, when δ = 0, The form of the relationship matrix proposed by Z by subtracting ijz is the jth SNP in the ith individuals, jkz is the jth SNP in the kth individual when m is the number of markers. The diagonals are treated differently than the off-diagonals in this form.The method proposed by jz is the i-element vector of the jth SNP.The method proposed by The classical identity-by-state definition is  regress , ASREML   hybrids genotyped at m = 2,829 SNPs with H = 0.348 (δ from n = 599 wheat (Triticum aestivum) fully inbred lines  with an independent model. Third, we analyzed data from n = 1,814 stock mice (M. musculus) for body mass index (BMI), body length, and weight and genotyped for m = 10,346 SNPs  ecotypes phenotyped for the mean (μ) and SD of flowering time under 10°C (FT10) and 16°C (FT16) and genotyped at m = 193,697 SNPs  population made available by PIC (a Genus company) with n = 3,534 entries genotyped at m = 52,843 SNPs , but the accuracy (bias) did not improve. It has been demonstrated ad nauseam that increasing n increases precision or lowers the sampling variance of the estimates but does not eliminate bias (H increased (H that impacted the precision of genomic heritability estimation did not affect H increased for high heritability traits and precision worsened as H increased for low heritability traits. For traits where The precision (variance) improved by increasing the population size  , average and hg2 .K, i.e. K that only deviated from n), whereas we used We found that the normalized variance . KGN, inulations . This woH = 0.5 by design or happenstance. It may be that the only reference population that is concretely defined is the sample population. In connection to Inbreeding changes the patterns of among and within entry genomic variance and drives deviations from HWE . In genoArabidopsis, or inbred per se evaluations in hybrid crops, such as maize, tomato, rice, the covariance among marker effects increases. K, which is taken into account using ASV.When the study populations are entirely, or partially, inbred as in wheat,  effects . We beli1 hybrids, unstructured GWAS populations, and animal herds or flocks  and exists even for enormous data sets. We derived a new relationship matrix, The interpretation of genomic variance and heritability estimates was systematically affected by the available methods used to estimate n yield more precise estimates of key variance components in research programs , which is equal to s = 0). While s = –1 yields more stable estimates of s for each locus.We did not explore differences that arise from population structure or rare alleles, which is a limitation to our simulation approach  and other forms of ted GRMs ; Table 1https://doi.org/10.5281/zenodo.6211739).The input and output data from simulations and analyses have been deposited, along with the code for the simulations, in a public Zenodo repository (


Pregnancy losses in dairy cattle result in impaired animal health and welfare, as well as economic losses due to increased culling, reduced milk production, calf losses, and increased reproductive costs, among others. Advances in the last few decades have allowed the dairy industry to make significant progress in reproductive efficiency, but pregnancy losses continue to be an unresolved problem. The origin of abortions can be infectious disease, metabolic disorders, heat stress, and a genetic predisposition among many others. We have developed genomic predictions (Z_Abort) to identify Holstein dairy cows with a greater risk of abortion. This allows dairy producers and veterinarians to select more productive and profitable cows. The objectives of the study were to (1) describe the development of the genomic predictions for cow abortions in lactating Holstein dairy cattle based on producer-recorded data and ssGBLUP methodology and (2) evaluate the efficacy of genomic predictions for cow abortions in commercial herds of US Holstein cows using data from herds that do not contribute phenotypic information to the evaluation. The results of the present study show that the genomic predictions for cow abortion trait (Z_Abort) can effectively predict the risk of abortion of lactating Holstein dairy cows and, hence, allow genetic selection towards healthier and more profitable cows.p < 0.0001). The inclusion of cow abortion genomic predictions in a multi-trait selection index would allow dairy producers and consultants to reduce the incidence of abortion and to select high-producing, healthier, and more profitable cows.Abortion in dairy cattle causes great economic losses due to reduced animal health, increase in culling rates, reduction in calf production, and milk yield, among others. Although the etiology of abortions can be of various origins, previous research has shown a genetic component. The objectives of this study were to (1) describe the development of the genomic prediction for cow abortions in lactating Holstein dairy cattle based on producer-recorded data and ssGBLUP methodology and (2) evaluate the efficacy of genomic predictions for cow abortions in commercial herds of US Holstein cows using data from herds that do not contribute phenotypic information to the evaluation. We hypothesized that cows with greater genomic predictions for cow abortions (Z_Abort STA) would have a reduced incidence of abortion. Phenotypic data on abortions, pedigree, and genotypes were collected directly from commercial dairy producers upon obtaining their permission. Abortion was defined as the loss of a confirmed pregnancy after 42 and prior to 260 days of gestation, treated as a binary outcome , and analyzed using a threshold model. Data from a different subset of animals were used to test the efficacy of the prediction. The additive genetic variance for the cow abortion trait (Z_Abort) was 0.1235 and heritability was 0.0773. For all animals with genotypes , mean reliability was 42%, and genomic predicted transmitting abilities (gPTAs) ranged from −8.8 to 12.4. Z_Abort had a positive correlation with cow and calf health traits and reproductive traits, and a negative correlation with production traits. Z_Abort effectively identified cows with a greater or lesser risk of abortion (16.6% vs. 11.0% for the worst and best genomics groups, respectively;  Reproductive success is one of the main drivers of profitability in dairy herds. Every day a cow remains non-pregnant beyond the established voluntary waiting period results in reduced profit. Pregnancy loss has a substantial negative impact on reproductive efficiency and, therefore, on-farm profitability . The ComIn the last few decades, advances in the understanding of reproductive physiology, the development of new reproductive management strategies, and genetic selection have allowed the dairy industry to drastically reverse a negative trend and increase pregnancy rates . DespiteTM (DWP$) index in 2016. DWP$ is an economic multi-trait selection index that was formulated to estimate the potential lifetime profitability an animal would generate under dairy economic conditions in the United States and includes cow and calf wellness, production, fertility, functional type, longevity, livability, calving ability, and milk quality traits [Considering the economic impact of pregnancy losses discussed in the previous paragraphs, the development of a multi-trait selection index that includes abortion risk would help select and breed more profitable cows. Selection indices allow dairy breeders and producers to select animals based on a combination of different traits, each of which receives a relative weight. Selection indices provide a way to combine information about many traits into a single number that can rank animals and inform breeding decisions. Initially, selection indices were built accounting only for production traits, hence indirectly selecting against fertility and health traits ,25 due ty traits ,27. ThisThe objectives of this study were to (1) describe the development of the genomic predictions for cow abortions in Holstein dairy cattle based on producer-recorded data and ssGBLUP methodology and (2) evaluate the efficacy of genomic predictions for cow abortions in commercial herds of US Holstein cows using data from herds that do not contribute phenotypic information to the evaluation. In the current study, we hypothesized that cows with the highest genetic risk for abortion would have a higher phenotypic incidence of abortion.Data from 1991 to date were available from 279 herds from 24 states in the USA with an average of 13,759 phenotypic records per herd. Signed consents were obtained from herd owners, and herds were not monitored or economically compensated by Zoetis. Herd performance and pedigree information was retrieved from the on-farm herd management software.The methodology used in this study was similar to that reported in McGovern et al. . The ZoeSimilar to McGovern et al.  and descZ_Abort) was defined as the loss of pregnancy between 42 and 260 days of gestation. Animals having recorded abortions before 42 days of pregnancy were removed from the data. Abortions recorded after 260 days of gestation were considered full-term pregnancies and the animals were defined as healthy. To be considered as aborted, a cow must have had a breeding event followed by a positive pregnancy diagnosis and a recorded abortion event. Healthy animals must have been confirmed pregnant and have reached at least 260 days of gestation without an abortion event. Animals sold or died before having an opportunity to reach 260 days of pregnancy were removed. Abortion was treated as a binary event . Only one abortion event per lactation was considered. Further, each animal was required to have a known service sire, as well as an estimated 305 days ME milk yield and days open within biological limits.The trait for cow abortion (Contemporary groups (HYS) were formed by combining herd, year, and season of calving, considering 4 seasons within each calving year: winter (December–February), spring (March–May), summer (June–August), and Fall (September–November). If within a herd by year and season of calving (HYS) group there were not at least twenty records and at least one recorded abortion event the group was omitted from the analysis because it was assumed that the herd did not record abortions at all or did not record them during that time period.β is the vector of fixed effects, with the corresponding incidence matrix X; fixed effects included parity , breed composition of the embryo , and the linear covariates of milk yield and days open; h is the random herd–year–season effect, where h ~ N, with the variance hσ2; s is the random effect of the service sire, with s ~ N; a is the random animal effect, with a ~ N, where aσ2 is the additive genetic variance and H is the pedigree relationship matrix augmented using genotypes; p is the random effect of the permanent environment with p ~ N, where pσ2 is the permanent environment variance, and e is the residual, where e ~ N. hZ, aZ, and pZ are incidence matrices corresponding to the random effects of herd–year–season, animal, and permanent environment, respectively; and I is the identity matrix.The analyses for the present study were conducted largely as described by Gonzalez-Peña et al. ; the folA−1, was replaced by the inverse of the H matrix that combines pedigree and genomic relationships [A−1 is an inverse of the pedigree relationship matrix, G−1 is an inverse of the genomic relationship matrix and A22−1 is an inverse of the pedigree–relationship matrix for genotyped animals only. The ‘algorithm for proven and young animals’ (APY) was applied [Variance components were estimated using the program THRGIBBS1F90 version 2.108 from the BLUPF90 family  without ionships ,32: (2)H applied . The pro applied  for detaThe transformation from raw EBVs (solutions from the CBLUP90IOD2 program) to predicted transmitting abilities (PTAs) was described in detail by McGovern et al. . BrieflyFor the purposes of this study, (1) the Z_Abort STA, its phenotypic correlations, and genetic relationships with other traits were estimated, (2) the economic value of the Z_Abort trait as it relates to its contributions to a dairy animal’s lifetime profitability was estimated , and (3) the STA for Z_Abort was multiplied by its corresponding economic weight, alongside all other traits in the lifetime merit selection index (DWP$ index), which were then summed together to determine an animal’s overall selection index value ,34.The efficacy of Z_Abort predictions was established using a subset of animals that did not contribute phenotypes to the genetic evaluation. Data from 6922 females  belonging to 5 commercial herds from the USA with good record-keeping practices for abortion events  were included. p < 0.05. The cost of an abortion was assumed as USD 555 [Importantly, Z_Abort STA predictions for the selected animals (lactations 1 to 4) were generated from phenotypic data available on 31 December 2012 to ensure that an animal’s own performance data were not contributing to the genetic evaluation and STAs would, in effect, be those of a heifer. Genomic predictions for cow abortion were used to rank animals within herd and birth year and season and assign them to quartiles based on their Z_Abort STA  similar to what was reported in McGovern et al. . As a siThe frequencies of reproductive Holstein haplotype (HH) carriers for AI sires and for cows within each Z_Abort STA quartile were calculated for HH0-HH5. The latter was analyzed using PROC GLIMMIX from SAS  with a binomial distribution and logit link function including Z_Abort STA quartile as a fixed effect. The frequency of the mating of two carriers for a given HH was calculated for cows that did and did not abort for cows bred to AI sires with known HH status . The number of phenotypic records, genotypes, animals in the evaluation, and the incidence of abortion as of April 2022 are described in Variance components estimations for cow abortion in Holsteins are shown in The means, standard deviations, and reliabilities of gPTAs, STAs, and reliabilities for Z_Abort are presented in The product–moment (Pearson) correlations of genomic predictions for cow abortion (Z_Abort STA) with predictions for the lifetime merit selection index (DWP$ index) and other Zoetis wellness and fertility traits, and the correlations of Z_Abort with economically important traits and indexes in the national genetic evaluation produced by the Council on Dairy Cattle Breeding (CDCB) are presented in p > 0.1) of milk production (305ME), the season of conception, type of semen used for breeding , or cow abortion group by lactation interaction on abortion incidence. Therefore, these effects were removed from the final model.A total of 6922 cows and 14,068 pregnancies were included in the analysis. The overall incidence of abortion was 12.8% . p < 0.0001). As shown in p < 0.05) abortion incidence, followed by the next quartile, and the best two groups were not statistically different. There was an effect of the lactation group  for the third and fourth than for first and second lactation cows. To better understand the added value of Z_Abort to the currently available fertility traits, we explored if there was any existing relationship between DPR gPTA and abortion incidence. We observed a significant effect of DPR gPTA quartile on abortion incidence , but the best genetic group was not different from the second worst group.The observed results demonstrated the association between the genetic prediction of cow abortion and phenotypic incidence of abortion. Differences in observed cow abortion  were statistically significant between Z_Abort genetic groups (p < 0.0001) and lactation (p < 0.0001) on the predicted probability of abortion, where the latter increased as Z_Abort decreased (There was an effect of Z_Abort STA (ecreased .p < 0.001) and was lesser (p < 0.05) in the best genetic group. The frequency of HH3 and HH4 tended to be affected by Z_Abort genetic group  (HH), we performed an analysis of the proportion of cows within each Z_Abort genetic group and AI sires that were carriers for HH0, HH1, HH2, HH3, HH4, and HH5. Results for HH6 were not available for cows at the time of the evaluation but no AI sire mates were carriers of this defect. Twenty-four cows were eliminated from this analysis because their HH results were not available, and their service sires were recorded as herd bulls. The frequencies of HH carriers for sires and the matings of carriers for cows that aborted and cows that did not abort are reported in Although genetic and genomic associations with abortion in cattle have been previously described in the literature ,23,35,36The additive genomic variance observed in this study was greater than previously reported by others for abortion and/or embryo loss ,35,36, wIncidences of abortion (42 to 260 days after AI) in the genetic evaluation 11.7%) and the validation population (12.8%) were similar to previous reports 1.7% and , but difThe influences of the HH defects in this study were minimal, with only four abortions involving mates of carriers. The low frequency of HH carriers among the genomically confirmed AI service sires, the lack of difference in the proportion of carriers among cows that did or did not abort, and the similarity in the frequency of carrier animals through Z_Abort quartiles for most HH allow us to assume that the abortion incidence was not influenced by the matings of HH carriers. Despite this, HH2 and HH4 were (or tended to be) less frequent in the best quartile for Z_Abort STA. This is not surprising because although HH need to be in a homozygous state to be lethal, the possibility that these markers are also related to some genes with an additive effect cannot be ruled out. Furthermore, we cannot disregard the possible existence of other unknown HH that could be associated with Z_Abort predictions.Genomic STA for Z_Abort showed a positive correlation with other wellness traits related to reproductive efficiency and animal health. The positive genetic correlation between reduced abortion risk and reduced risk of twin gestation has been previously described by our group , and a pInterestingly, although previous studies have shown an increase in pregnancy loss in cows suffering from mastitis ,45 and wThe positive genetic correlation of Z_Abort with DPR and CCR gPTA was relatively low, but it should be noted that the correlations are not adjusted for the reliability of the predictions (42% for Z_Abort). The magnitude of the correlation between DPR gPTA and Z_Abort STA and the observation that the maximum overlap between quartiles is 8%  suggest There is strong evidence supporting that high-yield dairy cows have lesser plasma concentrations of progesterone , which iThe negative correlations with production traits might be a drawback for including Z_Abort as a selection trait in a genetic improvement program. Including Z_Abort (5% weight) in the DWP$ index, along with other fertility and health traits, resulted in positive selection towards cows with fewer abortions. Estimated response to selection for DWP$ (updated April 2022) shows that an increase of 1 SD would result in an increase of 219 pounds for Milk gPTA, 20 pounds for Fat gPTA, and 11 pounds of Protein gPTA coupled with an increase of 0.19 in Z_Abort STA . ConversThe magnitude of the improvement gained in Z_Abort through DWP$ might seem marginal if only the female selection is considered. Having the abortion trait predictions for sire selection will likely lead to the removal of some outliers with poor genetic merit and the impact could be of greater magnitude. Over the last decades, advancements in reproductive management and genetic selection have allowed the dairy industry to reverse a negative trend in reproductive performance and increase pregnancy rates. Despite this, controlling pregnancy loss and abortion are still a pendent assignment. The evaluation presented and validated in the present study provides the industry with a new tool that could greatly impact reproductive efficiency and cow profitability for future generations of dairy cows. To assess the impact of this trait, we performed a simulation analysis using the model described by DeVries  in whichResults from the current study provide additional evidence that on farms, producer-recorded data can be successfully used for performing genetic evaluations in Holstein cows. Furthermore, the results support our hypothesis that the newly developed genomic predictions can effectively identify cows with high, low, and intermediate risks of abortion within a Holstein cattle population. This indicated that animals with higher Z_Abort STA predictions had lower observed abortion values than animals with lower Z_Abort STA predictions. It follows that decisions made in selection, management, and breeding to increase the average Z_Abort STA value within a given herd would be expected to decrease average abortion incidence. Decreasing the incidence of abortion through direct selection on genetic prediction for abortion (Z_Abort) can play an important role in a comprehensive reproductive management strategy for dairy operations. Including the Z_Abort trait in selection indexes and programs, coupled with state-of-the-art reproductive and health management, can help the dairy industry overcome the difficult challenge of reducing pregnancy loss in high-yield dairy cows.


Vitis vinifera L.) has only been evaluated in non-breeding contexts mainly through cross-validation within a single population. We tested across-population genomic prediction in a more realistic breeding configuration, from a diversity panel to ten bi-parental crosses connected within a half-diallel mating design. Prediction quality was evaluated over 15 traits of interest , for both the average genetic value of each cross (cross mean) and the genetic values of individuals within each cross . Genomic prediction in these conditions was found useful: for cross mean, average per-trait predictive ability was 0.6, while per-cross predictive ability was halved on average, but reached a maximum of 0.7. Mean predictive ability for individual values within crosses was 0.26, about half the within-half-diallel value taken as a reference. For some traits and/or crosses, these across-population predictive ability values are promising for implementing genomic selection in grapevine breeding. This study also provided key insights on variables affecting predictive ability. Per-cross predictive ability was well predicted by genetic distance between parents and when this predictive ability was below 0.6, it was improved by training set optimization. For individual values, predictive ability mostly depended on trait-related variables (magnitude of the cross effect and heritability). These results will greatly help designing grapevine breeding programs assisted by genomic prediction.Crop breeding involves two selection steps: choosing progenitors and selecting individuals within progenies. Genomic prediction, based on genome-wide marker estimation of genetic values, could facilitate these steps. However, its potential usefulness in grapevine ( Breeding for perennial species is mostly based on phenotypic selection and is hindered by cumbersome field trials and the long generation time. Genomic prediction (GP), based on genome-wide prediction of genetic values , has beeBreeding schemes typically involve first the choice of parents  and then the selection of offspring within crosses. GP is adapted both for predicting cross mean and for ranking genotypes within a cross (Mendelian sampling). These steps correspond to the components of the predictive ability (PA) of GP. It is indeed defined as the sum of cross mean and Mendelian sampling terms, as detailed in Werner et al. .Cross mean is the sum of the breeding values of parents if allelic effects are only additive, but in practice some deviation may result from dominance or epistasis . So far,In contrast, the prediction of genetic values within a cross (Mendelian sampling), has been widely studied, both with simulated and real data, and various parameters affecting PA have been pointed out, including the statistical method used , the comVitis vinifera subsp. vinifera), very few authors have assessed the potential interest of GP. Viana et al. [V. vinifera accessions to perform both GP and genome-wide association study (GWAS) for 33 phenotypes. More recently, Brault et al. [In grapevine  subpopulation from the diversity panel , which w2) for 15 traits related to yield, berry composition, phenology and vigour. Overall H2 values were medium to high, ranging from 0.49 for mcwi  in the half-diallel to 0.91 for mbw in the panel . This might be due to the difficulty to phenotype this specific trait because of the presence of lateral wings in some individuals.We then investigated broad-sense heritability values . Predictive ability (PA) was assessed as Pearson’s correlation between the observed mean genotypic value per half-diallel cross and the one predicted based on parental average genotypes . Three snbclu and vigour . Unlike for traits, no cross had constantly high or low PA , with an overall average of 0.36. Most often, PA was lower in scenario 1b than in scenario 1a, likely because no full-sibs were included in the training set. However, there were several cases with PA values similar or higher in scenario 1b for one parental TS compared to scenario 1a. RR method produced the best PA in 80% of the 30 combinations (2 parents x 15 traits).In scenario 1b , there wvigour, clucomp and maltar.ripe displayed a particularly marked decrease. On the opposite, mcwi and vermatu reached equivalent PA values in both scenarios. RR provided the best PA for 11 traits.In scenario 2 , overallWhen only WW genotypes from the diversity panel were used as TS, PA was lower by 0.05 compared to scenario 2 .We sought those variables affecting the PA values observed above, both for prediction of cross mean and Mendelian sampling. We then implemented training set (TS) optimization in an attempt to increase PA.In scenario 2, per-cross PA was highly correlated (0.85) with the cross parents’ additive genomic relationship . No suchSince variation in per-cross PA for scenario 2 was extremely large, from −0.15 for GxCS to 0.73 for SxPN , we implThe variable that most affected per-trait PA was the  2 0.53, .No other explanatory variable displayed any significant impact despite a fairly high correlation with per-trait or per-cross PA, which could be due to low sample sizes .2, per-cross H2 and the proportion of non-segregating markers. Surprisingly, half-diallel overall H2 was not selected in scenario 2 with either RR or best method, while it had a strong effect in other modalities.To model Mendelian sampling PA for each scenario and method selected for each trait , we applied multiple linear regression on six to nine variables depending on the scenario, as detailed in Material and Methods. The highest coefficient of determination (37.8%) was obtained in scenario 1a with the best method . Coeffic2, but differed in scenario 2 in which more variables were selected. Overall, most of the relative importance came from variables related to the trait and not to the genetic composition of TS or validation set (VS).The selected variables were quite similar between scenarios 1a and 1b, with a high effect of half-diallel overall and per-cross HWe also calculated individual PA with optimized TSs derived from the diversity panel . However2 and phenotypic structure (subpopulation or cross effects on phenotypic data)  with 15 weakly related traits with variable levels of Hic data) , (ii) inFor the prediction of cross mean, overall PA was 0.45 in scenario 2, average per-cross PA of 0.36, while the average per-trait PA was twice as high (0.6) . In studmbw was 0.56, whereas in the present study, we obtained 0.35 in the Grenache x Syrah progeny (n = 59). We further investigated such discrepancy, and found it related to a sampling bias due to the small VS size in Flutre et al. [For the prediction of Mendelian sampling, overall average PA was lower than overall PA for cross mean in scenario 2 . Yet, Mendelian sampling PA was still quite high, considering that TS was essentially unrelated to VS for most genotypes and with no first-degree relationship with predicted progenies. When WW subpopulation was used as TS , PA was e et al.   was consistent with those described on fruit perennial species where individual prediction was performed with a TS not directly related to the VS . In o et al.  reportedo et al.  reportedo et al.  found PAo et al. , as suggo et al. , while hSeveral factors may influence Mendelian sampling PA in our study compared to others. Among potential inflating factors, we can mention a slight over-representation of phenotyped individuals from the WW panel subpopulation, to which four out of the five parents of the half-diallel belong, leading to a higher genetic relationship between effective TS and VS. Factors potentially decreasing PA could be differences between TS and VS experimental designs since the diversity panel and the half-diallel were not phenotyped on the same years, had different plant management systems  and were planted a few kilometers apart. Nevertheless, for most studied traits, two years of phenotyping were used to compute genotypic BLUPs, which could at least compensate for differences between years, usually referred to as the millesime effect.We focused on PA obtained with the best method between RR and LASSO, to take into account the part of variability among traits associated with genetic architecture. Indeed, LASSO is supposed to be better adapted to traits underlined by few QTLs, while RR would yield better PA for highly polygenic traits . HoweverStudying both per-cross and per-trait PA allowed us to characterize different variables affecting PA. Regarding the other factors affecting PA, for cross mean prediction in scenario 2, we found no other variable significantly affecting per-trait PA . ConversFor the prediction of Mendelian sampling, the variables explaining individual PA in scenario 2 were quite different from those explaining cross mean PA. Trait-related variables had a large impact on individual PA: half-diallel overall and per-cross heritability, but also the relative variance of cross effect . SurprisAcross-population GP with model training in a diversity panel appeared to be promising in grapevine breeding for some traits and crosses, particularly for parent choice .The usefulness of GP for better selecting parents for future crosses can be at first assessed by the low overall correlation between mean parental genotypic values (BLUPs) and mean offspring BLUPs  genotype of interest with dense genotypic data could be used for this purpose as exemplified with the half-diallel, since its five parents were not part of the diversity panel.Since our results show that prediction of cross mean can be quite accurate and useful in scenario 2, we decided to go one step further and implemented cross mean prediction for all 38 781 possible crosses between the 279 genotypes of the diversity panel, based on parental average genotypes  and on mBased on our results, the following improvements could be tested: i) increase SNP density , 37 and Predicting cross variance could also prove useful to design the offspring selection step, more specifically for choosing the number of offspring to test or produce for a given cross. Depending on the available funds and breeding program, a breeder may want to select crosses with high genetic variance, in order to maximize the probability to generate top-ranking genotypes. Conversely, choosing a cross with low variance could limit the risk of breeding poor genotypes.We implemented GP in grapevine in a breeding context, i.e. across populations, on 15 traits, in ten related crosses, and obtained moderate to high PA values for some crosses and traits, thus showing GP usefulness in grapevine. Never before had genomic prediction been implemented for so many traits and crosses simultaneously in this species. We showed that per-cross PA was strongly correlated with the genetic distance between parents, whereas Mendelian sampling PA was largely determined by trait-related variables, such as heritability and the magnitude of the cross effect.V. vinifera cultivars: Cabernet-Sauvignon (CS), Pinot Noir (PN), Terret Noir (TN), Grenache (G) and Syrah (S) [The half-diallel consists of 10 pseudo-yrah (S) . Each faThe diversity panel consists of 279 cultivars selected as maximizing genetic diversity and minimizing kinship among cultivated grapevine. Grapevine genetic diversity is highly heterozygous with a weak to moderate structuration into three subpopulations: WW (Wine West), WE (Wine East) and TE (Table East) [The half-diallel was created in 1998 at INRAE Montpellier, grafted on Richter 110, and planted in 2005, at the Institut Agro experimental vineyard “Le Chapitre” in Villeneuve-lès-Maguelone (Southern France). The progenies were planted in two randomized complete blocks, with plots of two consecutive plants per offspring per block.The field design for the diversity panel was previously described in Flutre et al. . Brieflymal.ripe), tartaric (tar.ripe) and shikimic acid (shik.ripe) concentrations in shiktar.ripe) and malic / tartaric acid ; morphological traits with mean berry weight  measured on 100 random berries, mean cluster weight , mean cluster length  and mean cluster width , measured on 3 clusters, number of clusters (nbclu) and cluster compactness (clucomp) measured on the OIV semi-quantitative scale; phenology traits with veraison date , maturity date corresponding to berries reaching 20° Brix  and the interval between veraison and maturity ; vigour , derived as the ratio between pruning weight and the number of canes. Phenotypic data were collected between 2013 and 2017 for the half-diallel and in 2011–2012 for the diversity panel. There was a slight over-representation of phenotypes from the WW subpopulation because of fertility issues in WE and TE subpopulations. Distribution of raw phenotypic data for both populations are shown in We studied 15 traits in both trials: berry composition with malic , from wFor the half-diallel, we used genotyping-by-sequencing (GBS) SNP markers derived by Tello et al. , 622 of Finally, we only retained the 32 894 SNPs common to both populations  broad-sense heritability for genotype-entry means  as:\docWe also estimated broad-sense heritability per cross . For that, we applied the same selected model, but removed all effects involving cross. Then, we estimated variance components within each cross, and heritability with the same formula, after removing variances involving cross.All information on analyses of phenotypic data and heritability of the half-diallel is detailed in We used the genotypic values previously estimated in Flutre et al.  with a sFor each of the two populations, genotypic BLUPs were scaled to a variance of 1, allowing comparison among traits.Marker effects were estimated using two methods to take into account varying genetic architecture among the traits studied. Ridge regression (RR) , best adWe assessed prediction within half-diallel crosses under three different training scenarios :Scenario 1a: whole half-diallel prediction. We applied random outer 10-fold cross-validation over the whole half-diallel population. In each fold, 90% of the phenotyped offspring were used as the training set (TS) and the remaining 10% as the validation set (VS). Cross-validation was replicated ten times.Scenario 1b: half-sib prediction. For each half-diallel cross used as VS, we trained the model with the three half-sib crosses of each parent in turn, thus predicting each cross twice.Scenario 2: across-population prediction. We used the whole diversity panel as TS and each half-diallel cross as VS. We also tested a variation of this scenario by using only genotypes from WW subpopulation as TS.In order to account for the effect of genetic architecture, we applied both RR and LASSO methods for each trait and cross and kept the best PA, for both cross mean and within cross individual prediction.Cross mean PA was assessed as Pearson’s correlation between the average value of observed total genotypic values (sum of genotype and cross BLUPs for each offspring) for each cross, and the mean predicted genotypic value per cross, calculated in two ways, as:average predicted value over all offspring of the cross. In scenario 1a, each offspring was predicted 10 times, thus we also averaged the predicted value over the 10 replicates.predicted value for the parental average genotype, defined at each locus and for each cross as the mean allelic dosage according to the expected segregation pattern based on parents’ genotypes .Genotypic values predicted with these two modalities were highly correlated (above 0.98) in the three scenarios and for the two methods , for each trait (per-trait PA) and for each cross (per-cross PA).We measured PA within each cross in each scenario as Pearson’s correlation between observed total genotypic values and predicted genotypic values.2 of correlated regressors with the R-package relaimpo [We tested the effect of several variables on within-cross individual PA, in each scenario. We built a multiple linear regression model with PA per trait x cross combination as the response variable and as predictors, a set of variables common to all three scenarios plus specific variables for scenarios 1b and 2. Common variables were: the proportion of non-segregating markers in the cross , overalle et al.  and Table et al. , which arelaimpo .2) of the model.The percentage of trait variance within the diversity panel explained by subpopulation  was evaluated by fitting for each trait the following linear model: PEVmean) and CDmean (based on the coefficient of determination) [MeanRel), as the mean additive relationship between each genotype in TS and all genotypes in VS. Each optimized TS was specific to a cross. The realized additive relationship based on marker data was estimated using the rrBLUP R-package [We tested three methods for optimizing TS in scenario 2, for both cross mean and within-cross individual prediction. We used the STPGA R-package  to impleination) . Moreove-package  with the-package . For eacMESO@LR-Platform at the University of Montpellier. Partial funding of Charlotte Brault’s PhD was provided by ANRT , IFV (Institut Français de la Vigne et du Vin) and Inter-Rhône .We thank Charles Romieu for his help on the acquisition of phenotypic data as well as Philippe Châtelet and Morgane Roth for their suggestions on the text. This work has been realized with the support of the SouthGreen platform and VS, AD, PT, TF, JPP and LLC conceived the idea of the study and contributed to funding acquisition; TP, PF, AD and JPP obtained the phenotypic data used in this work; CB performed and interpreted results; AD conceived the half-diallel population; PT is the PhD supervisor of CB; CB wrote the original draft, which was reviewed and edited by all authors. All authors read and approved the final manuscript.https://doi.org/10.15454/PNQQUQ.All analyses were conducted using free and open-source software, mostly R. Phenotypic and genotypic data, R scripts and result tables are available at The authors declare that they have no conflict of interest. The authors declare that the experiments comply with the current laws of the country in which they were carried out.Horticulture Research online.Web_Material_uhac041Click here for additional data file.


The use of genomics has improved response to selection for functional traits with low heritability such as fertility traits. Much of the work on fertility traits has been performed through use of genome-wide association studies (GWAS) to identify genetic loci associated with reproductive traits. Under a GWAS approach, the assumption is that the markers on the panel are in linkage disequilibrium with causative mutations. In many cases, identification of the causative mutation is difficult because an associated genetic marker can be in intergenic regions and can be in linkage disequilibrium with variants in several nearby genes. Another approach is to identify candidate genes using knowledge of the biological pathways controlling a trait to search for single nucleotide polymorphism (SNP) in genes in those pathways. This should reveal putative causative markers responsible for genetic variation in biological function, and it is expected that the marker will be more strongly associated with a trait than one in linkage disequilibrium. An example of how a series of candidate gene studies demonstrate that identification of markers in genes involved in reproductive processes can lead to discovery of additional markers associated with genetic variation in reproductive traits is presented. In addition, the inclusion of candidate markers for fertility can improve reliability of genetic estimates for fertility traits, and the repeatability of the effects across a separate population of animals gives confidence that association elucidated by this set of markers is likely to be real. More importantly, the use of candidate genes can provide insights into the biology underpinning genetic variation in fertility, and that this understanding can lead to physiological interventions to improve reproductive function. Fertility is a complex trait and, it is regulated in part by genetics. In the dairy cow, genetic merit for fertility and production are negatively correlated ranging from 0.35 - 0.60 . NeverthMost reproductive traits are controlled by many genes, each of which has a small effect. This is evident from genome wide association studies (GWAS) in which genetic variation in a trait is partitioned into associations with individual single nucleotide polymorphism (SNP). The low heritability characteristic of reproductive traits is indicative that only a small proportion of phenotypic variance is due to additive actions of individual genes and that reliability estimates of breeding values are prone to be low. It does not, however, mean that reproductive traits are not under genetic control, many specific genes have been identified that contain mutations that are associated with reproductive function. Furthermore, clear differences in fertility have been found between genetic lines of animals. In Holstein, for example, cows with higher genetic merit for fertility had fewer services per conception, and shorter intervals from calving to conception compared with cows with low genetic merit for fertility , cow conception rate (CCR) and heifer conception rate (HCR). DPR is defined as the percent of cows eligible for breeding that become pregnant in each 21-day period . Conceptually, DPR is the product of estrous detection rate (the percent of cows in estrus that are detected in estrus) and pregnancy rate per insemination (the percent of inseminated cows that become pregnant). Practically, DPR is calculated from the term days open, which is the interval from calving to conception. Predicted transmitting ability (PTA) for DPR and days open are nearly linear function of each other. An increase of 1% in PTA for DPR equals a decrease of 4 days in the PTA for days open . As of December 2017, there were 102,499,615 SNP and 10,462 other genetic structural variations (>50 base pairs) including deletion/insertions, copy number variant, duplications, inversions, translocations and complex chromosomal arrangements  was associated with increased ovulation rate in daughters of bulls carrying the haplotype. After identification of a deficit of homozygotes for a JH1 haplotype associated with reduced fertility in Jersey using GWAS, sequencing performed in Jersey bulls revealed a nonsense mutation in CWC15 which is embryonic lethal, as no homozygous individuals are present in the population , studied the involvement of SNP in FGF2 on embryonic survival because of the role of the FGF2 in regulation of IFNT expression in the trophectoderm  and 12 SNP previously associated with fertility in the literature including More recently, SNP with significant associations with fertility found by There was a modest increase in reliability of genetic estimate for DPR (0.2%) when the SNP were included in the markers currently used for the national genetic evaluation system . From the 12 genes, only two: WBP1 and PARM1 had increased expression at the moment of genome activation. Since the previous associations were based on the paternal SNP genotype, these were the genes most likely to represent actual effects of the SNP on embryonic development. Further evaluation showed that the SNP in WBP1 caused changes in predicted protein structure. By reducing transcript abundance of this gene using Gapmer antisense oligonucleotides, it was revealed that WBP1 plays a critical in trophectoderm formation. WBP1 is a single transmembrane adaptor protein  in cells when exposed to high temperatures (HSPA1A/HSPA1L was high at the 2-cell stage in the bovine embryo, and when putative zygotes were exposed to heat shock or high oxygen conditions, those embryos inheriting the deletion mutation in HSPA1L had greater survival after being exposed to adverse conditions. Perhaps embryonic survival during heat stress could be improved by selecting for thermotolerant genotypes.Evidence was also provided that the SNP in the promoter region of eratures . In thisCOQ9, the use of candidate genes can provide insights of the biology underpinning genetic variation in fertility, and that this understanding can lead to physiological interventions to improve reproductive function.Taking all together, this series of studies demonstrated that identification of SNP in genes involved in reproductive processes can lead to discovery of additional markers associated with genetic variation in reproductive traits. Inclusion of these markers in current genomic evaluations also can increase reliability of genetic estimates for fertility. The fact that SNP effects were frequently repeated among two independent populations of animals and that phenotype as well as genotype was affected provides confidence that selection of these markers will improve genetic merit for fertility. As shown for the SNP in The introduction of genomic selection in dairy cattle has increased rates of genetic gain, particularly for low heritability traits such as fertility. The use of GWAS as a tool for genomic selection has been very successful in improving accuracy of genetic selection in dairy cattle. The pathway to choose for gene discovery will depend on several variants: available information of the phenotype or trait of interest, population size and overall goal of the work. Without previous knowledge of genes involved in the phenotype of interest, GWAS are a powerful tool to identify regions associated with the trait. This also could elucidate candidate genes for further study as GWAS by themselves are not designed primarily to illuminate the underlying biology of the studied phenotype. The use of candidate genes in turn, allow also to improve the SNP panels used for genetic evaluations, by finding markers with stronger associations with the traits of interest that can be included in genomic evaluation schemes. Furthermore, with the identification of candidate genes, functional studies involving gene editing or gene knockout modifications can be developed to understand the tight regulation of reproductive function in cattle. As genotyping cost decrease, more datasets and whole genome sequence data becomes available that can be used to validate markers in different populations; and in the case of sequencing, identifying causal mutations of the phenotypes of interest.


FROH) and the Spearman coefficient between FROH and reproduction traits. We completed a mixed linear model association analysis to identify the effect of high-frequency copy number variation  on Bama Xiang pig reproductive traits using TASSEL software. Across eight chromosomes, we identified 29 significant single nucleotide polymorphisms, and 12 genes were considered important candidates for litter-size traits based on their vital roles in sperm structure, spermatogenesis, sperm function, ovarian or follicular function, and male/female infertility. We identified 9,322 ROHs; the litter-size traits had a significant negative correlation to FROH. A total of 3,317 CNVs, 24 CCNVR, and 50 HCNVR were identified using cnvPartition and PennCNV. Eleven genes related to reproduction were identified in CCNVRs, including seven genes related to the testis and sperm function in CCNVR1 (chr1 from 311585283 to 315307620). Two candidate genes (NEURL1 and SH3PXD2A) related to reproduction traits were identified in HCNVR34. The result suggests that these genes may improve the litter size of Bama Xiang by marker-assisted selection. However, attention should be paid to deter inbreeding in Bama Xiang pigs to conserve their genetic diversity.Litter size and teat number are economically important traits in the porcine industry. However, the genetic mechanisms influencing these traits remain unknown. In this study, we analyzed the genetic basis of litter size and teat number in Bama Xiang pigs and evaluated the genomic inbreeding coefficients of this breed. We conducted a genome-wide association study to identify runs of homozygosity (ROH), and copy number variation (CNV) using the novel Illumina PorcineSNP50 BeadChip array in Bama Xiang pigs and annotated the related genes in significant single nucleotide polymorphisms and common copy number variation region (CCNVR). We calculated the ROH-based genomic inbreeding coefficients ( Bama Xiang pigs, an indigenous Chinese pig breed, are famous for their excellent meat quality and early maturation . Owing tAHR had a positive effect on reproduction traits. The copy number variation in GPER1 might be related to the litter size in the Large White pig breed  are a subtype of genomic structural variation ranging from 50 bp to several Mb in length. The copy number variation region (CNVR) is the area adjacent to the copy number with overlapping regions . The CNVig breed . Bovo etig breed  showed tSingle nucleotide polymorphism (SNP) arrays can genotype hundreds of thousands of SNPs distributed throughout the genome . Based oLitter size and teat number, which are the base index, are typically associated with economic benefits and production ability in the porcine industry. While the teat number has a medium level of heritability, the litter-size heritability is low. During breeding, the teat number trait increases with an increase in the litter-size trait , 20. LitFROH) of Bama Xiang pigs using SNP array data. We also performed CNV detection and CNVR-based association analysis of litter size and teat number of Bama Xiang pigs. We identified the genes in significant SNPs, ROH, and CNVR and provided the candidate genes associated with litter size and the teat number of Bama Xiang pigs. The information on the Bama Xiang pig can provide the development of the molecular mechanisms of litter size and teat number. Understanding the genetic basis of litter size and teat number in Bama Xiang pigs should help us improve their reproductive capacity.In this study, we completed the genome-wide association study (GWAS) and the ROH analysis to evaluate the genomic inbreeding coefficients  for genomic DNA extraction. Parity and teat number data from 297 sows  were also obtained to calculate phenotype statistics of 14 litter-size traits and five teat-number traits .Using a tissue DNA isolation mini kit , the genomic DNA was isolated from the ear tissue. Porcine SNP50 BeadChip  containing 51,315 SNPs was used to genotype the genomic DNA. The raw data were called using the GenomeStudio 2.0 software. Single nucleotide polymorphism arrays with call rates less than 0.9 or with minor allele frequencies of <0.05 were removed in PLINK, version 1.90. Single nucleotide polymorphism arrays without location information were also deleted. After quality control, 403 sows and 24,123 autosomal SNPs were used for analysis. Beagle, version 5.0, was used to impute missing alleles.For each trait, we implemented GWAS using a univariate linear mixed model in GEMMA. The GWAS model was as follows :y is an n-vector of reproduction traits, W is a matrix of fixed effects including three principal constituents and the parity effect, x is the SNP genotype, α and β are the corresponding coefficients, u is the random effect, ε is the random error, τ−1 is the variance of residual errors, λ is the ratio between the two variance components, K is the kinship matrix, In is the n × n identity matrix, and MVNn denotes the n-dimensional multivariate normal distribution. Thresholds for Bonferroni-adjusted genome-wide significance and suggestive significance were defined as –log10(p) = 5.68  and –log10(p) = 4.38 , respectively (Sus scrofa 10.2).where ectively –29. We dFROH for Bama Xiang pigs was estimated using the following formula  was used to annotate the traits related to the CCNVR.The CNVs were detected using cnvPartition 3.2.0 and PennCNV 1.0.5 software. As a plug-in software in GenomeStudio 2.0, cnvPartition detected different copy numbers using Gaussian distribution by Logp = 0.001 (0.05/50) and p = 0.02 (1/50) as the significance thresholds and suggestive significance thresholds, respectively , including ABN (−0.28), BN1 (−0.19), BN2 (−0.19), BN3 (−0.25), BN4 (−0.15), BN5 (−0.20), BN6 (−0.23), BN8 (−0.17), BN9 (−0.22), MAXBN (−0.22), and the minimum numbers of birth (MINBN) (−0.25) . The number of ROH for 0–6, 6–12, 12–24, and 24–48 Mb was 8,369 (89.77%), 831 (8.91%), 110 (1.18%), and 12 (0.13%), respectively. The genomic inbreeding coefficients per sow ranged from 0.0013 to 0.24, with the average genomic inbreeding coefficient as 0.036 ± 0.024 (mean ± SD). A total of 12 litter-size traits had a significantly negative relation with  (−0.25) . The genp < 0.05) in the cilium movement and outer dynein arm assembly pathway. We located 637 QTLs in CCNVRs, including 26 average backfat thickness QTLs, 21 backfat at last rib QTLs, and 17 loin muscle area QTLs  related to reproduction traits located in HCNVR34.With cnvPartition and PennCNV software, we got 242 CNVRs in Bama Xiang pigs, including 50 HCNVR . After e HCNVR34 . The delMAPK14 was the only gene that was not associated with a specific sex; MAPK14 promotes phosphorylation and is therefore involved in both male and female reproduction  mice are sterile because haploid differentiation becomes impaired  with asthenozoospermia  contained NEURL1 and SH3PXD2A gene may be the candidate CNVR and candidate genes, which is related to litter size and teat number in Bama Xiang pigs.We identified 3,317 CNVs, 242 CNVRs, and 13 CCNVRs in Bama Xiang pigs. A total of 11 genes related to reproduction, TUBB4B , STPG3 , the National Natural Science Foundation of China (81860150), and the Science and Technology Major Project of Guangxi (Guike-AA17292002).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.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.