Genomic selection (GS) can accelerate variety improvement when training set (TS) size and its relationship with the breeding set (BS) are optimized for prediction accuracies (PAs) of genomic prediction (GP) models. Sixteen GP algorithms were run on phenotypic best linear unbiased predictors (BLUPs) and estimators (BLUEs) of resistance to both fall armyworm (FAW) and maize weevil (MW) in a tropical maize panel. For MW resistance, 37% of the panel was the TS, and the BS was the remainder, whilst for FAW, random-based training sets (RBTS) and pedigree-based training sets (PBTSs) were designed. PAs achieved with BLUPs varied from 0.66 to 0.82 for MW-resistance traits, and for FAW resistance, 0.694 to 0.714 for RBTS of 37%, and 0.843 to 0.844 for RBTS of 85%, and these were at least two-fold those from BLUEs. For PBTS, FAW resistance PAs were generally higher than those for RBTS, except for one dataset. GP models generally showed similar PAs across individual traits whilst the TS designation was determinant, since a positive correlation (R = 0.92***) between TS size and PAs was observed for RBTS, and for the PBTS, it was negative (R = 0.44**). This study pioneered the use of GS for maize resistance to insect pests in sub-Saharan Africa. Insect damage on maize plants and stored grains potentially impedes food security in Africa ,2,3. TheThe complex nature of insect resistance traits makes PS slow and expensive, and thus, difficult to implement, especially for resource-constrained breeding programs . ApplicaSeveral statistical and machine learning GP models with various strengths and weaknesses have been developed to adapt to different contexts that are partly influenced by the genetic architecture of traits  and reproductive classes of plants  ,35,36. Thttps://kdcompute.igss-africa.org/kdcompute/home), an online database developed by Diversity Array Technologies  for the analysis of DArT marker data, presents great interest for this purpose. It hosts a suite of parametric, semiparametric, and nonparametric GP methods that can be run simultaneously on genotype-phenotype datasets.Representative parametric methods are ridge regression best linear unbiased predictors (RR-BLUP)  and genoAdditional factors that influence PAs are the different sizes of the training sets (TSs) and breeding sets (BS) and their genetic relationships, the number of markers used to estimate genomic estimated breeding values (GEBV) of lines, the population structure, and the extent of linkage disequilibrium ,31,41,60Furthermore, in maize, GPs were previously conducted using either genotypic best linear unbiased estimators (BLUEs) ,68,69 orThe panel used in this study consisted of 358 maize lines with diverse genetic and geographic backgrounds, and they were sourced from the National Crop Resources Research Institute , the International Institute for Tropical Agriculture , and The International Maize and Wheat Improvement Center . The panel consisted of 71 inbred lines developed for various purposes at NaCRRI; 28 and five stem borer (SB)-resistant inbred lines from CIMMYT ,13,14 anThe panel was planted and evaluated in three environments, at Mubuku Irrigation Experimental Station in Kasese, western Uganda in 2017 (316 lines) during the second rainy season (2017B) and the National Crop Resources Research Institute (NaCRRI), Namulonge, central Uganda in 2018 (92 lines) and 2019 (252 lines) both during the first rainy seasons . Detailed information on these locations is presented in Each combination of location and season was considered an environment, resulting in a total of three environments. An augmented experimental design was adopted in all three environments using six checks in 2017B, two in 2018A, and four in 2019A replicated in all the blocks. The experiments in 2017B, 2018A, and 2019A consisted of twelve, five, and ten blocks, respectively, containing the replicated checks and unreplicated lines and the experiment in 2018A was replicated twice.Genotyping of the panel and SNP quality were described in our previous study . In briehttps://kdcompute.igss-africa.org/kdcompute/home), an online database developed by Diversity Array Technologies  for the analysis of DArT marker data. KDCompute uses a suit of imputation methods to impute the SNP dataset and scores the imputation results by calculating simple matching coefficient (SMC). The method with the highest SMC is considered as optimal and used to impute the original genotypic dataset.The DRSNP dataset was imputed before GP using KDCompute 1.5.2. beta  population to build up. FAW damage scoring in all the three environments was carried out two months after planting when adequate natural FAW infestation levels had manifested, and scoring was based on a visual assessment using a scale of 1 (no or minor leaf damage) to 9  , illustr3 plastic jars incubated for 14 days in the laboratory at a temperature of 28 ± 2 °C and relative humidity of 70% ± 5%, to enhance oviposition. The lids of the jars were perforated and a gauze-wire mesh with a pore size smaller than one mm was fitted on each lid to allow proper ventilation while preventing the weevils from escaping.Rearing of and bioassays for MW were performed as described in previous experiments carried out at NaCRRI ,77. Weev3 glass jars and infested with 32 unsexed weevils. After 10-days of incubation to allow oviposition, all dead and living adult insects were removed. One month after infestation (MAI), each sample was removed from its jar, and the grains and the flour were isolated and their weights were recorded. The total number of holes inflicted by the weevils on the grains was counted along with the number of grains affected by such damages. Additionally, the numbers of dead and living weevils were recorded. After these measurements were collected, the grains were returned to their respective jars and all the measurements were repeated at two and three MAI. The collected data were used to infer, for each sample, the cumulative grain weight loss (GWL), the cumulative number of emerged adult weevil progenies (AP), and the final number of damage-affected kernels (AK).After harvesting and shelling, grains of each line were bulked across environments. Then, samples of 30 g were weighed from each grain bulk, aiming to produce three replicates per line for the MW bioassay experiment. However, due to the lack of an adequate amount of grains for most of the lines of the panel, only 64, 123, and 132 lines could generate three, two, and one replicates, respectively, and were therefore considered for the MW bioassay experiment. Each of these samples was wrapped in polythene bags and kept at −20 °C for 14 days to eliminate any weevil infestation prior to the start of the experiment. After this disinfestation process, samples were left to thaw and transferred into 250 cmranef function of the R package [Both best linear unbiased estimators (BLUEs) and predictors (BLUPs) were generated using the general linear model with only phenotype option of the software Trait Association through Evolution and Linkage (TASSEL)  and the  package  lme4 [80The mixed model for generating BLUEs  and BLUPs  for FAW damage scores across environments model was:Due to inadequate amount of seeds, only 37% (126 out of 341 that had genotypic data) of lines from the panel had phenotypic data on grain weight loss (GWL), adult progeny emergence (AP), and number of affected kernels (AK). Therefore, to estimate GP accuracies for MW resistance, these 126 lines were used as the TS and the remaining 215 lines with only genotypic data constituted the breeding set (BS).The GP analyses for FAW resistance were carried out on the 341 lines of the panel that were genotyped and phenotyped for FAW damage resistance. To determine TS and BS sizes and compositions for the evaluation of maize resistance to FAW damage, two strategies, namely, random-based TS (RBTS) and pedigree-based TS (PBTS), were used.=INDEX),1)” and dragging until the adequate number of lines for each percentage determined above was obtained.For the RBTS, 126 (37%) lines used for GPs of MW-resistance traits were used as the TS for FAW to predict the GEBVs of the remaining 215 lines first. To build the second TS for FAW, the 215 (63%) lines used earlier as BS were considered as a TS. Then to determine the third and fourth TSs for FAW, random selections of 75 and 85% of the lines in the entire panel were performed through the Excel formula “The four datasets determined based on the pedigrees of the lines in the panel (PBTS strategy) are presented in The GP analyses were performed using the BLUEs and BLUPs of the phenotypes and the 28,919 DRSNPs. Sixteen algorithms available in 10 GP methods were implemented using the Genomic Prediction 0.2.6 plugin of the KDCompute 1.5.2. beta. The 10 methods were directly translated from functions of five R packages designed for GP analyses:y is the vector of observations, Z is the design matrix for random effects, and µ is the vector of random effects [Bayesian models have different prior distributions with a general model that can be as follows:  effects .2, where σ2 is unknown and assumed to have scaled x2 distribution. In the KDCompute genomic prediction 0.2.6 plugin, the Gibbs sampler is run with 4000 iterations and 1000 iterations for burn-in period as default parameters.The BLR (Bayesian Linear Regression) algorithms from the BLR R Package  are usedThe Bayesian Generalized Linear Regression (BGLR) package fits various types of parametric and semi-parametric Bayesian regressions. The parametric Bayesian algorithms used from this package rely on different prior distributions that induce different types of shrinkages of the marker effects , includiμ represents the fixed effects vector and ε is a vector of random residuals. The parameters α and ε are assumed to have independent prior distributions h. The parameter h measures the genomic distances among genotypes that can be interpreted as a correlation matrix and it controls the rate of decay of the correlation among genotypes [Reproducing kernel Hilbert space (RKHS) ,48 is a enotypes . To perfmmer (mixed model equations in R) function on the KDCompute genomic prediction 0.2.6 plugin. The package solves mixed model equations proposed by Henderson [The Sommer (solving mixed model equations in R) package  was usedenderson . It workenderson , averageenderson , expectaenderson , and theenderson .K is the additive or genomic relationship matrix (A or gA) in the genomics context, X and Z are incidence matrices for fixed and random effects, respectively, and R is the matrix for residuals (here K(A). The genomic relationship matrix was constructed according to VanRaden where The model by Sommer can be formulated as : y=Xβ+Zμpi(1−pi) .the mixed model solution (MMS) that calculates the maximum-likelihood (ML) or restricted-ML (REML) solutions for mixed models to perform GP [The ridge regression best linear unbiased predictor (rrBLUP) packages can either estimate marker effects by ridge regression, or alternatively, BLUPs can be calculated based on an additive relationship matrix or a Gaussian kernel. Additionally, using the rrBLUP package, rform GP  was fittβ is a vector of fixed effects and µ is a vector of random effects with variance https://kdcompute.igss-africa.org/kdcompute/home).The mixed models fitted by rrBLUP can be formulated as:mtry, square root and regression (sqrt(p) and p/3, respectively, where p is number of variables in x), for the classification of the number of variables randomly sampled as candidates at each split were implemented in this study. Additionally, the trees to grow (ntree) was set to 10, while node size  and max nodes  were set to 5 and 10, respectively. The 16 methods used in this study and their statistical characteristics are presented in The R package RandomForest that implements Breiman’s random forest algorithm for classification and regression  was used2) averaged across the 50 cross-validation replications between the observed phenotypic values and the predicted genomic-estimated breeding values (GEBV) (https://kdcompute.igss-africa.org/kdcompute/plugins).To calculate the predictive accuracies of each of the 17 methods, a cross-validation approach was performed using the data for the TS with 10 folds and five repetitions amounting to 50 replications. The PAs were estimated as the correlation coefficient (Rp < 0.001) correlations between BLUEs and BLUPs for each trait ranging from 0.93 for FAW to close to 1 for AP, AK, and GWL  positive correlation of 0.92  of the panel and highest with the largest TS (85% of the panel). Even with a TS of 37%, the PAs were still high, ranging from 0.694 to 0.714 for mms_ML and BLR methods, respectively . However of 0.92  between  of 0.92 .Although the PAs did not vary much among GP algorithms, especially when the analyses involved larger TS sizes equal or bigger than 63% of the panel, the machine learning methods slightly outperformed other GP algorithms for all the traits, except for the TS of 37% where Bayesian methods such as BLR and BayesC showed a slight advantage over the machine learning methods . The PAsp > 0.0036) negative relationship of r = −0.45 , eight of the 10 algorithms achieved low PAs (below 0.20) and only missForest_Reg and missForest_Sqt attained PAs of 0.749 and 0.750, respectively. Thus, the Pearson correlation between the sizes of the PBTS datasets and the predictions accuracies for the 10 GP algorithms revealed a significant  decay with high diversity . These gWith a RBTS of 37% of the panel, which was the smallest and expected to give the worst PAs, PAs were higher (at least two-fold) across both FAW and MW-resistance traits and for all GP models when trait BLUPs were used as phenotypes compared to BLUEs, although there were high Pearson correlations between these two categories of phenotypic data for each trait. In general, BLUPs were reported to have higher predictability than BLUEs owing to better accounting for outliers and environmental variabilities permitted by the shrinkage procedure in BLUPs, which results in more accurate estimates of individual genetic effects ,71,72,73The obtained PAs were high for both MW and FAW-resistance traits even with TS of moderate sizes confirming the potential of genomic selection (GS) in Africa-adapted germplasms ,29,30,33The PAs increased up to above 0.85 in proportion to the increase in TS (RBTS approach) size for FAW resistance which was the only trait phenotyped for all the lines of the panel. It would be interesting to phenotype other lines of the panel that were not evaluated for MW-resistance traits to establish larger TS which may improve the PAs ,65,97,98In this study, several GP models that included statistical and machine learning algorithms from parametric, semi-parametric, and nonparametric approaches were used to predict FAW and MW-resistance traits. These GP algorithms, as expected, performed differently on the different traits although the predictive variations were generally minimal, especially when large TS were involved, similarly to earlier model benchmarking reports ,101. BayThis supposed genetic architecture difference between FAW and MW-resistance trait could be the reason for non-linear methods such as random forest performing better at predicting FAW resistance, since these are more capable of integrating epistasis in the statistical modelling ,51. Howep > 2.2.10−16) positive correlation (R = 0.92) between TS size and PAs. Similarly, positive correlations between the number of lines in the TS and the PAs, and plateau for the PAs were also reported by Edwards et al. [Two factors, the relative sizes of the TS and BS (RBTS approach) and their genetic relationship (PBTS approach), influenced the levels of PAs across FAW-resistance datasets, corroborating earlier reports ,107,108.s et al. .p < 0.0036) negative correlation (R = −0.45) between the sizes of the PBTS and the achieved PAs.The composition of the TS and its relationship with the BS are determinant factors for the genomic predictability of complex traits ,113,114.However, it is not very clear why the predictions for the BS FAW.Ped3 (47 CIMMYT SB and SP-resistant lines) and the TS  led to lower PAs for FAW.Ped3. A possible explanation could be that these two sets were distantly related since only two and one CIMMYT SB and SP-resistant lines, respectively, were used as parents to develop the DH lines. Spindel et al.  argued tThis study assessed prediction accuracies of genomic-estimated breeding values for fall armyworm (FAW) and maize weevil (MW)-resistance traits in a diverse Africa-adapted maize panel using several parametric, semi-parametric, and non-parametric genomic prediction models. Prediction accuracies for maize resistance to FAW and MW traits were relatively high, even with a moderate training set size. For FAW resistance, although the prediction accuracies were positively correlated with the size of the training set, the composition and the relationship of the training set with the breeding set were more influential in predicting line performance. Additionally, TS determination-related parameters were more important than the type of genomic prediction models in predicting FAW and MW-resistance traits. However, Bayesian models on MW-resistance traits and machine learning models on FAW damage resistance outperformed mixed linear models in almost all the datasets used in this study. Therefore, future genomic selection programs for maize resistance to insect pests such as FAW and MW in Africa should put more effort into designing effective training sets and use selected Bayesian and machine learning GP algorithms to improve genetic gains, shorten breeding cycles, and accelerate variety release. Such programs could greatly benefit from using the genetically diverse maize panel used in this study as a base population, since it consists of lines adapted to several African agro-ecologies.


P. vannamei) hatcheries in China. Our objectives were to determine the additive genetic variance associated with reproductive traits, and to anticipate any potential impacts on reproductive performance when selecting for increased body weight by assessing genetic correlations between post-spawning body weight and specific female reproductive traits. Data were collected on 595 females from 78 full-sib families over 30 days, with a total of 1,113 spawning events recorded. Traits studied included: body weight after spawning (WAS), number of eggs per spawn (NE), number of nauplii per spawn (NN), egg hatching rate per spawn (HR), number of eggs produced relative to female weight (g) (FE), and spawn frequency over 30 days (SF). Estimated heritability was high  for WAS (h2 = 0.64 ± 0.10) and moderate for NE (0.26 ± 0.07), NN (0.18 ± 0.06), and SF (0.15 ± 0.06), respectively. In contrast, h2 for HR (0.04 ± 0.03) and FE (0.05 ± 0.04) were low. The genetic correlations between growth trait (WAS) with NE, NN and SF were 0.93 ± 0.10, 0.84 ± 0.10, and 0.57 ± 0.18, respectively. While the genetic correlation between WAS and HR was low (0.02 ± 0.33), a negative genetic correlation was found between WAS and FE (−0.50 ± 0.27). Overall, we concluded that it is possible to improve the key female reproductive traits  in cultured white shrimp lines via genetic selection, but not for HR or FE. The genetic relationship between the growth trait and reproductive traits predicts that selection on fast growth would increase the production in the seed sector, with little or no compromise on the eggs quality.Seed production can be improved if genetic selection is applied to key reproductive traits when a substantial amount additive genetic variation is present that can be exploited in a selective breeding program. Despite the commercial importance of reproductive traits to the seed production sector currently, few quantitative genetic studies have been conducted to address these traits in farmed penaeid shrimp culture lines. Here, we investigated genetic parameters for a number of key reproductive traits that directly impact nauplii production in Pacific white shrimp ( This is especially true for penaeid shrimp species that possess many unique reproductive characteristics; in particular, at maturation in hatcheries, many females may spawn relatively infrequently or may never spawn, while a small proportion of females spawn multiple times, hence these females are likely to contribute the majority of nauplii produced6. Having knowledge about genetic parameters (heritability and genetic correlations) for key reproductive traits will be essential when designing better breeding strategies for improving broodstock reproductive capacity and quality via genetic selection. For example, a recent experimental study of a small marine copepod crustacean  reported that total egg production was increased by 24.5%, following selection over five generations with heritability (h2) for this trait estimated at 0.387.Reproductive characteristics constitute a set of commercially important traits that are yet to receive much attention when genetic improvement is applied to farmed aquatic species9, most breeding programs to date have focused primarily on growth traits11. There are many examples of this practice however, that have also reported undesirable (cor)related effects on other fitness traits in domesticated animals, particularly with respect to metabolic, reproductive and health status traits12. For example, negative correlations were reported in pigs for reproductive traits when individuals were selected for high meat production efficiency. This resulted in a significant reduction in both fertility and litter size12. In contrast, studies in a wide variety of animal species  have reported positive relationships between growth traits and some reproductive traits (e.g. litter size and fecundity)13. While the practice of genetic selection works essentially via a ‘black box’ approach, the opportunity still remains to understand, to anticipate and to prevent any potentially negative impacts of selection based on developing knowledge about genetic correlations (rg) between growth traits and important reproductive traits12.While application of genetic selection to farmed aquatic species has increased productivity significantly in a number of species19 and tilapias22. In salmonids, the majority of production traits that have been investigated show relatively high levels of additive genetic variance with most genetic correlations indicating positive relationships between growth-related traits and the reproductive traits examined. As an example, Gall and Neira15 reported h2 estimates for weight, number of green eggs, and number of eyed eggs in coho salmon (Oncorhynchus kisutch) ranging between 0.32 to 0.42, and genetic correlations between harvest weight and reproductive traits of egg weight and weight of eggs spawned were the same at 0.46. In domesticated rainbow trout (Oncorhynchus mykiss), h2 estimates for female egg number and egg size were 0.32 and 0.28, respectively14, while h2 estimates for traits including spawning date, egg size, number of eggs, and egg volume were all moderate to high19. In contrast in a Nile tilapia (Oreochromis niloticus) breeding program in Vietnam, h2 estimates for both fecundity traits and fertility were low21, while spawning success (h2 = 0.20–0.22) was an exception22. Likewise, Thoa et al.20 reported low h2 estimates for number of fry at hatching, total fry weight, and fry mortality in a base population of red tilapia (Oreochromis sp.). In addition, a case study that applied selection on reproductive traits in female channel catfish to produce hybrid catfish embryos reported realized h2 estimates for fecundity that ranged from 0.10 to 0.42 while h2 for percentage hatch and fry/kg were low23.To date, few studies have investigated genetic parameters for reproductive traits in farmed aquatic taxa, and of those studies, most have focussed on salmonid species6, there has been a noticeable lack of research that has investigated capacity of females to spawn multiple times in penaeid shrimp. This trait has the potential to double or even triple nauplii production by individual females. Until recently however, there have only been a few reports that have investigated genetic parameters for this trait in penaeids25. Reproductive traits in farmed penaeid species , are among those that can contribute the most to increasing profitability of the hatchery sector but to date, only a single study has reported h2 estimates for the above traits under commercial hatchery conditions26. While there have been two studies estimating genetic parameters for reproductive traits in Pacific white shrimp (P. vannamei) following artificial insemination28, more information will be required for the seed production sector because these studies indicate that there are differences in reproductive trait data when applying artificial insemination vs natural mating in penaeid species. Moreover, high levels of additive genetic variance in reproductive traits for mean oocyte number, diameter, ovary maturity stage29, and high genetic correlations between levels of vitellogenin in haemolymph and mean diameter of oocytes have been reported for Pacific white shrimp30. In black tiger shrimp (P. monodon), h2 estimates for days to spawn, number of eggs, number of nauplii, and hatching rate ranged from 0.18 to 0.47, indicating that these traits can be improved to increase total reproductive output via genetic selection31.While a number of studies have demonstrated the potential capacity to improve seed production via genetic selectionP. vannamei broodstock under commercial maturation conditions using the family line, and (2) to estimate genetic correlations between individual body weight after spawning with specific reproductive traits. Knowledge generated in this study can be applied to improve production of nauplii via genetic selection and to minimize any negative impacts on reproductive performance that may result from selection for fast growth.The aims of the current study therefore were: (1) to examine genetic variance for key reproductive traits in female 3) and number of nauplii  per spawn were in general terms, comparable with that obtained during commercial Pacific white shrimp nauplii production elsewhere in China (pers. obs.). A relatively high mean hatch rate (HR = 84.60%) estimate here indicates that the experimental broodstock management protocols employed had been appropriate.Across a 30-day experimental period, 950 successful spawning records were observed out of a total of 1,113 spawning events. The basic statistics for each trait  are presented in Table r = 0.45 ± 0.03) yet highly significantly different from zero (P < 0.01). Similarly, the number of nauplii per spawn (NN) was also positively correlated with post-spawning weight  for each reproductive trait. h2 for body weight after spawning (WAS) was very high (0.64 ± 0.10), while h2 for the number of eggs per spawn (NE), number of nauplii per spawn (NN) and spawn frequency (SF) were all moderate (0.15 to 0.26). h2 estimates for hatching rate of eggs (HR and HRat) and the number of eggs per unit body weight (FE) were in general, low (0.04 ± 0.03) and not significantly different from zero. This result indicates that only limited additive genetic variance was present in the line for HR and FE traits. Estimates for repeatability variance and repeatability (rep) are presented in Table Table rg) and phenotypic (rp) correlations between pairs of reproductive traits. The genetic correlations between WAS and reproductive traits  were high-medium, with 0.93 ± 0.10, 0.84 ± 0.10, and 0.57 ± 0.18, respectively. Genetic correlation between WAS and HR was low (0.02 ± 0.33) with large standard errors. However, a negative genetic correlation (−0.50 ± 0.27) was observed between WAS and FE, suggesting that while NE and NN will be increased with body weight, FE, the ratio of number of eggs per biomass, will be decreased. Regarding reproductive traits of NE, NN, and SF, these directly determine the production for nauplii hatcheries, and HR is an important index for egg quality. The above genetic relationships suggest that selection on fast growth will also benefit the seed sector, with no negative impact on egg quality. A negative genetic correlation between WAS and FE however, indicates that selection on fast growth may involve a trade-off in relative fecundity. Across all pairwise comparisons among reproductive traits, the highest genetic correlation were 0.97 ± 0.03 (NE and NN), 0.86 ± 0.18 (SF and NE), and 0.70 ± 0.24 (SF and NN), respectively.Table rp) as that seen for genetic correlations among the traits evaluated. Except for the comparison of FE and WAS, all phenotypic correlations were positive, with the highest estimate evident between NE and NN and the lowest estimate observed between SF and FE. It is clear that the positive rg estimates between WAS and reproductive traits were significantly higher than the corresponding rp estimates.A similar pattern was evident for phenotypic correlations 34. Our relatively low average accumulated matings per night may have resulted from a size effect of female broodstock used in the experiment as no body size selection of experimental animals was practiced here from PL to maturation stage. A large proportion of small sized female broodstock used here potentially have produced a relatively low spawning frequency compared with that possible if larger individuals had been chosen for the study specifically. While we observed this effect in our study , positive correlations between body size of broodstock and spawning frequency have also been reported previously in a variety of farmed penaeid species36.The major difficulty associated with studying reproductive traits in penaeid species is establishing optimal environmental conditions for maturation over an experimental test period because the majority of reproductive traits tested are highly sensitive to even small variation in physical conditions; in maturation tanks, nutritional factors in broodstock diet and the physiological condition of experimental animalsts Table  were ver3) was consistent with the estimates reported in two other studies on reproductive traits in female P. vannamei in Mexico27 , and higher than the values (160.7 × 103) reported by Tan, et al.28. The estimates of nauplii per spawn (NN) and hatching rate of eggs (HR) in our study were similar to the estimates reported by Arcos et al.26 , but significantly higher than that reported by Caballero-Zamora et al.27  and Tan et al.28 , respectively. The different results likely arise from the differences in the mating design methods used for data collection between studies as the latter two studies employed artificial mating while our study and that of Arcos et al.26 relied on natural matings. Many factors, including physical condition of male/female broodstock or the artificial insemination (AI) skills of technicians, can significantly impact performance, which can lead to low hatching rates and a low number of nauplii produced. Because our experiment relied on natural matings, the conditions were very similar to practical commercial production conditions for nauplii production. We would expect therefore, that the data produced here would be more applicable to improving seed reproduction in industrial environments.The mean number of eggs per spawn (NE) reported here  across the 30 day trial was 1.44, lower than reported in the study by Arcos et al.26 where mean SF was 1.71 per female per month. This difference may result from the different culture conditions used for broodstock in the two studies. In the Arcos et al.26 study, broodstock were cultured in an earthen pond while broodstock used in this study were cultured from PL to maturation stage in recirculating tanks. It is quite common for broodstock cultured in earthen ponds to show higher mean spawning frequency than broodstock cultured in tank systems. This effect was observed in our earlier study where we compared data on reproductive traits between broodstock reared in earthen ponds and recirculating tanks and confirmed the finding . In this comparison, mean SF for broodstock raised in earthen ponds was 1.93, a result similar to that reported by Arcos et al.26, but significantly higher than that of broodstock raised in recirculating tanks (SF = 1.34). While selecting for spawning frequency shows promise with a moderate degree of heritability (0.15), it should be recognised that very few females actually contribute to the next generation  was high (0.64 ± 0.10), and while higher than many reported for this trait in other penaeid species, it was still within the normal range. For Pacific white shrimp, mean h2 estimates for body weight during insemination are also high at 0.44 ± 0.0827, 0.49 ± 0.1428 and 0.58 ± 0.0825, respectively. While in black tiger shrimp, h2 for body weight at 54 weeks was 0.53 ± 0.1431. For the same trait in Nile tilapia, h2 was 0.68 ± 0.1021. h2 for body weight prior to spawning in red tilapia was higher 0.80 ± 0.1620. While levels of quantitative genetic variation for specific traits do vary among farmed populations and species (e.g. crustaceans vs fish), in general there are some consistencies41. In coho salmon, h2 estimates for both body weight at spawning and post-spawn weight were only moderate15. So comparatively, based on our estimates of Pacific white shrimp and the most recent published studies in most aquaculture species, body weight at spawning stage in most aquaculture species appears to be a highly heritable trait, indicating that a large amount of additive genetic variance is available that can be exploited in breed improvement programs in most aquatic species that have been tested in this way. Taken together, in general high heritability for weight/size at maturation stage provides good support for Hill’s (2010: p79) argument that ‘Heritabilities (h2) tend to be highest for conformation traits and mature size, typically 50 per cent or more, and lowest for fitness-associated traits such as fertility ’44.h2 estimate for SF was moderate (h2 = 0.15) and is similar to the estimates in earlier reports for this trait in P. vannamei24, but higher (h2 = 0.07) than a reported for females cultured in brackish water25. Moderate levels of additive genetic variation for SF indicate that multiple spawning capacity is an inherited trait and can therefore in theory, be improved via selection. h2 for NE (h2 = 0.26) and NN (h2 = 0.18) here were comparable with estimates reported for black tiger shrimp31, but higher than estimates reported in earlier Pacific white shrimp studies28. Differences between our estimates and those of Caballero-Zamora et al.27 and Tan et al.28 on the same species, once again, likely result from the different mating designs employed, in particular use of natural mating vs an artificial insemination approach. In salmonid species, h2 estimates for number of eggs and eyed eggs are usually moderate to high19. While in contrast, in tilapia, estimates for fecundity related traits are often quite low21. This however, is not always the case for farmed tilapia strains because number of eggs (h2 = 0.20) and number of hatched fry (h2 = 0.16) showed moderate heritability estimates in the GIFT tilapia strain45.The h2 estimate for relative fecundity, FE (h2 = 0.05), is the first report for this trait in a penaeid species. A low FE heritability estimate for Pacific white shrimp is consistent with estimates for this trait in Nile tilapia21. Likewise, nearly zero additive genetic variance was reported for a similar trait (fry/kg of broodstock) in channel catfish23. In general, low and non-significant additive genetic variance for FE traits suggest that relative reproductive output would most likely be a difficult trait to improve via genetic selection in most aquatic species.Our h2 estimates for egg hatching rate (HR) estimated in our study were also low, a result consistent with similar estimates in both tilapia21 and channel catfish23. A related trait  reported for giant freshwater prawn also showed low additive genetic variance46. In general, traits that involve fertilization and/or survival of larvae at hatching are essentially group fitness traits rather than individual ones, indicating that potentially many non-genetic factors can have significant effects on such traits. Overall, limited additive genetic variation for HR indicates that this trait in Pacific white shrimp is unlikely to be improved via genetic selection.P. vannamei, e.g. correlations of 0.49 and 0.54 between body weight at insemination and NE, and NN, respectively27. Positive genetic correlations that are in general, moderate in degree between bodyweight at spawning and fecundity traits have also been reported in tilapia21 and some salmonids19. The genetic correlation between WAS and HR in our study was low and not significantly different from zero, which suggests that the genetic control of these two traits are not linked. Genetic correlations between WAS and reproductive traits of NE, NN, SF, and HR tested here were all positive, a result that suggests that selection to increase body weight of female broodstock will not have any negative impacts on their individual reproductive performance, and in fact could actually increase overall female broodstock reproductive output via indirect selection. In aquatic species, broodstock with relatively high body weight at spawning usually have experienced good nutrition and are likely to be in a robust physiological condition, as a consequence their fecundity should be higher than individuals that have experienced poorer nutrition. The genetic correlations results here for P. vannamei females however, suggest that high body weight and better reproductive performance are linked.The estimated genetic correlations between body weight of WAS and fecundity traits  were all positive and medium-high in level (from 0.57 to 0.93), a result higher than earlier reported results for P. vannamei27. For black tiger shrimp Macbeth et al.31, reported negative genetic correlations between NE and NN, and NE and HR, but moderate and positive correlations between NN and HR. In other aquaculture species, results of estimates for genetic correlations among reproductive traits have been very diverse21 and most may be species specific and will also depend on the specific pairs of traits examined.Genetic correlations among reproductive traits  were all positive except for that of SF vs HR, and ranged from low (NE vs HR) to high (NE vs NN). These results show clearly that genetic selection on individual reproductive traits is unlikely to have any potentially negative impact on other reproductive traits. While this set of reproductive traits is very important for nauplii production in commercial Pacific white shrimp hatcheries, to date no published studies have reported on genetic correlations among these traits. Data from other studies have reported on correlations between some of these traits however, that have employed artificial insemination rather than natural matings in penaeids. As examples, the genetic correlation between NN and NE was reported to be moderate (0.24 ± 0.41) in P. vannamei e.g. rp 0.3426 and 0.2727. A relatively high rp between WAS and NE has also been reported in some other penaeid species31. The correlation between WAS and NN was lower than between WAS and NE but was still moderate and positive , that have always been observed to show a small percentage of spawns that do not result in hatched nauplii. This results from otherwise successfully mated females losing their adhered spermatophore before mature eggs can be released. In this study, the phenotypic correlations between WAS and other reproductive traits were also all positive which indicate that larger females in general spawn more often, release a larger number of fertilized eggs and produce a larger number of nauplii than do smaller females37. Therefore as a general rule, large body size for mature females is a good practical and measurable characteristic for inferring likely relative reproductive performance of individual female P. vannamei broodstook.The phenotypic correlation between WAS and NE was moderate (0.45), a result that is comparable with other estimates for P. monodon), as this species has a similar reproductive cycle to that of Pacific white shrimp and there are still major difficulties associated with nauplii production in black tiger shrimp farming.Improving reproductive performance of Pacific white shrimp strains is a key objective for the broodstock market in China in the future. Fresh, nutritional food for broodstock maturation is a major financial constraint on hatcheries, and the nauplii production sector would benefit significantly from strains with improved reproductive output. This is because it would allow hatchery managers to maintain smaller broodstock populations while achieving comparable seed production output or allow them to invest the same resources but produce more seed. Both options would result in a significant increase in hatchery profit. The capacity to improve nauplii production from each female broodstock individual has huge commercial potential, with the possibility that spawning frequency could be trebled. Breeders can also include reproductive traits in addition to current selected traits via either a multiple trait selection approach or a two stage selection approach. Additionally, a genome selection (GS) approach has recently been very successful at improving total egg production in the poultry industry, so trialling GS in penaeid hatcheries may offer new potential for improving the reproductive traits in shrimps. Results may also be useful for genetic improvement of black tiger shrimp  of individual broodstock females, so these two latter traits are unlikely to be improved via genetic selection. Evidence for both positive and moderate genetic correlations and phenotypic correlations between body weight after spawning and some reproductive traits also suggests that there is only very limited potential for negative correlated impacts on individual reproductive performance of female broodstock by selection to increase mean body weight. It is clear however, that data will need to be collected over future multiple generations of selection from our domesticated line to investigate any potential for deterioration in reproduction performance due to the cooperative impacts of selection for improved mean body weight and accumulation of inbreeding over time.P. vannamei was produced following a complete 4 × 4 diallel cross of four domesticated culture lines obtained in China between June and July 2015. Details of the strains and maintenance of families generated are described in Ren et al.47. On May 4th 2016, when shrimp had reached maturation, 660 test animals were selected randomly from each of 78 full-sib families with individuals transferred to maturation tanks (10 m2). Test females were then subjected to unilateral eyestalk ablation to induce ovarian maturation, and broodstock males and females reared separately with 110 individuals per tank.The experiment was conducted at a Beijing Shuishiji Biotech. Ltd. maturation facility in Wanning (Hainan Province), China. A base family line of In total, data from 595 females that survived 30 days of experimentation were recorded in the study. Number-coded silicon eye rings were placed on the remaining eyestalk for individual female identification. A biological water recirculating system was used to maintain water quality at an exchange rate of 600% to 800% per day. Daily feed composition consisted of a mixture of fresh meal diet  delivered at a rate of approximately 5% of total biomass per tank. Tank water was maintained at 28 ± 2 °C and 31–35 ppt salinity. Data collection commenced in June 2016 and continued over a 30 day period.Females presenting with mature ovaries (stage IV) were collected daily at 10:00 and transferred to tanks containing male broodstock. At 19:00, successfully-mated females with attached spermatophores were placed in individual 500 L fibreglass tanks filled with 300 L of clean seawater. Environmental conditions for spawning were maintained at 28 ± 0.5 °C and a salinity of 32–36 ppt. At 24:00, all females in spawning tanks were returned to maturation tanks and eggs incubated with gentle aeration.Body weight after spawning (WAS) was measured after successful spawning at 12:00. Five reproductive traits were measured and recorded per female: (i) number of eggs (NE) per spawn - measured in three replicate 200 ml breaker samples after being thoroughly homogenized in seawater taken from spawning tanks (300 L in volume); (ii) number of nauplii (NN) per spawning - measured in the same way as for NE after nauplii had hatched on the second day at 11:30; (iii) relative fecundity - measured as the number of eggs per unit body weight (FE) - calculated by dividing the number of eggs per spawn by WAS; (iv) egg hatching rate per spawn ; and v) female spawning frequency (SF) - calculated as the total number of successful spawning events per individual female at the end of the experimental period.48. For comparative purposes, both the original data (HR) and arcsine transformed data (HRat) were used in subsequent statistical analyses. For all other traits , untransformed values were used in the data analysis. Genetic variance and covariance components and h2 for targeted traits were estimated using an animal model applying the restricted maximum likelihood (REML) methodology in WOMBAT49. For trait of SF, the linear mixed animal model can be written as follows:Prior to formal data analysis, raw HR percentage data were arcsine transformedy is a vector of observations for a reproductive trait per spawn event (SF), β is a vector of fixed effects consisting of maturation tanks, the recorded spawn event batches, and regression coefficient of age of shrimps, α is the vector of random additive genetic effects of the animals, e is the vector of random residual errors andX and Z are known incidence matrices relating observations to the fixed effects mentioned above, and animal effects, respectively. Both α and e follow a normal distribution with mean zero and variance Aσa2 and Iσe2, respectively. Here, σa2 and σe2 are the additive genetic and residual error variances while A is the numerator relationship matrix based on pedigree information.at and FE resulted from multiple observations for some female individuals. Repeated measures for these traits were across 30 days, with these data recorded from different spawning order, i.e. first spawn, second spawn, up to sixth spawn for some females. Therefore, we also used a repeatability animal model (Model 2) to account for replication within individuals:In this experiment, estimates of WAS, NE, NN, HR, HRy is a vector of observations for a reproductive trait per spawn event , β is a vector of fixed effects consisting of maturation tanks, the recorded spawn event batches, and regression coefficient of age of shrimps, α is the vector of random additive genetic effects of the animals, pe is the vector of random maternal permanent environment effects contributed by individual females to their offspring families, e is the vector of random residual errors and X, Z1 and Z2 are known incidence matrices relating observations to the fixed effects mentioned above, animal effects and permanent environment effects, respectively. α, pe and e follow a normal distribution with mean zero and variance Aσa2, Iσpe2 and Iσe2, respectively. Here, σa2, σpe2 and σe2 are the additive genetic, permanent environment and error variances while A is the numerator relationship matrix based on pedigree information.h2 was calculated as the ratio of additive genetic variance to total phenotype variance (h2 = σα2/ σp2). In Model (2), heritability (h2) and repeatability (rep) were calculated as follows:In Model (1), yWAS, yNE, yNN, yHR, yFE and ySF are the same as defined in Model 1, respectively. Total phenotypic variance (σp2) was estimated as the sum of additive animal genetic variance (σα2) and random residual components (σe2). Genetic or phenotypic correlation between two traits was calculated as: 12 was the genetic or phenotypic covariance between two traits, and σ12 and σ22 were either additive genetic variances of trait 1 and 2, or phenotypic variances of the two traits, respectively.In the primary analysis, the results were similar between the linear mixed animal model and the repeatability animal model, which were also supported by comparing the log-likelihood ratio of the models. Therefore, a multivariate mixed animal model was fitted to estimate the genetic and phenotype correlation between examined traits, expressed in matrix notation as:


PPIL4), which was shown to be associated with milk production traits in US Holstein cattle but not known for fertility-related functions. Simulations indicated that the current sample size had limited power to detect QTL with dominance effects for female fertility probably due to low QTL variance. More females need to be genotyped to achieve reliable mapping of QTL with dominance effects for female fertility.Exploring dominance variance and loci contributing to dominance variation is important to understand the genetic architecture behind quantitative traits. The objectives of this study were i) to estimate dominance variances, ii) to detect quantitative trait loci (QTL) with dominant effects, and iii) to evaluate the power and the precision of identifying loci with dominance effect through post-hoc simulations, with applications for female fertility in Danish Holstein cattle. The female fertility records analyzed were number of inseminations (NINS), days from calving to first insemination (ICF), and days from the first to last insemination (IFL), covering both abilities to recycle and to get pregnant in the female reproductive cycle. There were 3,040 heifers and 4,483 cows with both female fertility records and Illumina BovineSNP50 BeadChip genotypes  after quality control). Genomic best linear unbiased prediction (BLUP) models were used to estimate additive and dominance genetic variances. Linear mixed models were used for association analyses. A post-hoc simulation study was performed using genotyped heifers’ data. In heifers, estimates of dominance genetic variances for female fertility traits were larger than additive genetic variances, but had large standard errors. The variance components for fertility traits in cows could not be estimated due to non-convergence of the statistical model. In total, five QTL located on chromosomes 9, 11 (2 QTL), 19, and 28 were identified and all of them showed both additive and dominance genetic effects. Among them, the SNP rs29018921 on chromosome 9 is close to a previously identified QTL in Nordic Holstein for interval between first and last insemination. This SNP is located in the 3’ untranslated region of gene peptidylprolyl isomerase like 4 ( Declining female fertility increases the costs for dairy farm management due to extra inseminations, veterinary treatments, and involuntary replacements2. Moreover, poor female fertility has been showed to be genetically correlated with increased methane production and negative climate impact3. Female fertility in dairy cattle can be generally divided into two component5. The first component is the ability to return to cycling and to go into heat after calving, which can be measured by the time interval from calving to first insemination. The second component is the ability to conceive and become pregnant, which can be measured by the time interval between the first and last inseminations or the number of inseminations per conception.Intensive selection on milk yield in dairy cattle has led to a decline in female fertility, due to unfavorable genetic correlations between milk yield and female fertility8. Apart from the genetic and environmental factors, management decisions can also influence the fertility phenotypes 7. It has been reported that higher estimated heritabilities were achieved using activity measurements to indicate estrus in dairy cows compared with using traditional measurements calculating from calving and insemination records9. Another reason could be that the non-additive part of the genetic variation was often not considered due to the application of additive-only models10. Dominance effects are an important part of non-additive genetic effects. They represent the effect of interactions between alleles at the same locus11. Dominance genetic effects have been reported to make a substantial contribution (up to 14% of phenotypic variance) to the genetic variation in yearling weight in cattle12. Thus, understanding the genetic architecture in the presence of dominance effects is helpful for planning breeding strategies and increasing genetic gain. For example, dominance effects can be utilized by designing mating schemes that optimize favorable allele combinations, especially for crossbreeding which benefit from heterosis13.Female fertility traits in cattle have low heritabilities , which has been well documented in various Holstein populations14. The availability of high throughput genotyping technology enables the investigation of dominance effect using genomic information. From the computational perspective, the investigation of dominance effect using a genomic-based approach is much simpler than using pedigree-based approaches. This is due to that heterozygotes and homozygotes can be directly distinguished by genomic information. For milk yield in dairy cattle, the dominance variance accounted for up to 7% of total phenotypic variance, while the additive variance accounted for up to 30% of total phenotypic variance14. Furthermore, including dominance effects in the analyses can improve the fitness of models and the reliability of genomic predictions15.The ability to estimate dominance variance using pedigree-based approach is limited by the requirement for data with large full-sib families and the high computational complexity involved17. By definition, recessive alleles have large dominance effects. One consequence of the existences of recessive alleles is the genetic variation in female fertility, as females carrying recessive lethal alleles will lose embryos that become homozygous for one of these alleles. In addition, female fertility traits tend to suffer from inbreeding depression18. This also suggests substantial dominance effects acting on female fertility. The estimation of dominance variance components for female fertility traits using pedigree-based approach has previously been reported20. In US Holstein, the broad sense heritability (2.2% to 6.6%) was reported to be at least twice as large as the narrow sense heritability for female fertility traits19. In Austrian Simmental and Brown Swiss dairy cattle, similar values for additive (1.00%) and dominance (0.32% to 1.36%) variances were observed for female fertility traits20. To our knowledge, however, the estimation of the dominance genetic variance using genomic-based approach has not previously been applied on female fertility in dairy cattle.In recent years, a number of studies have identified recessive alleles, including embryonic recessive lethal allele segregating in modern cattle populations21. However, few GWAS for dominance effects have been performed in dairy cattle, despite large dominance genetic variances for some traits15. In contrast to GWAS for additive effects which were commonly performed on estimated breeding values, the detection of dominance effects requires genotyped animals having their own phenotypic records. Recently, the accumulation of cows with both phenotypes and genotypes has enabled the investigation of dominance genetic effects by GWAS. For example, suggestive QTL for dominance effects located on chromosome 2, 3, 5, 26 and 27 for milk yield and located on chromosome 1, 2, 3, 7, 23, 25 and 28 for female fertility have been reported in dairy cattle22. The statistical power for detecting QTL with dominance genetic effects is expected to be low, due to reliability of estimated genetic value of cows is much lower than those of proven bulls.Genome-wide association studies (GWAS) have become a useful tool to reveal the genetic architecture for complex traitsIn Danish Holsteins, large numbers of heifers and cows have been recently genotyped with low-density SNP chips for the purpose of genomic evaluation. Simultaneously, large amounts of phenotypic information are available for farm management and for breeding value estimation. These data open the opportunity for the estimation of dominance variances and the detection of QTL with dominance genetic effects in dairy cattle, in contrast to pseudo phenotypes such as estimated breeding values or de-regressed proofs where dominance genetic effects are not included.The objectives of this study were to 1) estimate additive and dominance variances for female fertility traits in Danish Holsteins; 2) detect QTL with additive and dominance effects; 3) evaluate the power and the precision using simulation when detecting QTL with dominance effects for our study design.All phenotypic and genomic data were recorded for the purpose of routine dairy cattle managements and genomic evaluations previously, followed guidelines and regulations by the Danish Animal Experiments Inspectorate. Ethics review and approval was not required for this study, because no additional animal handling or experiment was performed specifically for this study.https://www.nordicebv.info/health/) with slight modifications. Only records for heifers with age at first insemination older than 270 days and younger than 900 days, NINSh less than 8 and IFLh less than 365 days were kept. Only records of cows with age at first calving older than 550 days and younger than 1100 days, NINSc smaller than 8, ICF less than 230 days, and IFLc less than 365 days were kept. After editing, there were 714,759 heifers and 905,447 cows left for further analyses. Approximately 15% of them had no confirmed successful insemination. Thus, the last insemination was taken as an unsuccessful insemination, and the corresponding records were considered as censored records. A penalty of 21 days was added to censored IFL and 1 “count” was added to censored NINS6.Insemination and calving records of Danish Holsteins born from 2004 to 2012 in 5,248 herds were used in our analyses. The raw data included insemination records for 738,049 heifers and 974,715 cows in lactations 1–3. The performances of heifers and cows were considered as different traits. The traits analyzed were number of inseminations (NINS), days from calving to first insemination (ICF), and days from the first to last insemination (IFL), which covered both abilities to recycle and to get pregnant in the female reproductive cycle. The ICF was only available in cows, while IFL and NINS were available in both heifers and cows. For IFL and NINS, a suffixes h (for heifers) or c (for cows) was attached to the trait abbreviations. The raw data were edited according to standard procedures of Nordic Cattle Genetic Evaluation  on 29 Bos taurus autosomes and the X chromosome were available. The numbers of SNPs per chromosome ranged from 894 on the X chromosome to 2,502 on the chromosome 1. A routine quality control was conducted using the software Plink24 to remove SNPs with minor allele frequencies <5%, call rate <90% or a significant deviation from the Hardy–Weinberg proportion . After quality control, the number of SNPs remaining was 35,391. The UMD v3.1 assembly25 was used as the reference for genomic position of the SNPs.Among the animals with phenotypic records, 3,040 heifers and 4,483 cows were genotyped with Illumina BovineSNP50 BeadChip version 1 or 2 26 was used to pre-correct phenotypes for heifers and cows separately.The original phenotypes were pre-corrected for fixed effects before estimation of variance components and association analyses. In this way, the fixed effects were estimated more accurately using all animals with phenotypes  rather than just using the genotyped subset . A pedigree-based sire model applied in the DMU softwareThe model for heifers was:b was the vector of fixed effects including herd, year-month of first insemination, age at the first insemination , age at the first calving  and parities (only for cows), The model for cows was:1 was the vector of ones, a was the vector of additive genetic effects, and d was the vector of dominance effects. The a and d were assumed to follow normal distributions, G was the genomic additive relationship matrix, G and D were built from genotypes, but excluding SNPs on the X chromosome10. In brief, the additive genomic relationship matrix was constructed following previous studies28, the dominance genomic relationship matrix 26 was used to estimate additive and dominance genetic variances. Asymptotic standard errors of variance component estimates were obtained from the average information matrix. The standard errors of heritabilities were estimated using an expansion of the Taylor series29.Genomic best linear unbiased prediction (BLUP) model was applied to estimate additive and dominance genetic variances using pre-corrected phenotypes. Both additive and dominance genetic relationship matrices were constructed from the genome-wide marker data. Compared with pedigree based relationship matrices, marker-based relationship matrices include both genetic links through unknown common ancestors and the Mendelian sample variation. The genomic BLUP model was:30 implemented in the DMU software26 was used to test associations between SNPs and pre-corrected phenotypes for each trait. The SNPs were fitted into the model one by one:A mixed model analysis31. First, the effects of the genotypes were tested against the null hypothesis (µAA = µAa= µaa) using a χ2 test with two degrees of freedom. The alternative hypothesis was that genotype effects were not all equal. False Discovery Rate (FDR) was applied  to correct for multiple testing instead of stringent Bonferroni correction. FDR <= 0.10 was chosen as significance threshold to detect SNPs associated with low heritable female fertility traits. The same significance threshold was also chosen in previous study of detecting dominance effects31. Second, the SNPs with significant associations were then tested for the mode of gene action (additive and dominance). The additive effects11 were calculated as a = (µaa − µAA)/2 and dominance effects11 were calculated as d = µAa − (µaa + µAA)/2. Testing of the significance was carried out using a t test against a null hypothesis of no additive and dominance effect. Additive and dominance effects were declared significant when they were different from zero . Under the assumption of Hardy-Weinberg equilibrium, the additive variance was calculated as 2p(1 − p)[a + (1 − 2p)d]2 and the dominance variance was calculated as [2p(1 − p)d]2, with p being the frequency of allele a.The additive and dominance effects of a SNP were tested in a two-step procedureF was the inbreeding coefficient of the known parent. Polygenic effects of offspring with two known parents was sampled as Simulations were carried out to test the power and precision and when detecting dominance effects, using the available genotypes from chromosome 25 (arbitrarily selected) and pedigree from 3,040 genotyped heifers. The simulated phenotypes included polygenic effects, 3 QTL effects (sum of additive effects and dominance effects), and residuals. The polygenic effects were simulated from the oldest to the youngest animal in the pedigree. The polygenic effects of founder animals were sampled from the standard normal distribution as h = d/a was simulated as −1, −0.5, 0.5, or 1. To mimic the low heritability of female fertility traits (<0.05) in Holstein populations, larger residuals were sampled as eThree SNPs located at 10,109,903 bp, 20,058,762 bp and 30,039,582 bp on chromosome 25 were chosen as quantitative trait nucleotide (QTN), and with minor allele frequencies of 0.43, 0.19, and 0.09. These three QTN were chosen to represent high, medium, and low MAF. The additive genetic variances for each of these QTNs were simulated as either 5% or 10% of the polygenic genetic variance to represent the scenarios of the small and large QTL genetic variance. The dominance ratio The descriptive statistics of female fertility traits for all animals with phenotypes  and for genotyped subset of animals  are presented in Table 2, while the additive genetic variance was 210 days2. Furthermore, large standard errors were observed for both additive and dominance genetic variances.The estimated additive and dominance genetic variances for heifer traits are summarized in Table P-value = 8.86E-6) for IFLc. On chromosome 11, there were two SNPs with significant additive effects for IFLh. They were rs109730886 located at 15,201,728 bp , and rs41592172 located at 21,081,322 bp . On chromosome 19, rs109922122 located at 55,191,677 bp had a significant additive effect  for IFLh. On chromosome 28, SNP rs109743925 located at 177,494 bp had a significant additive effect  for IFLh.A summary of significant SNPs is presented in Table P-value of 2.01E-5 for additive genetic effect, but only had a P-value of 0.003 for dominance effect. The estimated dominance ratios h for five QTLs ranged from −1.25 to 0.97.The SNPs with significant additive genetic effects also had significant dominance genetic effects Table . The Manh = −1, while the lowest power (0.02) was achieved with h = 0.5. In the scenario with large QTL variance, the power to detect dominance effects was larger compared with that in the scenario of small QTL variance. Maximal power (0.46) was achieved when h = −1, while the lowest power (0.1) was achieved when h = −0.5.The power and precision of the QTL mapping of dominance effects are shown in Fig. h was −1, while the lowest precision (0.42) was achieved when the h was −0.5. In scenarios with large QTL variance, the precision was in general higher than that in the scenarios with small QTL genetic variance except when h was 0.5. The highest precision (0.14 Mb) was achieved when the h was −1, while the lowest precision (0.4) was achieved when the h was 0.5.In the scenario with small QTL variance, the highest precision (0.18 Mb) was achieved when post-hoc simulations using existed genotype dataset provided a justification for the power and precision to detect dominance effects with current datasets.The genetic architectures of dominance effect for female fertility traits in Danish Holstein were investigated in this study. Several QTLs discovered for dominance effects provided novel variants for further investigation. Besides, our 33. Other possible reasons for larger dominance genetic variance could be due to recessive lethal alleles. It has been reported that recessive lethal alleles play an important role on fertility traits in modern dairy cattle34. At low frequencies of the recessive allele, the recessive lethal would contribute mostly to dominance genetic variance in fertility traits. However, the large standard errors for both additive and dominance genetic variance hinder us to make a fair comparison between these two estimates. Low heritability and limited numbers of genotyped heifers could make the accurate estimation of variance components challenging14.The substantial dominance genetic variance in heifers indicates that dominance effects are important for genetic architecture of female fertility traits, at least for heifers. For example, both IFLh and NINSh had larger dominance genetic variances than additive genetic variances. A previous study demonstrated that the dominance genetic variance was moderate smaller than additive genetic variance in real data for number of teats, back fat, and average daily gain in pigs2, where r is the correlation between the observed SNP and the causal variant. In comparison, the dependence on high LD between observed SNPs and causal variants is much stronger (r4) when detecting dominance effects34.Additive and dominance effects were both significant in each of the identified QTL. This probably indicates that both additive and dominance effects jointly affect the genetic architecture of female fertility traits. This could also be that additive and dominance effects are not statistically independent. In our study, the significances of dominance effects were in general smaller than those of additive effects. This probably indicates that the power to detect dominance effects was lower than the power to detect additive effects. This might be explained by that the success of detecting additive effects depends on the presence of high linkage disequilibrium (LD) r35. In their study, a SNP located at 87,568,944 bp on chromosome 9, in the vicinity of rs29018921 detected in this study, was reported to be associated with IFLc (p = 1.34 × 10−8). The rs29018921 is located in the 3′ untranslated region of gene peptidylprolyl isomerase like 4 (PPIL4). This gene was shown to be associated with milk production traits in a selection signature study in US Holstein cattle36. However, no female fertility-related functions of this gene are known.A previous GWAS used data from 3,475 Nordic Holstein bulls genotyped with the BovineSNP50 Beadchip to discover additive associations between SNPs and eight female fertility-related traits38. The genes near these SNPs do not have known female fertility-related functions. The discrepancies with previous studies might indicate that they are novel genes for female fertility traits, or they are false discoveries due to low number of genotyped records in our dataset. However, these newly identified associations might be served as candidate SNPs for future investigations.This study also showed that rs109730886 and rs41592172 on chromosome11, rs109922122 on chromosome 19, and rs109743925 on chromosome 28 were associated with IFLh. However, these regions were not reported in previous studies for Nordic Holsteinsh) increased. For example, in the scenario with low QTL genetic variance, power increased from 0.04 to 0.16 when h changed from −0.5 to −1; in the scenario with high QTL genetic variance, power increased from 0.1 to 0.46 when h changed from −0.5 to −1. This clearly demonstrated that if there was more weight on dominance in the mode of gene action, more detection power will be achieved. Overall, it was difficult to discover dominance effects if the dominance genetic variance was low as a result of low QTL variance. In the scenario with low QTL variance, the power to detect dominance effects was only 0.02 when h was 0.5. The simulations also showed that the current study did not have high power to detect dominance effects, probably due to the low QTL genetic variance. The effect of sample size was not explored in this study. However, the limited sample size might have led to inaccurate estimates of additive and dominance genetic variances. For example, limited QTL detection power for additive genetic effects of female fertility was observed in the GWAS for Chinese Holsteins37, which had a similar reference population size . Thus, for female fertility traits, more animals need to be genotyped for future studies. Besides, we need to pay attention to the possible biased selection of cows to genotype.The simulations estimated the power and precision based on the current heritability, genotyping data and sample size. Power increased with the absolute value of degree of dominance (5. Furthermore, the genotyped animals had poorer fertility performance compared with all animals having phenotypes, but with a large standard deviation. The reason might be that genotyped cows were pre-selected for higher milk yield, which had negative genetic correlation with female fertility.Female fertility performance of heifers was superior to that of cows in Danish Holsteins, which was also observed in a previous studyDominance genetic variances were larger than additive genetic variances in heifers, but with large standard errors. Five QTL located on chromosome 9, 11, 19 and 28 were detected for female fertility in Danish Holsteins, which were significant for both additive and dominance effects. Simulations indicated that the current sample size had limited power to detect dominance effects for female fertility. More females need to be genotyped to map genetic variants with dominance effects for female fertility.Supplement File S1.


R2s = .074 vs. .037, p = 8.23× 10−24). Individuals in the lowest decile of polygenic scores foreducation attained significantly more education if they were adopted, possiblybecause of educationally supportive adoptive environments. Overall, theseresults suggest that genetic influences on education are mediated via the homeenvironment.Polygenic scores now explain approximately 10% of the variation in educationalattainment. However, they capture not only genetic propensity but alsoinformation about the family environment. This is because of passivegene–environment correlation, whereby the correlation between offspring andparent genotypes results in an association between offspring genotypes and therearing environment. We measured passive gene–environment correlation usinginformation on 6,311 adoptees in the UK Biobank. Adoptees’ genotypes were lesscorrelated with their rearing environments because they did not share genes withtheir adoptive parents. We found that polygenic scores were twice as predictiveof years of education in nonadopted individuals compared with adoptees( An important process by which genes and environments work together to influence behavioris gene–environment correlation . Gene–enIt is essential to investigate gene–environment interplay in educational attainment forseveral reasons. First, educational attainment is an important trait for individuals andsociety, partly because of its significance for health and health inequalities. Second,gene–environment correlation clearly matters for educational attainment. Adoption, twin,and instrumental-variables research suggest that shared genes largely explainassociations between parent and child attainment . Third,Behavior-genetic study designs are needed to disentangle causal processes affectingeducational attainment. Adoption studies do this by removing overlapping genetic andenvironmental influences (passive gene–environment correlation). This is achieved bymeasuring the resemblance of adopted children to their birth parents and to theiradoptive parents. The former gives an estimate of direct genetic influence independentof passively correlated environmental effects. The latter gives an estimate of sharedenvironmental influence, free of correlated genetic effects. Passive gene–environmentcorrelation may be estimated as the extent to which genes contribute more to thecovariation between measures of the family environment and offspring traits innonadoptive than adoptive families . NotablyMore recently, researchers have applied genomic tools to family data to estimate directand indirect effects on educational attainment . These dThe present study drew on an unusually large and relatively unexplored sample of adopteesand harmonized a traditional quantitative genetic approach with modern genomic tools.Our main aim was to use the natural experiment created by adoptive placement to measurethe importance of passive gene–environment correlation for educational attainment. Whenchildren are adopted by nonrelatives, the indirect genetic path between the rearingenvironment and their traits is not present because adoptive parents are not geneticallyrelated to adopted children. Three hypotheses follow. First, the phenotypic varianceshould be lower in adoptees compared with nonadopted individuals, because adoptees donot have the additional source of variance of passive gene–environment correlation. This diThe UK Biobank is an epidemiological resource including British individuals fromthe ages of 40 to 70 at recruitment . UK BiobGenotype quality-control criteria were common genetic variants of minor allelefrequency greater than 0.01 that were directly genotyped or imputed with highconfidence (information-content metric > 0.4), individuals with a genotypecall rate greater than 98% who had concordant phenotypic and genetic genderinformation, and individuals who were unrelated to others in the data set (lessthan third-degree relatives). We removed relatives using a greedy algorithm tominimize the exclusion of adoptees. To reduce confounding from populationstratification, we limited all analyses to individuals of European ancestry, asdefined by four-means clustering on the first two genetic principal componentsprovided by the UK Biobank. We also controlled for 10 ancestry principalcomponents of the European sample in all genomic analyses.Years of education, a proxy for educational attainment, was defined according toInternational Standard Classification of Education categories, as in previousgenomic studies of the phenotype in UK Biobank and other samples . Theresz test, andWilcoxon test, respectively.First, we formally tested the hypothesis that nonadopted individuals showgreater phenotypic variance than adopted individuals because of the presenceof an additional source of variance (passive gene–environment correlation).A nonparametric test was used given the nonnormal distribution of theyears-of-education variable . Thistedplyr package in the R programming environment analysis. The purpose of this was to estimate the effect sizes ofassociations between genome-wide genetic variants and years of education forthe creation of individual-level polygenic scores. We derived our basesummary statistics file for years of education by meta-analyzing summarystatistics from our own GWA analysis in this subsample with independentsummary statistics obtained from the Social Science Genomics Consortium.Our third independent sample contained 6,500 individuals, to match the samplesize of adopted individuals, on which to run polygenic-prediction models. Inthese prediction models, we regressed the years-of-education phenotype inthe UK Biobank on polygenic scores for years of education in adoptees andthen repeated the analysis in the 6,500 nonadopted individuals. In thisthird set of analyses, we used a set p-value threshold in our two independent and similarlysized samples of adopted and nonadopted individuals.As a negative control, we tested the polygenic-prediction comparison betweenadopted and nonadopted individuals for height, which has not shown evidenceof passive gene–environment correlation in previous studies . As withN = 381,654). The genetic “influence” onadoption largely arises in the biological-parent generation becauseheritable traits influence the likelihood of adoption of theirchild.Substantial heritability of our environmental moderator might haveaffected the interpretation of our main results. To explore this, wealso estimated the heritability of adoption status using LDSC in thefull sample  into deciles and tested for meandifferences in years of education between adopted and nonadopted groupsin each decile.Differences in genetic influences on the same trait across contexts—inthis case, adoption—can also be conceptualized as gene–environmentinteraction, whereby the impact of genes on educational attainment maybe contingent on adoption status. We aimed to further explore our mainresults by testing a formal polygenic-score-by-adoption interactionregression model. The model contained main effects for polygenic scorefor years of education, adoption, and covariates, plus the interactionterm, as well as interaction terms for polygenic score and adoption witheach covariate . We testN = 375,343) and in the sampleof adoptees, and then estimated the genetic correlation between themusing LDSC. Second, we tested whether education is genetically linked todifferent traits between adoptees and nonadopted individuals. To thisend, we estimated genetic correlations between years of education and247 traits, available on LD Hub , access to education increased, and there was great changein the norms and regulations surrounding reproduction, contraception,and adoption. Previous studies have found that genetic influence onyears of education increased in this period in the United Kingdom,because environmental differences between people had less influence onwhether they stayed in education . WeinveR2 statistics using the boot package inR, with 1,000 replications. Genome-wide genetic correlations wereestimated using LDSC  controlled forthe following covariates: sex, age, 10 ancestry principal components,and factors capturing genotyping batch and center. The majority of theanalyses were completed in R Version 3.5. GREML was performed in theGCTA software . GWA meting LDSC  and LD Hing LDSC . The UK The total sample of individuals with education-phenotype data andquality-controlled genotype data was 381,654. As described in the Methodsection, individuals were split into four mutually exclusive groups: (a) 6,311individuals adopted as children, (b) 318,843 nonadopted individuals for GWAanalysis, (c) 50,000 nonadopted individuals for training of polygenic scores,and (d) 6,500 nonadopted individuals for genomic analyses for comparison withadoptees. Nonadopted individuals were randomly placed into groups b, c, andd.p = .002compared with 6,500 nonadopted individuals in group d; p = 3.2× 10−5 compared with all nonadopted individuals). p = .026 compared with group d; p = .009compared with all nonadopted individuals), although point estimates were similar(56.4 vs. 56.7). There were significantly more males in the adopted group, but the magnitude of the differencewas small . Adoptees had significantly fewer years ofeducation . This is also reflected in the lower percentageof college attendees , compared with adopted individuals . However, confidence intervals were wide andoverlapped, so the difference in heritability was not significant.SE = 0.005) in the full sample ofnonadopted individuals  and 0.14(SE = 0.073) for adoptees, corroborating the pattern ofresults found using GREML. LDSC estimates are typically lower than GCTA andGREML-derived estimates . The optimal significance threshold (p)for inclusion of SNPs was 1 . Table S2 in the Supplemental Material shows the full results from thepolygenic-prediction analyses.SE = 0.008) versusnonadopted individuals  was notsignificantly different (p = .62). The optimal significancethreshold (p) for inclusion of SNPs in the polygenic score was.001.For our negative control analysis of height, as expected, the variance explainedby the polygenic score in adoptees , assuming the population prevalence ofadoption is identical to the sample prevalence (1.7%). If the actualpopulation prevalence differed and was, for example, 0.7% or 2.7%, theliability-scale SNP heritability would become 0.047 (SE =0.002) or 0.066 (SE = 0.005), respectively. Adoption statusshowed significant genetic correlations with education, age at first birth,depression, and obesity after analyses corrected for multiple testing , although these correlations shouldbe viewed with caution given the low SNP heritability of adoption. Adoptionstatus could be significantly predicted by the polygenic score for years ofeducation . The heritability of adoption was low but may haveconfounded our between-groups comparisons.We found a liability-scale SNP heritability of being adopted of 0.059. This meansthat polygenic scores had a smaller association with education in adoptees.Then, using logistic regression instead of linear regression, we also foundthat the interaction exceeded multiplicativity . The finding of interaction exceedingboth additive and multiplicative models means that the combined effect ofpolygenic score for education and adoption status is not scale dependent andis greater than either the sum or product of their individual effects,respectively.We tested a formal interaction model to further examine the finding thatgenetic influences on education are weaker in the sample of adoptees. Theinteraction between polygenic score and adoption status in predicting yearsof education is shown in SE =0.03; standardized) compared with nonadopted individuals . This mean difference between adopted andnonadopted individuals was significant in the bottom decile(p = 7.05 × 10−5) but not for other decilesof polygenic load. See Table S4 in the Supplemental Material for full results of the decileanalysis.To further explore the interaction, we plotted the mean years of educationper decile of polygenic score for years of education, separately for adoptedand nonadopted individuals. SE = 0.21). Second, we found noevidence that educational attainment was associated with different traits inindividuals who were adopted. Figure S1 in the Supplemental Material presents estimates of geneticcorrelations between years of education and 247 external traits, separatelyfor the adopted and nonadopted samples. None of these were significantlydifferent between adoptees and nonadopted individuals after multiple-testingcorrection. Because of the relatively small sample of adopted individuals,these results should be interpreted with caution.We found that largely the same genetic influences were operating on educationregardless of adoption status. First, the genetic correlation between yearsof education in adopted and nonadopted individuals was not significantlydifferent from 1, 0.81  versus from passive gene–environment correlation. We found small, nonsignificant differences in thevariance explained by polygenic scores for education depending on theyear-of-birth group considered. R2 = .04) compared with individuals reared withtheir relatives . The variance explained by polygenic scores in years ofeducation in adoptees (R2 = .04) approximated the prediction from thedirect effects of individuals’ own DNA. The difference between the varianceexplained in nonadopted individuals and adoptees suggests that about half of thepredictive power of polygenic scores for educational attainment comes from passivegene–environment correlation. We also found that individuals in the lowest decile ofpolygenic score attained significantly more years of education if they wereadopted.Cumulatively, our findings suggest that the family environment provided by relativesplays an important role in the manifestation of genetic effects on education.Polygenic scores explained significantly less variance in the educational attainmentof individuals who were adopted away from their parents as children. However, future progress in understanding themechanisms driving the transmission of educational attainment will requireintergenerational, longitudinal, and genetically informative data sets, includingdetailed characterization of the home environment. A developmental approach isuseful, because gene–environment correlations likely arise early in childhood, andthere will be complex reciprocal effects across time. Researchers have alreadystarted to pinpoint genetically influenced aspects of families that are associatedwith children’s polygenic scores for education .The evidence presented in this article highlights the importance of the familyenvironment to causal mechanisms influencing individual differences in educationalattainment. This can be through possessing genes that shape the educationalenvironment provided for offspring that also directly influence attainment in thechild or through providing an educationally supportive environment for an adoptedchild.Click here for additional data file.Supplemental material, Cheesman_Supplemental_Material_rev for Comparison ofAdopted and Nonadopted Individuals Reveals Gene–Environment Interplay forEducation in the UK Biobank by Rosa Cheesman, Avina Hunjan, Jonathan R. I.Coleman, Yasmin Ahmadzadeh, Robert Plomin, Tom A. McAdams, Thalia C. Eley andGerome Breen in Psychological Science