Each root trait was assigned a predicted importance rank based on the trait’s contribution to the cumulative reduction in the mean square error (MSE) in the RF tree regression models for SWt. The root traits were further prioritized for potential selection based on the rg and SWt correlated response (CR). The predicted importance of the eight root traits showed that the number of root tips (Tips) and root length (RLength) under HN and crossings (Xsings) and root average diameter (RAvdiam) under LN were the most relevant. SWt had a highly antagonistic rg (− 0.83) to RAvdiam, but a high predicted indirect selection efficiency (− 112.8%) with RAvdiam under LN; RAvdiam showed no significant rg or rp to SWt under HN. In limited N availability, we suggest that selecting against larger RAvdiam as a secondary trait might improve biomass and, hence, NUE with no apparent yield penalty under HN.The efficient acquisition and transport of nutrients by plants largely depend on the root architecture. Due to the absence of complex microbial network interactions and soil heterogeneity in a restricted soilless medium, the architecture of roots is a function of genetics defined by the soilless matrix and exogenously supplied nutrients such as nitrogen (N). The knowledge of root trait combinations that offer the optimal nitrogen use efficiency (NUE) is far from being conclusive. The objective of this study was to define the root trait(s) that best predicts and correlates with vegetative biomass under differed N treatments. We used eight image-derived root architectural traits of 202 diverse spinach lines grown in two N concentrations  in randomized complete blocks design. Supervised random forest (RF) machine learning augmented by ranger hyperparameter grid search was used to predict the variable importance of the root traits. We also determined the broad-sense heritability (H) and genetic ( Most plants can utilize only half of the applied N, losing it in the form of nitrates (NO3−), which can cause environmental hazards3. Spinach requires high rates of N fertilizer to produce high biomass and quality. It is estimated that about 60% of N applied to spinach in commercial production is lost through leaching4 due to its shallow root system5 and short production cycle. Spinach is also relatively poor in its NO3− reducing capacity7. About 80% of the total root length of spinach settles in the upper 0–15 cm soil layer, and the root distribution is not affected even by the addition of usable nitrates below 15–30 cm5. Thus, the rooting structure and the growth patterns that define roots are essential considerations to delineate the differences in nutrient absorption and efficiency. This is even more important in spinach due to its high affinity for N8. The morphological changes in the root system are regulated by the plant's nutritional status and interaction with the surrounding environment as detected through the localized signals by roots. Several studies have discussed the N-dependent  changes in the root architecture across species13. Therefore, investigation of root development is of importance for understanding plant responses to low-N stresses.Being the first tissues that intercept various nutrients and water uptake, roots play an essential role in plant growth and development. Root architecture highly varies in response to different nutrient deficiencies15, root development in the soilless media is entirely reliant on an exogenous supply of nutrients. Due to their inert nature, the soilless systems minimize the changes that could occur due to gradients in temperature, oxygen status, water availability, pH, bulk density, or seasonal variations. In these cases, the root structure and appearance are a function of genetics as modified by the soilless matrix, and the concentration of the nutrients applied16. Different studies have profiled root systems and their association with the environment in field conditions, non-soil media and microbes19. Modeling techniques for root feature diversity, structure, and activity have been attempted, including multivariate and machine-learning techniques22. However, much remains to decipher the genetic and potential importance prioritization of the assigned root traits in influencing the above-ground biomass.Unlike soil, where the complex root-microbial association may naturally facilitate the plant absorptive capacity of hitherto unavailable N23. However, the shorter crop duration of spinach allows only a short time for root development25. To date, much research on developing breeding strategies to improve N uptake or utilization is focused on modifying the root architecture of main crops like maize, rice, and wheat. Although several root architectural, topological, and developmental traits such as deeper and longer roots, rapid growth, and higher root density associated with higher N use efficiency have been identified27 in cereal crops, such efforts to identify root traits that respond to N stress to capture the N available at depths in vegetables are limited.Root structure and its functioning are associated with N uptake, which influences plant performance and yield. Although improving root performance is relevant to all crops, it is particularly relevant to short-cycle vegetable crops like spinach that would benefit from early below-ground vigor29. Since a soilless indoor system relies on the artificial supply of essential nutrients30, nutrient management is critical for the harvestable quality and quantity of a crop32. The differences in the value for money' between varieties of the same species may sometimes narrow down how efficiently the crop can uptake and convert the nutrients into harvestable products. Rooting system and architecture are important determinants of efficiency that maintain a favorable balance between resource investment (photosynthates) and resource acquisition 34. Varieties with favorable root architecture that enhance nutrient uptake and photosynthate use will reduce operating costs while balancing nutritional content and yield. This study investigates root traits and their relationship to the harvestable 'above-ground' biomass of spinach grown in two contrasting N supplies in a uniformly controlled indoor environment. Our assumption here is that in a uniform soilless matrix, genetics and the N management are the two primary sources of variation defining root architecture. We have used supervised random forest optimized machine learning algorithm by 'ranger'35, to predict the importance of eight root traits on the spinach's harvestable biomass at the 'baby-spinach' stage. We have also applied META-R36 to determine the genetic and phenotypic correlations and heritability to prioritize the root traits in influencing the harvestable shoot biomass. Finally, we compare the machine learning classification and the prioritization based on genetic correlations and present the top trait(s) with the highest selection potential.Soilless indoor farming is becoming increasingly popular in the recent yearsS. oleracea) accessions maintained and provided by the USDA-National Plant Germplasm System (NPGS) (https://npgsweb.ars-grin.gov/) at Ames, Iowa, U.S.A was used in the present study. The plants were grown in a growth chamber under controlled conditions of 12/12 h (light/dark), 22 °C, and 75% relative humidity. The seeds of each accession were sown in triplicate in turface  in small pots (10.2 cm × 10.2 cm and 8.9 cm deep). Each set of replicates was completely randomized across separate shelves. After the seedling emergence, plants were fertilized with Peters professional ready mix  every after four days. Two concentrations of nitrogen (N), low N (50 ppm), and high N (200 ppm) were used for low and high N management, respectively. An additional N for the high N-management was provided using calcium nitrate, and equivalent calcium (3.85 mM) was replaced by calcium chloride in the low N-management. The concentrations of the macro/micro-nutrients present in the fertilizer solution are provided in Supplementary Dataset Table A collection of 202 spinach  and the University’s Rule for the use of Biohazards and Dual Use Research of Concern , approved by the Texas A&M Institutional Biosafety Committee (IBC).37 classification and included: (1) morphology for root length (RLength) and average root diameter (RAvdiam); (2) an indication of the complexity of the root system architecture measured using number of tips, forks (number of root bifurcations), and crossings ; (3) root system of the standing crop (RSSC) for root volume (RVol), root surface area (RSarea) and root weight (RWt). The harvestable above-ground biomass was determined as fresh shoot weight (SWt)  after removing the excess surface moisture by gently paper-bloating the wet roots followed by a two-minute air drying.The plants were harvested at the physiological maturity of baby spinach (5–6 leaves) after 41 days of sowing. Each plant was carefully pulled from the turface and washed with running water to clear any debris off the roots. The roots were separated from the shoot at the cotyledonary nodes and floated in water. The lateral roots were separated gently using a fine tip paintbrush to minimize the overlapping of roots. The images were taken by digitally scanning roots of individual plants  between root traits and rg and rp between the root traits and the SWt within and between the two N managements. Parallel to the correlation analyses, we used a supervised random forest machine learning39 technique to estimate the variable importance of each root phenotype in predicting the above-ground shoot biomass. The details of the parallel procedures are described below.The analysis pipeline was designed to define the phenotypic, genotypic, and predictive relationship between the root traits and between the root traits and the SWt of spinach plants grown in a soilless system. We determined the lmer from package lme4 of R using REML via Multi Environment Trial Analysis with R, META-R36, to calculate the adjusted means  for each root and shoot variable, under the two N managements.For individual analyses, we used the model isijk is the trait of interest, µ is the mean effect, Repi is the effect of the ith replicate represented by the complete blocks, Genk is the effect of the kth genotype, εijk is the error associated with the ith replication, jth incomplete block and the kth genotype, which is assumed to be normally and independently distributed, with mean zero and homoscedastic variance σ2. For the combined analyses across the two N-managements, the model was adjusted toMgti and Mgti × Genl are the effects of the ith N-management and the N-management by genotype interaction, respectively. Genotype and N-management were both treated as random effects, and BLUPs were used to estimate random effects and BLUEs to estimate the fixed effect. Grand means were separated based on Fisher’s Least Significance Difference (LSD) at α = 5%. We also determined the coefficients of variation (CV) for all traits.Linear mixed models were implemented in H) of three replicates in each N-management, which is also an estimate of correlation expected between line means from the three replicate trials conducted in the two N-managements. H was determined40 on a line mean basis asσ2g and σ2e are the genotype and the residual error variance components, respectively; nReps is the number of replicates, σ2ge is the variance component of genotype by N-management interaction, and nMgt is the number of N-managements in the analysis.We estimated the average broad-sense heritability  is the phenotypic correlation between N-managements j and j0; and Hj and Hj0 are the heritability of N-managements j and j0 respectively, σg(jj0) is the arithmetic mean of all pairwise genotypic covariances between trait j and j0, and σg(j)σg(j0) is the arithmetic average of all pairwise geometric means among the genotypic variance components of the traits.Genetic and phenotypic correlations were calculated for each trait pair, within and across the N-managements. The 42, creating a dendrogram. In each case, a minimum heritability threshold was set at 0.1; any trait whose heritability within or between the two N-managements was lower than 0.1 was excluded from the analysis and was not plotted. For phenotypic correlations, simple Pearson correlations between different pairs of N-managements or traits were used.For graphical illustrations, cluster analysis based on the environment distance matrix (1—Genetic Correlation matrix) was also performed using the ‘Ward’ methodCRswt is the correlated response of SWt, rg is the genetic correlation, HRT is the repeatability of root traits, Vg(swt) is the genetic variance of SWt, and i is the selection intensity whose estimate we assumed would be similar between traits. Thus, CRswt was compared to direct response (R),CRswt/Rswt = rg√HRT/√ Hswt. That is, if rg × HRT > Hswt, then indirect selection would be superior46.Correlated response (CR) was predicted for SWt to determine if direct or indirect selection resulting from selecting a root trait would be superior under similar N-managements. We used the formula:randomForest47 package and first ran the regression on default tuning parameters. We also invoked a user-defined hyperparameter tuning in the ranger35 package to optimize our models; ranger is a C++ implementation of Breiman's FORTRAN-based random forest algorithm39. Finally, we compared the accuracy of the model from the randomForest default tuning and that from ranger hyperparametric search tuning. The function missForest48 was used to impute missing data. Outliers were normalized by an internally derived proximity matrix procedure built into the RF. In the normalization, if an outlier case i and case j both end up in the same tree node, increase proximity prox(ij) between i and j by 1 and accumulate over all trees in RF, the outliers are normalized by twice the number of trees in RF. This creates a proximity square matrix where observations that are ‘similar or alike’ in value have proximities close to 1 and the dissimilar proximity closer to 0.To rank the root traits by importance in the prediction models for SWt, we used the random forest (RF) modeling in R. RF is a powerful ensemble machine learning tool that combines the outputs of numerous decision tree classification models. We applied the regression type to the 49. The typical range is ~ 60 to 85%, where smaller sample sizes can reduce the training time but may introduce more bias than necessary, while too large a sample size can increase performance but at the risk of overfitting because it introduces more variance39. An F-fold cross-validation feature in RF invokes the evaluation of model performance by training it on a number of different smaller datasets and evaluating them over the other smaller testing sets. By default, randomForest randomly splits the number of datasets of almost the same sized k-folds, and each of the folder models is evaluated over the number of folders and tested on the remaining test set47. This process is repeated until all the subsets have been evaluated. The regression tree parameters are tuned further by choosing the number of independent variables (m) using the default as m = p/3, where p is the total number of root traits in our analysis. This helps generalize the data best to return the least out-of-bag (OOB) error rate and provides a built-in validation set. Further, it identifies the number of trees (ntree), required to stabilize the error rate during tuning more efficiently49. OOB error is an internal error estimate of a random forest as it is being constructed39. It is estimated by testing each tree built from the bootstrap aggregation (bagging samples) from the training set on the remaining  of the samples not used in building that tree; randomForest chooses a random subset of features and builds many regression trees, and the model averages out all the predictions of the decision trees.The default data split  were applied to train each N-management. The 63.25% is the proportion expected of unique observations in a bootstrap samplentree), producing the least OOB error rate. The term ‘Optimal’ refers to the number of trees that were just enough to stabilize the OOB error and improve efficiency by avoiding unnecessary runs, as determined from the ntree function and which.min argument. The optimal number of trees was delineated first by running 500 trees with the default 63.25:36.75 split for each N-management. A hypergrid search was then constructed across several hyperparameter combinations and looped through each combination (details are in Supplementary Dataset Table mtry (4 variables from 2 to 48), for the number of random root trait variables to include in each tree. The primary concern was to tune the number of candidate variables (features) to sample at each tree node split randomly; 2) sampsize  denoting the number of samples to train, 3) model nodesize (8 variables from 1 to 48), which determines the minimum number of samples within the terminal nodes and thus controls the complexity of the trees. This was necessary to set a bias-variance tradeoff where smaller node size allows for deeper, more complex trees with the risk of introducing more variance (risk of overfitting) and larger node results in shallower trees which may introduce more bias (risk of not fully capturing unique patterns and relationships in the data)39. The minimum OOB root mean square error (OOB_RMSE) was set at zero (0). For ntree, we used 500 because the OOB_RMSE from hypergrid searches stabilized with less than 500 trees  was used as our prediction model in a new regression run in randomForest to predict the new test set. The validation set was used as the independent test set since the sampsize split was done before bootstrapping and before sampsize split-variable randomization of the predictor root traits. Furthermore, we set importance as equals impurity' in the above modeling, which allows us to assess the variable importance of the root traits. Variable importance is measured by recording the decrease in mean square error (MSE) each time a variable is used as a node split in a tree39. The remaining error left in predictive accuracy after a node split is the ‘node impurity,’ and a variable that reduces this impurity is considered more important than those that do not. Consequently, the root variable with the greatest accumulated reduction in MSE was considered the more impactful39.We applied all the above models on the same independent test  dataset to evaluate the accuracy of the grid-tuned model compared to the default model. The best of the two , we ranked root traits based on the predicted importance of each in the models in describing its relationship with SWt. The traits with the greatest variable importance (Tips under HN and Xsings under LN) identified by ML also had the largest nts Fig. . The trarg between all traits within and between N-managements are summarized in Tables rg is to determine if a greater response on SWt would result by selecting a root trait as a secondary trait. The pairwise rg and rp between root traits and SWt were nearly identical under HN except for correlations between RAvdiam andSWt where rg = 0.045 and rp = 0.168. Under LN, the similarity was also high except for correlations between RAvdiam and SWt where rg =  −0.83 and rp =  −0.48, and between RSarea and SWt where rg = 0.05 and rp = 0.28. With the exception of RAvdiam and Xsings, the rg and rp between the other root traits and SWt were generally larger under HN compared to the corresponding rg and rp between root traits and SWt under LN  and having the largest H difference between the N-managements (53.6% in LN and 95.7% in LN). RWt had the least difference (50.3% in HN and 50.6% in the LN). H between the N-managements was very low, yet the genetic correlation was very high, suggesting that H is affected by the environmental noise between the two N-managements.The mean ts Table . Some shrg and rp were positive and highly significant in both managements, while H was medium' in the LN, 0.588; in the HN, 0.658). These observations suggest that selecting for small root diameter may be desirable for improving shoot weight of baby spinach in low N. In fact, of all the root traits in this report, only RAvdiam had a predicted high indirect selection efficiency (113%) for SWt  to SWt under LN, while the correlations were positive but not significant under HN. It was ranked among the highest in the RF regression under LN but ranked bottom in the HN. The heritability was very high (0.957) under LN compared to 0.536 under HN. On the other hand, Xsing, was ranked highest ranked by the RF regressions under LN, but lower under HN  between root traits and between the root traits and the SWt within and between the N-managements. Parallel to the correlation analyses, we used the predictive random forest machine learning technique to rank the root phenotypes according to their strength to predict SWt.The analysis pipeline was designed to define the phenotypic, genotypic, and predictive relationship between root architecture traits , root morphological traits , the root system of the standing crop  and between the root traits and the SWt of spinach grown in a soilless system. The objective was to determine root traits that have the greatest effect on the harvestable shoot under low N and thus can be used as a secondary trait to select for high NUE germplasm. We determined the phenotypic and genetic correlations  was not as high compared to H of RAvdiam (~ 96%), and with a genetic correlation of − 0.827 between them, the correlation in environmental values within N-management which dominated the phenotypic correlation (− 0.481) between RAdiam and SWt may have been mainly due to LN-management effect on SWt. Thus, an LN environment that minimizes the devaluation of the breeding values between the RAvdiam and SWt must be maintained, and we believe indoor environments may provide this condition.We predicted the correlated response (CR) in SWt resulting from selecting any of the eight root traits to speculate its suitability as a secondary trait. An important component in defining CR is the CRswt/Rswt  and RLength, but significant negative rp with Tips (− 0.238) and Xsings (− 0.310)  and the highly negative rg (− 0.827) with SWt under LN management  in our study, the RAvdiam measure can be used to indicate the ratio of axial: lateral roots.We have noticed that under HN, RAvdiam did not have significant ol Table . Meanwhiips − 0.28 and Xsiips − 0.28 and Xsirg but significant rp between RSarea and SWt, our data suggest that only a limited genetic linkage drag or pleiotropy45 on shoot yield might result from selecting against large RAvdiam. Moreover, RSarea and RVol are standing crop traits37 for ‘root bulk’, which are a product of morphological traits (RAvdiam and RLength) and root architectural traits . The significant small positive rp between RSarea and SWt may be a combined artifact of these other morphological and architectural components when we also consider a significant negative rp existed between RAvdiam and SWt in the LN management. This position is also supported by the fact that RVol had a negative rg (− 0.296) and an insignificant rp to SWt, and yet RVol had positive rg (0.439) and rp (0.931) to RLength; RLength, on the other hand, had significant rg (0.539) and rp (0.529) to SWt. RAvdiam was also highly heritable with H ~ 96% under LN, Table The genotypic correlations between RAvdiam and RSarea (0.533) and between RAvdiam and RVol (0.794) were also highly significant and positive. This implies that selecting against large root diameter may also select against RSarea and RVol under low N-management. Since there was non-significant rg − 0.29 and an iH (Table . The rg between SWt and RAvdiam can be high (Table 46. In this study, the RAvdiam met these two critical criteria. However, for practical use in a breeding program, the secondary trait must also be inexpensive and easy to measure in large trials45. In that case, shoot biomass estimate could be used to select for roots bulk traits in production systems that target spinach roots as the end product. Because precision in imaging techniques for roots and shoot is rapidly evolving58, we believe that soilless systems can be designed to facilitate robust root metrics characterization to match the ease with which above-ground biomass can be phenotyped. It would also be worthwhile to determine if further selection for/ against other root traits would eventually result in a superior secondary selection for shoot biomass. How these relationships would play along as the plants mature under different indoor growth conditions or in the field conditions require further studies.Compared to SWt, RAvdiam has shown greater H Table . The rg gh Table . In othe51. The possible complex interactions between the root traits that may have influenced the SWt were not explicitly considered in our interpretations. However, we have alluded to such complexity by describing the trait to trait correlations, which we hope should serve as an impetus for further inquiry. Although the expected genetic correlation between estimates of cultivar means are best obtained from independent sets of trials59, we hypothesize that under similar N treatments, manipulation of other growth conditions in independent indoor growth environments may lead to some deviations from the response to selection predicted here. With the advent of techniques in processing images and the deep learning60 frameworks that use advanced optimization and features from data, such prediction accuracy is likely to improve continually63. Nonetheless, machine learning recognized root traits would continue to rely on vigorous calibrations and field-based validation in systems of interest.Although a soilless system reduces the complexities associated with soils, we believe that the selection of a root trait needs to be understood in the context of the possible complex interplay among root traitsIn conclusion, we report on the investigation of eight root traits genetic and phenotypic correlations with fresh shoot biomass of spinach grown in a soilless system in a controlled indoor environment. The plants were harvested at 41 d after sowing, a stage corresponding to the marketable baby spinach. We have used both genotypes by management and other conventional breeder statistics and a machine learning predictive technique to define candidate root traits with the potential for indirectly selecting for spinach shoot yield. The experiments were set up under two separate and contrasting N-managements. Of the eight root traits, the root average diameter emerged as the only candidate with a predicted indirect selection efficiency good enough to improve shoot biomass. However, it had a robust negative genetic correlation with shoot yield, making us believe that selecting against large root diameter may improve the fresh shoot yield of baby spinach. We have exercised caution in this interpretation by recommending further studies into the possible complex interactions among the root traits considered in improving shoot biomass yield in baby spinach.Supplementary Information.


Poecilia reticulata) are typified by extreme variation governed by both natural and sexual selection. Since guppy colour patterns are often inherited faithfully from fathers to sons, it has been hypothesised that many of the colour trait genes must be physically linked to sex determining loci as a ‘supergene’ on the sex chromosome. Here, we phenotype and genotype four guppy ‘Iso-Y lines’, where colour was inherited along the patriline for 40 generations. Using an unbiased phenotyping method, we confirm the breeding design was successful in creating four distinct colour patterns. We find that genetic differentiation among the Iso-Y lines is repeatedly associated with a diverse haplotype on an autosome (LG1), not the sex chromosome (LG12). Moreover, the LG1 haplotype exhibits elevated linkage disequilibrium and evidence of sex-specific diversity in the natural source population. We hypothesise that colour pattern polymorphism is driven by Y-autosome epistasis.Male colour patterns of the Trinidadian guppy ( Extreme colour pattern variation in male Trinidadian guppies are influenced by natural selection and sexual selection. Here, the authors phenotype and genotype four guppy lineages finding that colour pattern is associated with a diverse haplotype on an autosome. However, this model neglects important factors such as pleiotropy and epistasis3. Sex-linked colour polymorphism provides a tractable trait for exploring the evolutionary and ecological drivers of balancing selection and sex-chromosome evolution5, and genome sequencing methods have hugely enhanced our ability to detect the genetic basis of colour traits6. Using a unique breeding strategy designed to delineate regions of the genome related to colour, we analyse whole-genome sequencing data to uncover the genetic basis of sex-linked colour polymorphism in the Trinidadian guppy (Poecilia reticulata).Understanding the genetic architecture of highly diverse and ecologically-important traits is a fundamental problem in evolutionary biology. This is particularly true for traits where the underlying genes are predicted to be on the Y chromosome. Because the Y-chromosome does not recombine, it is expected to degrade over time, whilst its unique inheritance from fathers to sons will select for genes that increase male fitness8. Guppy colour patterns exhibit high levels of standing genetic variation11, despite evidence that mate choice and predation impose directional selection15. Considerable evidence suggests that genetic diversity is maintained by negative frequency dependent selection (NFDS), driven by female mate preference for rare or novel morphs20 and also frequency-dependent survival22. Despite this great diversity in colour patterns, and our understanding of the evolutionary processes maintaining it, the underlying genetic architecture remains largely unknown.Guppy colour traits have fascinated biologists for a hundred years, and present an exciting system for testing predictions of sex-linked polymorphic traits. Males display a mosaic of complex and diverse colouration patterns, varying in colour, number, shape, size, and position of spots, while females are a drab and uniform tan colour24. The supergene-hypothesis originates from early pedigree studies that found patrilineal inheritance for many guppy colour pattern elements26. While clearly demonstrating the importance of the Y-chromosome for colour, this early work also reported among-population variability in the strength of Y-linkage, indicating a more complex genetic architecture. Indeed, although there is an enrichment of pigment genes on male-specific contigs27, recent studies have also highlighted the importance of X-linked and autosomal inheritance of colour traits. A QTL mapping study found that only 13% of colour trait loci mapped to the sex chromosome (LG12)28 and a pedigree analysis of colour pattern inheritance showed that ornaments are not completely Y-linked, hypothesising a potential role for Y-autosome epistasis29. Combined, this work suggests that a non-recombining, male-specific region on LG12 plays an important, but not exclusive role in guppy colour patterning.It has long-been hypothesised that colour patterning genes and the sex determining locus (SDL) form a Y-linked ‘supergene’ in the guppy32. Indeed, sex has been mapped to the distal end of LG12 in multiple mapping and pedigree crossing studies33. Other studies however, conclude that the non-recombining region extends beyond this distal region in some populations based on similar sex-specific genomic diversity measures35. Intriguingly, the distal end of LG12 has been found to be highly diverse among males with many segregating male-specific variants, indicative of multiple Y haplotypes, as would be predicted under NFDS for Y-linked colour traits35. Within this candidate region, however, no gene associated with colour or sex has been found. Clearly, more work is needed to delineate the Y-linked genomic architecture of this important trait.Recent genomic studies have therefore focussed on identifying the boundaries and genetic content of the non-recombining Y-region. Using male specific diversity across multiple populations, the Y-specific region was concluded to be small, possibly only a single gene, occurring near the distal end of LG1236. Each Iso-Y line was founded by one male showing a distinct colour pattern. This colour pattern was introgressed onto a randomised genetic background by mating males that resembled the founder, to females from a randomly-mating stock population. Outcrossing to stock population females occurred every 2–3 generations over the 40 generations that the lines were propagated. Given that each backcrossed generation theoretically reduces the parental genome by half, we expect more than 99.99% of the genome to be homogenised through this approach37. This experimental design allows us to delineate regions of the genome related to colour pattern, as it should homogenise regions unrelated to the colour differences among lines. Using a Pool-seq approach on each Iso-Y line, we find that the lines are consistently different on an autosome (LG1), not the sex chromosome (LG12). In order to examine the LG1 colour-linked candidates in a natural population, we then conduct an analysis of whole-genome sequencing (WGS) data from the source population, finding that a large and diverse autosomal haplotype is maintained in nature. We hypothesise that colour pattern variation is driven by Y-autosome epistasis. This genetic architecture could help to explain how high levels of Y-linked diversity is maintained in guppy colour patterns.In this work, we use an innovative approach to identify genomic regions associated with highly variable, sex-linked, colour polymorphism in guppies. We phenotype and genotype four ‘Iso-Y’ lines, which originated from a natural population, and show strong Y-linked parental heritability in colour pattern38. Consequently, we used multispectral digital photography to capture human-visible and ultraviolet images of males from each Iso-Y line. We used geometric morphometrics to correct for individual differences in body size and shape among fish so that colour patterns could be measured as though they existed on identical male bodies. We then used the Colormesh pipeline39 to extract colour measurements from these images at sampling locations across the body and caudal fin.Male guppies have an ultraviolet component to their colour patterns, and guppies can detect and adjust their social behaviour based on ultraviolet colouration41 (see ‘Methods’ for details) revealed that males from the different Iso-Y lines were well-separated based on colour pattern. Discriminant functions (DF) 1, 2 and 3 accounted for 51.9%, 36.8%, and 11.4% of the variation among the Iso-Y lines, respectively ely Fig. , and disely Fig. . Variatiely Fig. .Fig. 1DiP < 0.001). Post-hoc pairwise tests revealed significant differences in colour pattern among all pairs  resulted in a final dataset of 3,995,905 SNPs. Mean pairwise FST between the Iso-Y lines was high overall (FST = 0.091). We first used pairwise FST values among the four Iso-Y lines, and then used a multivariate approach by normalising FST to Z-FST and summarising these with PCA FST42. The aim here was to summarise covariance of FST among comparisons and assess whether certain regions were consistently differentiated among the Iso-Y lines. Z-FST PC1 accounted for 37% of the total variance and reflected positive covariance in all pairwise FST comparisons (Supplementary Table Using a pooled whole-genome sequencing (Pool-seq) approach and summarising all pairwise comparisons with a PCA, we were able to identify where along the genome the Iso-Y lines were consistently different Fig. . Pool-seFST PC1 scores  and the highest percentage of SNPs with a Z-FST PC1 score above an upper 95% quantile of 3 . The remaining 47% of high-scoring SNPs were distributed across the genome, with other individual chromosomes or scaffolds accounting for <7% of high-scoring SNPs  showed high positive loadings among five of the six pairwise comparisons  highlighted the same regions of differentiation as PC1  and thus high Z-FST-LG12 PC1 scores reflected the haplotype associated with the Iso-Y9 phenotype. Z-FST-LG12 PC2  loadings were high for the remaining two comparisons with Iso-Y6. This suggests SNPs with high Z-FST-LG12 PC2 scores reflect the haplotype associated with the Iso-Y6 phenotype. Z-FST-LG12 PC3 reflected the final comparison, Iso-Y8-Iso-Y10. Z-FST-LG12 PC2 and PC3 also reflected Iso-Y line-specific loadings  on the allele frequencies  and Z-PC1 Fig. . Region PC1 Fig. .31.Next, to explore diversity within the Iso-Y lines, we calculated π across 10 kb windows for our two focal chromosomes (LG1 and LG12) and performed the same multivariate approach as above. On LG1, we found that regions of differentiation could be explained by a shared chromosomal landscape of diversity among all Iso-Y lines with Z-π-LG1 PC1 (PC1 captured 74% of the variance) accounting for the majority of variance in diversity  in Region 2 , two bands of  Mb, two FST Fig. . CorrespWe found several strong candidates for colour, male-specific fitness and vision in the three differentiated regions on LG1  contained 291 predicted genes. Genes with a potential role in colour included xpa, involved in pigmentation and photosensitivity to UV light48, pcdh10a involved in melanocyte migration, crebbpa, which has been identified as a candidate for plumage colouration in chickens49, and shoc2, which causes pigmentation abnormalities50, as well as five keratin genes, which have a role in pigmentation51. We also identified five retinal genes , and three genes involved in spermatogenesis or sperm motility 59. Region 3 (21.9–24.9 Mb) contained 94 predicted genes. This region also contained several promising candidates including two paralogs annotated as kita, previously identified as a key gene involved in pigment pattern formation in guppy strains60 and zebrafish61, sox10a, a sex determining region Y-box that regulates the expression of the mitf gene, which is the master regulator of melanophore–melanocyte differentiation in teleosts62, and is also responsible for colouration in rock pigeons63, mchr1, a melanin-concentrating hormone receptor, and a TRYP, located in melanocytes and involved in the production of melanin64. We also performed an assessment of Gene Ontology (GO) enrichment and KEGG mapping for the three regions on LG1 (see Supplementary Data Region 1 (4–5.9 Mb) contained 62 predicted genes. Of interest was nfemales = 16, nmales = 10, average coverage ≥13×, final dataset = 1,021,495 SNPs). Using multiple lines of evidence, we found a large haplotype on LG1 (11.1–15.9 Mb) segregating in the natural source population, which lies within ‘Region 2’ identified in the Iso-Y analysis (9.6–17 Mb). We term this area ‘Region 2-NP’   on LG1 revealed an area of high linkage between 11,114,772 and 15,890,374 bp, where it was apparent that several overlapping linkage blocks exist Fig. . We also LD Fig. , with a FST showed differences between the sexes within Region 2-NP   Fig. . A localMb) Fig. . MDS1 ouMb) Fig. .FST was observed , where male-specific Da was notably higher in high-predation (HP), compared to low-predation (LP) populations31. Moreover, the LD in this region extends across 4.6–6 Mb which includes another previously identified male-biased candidate region (LG12: 4.8–5.2 Mb)31. An assessment of the gene annotations within the MDS2 coordinates identified only a few candidates of interest , which is responsible for caudal fin patterning in Danio rerio73, and two male-trait candidates: AIG-1 (androgen-induced protein-1) family, and spag16 (sperm-associated antigen 16) ion Fig. , and anaity Fig. . In contFST and a reduction in male diversity. Structural variant (SV) analyses using short-read and long-read data did not show support for SVs in Region 2 nor Region 2-NP , 17  shared the same overall genotype signature of HOM ALT genotype blocks as seen in Iso-Y9. Seven individuals  showed genotype blocks alternating between areas with the Iso-Y9 HOM ALT genotype signature, and areas of heterozygosity. Lastly, only two individuals showed a signature of extended blocks of HOM REF genotypes: NAT08 and NAT16 , yet HOM REF genotypes were only maintained for a proportion of the entire region.Individual genotypes of the Iso-Y lines and the natural population data across LG1 revealed long stretches of maintained genotype states within Region 2-NP Fig. . In the ntotal = 9), we found evidence of two large divergent haplotypes encompassing the entirety of Region 2-NP with subsequent recombination at conserved breakpoints ; BP2: 11.7 Mb ; BP3: 12.2 Mb ; BP4: 13.1 Mb ; BP5: 14.4 Mb ; BP6: 15.4 Mb .By phasing the heterozygous individuals , there was a distinct difference in zygosity between males and females . Therefore, males are out of HWE; based on the female AFs, we would expect 5 HOM ALT, 3 HET and 2 HOM REF in males. The region delineated by BP3 to BP4 overlaps with a high density of SNPs showing signatures indicative of sex-differential selection (12.2 Mb to 13.1 Mb). The only breakpoint consistent between males and females (BP4) also distinguishes the break in LD in males, the drop in gene density, and a break in derived ancestry estimates of 100 bp windows , consistent genetic differences are most pronounced on an autosome, LG1. Analysis of the phenotype data showed that the breeding design was successful in producing four distinct Iso-Y lines with marked differences in colour pattern. Using these unique Iso-Y lines, we delineated three regions on LG1 that were consistently different among the differently coloured lines, and within these regions we identified many genes known to be linked to colour in model species. Then, using extensive WGS from the source population, we further highlight just one of these regions (Region 2-NP: 11.1–15.9 Mb), as having strong linkage and significant local ancestry, finding that a large and variable haplotype is maintained in nature.FST across the chromosome is expected due to sex linkage, we found no evidence of a consistently differentiated region on LG12. Moreover, all guppy chromosomes are acrocentric and show evidence of male heterochiasmy74; yet recombination events are particularly rare on LG12, implying that LG12 may decompose at a slower rate compared to autosomes. Our LG1 haplotype on the other hand, shows consistent differentiation between the lines. The near fixation of the LG1 Region-2 haplotype between the lines is strong evidence for this region harbouring genes involved in colour.We had hypothesised that the Y-linked colour pattern genes in our Iso-Y lines would be located on the sex chromosome, LG12. If colour pattern traits are fully Y-linked, and each Iso-Y line’s unique Y haplotype is fully inherited through the patriline, then with this breeding design we would predict a consistent pattern of high differentiation in the Y-linked region on LG12 between all Iso-Y line comparisons. Instead, we see that overall, the chromosome shows moderate divergence, driven by elevated differentiation in comparisons to Iso-Y9 and localised regions of differentiation in comparisons with Iso-Y6. Whilst elevated 33 . Previous research on this population of guppies (Paria) also supports our working hypothesis. Testosterone-treated females from Paria displayed high amounts of colour, suggesting an autosomal component to colour expression77. However, it has also been found that males in Paria exhibit strong patrilineal inheritance of colour pattern, suggesting the importance of the Y36. Given the success of our breeding design, where introgressed Iso-Y lines were significantly different in colour, we also found strong evidence for Y-linkage for colour. Ongoing work is directly testing the roles of Y-autosome epistasis versus Mendelian inheritance on guppy colour pattern by conducting crosses between Iso-Y lines with different LG1 haplotypes. Furthermore, it would be interesting to quantify the colour patterns of testosterone-treated females derived from these lines to more fully explore inheritance patterns in females.Our hypothesis is that colour pattern is controlled by the epistatic interaction between Y-specific regions and our candidate region on LG1 in this population. Y-autosome epistasis has been reported previously in other systems. For example, polymorphisms on the gene-poor Y chromosome in 31. We found that this difference is caused by a reduction in expected diversity in males, where males were not in HWE in the region from 11.1 Mb to 13.1 Mb (start of Region 2-NP to BP4), although females were in HWE. This could be indicative of a deleterious Y-autosome interaction, where certain Y haplotypes are incompatible with the ‘REF’ LG1 haplotype. Guppy adult sex-ratios, are indeed, generally female-biased81, and show a stronger female-bias in upstream low-predation (LP) environments, like Paria, albeit with sampling variability81. We found no evidence for large structural rearrangements (such as inversions) underlying the maintenance of our candidate region, LG1 Region 2-NP, and did not detect any relationship with our predicted conserved recombination points, nor increased GC or TE content. Therefore, exactly which molecular traits are driving this haplotype structure is unclear. By examining phased heterozygous individuals, it is however, apparent that crossing-over is restricted to key points along the haplotype and overall linkage is maintained in the population. Models of balancing selection show that balanced variants produce diversity patterns similar to those caused by positive selection82, and simulations suggest that balancing selection alone can maintain high-LD, and in particular, high divergence between colour phenotypes83. Taken together, our natural source population data reveals interesting signals in this region but determining the selective forces responsible for its maintenance requires a larger sample size, and colour pattern phenotype data from the natural source population, particularly for recombinant males.By further exploring our natural source population data, we can begin to hypothesise how this epistatic interaction might operate and how it may lead to the maintenance of Y-linked variation in colour. We recorded differences between the sexes in LG1 Region 2-NP, although this region did not appear in a previous analysis examining consistent differences between the sexes across multiple populations85. On the other hand, it is also contended that sex differences on autosomes are artefacts caused by duplications or translocations onto the Y chromosome86. Read coverage was not increased in the LG1 region, and we found no evidence of reduced mapping quality, which would be expected if this region was the result of a duplication or translocation event. Nor do we find evidence that our candidate region on LG1 is misassembled; we previously found strong Hi-C contact across the chromosome, although the genome assembly is derived from an individual from a different population31. We also found no evidence that a translocation from LG1 to LG12 had occurred uniquely in this population in our SV analyses, and we did not observe elevated inter-chromosomal LD in the natural data , but these results were not repeated across other HP-LP pairs32. Our candidate region on LG1 may explain differences in Y-linkage between predation ecotypes. Specifically, we identified a region between 12.2 Mb to 13.1 Mb with reduced diversity in males, compared to females, which also corresponded with a break in male patterns of LD. Previous analysis of molecular convergence between HP and LP populations identified two outlier windows in this area (12.17–12.18 Mb and 12.21–12.2 Mb), indicating that this particular region may be under divergent selection for HP-LP phenotypes92. We further compared WGS data from other populations across Trinidad at LG1, and detected a strong signal of HP-LP association within 12.2 Mb to 13.1 Mb, but the large haplotype structure is unique to the population studied here  environments and X-linkage in the upstream, low-predation (LP) environments. Whether Y-linkage varies by predation environment has been indirectly studied across Trinidad, where females treated with testosterone exhibited more colour patterns in LP populations compared to their HP counterparts93. Recognition of the importance of epistasis in response to selection is growing, and epistasis may be responsible for an increased, or non-linear rate, of adaptation in natural populations or artificial selected lines94. Additionally, having loci under NFDS not physically linked to the Y can shield them from increased drift experienced on the Y, allowing for higher levels of variation to be maintained95. Finally, for NFDS to operate, we would hypothesise that there should be a balance between keeping coadapted alleles together and breaking them apart to create variation. Together, this suggests that Y-autosome epistasis acting on a diverse autosomal haplotype presents a feasible hypothesis for the maintenance of colour pattern traits. The Iso-Y lines offer a unique resource to explore interactions between LG1 and LG12, and also to further distinguish the role of the three different regions on LG1 by performing focussed crosses between Iso-Y lines. Future studies should also aim to fully characterise the diversity of LG1, including additional long-read sequencing of multiple individuals from both LP and HP environments in order to determine the reservoir of variable haplotypes present in this region.Based on our Iso-Y lines and natural population data, we hypothesise a Y-autosome epistatic genetic architecture for guppy colour traits. This architecture may be particularly well-suited to a Y-linked trait under NFDS, such as guppy colour pattern. Models suggest that sex-linked polymorphism can only be maintained by natural selection in unusual genetic systems, where the maintenance of Y-linked variation in Y-autonomous models involves frequency-dependent selection, or interactions with other chromosomes19. Each Iso-Y line was maintained by breeding males with colour patterns similar to that of each line’s founder; hence, the colour patterns of the Iso-Y lines are ecologically relevant. Every generation, males were mated to females sired by males from the same line, or, every 2–3 generations, backcrossed into the stock population derived from the same Houde tributary. The lines have been maintained at Florida State University since 2012.All procedures involving live animals were reviewed and approved by the Florida State University Animal Care and Use Committee (protocol no. 1442 and no. 1740). The Iso-Y lines were kindly provided by AE Houde, who established them by choosing male lineages in which colour pattern on the body was strongly Y-linked. Each line was founded by a single male drawn from the ‘Houde’ tributary of the Paria River in Trinidad . Males from this tributary are known to show strong Y-linkagen = 41; Iso-Y8n = 48; Iso-Y9n = 42; Iso-Y10n = 42). Fish were lightly anesthetised by immersion in a Tricaine mesylate (Pentair) solution and placed on a clear petri dish above a grey background with the left side of the body facing upwards. A soft tip miniature paint brush was used to raise the dorsal fin, flare the caudal fin, and lower the gonopodium so that these appendages were visible. Fish were illuminated by four metal halide lights  that simulate the natural photic environment. A size standard and two full-spectrum colour standards  were included beside the fish. Glare and shadow were minimised by placing a diffuser (cylinder of 0.015” polytetrafluoroethylene) around the fish and colour standards. We photographed each fish once in the human visible spectrum (Baader UV/IR cut / L-Filter) and once in the UV spectrum (Baader U-Venus-Filter 350 nm).We used multispectral digital photography  to capture human-visible and ultraviolet images of males from each Iso-Y line . Images of each individual were unwarped to this consensus shape, thereby mapping every pixel from the original image to an analogous location on the consensus shape.Morphometrics were performed using the TPS Series software39 was performed in R v4.0.2. We first performed Delaunay triangulation, which is used to reconstruct a complex shape (i.e. the shape of the unwarped fish) using a concise number of points distributed across the surface of that shape. We then measured the average colour of pixels in a radius around each of these sample points. We used cross-validation to determine the optimal number of Delaunay triangulations (more triangulations result in more granular colour pattern data) and sample circle radius (see below). At each sample point, we extracted linear colour measurements for four colour channels: R (red), G (green), and B (blue) and UV. We accounted for any minor fluctuations in the lighting environment by calibrating the colour values for each channel by subtracting the average deviation of colour measured in the photo on the white and grey colour standards from the known reflectance values of those standards.Analysis using Colormesh v2.040 to perform a Principal Components Analysis (PCA), followed by a discriminant analysis to define the linear combinations of PC scores that minimise within and maximise between group variances.We used Discriminant Analysis of Principal Components (DAPC) to describe the properties of colour pattern as this analysis is recommended for characterising the properties of groups using high dimensional data sets. We used the dapc function in adegenet v2.1.339. We used cross-validation to determine the optimal number of PC’s to retain, number of Delaunay triangulations to perform, and sample circle radius. Using the xvalDapc function, we performed DAPC on training and validation data, and examined the average proportion of successful assignments for a varying number of retained PC’s. We defined the training and validation populations each as 50% of the individuals from each line. We set the maximum number of PC’s to retain for cross-validation as n.pca = 173 (the number of fish), with cross-validations performed at 17 different retention levels in increments of 10 PC’s (up to 170). We performed 100 replicates per PC retention level. The average proportion of successful placements was maximised (at 98.8% successful) by retaining 10 PC’s, using four Delaunay triangulations, and a sample circle radius of one pixel. Consequently, we used this sampling scheme to measure colour pattern for all phenotypic analyses, retaining 10 PC’s for DAPC. This scheme resulted in 9904 colour measurements per fish (four colour channels * 2476 sampling locations), with colour averaged over 5 pixels per sample point.We used DAPC in a cross-validation framework to determine the scheme for capturing colour data that allowed us to best discriminate among the Iso-Y linesTo visualise the colour variation summarised by the discriminant functions, we generated heat maps depicting the correlations between position on each discriminant function and colour for each colour channel at each sampling location.98, which computes the pairwise distances among observations and then performs a permutation test (randomly assigning labels among factors) to partition the distance matrix among sources of variation. P-values were then calculated using two-sided pseudo-F ratio tests. We used Euclidean distance and created 10 000 permuted samples per test. We additionally visualised the differences in phenotype among Iso-Y lines by generating density plots of each Iso-Y line for all 17 PC’s used in permutational MANOVA . We then used permutational t-tests to determine whether phenotypic variance differed between each pair of lines, using the sample function. We permuted the line labels for each whole-fish colour pattern, thereby accounting for the fact that different colour measures on the same fish are not independent of one another. We created 10 000 permuted samples per test and performed two-tailed tests.99. DNA quality was assessed using gel electrophoresis and DNA concentration calculated using Quant-iT Picogreen dsDNA reagent (Invitrogen) on a Glomax Explorer Microplate reader (Promega). DNA of each individual was diluted to 18-22 ng/µl and 4 µl of each added to a pooled sample per Iso-Y line. Pools were cleaned using a NEB Monarch clean up kit, with final concentration and quality of each confirmed using a Nanodrop ND-1000 (Thermo Fisher) and a Bioanalyser (Agilent). Library preparation and sequencing was performed at the University of Exeter Sequencing Service, using a NextFlex RAPID PCR-free library preparation protocol. Each of the libraries were sequenced across multiple lanes on a HiSeq 2500 in standard mode, with a 125 bp paired-end metric  with bwa mem v0.7.17101 and converted to sorted bam alignment format with samtools v1.9102. Coverage was calculated using qualimap v2.2.1103. Variants were called using Freebayes v1.3.1104 with GNU parallel105 by chunking the alignment files into regions based on coverage using sambamba v0.7106. Freebayes was run with the options: --use-best-n-alleles 4 -g 1000. The raw variant output was filtered for bi-allelic SNP variants at QUAL > 30 and DP > 10, followed by a maximum missing filter of 80% applied to each pool separately followed by the application of a minor allele frequency (maf) of 25% applied across all pools using vcftools v1.9107. The VCF file was used as input to poolfstat v1.2108, where the variants were filtered to exclude sites at <30× minimum coverage and <500× maximum coverage per pool, with a minimum read count per allele of 10 . We used the curated liftover for LG12 for all analyses and plots of LG12109.Raw reads were cleaned using cutadapt v1.13n = 9) and used these with previously available data31 (Supplementary Data n = 17)31. Although the Paria and LP Marianne guppies are sampled from different sites, there is strong evidence that gene flow occurs between the populations occupying the upper reaches of these rivers111. We found that genome-wide mean FST calculated between populations in this dataset was 0. Importantly, there was no effect of river on haplotype structure . Variants were phased individually with Beagle v5.0113, and then phased again using Shapeit v2.r904115 making use of phase-informative reads (PIR)116. We used the curated liftover for LG12 for all analyses and plots of LG12109.For the WGS of 26 wild-caught guppies, we sequenced individuals from the Paria river  we generated 20 Gb of long-read Pacbio data from one of the Iso-Y individuals (Iso-Y6). High molecular weight DNA was extracted using DNeasy Blood & Tissue Kit  with modifications (10× Genomics Sample Preparation Demonstrated Protocol and MagAttract HMW DNA Kit handbook). Data were sequenced on 3 SMRT cells of a PacBio Sequel at the University of Exeter Sequencing Service. For phasing, reads were aligned to the guppy genome using minimap2 v2.17FST was calculated using the Anova FST method implemented in poolfstat v1.2108. Per SNP FST values were compared pairwise between each Iso-Y line. To identify chromosomes with the highest mean variance in FST differentiation across our dataset, mean Z-scores of each PC were summarised for each chromosome42. These were calculated using the prcomp function using stats v3.6.2, centering and scaling the results.Analyses were conducted in R v4.0.1. Pairwise FST analysis, we evaluated the allele frequencies (AFs) of each line. AFs were extracted from the Pool-seq object generated by poolfstat and were polarised to Iso-Y9 (the line which showed the highest genetic differentiation). To explore delineation breakpoints in the AFs, we adopted the use of change point detection (CPD) analysis. CPD was conducted in R using changepoint v2.2.2119. We used individual AFs from each Iso-Y line as input to detect mean changes, using the BinSeg method and SIC criterion. The number of changepoints identified is Q; in cases where several change points were detected, we increased the value of Q to 10. To add support to the change points detected using the AFs, and to ensure we were not missing any additional breakpoints, we also used PC1 FST scores as input. In cases where multiple change points were detected within close vicinity of one another, caution was taken to delimit the smallest region in each case; this was to correctly identify the minimum unit of inheritance. Within the identified CPD regions, we further inspected the segregation of Iso-Y line alleles responsible for driving differentiation by plotting the AFs of each identified region120.To delineate line-specific blocks apparent from the distinct patterns of differentiation observed in the 121. To summarise the among-Iso-Y line variation, per SNP π values were used as input to PCA, calculated using the prcomp function.To assess diversity among the Iso-Y lines, π was calculated from the Iso-Y line allele frequencies on a per base pair basishttps://www.ebi.ac.uk/ena/browser/view/GCA_904066995) using samtools faidx (v1.9)102 and aligned them to the previous guppy genome assembly (https://www.ebi.ac.uk/ena/browser/view/GCA_000633615.2) using minimap2 v2.17117 and pulled the uniprot gene IDs from the annotation using biomaRt v2.44122. GO enrichment and KEGG mapping were performed using clusterProfiler v3.18.1123. For KEGG mapping, we used Ensembl’s gene dataset for the species as the universe. For GO enrichment, we used the AnnotationHub v2.22.1 to pull the latest available OrgDb (AH86018).For functional gene annotation, we extracted the regions of interest from the guppy genome  was calculated among polymorphic SNPs for LG1 and LG12. Invariant positions were removed using bcftools v1.865. Local PCAs were run with three PCs mapped onto three MDS. Mapped eigenvalues > 0.01 were assessed for saturation before defining significant MDS. Significant outlier windows of each MDS were defined by first calculating 3 standard deviations of the mean of the MDS distribution after trimming the 5% tails of each distribution, followed by returning all windows at the extremes of the distribution. To balance loss of power and sensitivity, local PCAs were assessed in both 10 bp and 100 bp windows  support > =median RG; manta SVs were filtered at a quality score > = 999 and only events where both paired-read and split-read support at values realistic of the overall read depth were retained; for Lumpy/smoove SVs, events that had evidence of both split read and paired end support at realistic read depth values were considered. We excluded SVs < = 10 kb. We also made use of our long-read sequencing data from one Iso-Y line individual (Iso-Y6) using sniffles v1.0.12132 and PBSV v2.3.0 (https://github.com/PacificBiosciences/pbsv). Any suspected SVs were manually inspected in the Integrated Genomics Viewer .For the medium-coverage WGS data derived from wild-caught individuals we used BreakDancer v1.4.5bamCoverage option of deeptools v3.3.1134. The first and last 100 kb of each chromosome were trimmed before estimating coverage with a binSize = 50, smoothLength = 75, and an effectiveGenomeSize of 528,351,853 bp (genome size minus masked and trimmed regions). The ends of chromosomes were trimmed because they often showed high peaks of coverage, thereby distorting the normalised measures across the chromosome. Coverage estimates were normalised using RPGC (reads per genomic context). Bins with normalised coverage >4 (four times the expected median of 1) were filtered. For the natural WGS data, coverage was averaged within populations. Outputs were converted to bed files with window sizes of 1 and 10 kb by taking weighted means.Coverage was estimated from bam files using the 135. For the haplotype-based analysis, we polarised the phased haplotypes to Iso-Y9. Breakpoints between the phases were quantified by identifying the location (in bp) where phase0 switched to phase1, and vice versa. Switchpoints were quantified in males and females and a switchpoint was considered to be conserved when the locations (within 50 kb) overlapped in two or more individuals.Genotype and haplotype plots were created using Genotype Plot in R120.Inter-chromosomal linkage was calculated as above for intra-chromosomal linkage calculating r2 values between LG1 and LG12 using the --inter-chr flag in plink v1.9, outputting a normal pairwise matrix. Results were plotted in R using custom scriptsFurther information on research design is available in the Supplementary InformationPeer Review FileDescription of Additional Supplementary FilesSupplementary Data 1Supplementary Data 2Supplementary Data 3Supplementary Data 4Supplementary Data 5Reporting Summary


Our objective was to identify the genomic regions and candidate genes associated with AFE, egg production at 43 weeks (EP43w), and egg production at 66 weeks (EP66w) in a Shaoxing duck population using genome-wide association studies (GWASs) and haplotype-sharing analysis. Single-nucleotide polymorphism (SNP)-based genetic parameter estimates showed that the heritability was 0.15, 0.20, and 0.22 for AFE, EP43w, and EP66w, respectively. Subsequently, three univariate GWASs for AFE, EP43w, and EP66w were carried out independently. Twenty-four SNPs located on chromosome 25 within a 0.01-Mb region that spans from 4.511 to 4.521 Mb were associated with AFE. There are two CIs that affect EP43w, i.e., twenty-five SNPs were in strong linkage disequilibrium region spanning from 3.186 to 3.247 Mb on chromosome 25, a region spanning from 4.442 to 4.446 Mb on chromosome 25, and two interesting genes, ACAD8 and THYN1, that may affect EP43w in laying ducks. There are also two CIs that affect EP66w, i.e., a 2.412-Mb region that spans from 127.497 to 129.910 Mb on chromosome 2 and a 0.355-Mb region that spans from 4.481 to 4.837 Mb on chromosome 29, and CA2 and GAMT may be the putative candidate genes. Our study also found some haplotypes significantly associated with these three traits based on haplotype-sharing analysis. Overall, this study was the first publication of GWAS on egg production in laying ducks, and our findings will be helpful to provide some candidate genes and haplotypes to improve egg production performance based on breeding in laying duck. Additionally, we learned from a method called bootstrap test to verify the reliability of a GWAS with small experimental samples that users can access at  Egg production traits, including age at first egg (AFE) and egg number (EN), have always been a focus of attention in laying ducks, as they directly affect economic benefits to farmers. EN has experienced considerable genetic progress in commercial laying ducks breeds through traditional selection for several decades, reaching a level at an egg on almost every day in highly efficient laying ducks. AFE is also a very important trait for egg production, as it is a partial determination of the laying period. Nowadays, young laying ducks as early as 16 weeks of age start to produce their first egg.https://www.animalgenome.org/cgi-bin/QTLdb/GG/index) reported 185 QTLs on 24 different chromosomes associated with AFE, EN, and egg production rate in chickens  has become an exceedingly effective and widely used approach in the identification of genetic variants associated with complex traits since the first application of GWAS research on age-related macular degeneration was performed successfully in 2005 by Klein et al. . ShaoxinA total number of 166 Shaoxing ducks from Hubei Shendan Co., Ltd.  were used in our study. Blood samples were collected from brachial veins using the standard procedure in week 66. All ducks were housed in individual cages of the same condition. The AFE and weekly egg production from the onset of laying eggs to 66 weeks of age for each duck were recorded, and then the data were used to define two egg production traits, as the EN from the onset of laying eggs to 43 weeks (EP43w) and the EN from the onset of laying eggs to 66 weeks (EP66w). Animal care and use protocol was approved by the Institutional Animal Care and Use Committee of the Zhejiang Academy of Agricultural Sciences , which was in accordance with the Guidelines for Experimental Animals established by the Ministry of Science and Technology .A standard cetyl trimethylammonium bromide (CTAB) method was used to isolate genomic DNA from blood, and agarose gel electrophoresis was used to examine the quality and quantity of DNA. After the examinations, paired-end libraries were generated for each eligible sample using standard procedures. Fragments were end-repaired, A-tailed, ligated to paired-end adaptors, and PCR amplified with 500-bp inserts for library construction. According to the manufacturer’s standard protocols, libraries were subjected to 150-bp paired-end sequencing on a HiSeq platform , to a mean sequencing depth of 10× for experimental animals. The depth ensured the accuracy of variant calling and genotyping and met the requirements for population genetic analyses.http://broadinstitute.github.io/picard) to avoid any influence on variant detection. For GATK SNP calling, standard preprocessing  and calling procedures were used  using default parameters . On averere used , each saere used . SNPs there used .p-values of markers was used to calculate the genome-wide false discovery rate (FDR) following Storey and Benjamini  was employed for the single-marker association test between variants and phenotypes underlining a univariate linear mixed model see  and is dtion see , and Inenjamini . The matf a GWAS . Quantil2 = 0.4. After the CIs were determined, an investigation of gene ontology (GO) for the genes within the CI was performed to determine biological processes associated with traits using the Database for Annotation, Visualization and Integrated Discovery (DAVID) (http://david.abcc.ncifcrf.gov/home.jsp) (To detect the linkage disequilibrium (LD) of SNPs near the most significant SNPs in the GWAS results, the 3-Mb region near the top SNPs in the whole-sequence association results was used to conduct LD analysis by extracting genotypes from the data set using plink 1.07 , and theome.jsp) .In addition, the haplotypes in the CI were constructed by fastphase with the default setting, and an attempt to find the sharing susceptibility haplotype was made by thoroughly scanning the haplotypes of all individuals .In this study, the bootstrap test was carried out to verify the reliability of GWASs, which was a resampling technique used to estimate statistics on a population by sampling a dataset with replacement. This method can be used to estimate summary statistics such as the mean, SD, CI, or correlation coefficient, which is done by repeatedly taking small samples, calculating the statistic, and taking the average of the calculated statistics. There were two steps for the bootstrap test in this study; first, random resampling was performed 1,000 times with replacement, in which some individuals can be sampled multiple times, while some may be sampled for 0 times. Then GWASs were conducted 1,000 times to see if there were still significant signals in the susceptibility region identified in our study. Our null hypothesis of bootstrap in our study is that more than 950 out of the 1,000 GWASs did not detect significant signals in the candidate region, which indicates that the fluctuation in the data structure of our experimental population has an effect on GWASs; in other words, the significant signals obtained in the GWASs were not accidental but were caused by differences in the genomes of the experimental individuals, which were reliable .p-values of those sites on chromosome 25, and all significantly associated loci that surpassed the FDR corrective threshold are shown in p-value = 2.91E−08, Qvalue = 1.881E−03) was located at 3,219,815 bp on chromosome 25 (λ) of the GWASs were 1.01, 1.02, and 1.01 in the three traits, indicating that population structures were properly corrected.After quality control, a total of 6,746,746 SNPs and 166 individuals were retained for further analyses. Association tests for AFE, EP43w, and EP66w were performed using a univariate linear model, and the threshold obtained by the naïve Bonferroni was 7.41E−09. The result showed that there was no SNP in the AFE and EP43w that surpassed this threshold, except for two SNPs on chromosome 29 that surpassed this threshold for EP66w . It was osome 25 . In addiosome 25 . For theosome 25 . In addiosome 25 . The avehttp://david.abcc.ncifcrf.gov/home.jsp), nine significant GO terms were identified  analysis, for AFE trait, we identified 23 SNPs that have strong LD status in the most significantly associated SNP 25_4513397 , which wentified , and most-test with haplotype 1 and chaotic haplotype , which indicated that haplotype 1 has a significant effect on EP43w. In addition, we also found four haplotypes in the CI  that were related to EP43w  is indicative that haplotype 1 has a significant effect of increasing EP66w. For EP66w , which indicated that haplotype 1 has a significant effect on EP66w.Through LD analysis, we obtained some corresponding CIs for AFE, EP43w, and EP66w, and then we performed a haplotype-sharing analysis of these intervals. The results are shown in to EP43w  and nameor EP66w , anotherAlthough these studies revealed some crucial discoveries, there were some limitations, such as the relatively small number of samples in our experimental population. Therefore, we herein carried out a bootstrap test to verify the reliability of GWASs in our study. For trait EP43w, there are 985 of the 1,000 GWASs that did not detect significant signals  in the interval from 3,216,505 to 3,238,808 bp on chromosome 25, and there are 931 of the 1,000 GWASs that did not detect significant signals in the interval from 4,442,034 to 4,513,397 bp on chromosome 25. For trait EP66w, there are 987 of the 1,000 GWASs that did not detect significant signals  in the interval from 129,826,588 to 129,903,609 bp on chromosome 2, and there are 992 of the 1,000 GWASs that did not detect significant signals  in the interval from 4,481,956 to 4500595 bp on chromosome 29. These results indicated that the fluctuation in the data structure of our experimental population has an effect on GWASs (FDR < 0.05); in other words, the significant signals obtained in our GWAS were not accidental but were caused by differences in the genomes of the experimental individuals, which were reliable.Egg production is an important economic trait. So far, many studies have focused on the genetic determinants of AFE, EP43w, and EP66w in chicken and have reported some candidate QTLs and genes . HoweverGenetic parameter estimates show that AFE, EP43w, and EP66w are medium heritable traits, which approximately coincided with the report by Chen et al. . Our resWe conducted a GWAS in Shaoxing duck population and provided strong evidence of the association of SNPs with 3 traits of egg production. There is an LD between the marker SNP and the causative variation within or near genes, as most SNPs found at genome-wide significance level in our study are within the known genes. Identifications of these loci may provide new insights into the genetic basics of egg production traits, though the characteristics and functions of these genes have not been studied in depth.N-methyltransferase (GAMT) has been shown to be associated with the reproductive system and development, which implies that GAMT may be a candidate gene underlying egg production traits (Number of eggs and AFE are two important production traits in laying ducks, and producing laying duck with earlier sexual maturity and a higher rate has always been the goal of laying duck breeding. Our study indicated that these reproductive traits are sex-limited and have low-to-moderate heritability, indicating that they can be genetically improved by marker-assisted selection and genomic selection. In this study, we found two candidate genes that affect AFE, including GRIK4 and ARHGEF12, and we found five candidate genes that affect EP43w, including B3GAT1, VPS26B, ACAD8, THYN1, and NCAPD3. ACADs are a family of mitochondrial flavoenzymes that catalyze the dehydrogenation steps of the α- and β-oxidation processes, which are related to fatty acid β-oxidation. Lv et al. have found that dietary genistein supplementation in feed inhibited fatty acid synthesis and enhanced β-oxidation in the livers of layers with fatty liver syndrome through the PPAR–ACAD pathways, thereby alleviating fat deposition and lipid metabolism disorder, resulting in significant improvement in the laying rate poultry . Yuan etn traits . In addihttps://github.com/xuwenwu24/Bootstrap-test.The relatively small number of samples in our experimental population is a limitation of this study. Therefore, we refer to a method called the bootstrap test to verify the reliability of GWASs in this study. The result showed that significant signals obtained in our GWASs were not accidental and were reliable. We have uploaded this method to the GitHub website, and users can access this method at In summary, this study demonstrates that AFE, EP43w, and EP66w have medium heritability, and there were strong correlations between them. We have located some significant confidence regions for those traits, and some genes, such as GRIK4 ARHGEF12, ACAD8, THYN1, CA2, and GAMT, may be the putative candidate genes underlying this interval based on its biochemical and physiological functions. In addition, our study also found some haplotypes that were significantly associated with these three traits. Post-study can identify causal mutations by enriching markers within the identified intervals and functional studies on related genes.


The importance of sheep production in Mexico has been increasing in recent years. Animal performance can be improved through continuous selection and cumulative genetic management. Studies on non-genetic factors that influence the growth characteristics of sheep, due to their positive genetic correlation with other live weights, can present data of great interest to small producers with limited resources. In the present study, genealogical and functional information from the historical archive of the Mexican Association of Sheep Breeders (AMCO) was used. The objective was to estimate the heritability and genetic correlations of the growth of ewes born and weaned at different times of the same year from different herds with pedigree registration. The expected results could be incorporated into genetic selection programs with a favorable impact on the local economy of small sheep producers in Mexico.Birth weight (BW) and weaning weight (WW) data from Pelibuey and Blackbelly lambs belonging to the Asociación Mexicana de Criadores de Ovinos (AMCO) were used with the objective of estimating genetic parameters (heritability and genetic correlations) and analyzing the growth characteristics of ewes born and weaned at different times of the same year from different herds with pedigree registration. In the case of Pelibuey lambs, the animal model included the weaning weight at 75 days of age, considering the direct additive genetic effect, maternal additive genetic effect, covariance between direct and maternal effects, as well as the permanent environmental effect of the mother. The direct estimators of heritability for Pelibuey were BW = 0.01 ± 0.021 and WW = 0.31 ± 0.074 and for Blackbelly they were BW = 0.05 ± 0.042 and WW = 0.41 ± 0.146. In the case of the maternal heritability estimators in Pelibuey they were BW = 0.02 ± 0.040 and WW = 0.21 ± 0.121 and for Blackbelly they were BW = 0.12 ± 0.054 and WW = 0.28 ± 0.121. The magnitude of the estimates of genetic correlations between direct and maternal effects for adjusted weaning weight at 75 days of age indicate that genetic progress may be slow in a breeding program. However, these selection results could be included in the short term in the breeding programs for the Pelibuey and Blackbelly breeds in Mexico, for livestock development in low-income rural areas. Ovis aries) is one of the earliest domesticated livestock species whose ancestors were primarily distributed in the fertile crescent approximately 10,000 years ago [The sheep  aims to increase precision and decrease generation intervals, obtaining genetic gains from young animals, allowing their early selection with a potentially favorable effect on reproduction . In the Sheep producers of the Pelibuey and Blackbelly breeds in Mexico need to implement selection systems based on productive records with characteristics of economic importance, which allows them to select their sheep based on estimates of the animal’s genetic value, especially recommended for those characteristics with low heritability . GeneticGenealogical and functional information used in this study belongs to the historical archives of the Mexican Association of Sheep Breeders (AMCO). A total of 285 Pelibuey rams and 114 Blackbelly rams were used to produce 8276 and 3890 evaluated lambs, respectively. The number of breeding ewes was 2910 for the Pelibuey breed and 1196 for the Blackbelly breed, belonging to 87 herds for Pelibuey and 52 for Blackbelly, covering the birth years from 2014 to 2020; only the weights at birth of lambs born alive and surviving at weaning were considered. Individual weaning weight records were adjusted at 75 days of age (WW), using the following Equation (1):The animal model for birth weight in both Pelibuey and Blackbelly (Equation (2)) included the direct additive genetic effect, the maternal additive genetic effect, and the maternal permanent environment effect, but did not include covariance between direct and maternal genetic effects.y = the vector of records of birth weight or weaning weight.β = a vector of fixed effects .a = an unknown direct additive genetic random effects vector.m = an unknown maternal additive genetic random effects vector.p = an unknown vector of random effects of the permanent maternal environment.e = an unknown vector of random effects of the temporal environment.a, Zm, and Zp are known incidence matrices that relate the records to β, a, m, and p, respectively.X = ZThe animal model for weight adjusted to 75 days of age (Equation (3)) included the direct additive genetic effect, the maternal additive genetic effect, and the covariance between the direct and maternal genetic effects. However, it did not include the effect of the mother’s permanent environment. Equation (4) considered the same effects as Equation (3), where the effect of the mother’s permanent environment was included.A = the Wright matrix of additive kinships between all animals in the pedigree:NI = an identity matrix of equal size to the total number of observations.As fixed effects, all animal models included the sex of the lamb, the type of lambing or weaning , the contemporary group, and the age of the mother at lambing as a linear covariate. The working hypothesis assumed that the direct additive genetic effects, maternal additive genetic effects, maternal permanent environmental effects, and residual effects were normally distributed with a mean of 0 and a structure of variances and covariances that depended on the assumptions of each model. The variance and covariance (Equation (5)) for the random effects of the animal model was:Heritability estimators were calculated from the estimators of the variance components. Heritability was calculated as the proportion of phenotypic variance due to additive genetic variance. The standard errors of the heritability estimators were approximate and calculated using the average information matrix  and the 1/2), fraction of the phenotypic variance due to effects of the permanent maternal environment (Estimators were obtained for phenotypic variance (−9 (where L represents the likelihood function) [The components of variance and genetic parameters were estimated with an animal model and Maximum Restricted Likelihood Free of Derivatives, using the MTDFREML program . Analyseunction) .On the other hand, for the birth weight in the Pelibuey breed, the maternal additive genetic variance was approximately two times greater than the direct additive genetic variance .2, while the maternal additive genetic variation was 0.024 kg2 for Blackbelly and 0.004 kg2 for Pelibuey approximately. Conversely, for weaning weight adjusted to 75 days of age in the Pelibuey breed, the direct additive genetic variance was greater than the maternal additive genetic variance . Furthermore, the variance of the permanent maternal environment (0.90 kg2) was lower than the direct and maternal additive genetic variances.However, the most important component in determining birth weight was the effect of the permanent maternal environment, since the variance of that effect was 0.025 kg2), as was the case for birth weight in the Pelibuey breed. Although they were estimated with different models, the direct and maternal additive genetic variances for weaning weight adjusted to 75 days of age in the Blackbelly breed were similar to the direct and maternal additive genetic variances for weaning weight adjusted to 75 days of age in the Pelibuey breed.For the birth weight in the Blackbelly breed, the maternal additive genetic variance was approximately two times greater than the direct additive genetic variance , which may have been due to the model, as it did not include the effect of the permanent maternal environment on the Blackbelly breed. The estimators of the genetic parameters for the growth characteristics evaluated in Pelibuey and Blackbelly are shown in The phenotypic variances for birth weight were similar, with values of 0.24 kgDirect heritability estimators for birth weight were close to zero in both breeds . The maternal heritability estimator for birth weight in the Blackbelly breed was higher than the maternal heritability estimator for birth weight in the Pelibuey breed (0.12 vs. 0.02); however, both heritability estimators were low, indicating that maternal additive genetic effects for birth weight are poorly heritable. For birth weight in Pelibuey, the variance of the permanent maternal environment with the proportion of phenotypic variance was 10 times greater than direct and maternal heritabilities (11 vs. 1 and 2%).For birth weight in Blackbelly, the variance of the permanent maternal environment with proportion of phenotypic variance and direct heritability were similar , contrary to what happened for birth weight in the Pelibuey breed. On the other hand, maternal heritability for birth weight in Blackbelly was 12% higher than direct heritability and variance of the permanent maternal environment as a proportion of phenotypic variance. The direct additive genetic effects for weaning weight adjusted to 75 days of age were moderately heritable in the Pelibuey (31%) and Blackbelly (41%) breeds, indicating that the selection of outstanding parents based on their expected differences in progeny  allows for the increase of weaning weights.Maternal genetic effects for weight adjusted at 75 days of age had heritability of about 25% in Pelibuey and Blackbelly, being less heritable than direct genetic effects. However, direct and maternal genetic effects for weaning weight adjusted to 75 days of age were highly and negatively correlated in both races, and were more strongly correlated in the Pelibuey breed than in the Blackbelly breed .In both the Pelibuey and Blackbelly breeds, genetic covariances between direct and maternal effects for adjusted weaning weight at 75 days of age were negative, indicating that offspring growth is antagonistic to milk production of the sheep, this means that, if we select for greater growth, we would demerit the milk production  of the sheep in both breeds . The resCloete et al.  presenteIn this context, Simm et al.  reportedPrevious studies with Merino, Romanov, Welsh Mountain, Targhee, and Suffolk sheep breeds have found maternal heritability estimators like those in the present study ,26,27,28In contrast, the direct heritability estimators reported by Lewer et al.  for Meriof −0.98 , −0.42 [of −0.98 , −0.78 [of −0.98 , −0.60 [of −0.98 , −0.90 [of −0.98 , and −0.of −0.98 .Delphino-Medrado et al.  performeMatebesi-Rantimo et al.  indicateThe scientific literature reports the importance of direct heritability factors for weaning weight, in this sense, Analla and Serradilla  report rThe estimators of direct heritability for weaning weight obtained in the present study may differ from those reported in the literature due to differences in breed, management, environment, number of records analyzed, intensity of selection, etc.Al-Shorepy and Notter  reportedIn the case of the Blackbelly breed, the results obtained in the present investigation were lower . However, Tosh and Kemp  obtainedVaez-Torshizi et al.  report tDirect and maternal heritability estimates for weight at 75 days of age for both Pelibuey and Blackbelly breeds were significantly higher than direct and maternal heritability estimates for birth weight. For adjusted weaning weight at 75 days of age, direct genetic effects were more important than maternal genetic effects, as direct heritability estimates were larger than maternal heritability estimates. The magnitude of the heritability estimators indicate that it is very feasible to improve (increase) the weight at 75 days of age through a selection program. This selection program could be based on expected differences in progeny or breeding values, as genetic evaluations of the Pelibuey and Blackbelly breeds are currently underway in Mexico.The magnitude of the estimates of genetic correlations between direct and maternal effects for adjusted weaning weight at 75 days of age indicate that genetic progress may be slow in a breeding program; however, this magnitude could be due to the influence on the data of certain effects not considered in the model . Finally, the differences between the genetic parameter estimators obtained in this study and some estimators published in the scientific literature could be due to differences in management, number of observations, breed, environment, and selection intensity, among other factors.