The performance of the proposed method was investigated using both synthetic and real data analysis. Simulation results showed that the proposed method performs better than both linear regression model (LRM) and LMM approaches in terms of powers and false discovery rates in presence of phenotypic outliers. On the other hand, the proposed method performed almost similar to LMM approach but much better than LRM approach in absence of outliers. In the case of real data analysis, our proposed method identified 11 SNPs that are significantly associated with the rice flowering time. Among the identified candidate SNPs, some were involved in seed development and flowering time pathways, and some were connected with flower and other developmental processes. These identified candidate SNPs could assist rice breeding programs effectively. Thus, our findings highlighted the importance of robust GWAS in identifying candidate genes.Genome-wide association studies (GWAS) play a vital role in identifying important genes those is associated with the phenotypic variations of living organisms. There are several statistical methods for GWAS including the linear mixed model (LMM) which is popular for addressing the challenges of hidden population stratification and polygenic effects. However, most of these methods including LMM are sensitive to phenotypic outliers that may lead the misleading results. To overcome this problem, in this paper, we proposed a way to robustify the LMM approach for reducing the influence of outlying observations using the  Trait variations in living organisms are related to genetic variations in genes. These variations are observed largely at physiological, developmental, and morphological stages. Identification of important genetic basis such as causal genetic variants for such distinction in phenotypic traits is identifiable at single nucleotide polymorphism (SNP) levels. The techniques to explore the SNP contribution in phenotypic variation are termed as Genome-Wide Association Studies (GWAS). SNPs, however, are usually tested for relationship study through the whole genome with the characters of important trait of interest. The SNPs identified by GWAS can be used for the treatment and prevention of certain complex traits in living organisms. A very large set of SNPs along with a very large number of accessions are simultaneously studied using different GWAS methods to uncover the significant relationship between genomic latent factors and phenotypic variations of interest2. The PLINK tool focused on parametric or nonparametric-based linear regressions which do not control population stratification. Population stratification is one of the main concerning issues when extensive genome-wide association analysis with numerous subjects is in consideration5. Some unidentified new population structures are probable to exist due to a large number of subjects that may perhaps liable for regular dissimilarities being selected in SNPs amongst cases and controls4. Due to the higher false discovery rate (FDR), it is imperative to correct the observed population stratification in GWAS6. There are, however, several statistical methodologies proposed earlier for GWAS to address the effects of population stratification. The most commonly used statistical methods to avoid the bias of population stratification (PS) or genetic relatedness are genomic control7, structured association8, and principal component analysis10. The genomic control (GC) method adjusts the statistical relationship by a common element concerning the whole set of SNPs for precise correction of PS4. If the consequence of population structure increases, the power of GC approach decreases14. The structured association (SA) analysis technique suggests locating the samples to separate subpopulation groups for collecting signs of a relationship in each group8. SA method is only useful for small datasets4. Principal Component Analysis (PCA) approach is also used to overcome the influence of population stratification in GWAS by using several topmost principal components (PCs) as covariates9. But none of the methods mentioned above can handle the influence of the polygenic effect. To overcome these issues, the linear mixed model (LMM) was proposed which is one of the most popular approaches in GWAS. It is widely using through several computer software such as TASSEL13, EMMA 15, EMMAX16, rrBLUP17, GAPIT18, and GAPIT Version 219.Linear regression model (LRM) is a popular approach in GWAS. It is implemented through PLINK software for detecting important SNPs associated with quantitative traitβ-divergence method21. The performance of the proposed approach has been investigated using both simulated and real rice genome datasets related to flowering time.However, all the methods as early discussed are very much sensitive to phenotypic outliers. So, they can produce misleading results in presence of outlying observations. To overcome these issues, an attempt is made to robustify the LMM based GWAS by using a new type of outlier modification rule based on the minimum We investigated the performance of the proposed method compare to two popular approaches (LMM and LRM) using both synthetic and real data analysis as discussed below:To investigate the performance of SNPs detections with the synthetic datasets, we considered two original clean simulated datasets that were generated with heritabilities 0.2 and 0.3 respectively, as described in the materials and method section. We contaminated 1%, 2%, 3%, 4%, and 5% phenotypic observations by outliers to generate five contaminated datasets with each clean dataset to investigate the performance against the phenotypic outliers. Before going to the performance comparison, first, we would like to discuss the preprocessing steps for the proposed method as follows.β-weight function for each genotypic group and then replace the outlying phenotypic observations with the corresponding group mean computed by the minimum β-divergence method. To show how β-weight function detects outliers, we plotted β-weight corresponding to each phenotypic observation in the Supplementary Fig. β-weights. Similarly, Supplementary Fig. β-weights. To select the outlying observations, we used the threshold value τj = pth quantile value of the empirical distribution of β-weight function correctly identified the outlying observations. Now we would like to discuss the consequence of outliers in the classical and proposed approaches by decomposing phenotypic variations as follows.To analyze these datasets by the proposed method, at first, we identified phenotypic outliers by using the d in Eq. . We obseTo discuss the consequence outliers on the partition of total phenotypic variations for both classical and proposed approaches, we considered the original clean dataset including two contaminated datasets based on 2% and 5% outlying observations. Table 2*) in presence of outliers becomes smaller than the heritability (h2) in absence of outliers by the classical approach, while the heritability (2) in absence of outliers by the proposed approach.We observed that variance proportions with respect to the genetic effect gradually decrease as increases the rate of outlying observations in the dataset by the classical approach, while the variance proportions with respect to the genetic effects are almost stable for each level of outlying rates in the dataset by the proposed approach. Therefore, the heritability  for each of the methods to investigate the performance of the proposed method in a comparison of the classical LRM and LMM approaches. We computed average power and FDR based on 1000 replication of each dataset. Figure 22. Thus we may conclude that both LRM and LMM approaches are very much sensitive to phenotypic outliers compare to the proposed method. This results also supported by the decomposition of phenotypic variations described in Table Figures 24 by the same datasets that were used in Fig. 24. Figure 25. Thus, the proposed robustification works well compare to 7σ and INT approaches.The proposed robustification technique was also compared with other two robustification techniques based on7-sigma rule (mentclass2pt{minimk). From the rest SNPs, we randomly selected 1996 SNPs as polygenic variants (effects). Finally the phenotypic observation were generated using Eq.  method. We have identified 11 significant SNPs using the proposed method (rGWAS) for rice flowering time with the threshold 27. Moreover, the analyzed trait contained seven phenotypic outliers  database and collecting necessary genomic information given in Table To investigate the biological significance of the identified 11 SNPs, we validated these SNPs by using literature review and gold benchmark data. The corresponding chromosome and position of the identified SNPs were used to annotate and find the candidate genes comparing with the reference genome from the Rice Genome Annotation Project (RGAP)  were identified those encodes the retrotransposon and transposon transposable elements (TEs). Several studies have reported that these TEs can be induced by heat and cold stress in plants33. For example, Ty1-copia like retrotransposon ONSEN was found to be activated by heat stress in Arabidopsis34. Temperature and photoperiod are also found as two key regulatory factors associated with the flowering time in plants including rice35.The SNP id2005644 was identified that located near the gene LOC_Os02g21070 which encodes pentatricopeptide repeats (PPR) domain-containing protein, and is assumed to take part in the biological molecule variation36 and found five SNPs comprised of four genes involved in the two pathways  and developmental process  of rice plant  and reproduction stages such as post-embryonic development  are functionally related to rice flower development  of the candidate genes along with their molecular functions (MF) and the cellular component (CC) of the genesGO:0,032,02 of ricant Fig. a. Regula42. Signaling components via signal transduction  chain activate the different plant steroid hormones namely Brassinosteroids to regulate various growth and developmental programs, including cell differentiation and elongation, reproductive development, senescence, skotomorphogenesis (seedling development in the dark), and vascular differentiation45. The hormonal signal transduction pathways are also responsible to control several yield-related traits, including leaf angle, plant height, tiller number, and grain size in rice47. The predicted metabolic routes in this study may execute metabolism activities to convert food to energy to run cellular processes, to build blocks for proteins, lipids, nucleic acids, and some carbohydrates49. Some enzyme-catalyzed reactions may allow rice plants to grow and reproduce, maintain their structures, and respond to various stresses. The GO pathway, response to stress  is predicted to play the role for controlling cellular activity in terms of movement, secretion, enzyme production, gene expression for the result of exogenous disturbance, temperature, humidity in rice plants.Abscission, a part of a multicellular organism , in GO enrichment analysis showed that it is directly related to the developmental process  in rice. Earlier studies showed that seed shattering is controlled by the development of the abscission layer pathways in rice that allows offspring dispersal in the natural environment51. The predicted result of subcellular localization (SCL) of the candidate genes implied that nine genes out of eleven are localized in cytosol . Out of the four genes the latter two genes were predicted to be located in extracellular (extra) and membrane (membr) of which LOC_Os07g45950 was predicted for vacuole (vacu) β-divergence method. This method introduced the β-weight function, which played a key role in the robustification procedure. For the convenience of the presentation, we call this method robust GWAS (rGWAS). Simulation results showed that the average power of correct identification of SNPs by LMM and the proposed method is almost the same and greater than 80%, which is much larger than the power of the linear regression model (LRM), in absence of outliers at heritabilities 0.2 and 0.3. The average power of LRM and the proposed method were slowly decreasing as gradually increasing the rate of phenotypic outliers with heritabilities 0.2 and 0.3, while the power of LMM was decreasing sharply and significantly. The false discovery rate (FDR) of LMM and proposed methods are almost the same and much smaller than the FDR of LRM in all cases of our simulation study. Thus, the proposed method outperformed the LRM and LMM in presence of outliers; otherwise, it shows the almost equal performance of LMM which is much better than LRM in absence of outliers. The demonstration of the proposed method with the real genome dataset against rice flowering time identified 11 important SNP makers. To investigate the biological significance of the identified 11 SNPs, we validated these SNPs by using literature review and gold benchmark data. We performed GSEA for the identified 11 SNP makers and SCL analysis to detect more valid SNPs out of 11 that have a significant association with the flowering time and other trait variations in rice. We also studied their expressions in various organs in rice to find the link with the flowering time. From GO analysis, it is observed that the gene LOC_Os06g18000 might play functional roles in flower development and response to stress in rice. Amongst the 11 genes, LOC_Os02g21880, LOC_Os06g18000, LOC_Os02g24134 exhibited larger expression in seedling, vascular cell, root, shoot, and panicle. Also, the gene LOC_Os08g25060 is predicted to provide maximum expression in vascular cell, root, and panicle. SCL results support that the cytosol contains the maximum number of genes. Plastid is an important molecular organ found in plant cells mostly involve in photosynthesis and other gene expressions. In our study, SCL analysis shows that the expression of the gene LOC_Os06g18000 in plastid may act as a flowering promoter. This gene expression in plastid likely to enhance the photosynthesis process which regulates the leaf anatomy for earlier flowering in rice. In GO analysis, it is also observed that this gene expression is associated with flowering in rice. Finally, it can be concluded that phenotypic outliers may significantly affect the analysis results in GWAS. Our proposed robust method outperforms the existing LRM and LMM methods in presence of outliers and the genomic information presented may however provide a basic platform for further biological investigations. To implement the proposed rGWAS method, the R-code and necessary instructions are available at the website.The GWAS is a powerful tool to explore the novel biomarker genes at the SNP level. The LMM approach has been considered as the leading statistical procedure to address the two main challenges of embedded population structures and genetic relatedness among individuals when GWAS is performed. It was however observed that this LMM approach is very much sensitive to phenotypic outlier that leads to misleading results. Therefore, in this article, we discussed a way to robustify the LMM procedure for controlling the outlying effect and reducing the puzzling effects of the population stratification and genetic relatedness in GWAS by using the minimum m genotypes with n measurements of a phenotype. Efficient mixed-model association (EMMA)15 is such a model generally expressed by the following :n × 1 vector of phenotypic observations, and X = (xij) is an n × q matrix of fixed effects including mean, SNPs, and other confounding variables.q × 1 vector representing coefficients of the fixed effects. Z = (zij) is an n × m incidence (design) matrix mapping each phenotype to one of the m genotypes. b is the vector of random polygenic effects which follows N, where σg2 is the polygenic variance component, and K = (kjt) is the m × m genomic relationship matrix. The genomic pairwise relationship coefficient between two individuals, j and t, is defined as followsxijand xit measure the numbers  of the minor allele(s) for the ith SNP of the jth and tth individuals respectively, and fi is the frequency of the minor allele. ε is the vector of random error which follows N, where σε2 is the error variance component and where I is the n × n identity matrix. The overall phenotypic variance–covariance matrix can be represented as The linear mixed model (LMM) approaches are extensively applied for genome-wide association studies (GWAS) for observable phenotypic variations in eukaryotic groups. If we consider that, there are I is the n × n identity matrix. The variance components for polygenic effects and errors were estimated by restricted maximum likelihood (REML) using spectraldecomposition instead of the iterative expectation–maximization algorithm 15. The full-likelihood function is maximized when δ as well and δ, defined by F-statistic for testing the null hypothesis Ma = 0 for an arbitrary full-rank p × q matrix M60.p numerator degrees of freedom and n-q denominator degrees of freedom. The Satterthwaite degrees of freedom are calculated to avoid computationally intensive matrix operations. Both ML and REML estimators are very much sensitive if one or more phenotypic observations in y are outliers. Thus, LMM based F-statistic in Eq. (F-statistic in Eq. (β-divergence methods61 as follows:where β-divergence based robust ANOVA62.(i) Select the top-ranking significant SNP associated with the phenotypic variations by using the minimum m groups corresponding to the m genotypic labels of the selected most significant SNP. For example, let(ii) Divide the phenotypic data into n = n1 + n2 + …….. + nm.be the partition of phenotypic observations corresponding to the selected SNP, where, lth  group using the β-weight function defined byi = 1, 2, ... , nl(iii) Detect the outlying observations from the β-divergence estimators The minimum θt+1 denotes the update of (t + 1)th iteration. The robustness of these estimators has been discussed in the background of influence function20 and their reliability61. It is noteworthy that the minimum β-divergence estimators β = 0.The notation 63. Therefore, in this article, an effort has been provided to develop a robust linear mixed model (LMM) method in which the classical MLEs β-divergence estimators θl in the mixed model. The minimum β-divergence method suggests two approaches for combining the robustness and efficiency of estimation in LMM. The tuning parameter β is selected through the cross-validation (CV) technique20. CV process produces β = 0 for the minimum β-divergence method estimators and is then equivalent to the classical estimators. When there are outlying subjects in the phenotypic traits, the technique generates β > 0 for the minimum β-divergence estimators. To overcome the challenges of outlying observations in GWAS, an alternative approach that is the β-weight function mentioned in (4) has been proposed with β = 0.2 for outlier detection. This weight function imposes smaller weights (≥ 0) to outlying observations and larger weights (≤ 1) to uncontaminated/usual objects.It is considered that the MLEs of a Gaussian distribution are consistent and asymptotically efficient in absence of outlying objectsd in Eq.  and 6)  63. Theryli in the lth group is defined based on the β-weight function mentioned below:τl is the pth quantile value of the empirical distribution of An outlying phenotypic observation lth group by its robust mean l = 1, 2,…,k), where m is the number of genotype in the selected SNP.(iv) Then replace the outlying phenotypic observations of (v) After that apply an efficient mixed-model association (EMMA) to the modified dataset discussed in the previous step.To investigate the performance of the proposed algorithm in a comparison of the conventional algorithms, we generated both the genotypic and phenotypic data as follows:m* = 2000 SNPs were generated for n = 1000 individuals, and these individuals were taken from k = 3 distinct population by considering different minor allele frequencies (MAFs). To do this, first, a set of latent vectors {v1, v2, …..vm*} was generated from a multivariate normal distribution with mean zero and variance–covariance matrix Cov = ρ|j-k|65. In our simulation, we considered ρ = 0.5 to avoid the linkage disequilibrium (LD) between the SNPs. Finally, two cutoff values s1 and s2 were used to convert the design matrix V =  = [vij] of latent vectors to the genotypic score matrix s1 and s2 determine the minor allele frequency.To explore how the proposed method performs, a set of synthetic genotype and phenotype data were generated. A synthetic genotype dataset was simulated that reflects population structure. For this purpose, m1 = 4 SNPs were considered as causal variants and the remaining m2 = m*-m1 = 1996 SNPs were allocated as polygenic variants (effects). The quantitative trait/phenotypic values were simulated using Eq.  was defined by the ratio of main genetic variance over the phenotypic variance and it is written asThe genomic outcomes of the SNPs were simulated from a normal distribution such that it satisfies a certain proportion of genetic variance for different genetic effects as given in Table To check the performance of the proposed method in a comparison of LRM and LMM approaches in presence of different rate of outliers, we contaminated 1%, 2%, 3%, 4%, and 5% of phenotypic data randomly by using theoutlying observations to generate five different contaminated datasets. We replicated these five contaminated datasets including original clean dataset 1000 times. Tthe outlying phenotypic observations was generated Let y* be the modified phenotypic response variable which is generated by replacing 5% observation of y by the outlying observations. Then var(y*) > var(y) obviously, which implies the Eq.  as12\docCombining Eq. , 11) an an11) an2*) in presence of outliers must be smaller than the heritability (h2) in absence of outliers as follows.Thus, error variance in presence of outliers must be larger than the error variance in absence of outliers. Conversely, the heritability (h2) in absence of outliers, sinceTherefore, both LMM and LRM approach losses the SNPs identification power in presence of phenotypic outliers. However, in the case of the proposed method, the error variance in presence of outliers must be almost same to the error variance in absence of outliers. Similarly, the heritability PT/PC) × 100 and FDR = [PF/(PT + PF)] × 100, respectively, where PT measures the truly detected SNPs and PC measures total causal variants and PF is the number of falsely detected SNPs. For each situation, 1000 replications were performed to account for the average value of the power and FDR for comparison.To investigate the performance, the statistical power and FDR of 3 methods were calculated by using the formula, Power = (www.ricediversity.org). The data set contain 413 accessions along with 36,901 SNPs of Oryza Sativa1. All selected SNPs were taken into consideration in the analysis with call rate > 70% and minor allele frequency (MAF) > 0.051. Missing genotypes were imputed with weighted k-Nearest-Neighbors method66 based on the five weighted nearest varieties. To compute the kinship matrix , LD-pruhttp://rice.plantbiology.msu.edu/) database was used to annotate the identified SNPs. Among the identified genes, six were annotated with protein-coding genes and the rest five were non-coding  Release 7 (https://www.ebi.ac.uk/QuickGO). A gene set was considered as significantly enriched for GO terms if ComplexHeatmap68.To characterized the candidate genes/SNPs that may have a significant association with the phenotypic variations, we performed gene ontology (GO) enrichment analysis of the candidate genes in terms of biological process (BP), molecular function (MF), and cellular component (CC) were performed using the on-line tool QuickGO  predictor55. The heatmap of the expression level of the genes was created via R package ComplexHeatmap68.We explored the expression profile of the candidate genes in different tissues. Tissue-specific expression of the genes were obtained from the database Rice Genome Annotation Project (RGAP)http://www.ru.ac.bd/biorgru/software/r-code-robustgwas-zip/To implement the proposed method, the necessary codes in R can be downloaded from the repository:Supplementary Information 1.Supplementary Information 2.Supplementary Information 3.


However, the analysis at chromosome level revealed a wide variability, with some chromosomes showing higher correlations than others. Interestingly, the correlation was stronger (−0.241) when we repeated the analysis in a reduced dataset including the 10% most and least fertile individuals, where the latter showed an increase in average inbreeding values (FROH) of around 30%. We also found 41 genomic regions  where homozygosity increased 100-fold, 13 of which were significantly associated with fertility after cross-validation. These regions encompassed 17 candidate genes previously related to oocyte and embryo development in several species. Overall, we demonstrated the relationship between increased homozygosis at the genomic level and fertility in mares. Our findings may help to deal with the occurrence of inbreeding depression, as well as further our understanding of the mechanisms underlying fertility in mares.The loss of genetic variability in livestock populations bred under strict selection processes is a growing concern, as it may lead to increased inbreeding values and lower fertility, as a consequence of the “inbreeding depression” effect. This is particularly important in horses, where inbreeding levels tend to rise as individuals become more and more closely related. In this study, we evaluated the effect of increased inbreeding levels on mare fertility by combining an SNP-based genomic approach using runs of homozygosity and the estimation of genetic breeding values for reproductive traits in a large population of Pura Raza Española mares. Our results showed a negative correlation between whole-genome homozygosity and fertility estimated breeding values (EBVs) at the genome level ( The increase in average inbreeding rates has become a serious concern in wild and livestock populations over the past two decades , 2. ThisIn horses, increased inbreeding is of particular concern. In closed studbooks, such as Pura Raza Española (PRE)  and ThorReproductive traits are extremely sensitive to problems derived from high levels of inbreeding . This caNowadays, horse breeding is entering the genomic era at full gallop. The number of individuals genotyped has increased exponentially over recent years, and it is now common to find studies including genotypes of hundreds of individuals –17. For In this study, we used an ROH-based methodology to analyze the relationship between homozygosity and fertility in a large cohort of PRE mares. In addition, we performed a complete genome scan to determine the existence, topological position, and putative function of genomic regions where increased homozygosity could negatively affect fertility.The initial reproductive dataset included 344,707 foaling records from 78,986 breeding mares belonging to 8,133 studs included in the PRE studbook. Records were obtained from the breed's creation until 2020, and only those of mares born after 1970 were kept, when the breed's official parentage control was established. Mares whose main activity was not foal production  were excluded, as were mares mainly devoted to leisure or sports activities .Individual horse fertility was determined by assessing the reproductive efficiency (Re), which was defined as the percentage relationship between the current and optimal parity number during a mare's entire reproductive life, or the last known age of mares which were still reproductively active. This reproductive trait was recently validated by our group as an indirect estimator of the mare fertility in a large population of PRE horses .EBV were estimated using a restricted maximum likelihood (REML) animal model as follows:Measurements of Reyi is the vector of the dependent variable (Re), μ is the overall mean, b is a vector of fixed effects, including stud, size of the herd in which the mare was born and year of birth; age and F, are the age and inbreeding of the mare respectively, included as lineal covariates, u is the vector of random effects due to the additive animal genetic effect, and e is the vector of the residual error, while X and Z are incidence matrices that relate the fixed and random effects with the dependent variable.where The expected variances of the model are:n = 87,227) included in the additive genetic relationship matrix (A)   averagedEBV were deregressed to pseudophenotypes (RedEBV), following the methodology proposed by Garrick et al. .The second step was to select 862 living individuals from 373 PRE herds for single nucleotide polymorphism (SNP) genotyping using diverse criteria, including sample availability, low average relatedness among individuals, and reliable Rebest genotyping practices” workflow with default parameters . Only SNP markers showing a high-quality genotyping rate (SNP CR > 95%) and quality (Fisher's Linear Discriminant (FLD) > 3.6) were kept, according to the manufacturer's recommendations  in 200 μl of whole blood according to the manufacturer's protocol. Genotyping was performed using the HD Axiom™ Equine SNP Genotyping Array , following the manufacturer's recommendations, in a Genetitan™ platform , Santiago de Compostela, Spain). The array included variant calls for 670,776 SNPs located uniformly across the entire genome . The genndations . We did ndations . The finslidingRuns procedure in the DetectRUNS Package  (percentage of the genome covered by ROH) per individual was estimated at genome and chromosome levels, following McQuillan et al.  and RedEBV in the 862 individuals genotyped. Next, we selected a reduced dataset (RD) which included individuals showing the top (High-Fert) and bottom (Low-Fert) 10% Re pseudophenotypes (n = 172), to increase the power of the association test. In both cases, the estimations were performed using the nlcor package  between High-Fert and Low-Fert individuals to find differences in homozygosity associated with variations in fertility traits.To test the relationship between whole-genome homozygosity and Re, we first estimated the non-linear correlations between F package  from R. 10 > 2] compared with a random occurrence probability were tagged as ROHi and further analyzed.The genomic regions of the RD in which the incidence of ROH increased significantly  were determined using a permutation test  as described by Goszczynski et al. . Only ret-test; ROHs with a t-value ≥ 2 were confirmed as significantly associated with mare fertility.The ROHi identified in the RD were validated in the whole dataset using the method described by Nani and Peñagaricano . BrieflyGRanges objects and intersected with the most recent version of the horse genome [EquCab 3.0,  was 0.25 ± 0.0031, revealing a substantial genetic effect. In addition, the standard deviation was nearly 80 times lower, which demonstrates their reliability. In addition, the ReEBV′s of the individuals genotyped showed a normal distribution , while displaying a wide range of variability  and High-Fert  clusters were highly divergent, which allowed us to perform a more robust analysis in terms of fertility (Reertility .ROH in the whole population was high (0.136 ± 0.07). However, it was nearly 30% lower in High-Fert individuals (FROH = 0.102 ± 0.06) compared with Low-Fert (FROH = 0.141 ± 0.07). Similar results were obtained in the analysis per chromosome, in which High-Fert individuals showed a lower FROH than Low-Fert in 19 chromosomes  (The average F < 0.05) .P < 0.0001, P < 0.01). However, differences were not evenly detected across the different chromosomes (The correlation between Re and the whole genomic homozygosity estimate (FROH) was negative and highly significant  showed a 100-fold increase in ROH abundance in the RD  and fertility (RedEBV), in line with previous reports in this species  contained 17 genes previously related to female reproductive competence in several species. None of them had been previously mapped as QTLs or harbored mutations and/or indels associated with fertility in horses . InteresedEBV was located on ECA3, including two major genes related to female fertility: alcohol dehydrogenase 5 (ADH5) and eukaryotic translation initiation factor 4E (EIF4E). In mice, inhibition of the ADH family reduced the de-novo production of retinol acid in the ovaries and the response to treatment with equine chorionic gonadotropin  gene. Its main function is to encode one of the subunits which form the canonical condensin complex (condensin I) in mitotic and meiotic cells  and therefore plays a key role in oogenesis progress and blastocyst formation  is related to ovarian regulation and the onset of decidualization during the pre and post-implantation periods in mice  and a PICT-2018-0227 grant .The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


Fourier-transform mid-infrared (FT-MIR) spectroscopy provides a high-throughput and inexpensive method for predicting milk composition and other novel traits from milk samples. While there have been many genome-wide association studies (GWAS) conducted on FT-MIR predicted traits, there have been few GWAS for individual FT-MIR wavenumbers. Using imputed whole-genome sequence for 38,085 mixed-breed New Zealand dairy cattle, we conducted GWAS on 895 individual FT-MIR wavenumber phenotypes, and assessed the value of these direct phenotypes for identifying candidate causal genes and variants, and improving our understanding of the physico-chemical properties of milk.ABO gene that has a potential role in changing milk oligosaccharide profiles. For the candidate causative genes implicated in these analyses, we examined the strength of association between relevant loci and each wavenumber across the mid-infrared spectrum. This revealed shared association patterns for groups of genomically-distant loci, highlighting clusters of loci linked through their biological roles in lactation and their presumed impacts on the chemical composition of milk.Separate GWAS conducted for each of 895 individual FT-MIR wavenumber phenotypes, identified 450 1-Mbp genomic regions with significant FT-MIR wavenumber QTL, compared to 246 1-Mbp genomic regions with QTL identified for FT-MIR predicted milk composition traits. Use of mammary RNA-seq data and gene annotation information identified 38 co-localized and co-segregating expression QTL (eQTL), and 31 protein-sequence mutations for FT-MIR wavenumber phenotypes, the latter including a null mutation in the This study demonstrates the utility of FT-MIR wavenumber phenotypes for improving our understanding of milk composition, presenting a larger number of QTL and putative causative genes and variants than found from FT-MIR predicted composition traits. Examining patterns of significance across the mid-infrared spectrum for loci of interest further highlighted commonalities of association, which likely reflects the physico-chemical properties of milk constituents.The online version contains supplementary material available at 10.1186/s12711-021-00648-9. Fourier-transform mid-infrared (FT-MIR) spectroscopy is a high-throughput and inexpensive method for predicting milk composition. The FT-MIR methodology determines the presence of specific chemical bonds in milk by measuring the absorbance of infrared light as the light interacts with molecules in the sample. Data from FT-MIR spectroscopy comprises a spectrum of absorbance values across the mid-infrared range that are readily available through routine milk testing. This technology is widely used to estimate the concentrations of major milk components such as fat and protein for incorporation into milk payment and animal evaluation systems. Over the last decade, there has been increased interest in using FT-MIR data to predict other milk composition and novel traits. Applications of FT-MIR spectroscopy as a phenotyping tool have been widely studied and reviewed –4. RecenSuccessful utilisation of FT-MIR data as a phenotyping tool depends on the strength of the phenotypic correlation between the predicted trait, and the trait as measured by a benchmarked standard; and successful incorporation of FT-MIR predicted traits into breeding programmes further depends on the heritability of the FT-MIR predicted trait, and the genetic correlation between the FT-MIR prediction and the benchmarked trait . StudiesAlthough there have been many genome-wide association studies (GWAS) for FT-MIR predicted milk composition traits such as fat, protein, and lactose concentrations –37, and . [DGAT1 K232A polymorphism had highly significant effects on wavenumbers associated with carboxylic and ester C=O bond stretching, triglyceride ester linkage C-O stretching and alkyl C-H stretching. In that same study, a polymorphism in the CSN3 gene had effects on wavenumbers that coincided with amide II, amide III and phosphate bands, and a polymorphism in the PAEP gene had effects on wavenumbers in a mid-infrared band that was attributed to C-N stretching [. [CSN3. Across those studies, association patterns varied widely for loci in different genes, with DGAT1 having highly significant effects across many wavenumbers, while PAEP had significant effects across fewer wavenumbers that were concentrated within a small number of spectral bands. Assessing association patterns across the mid-infrared spectrum for a wider range of loci could improve our understanding of the impact that different genes have on the molecular structure of milk. Moreover, comparing these association patterns could provide insights into commonalities in the way genes influence milk composition and how these impacts are detected.Previous studies have examined the effects of variants in individual genes and their encoded proteins on FT-MIR wavenumber phenotypes , 42. Wan.  observedN = 38,085) than previous such studies and at a higher genomic resolution, with imputed whole-genome sequence consisting of 17,873,880 variants. We further report molecular dissection of these signals through the use of variant annotation information and a large mammary RNA-seq resource, identifying candidate causative genes and variants for a substantial number of loci. Finally, we evaluated patterns of significance across the mid-infrared range for different loci, highlighting clusters of QTL that are broadly defined by the biochemical properties of the molecules that they encode.The purpose of the current study was to investigate the underlying genetics of milk composition, by conducting GWAS on 895 individual FT-MIR wavenumber phenotypes, and comparing these results to GWAS conducted on three FT-MIR predicted major milk composition traits. We report the use of a much larger sample  instruments as part of routine milk testing conducted by Livestock Improvement Corporation (LIC), over the period from September 2017 to May 2018 [Prior to conducting GWAS, adjusted cow phenotypes were generated for 895 individual FT-MIR wavenumbers and three FT-MIR predicted milk composition traits. Adjusted phenotypes were generated from one or more test-day samples on the same cow by fitting repeated measures models in ASReml-R , compriswhere N = 138; ~ 777 k SNP), Illumina BovineSNP50k , and/or custom GeneSeek Genomic Profiler LDv3 BeadChip  panels, with the resultant genotypes imputed to sequence density as part of a wider set of 153,357 animals, as described by Jivanji et al. [Bos taurus reference genome using BWA-MEM (v0.78-r455) [Bos taurus autosomes were considered, and phasing with genotype probabilities was undertaken using Beagle 4.0 [Animals were genotyped on Illumina BovineHD  , and GAT78-r455)  respecti78-r455) , 47. Thee dosage  for missN = 3389), with 675,321 SNPs remaining after eligibility filters were applied.The reference sets for SNP chip panels used at each imputation step were generated based on a uniform set of criteria. Genotypes were eligible for inclusion in a reference if the sample call rate was ≥ 0.95, and the proportion of Mendelian inconsistences observed between parent–offspring pairs of genotypes was lower than 0.005. The 50 k reference included eligible Illumina BovineSNP50 BeadChip genotypes for all males, and females that were a dam of a genotyped sire or had at least five recorded progeny . The GGP reference included eligible GGP LD BeadChip genotypes for all males, and females that had recorded progeny . Additional 50 k reference SNPs that were not on the GGP panel were also included as a background scaffold, resulting in a reference with 57,493 SNPs across 11,872 animals. The HD reference included all available Illumina BovineHD BeadChip genotypes, predominantly from widely-used sires and/or sequenced animals (ref) and the MAF in the overall population  satisfied the criteria: |MAFref-MAFoverall|/MAFref < 0.4. This resulted in the removal of 12 SNPs from the Illumina BovineSNP50 BeadChip, and three SNPs from the GGP LDv3 BeadChip. In addition, for all references, SNPs that were in common with sequence variants with more than 30 × depth coverage were removed if the concordance between genotype and sequencing calls was ≤ 0.7. Likewise, for GGP and 50 k references, any SNPs that were shared with the BovineHD panel were removed if the concordance between genotype calls from each panel was ≤ 0.7; and for the HD reference, any SNPs that were shared with the BovineSNP50 panel were removed if the genotypic concordance between panels was ≤ 0.7.For all references, SNPs that were monomorphic or had a batch call rate lower than 0.9 were excluded. Quality checks were made to ensure that allele frequencies in the reference population reflected those in the wider population. That is, for SNPs with a count of more than 1000 minor alleles in the overall population, the relationship between the minor allele frequency (MAF) in the reference population  = 12.21. The proportion of phenotypic variance explained by each SNP was evaluated as Separate GWAS were conducted using the Bolt-LMM software  for eachp-value based on the Bonferroni threshold were identified; and for each of these chromosomes, the most significant variant was identified and added to the set of covariates included in the next iteration. These subsequent iterations were only conducted on chromosomes that retained significant effects, whereby the process was repeated until these analyses ceased to highlight significant effects. For each of these iterations, the set of 43,851 SNPs representing genomic relationships continued to be fitted (using the LOSO approach) to account for population structure. These analyses resulted in a list of variants for each phenotype that aimed at capturing all the significant association analysis signals.To distinguish between multiple QTL segregating within the same region of a chromosome, an iterative conditional approach was undertaken for each phenotype. After running an initial GWAS that we refer to as the ‘base GWAS’, chromosomes with a significant Bos taurus reference genome using the Tophat2 program (version 2.0.12) [2 statistics with 1 degree of freedom were used to identify eQTL p-values. The Bonferroni significance threshold had been set at –log10(2.53e-07), based on α = 0.05, corrected for 197,338 tests.Gene expression phenotypes and the resulting eQTL were generated as part of a previously described study . Briefly 2.0.12) , and fil 2.0.12) . Genetic10 for the effect was greater than 1.5 × the Bonferroni threshold; or the correlation between the PIV and the QTL was in the range  for the effect was greater than 2 × the Bonferroni threshold; or the correlation between the PIV and the QTL was in the range  for the effect was greater than 2.5 × the Bonferroni threshold. All other variants in QTL regions where the correlation between the PIV and the QTL was higher than 0.9, and the –log10 for the effect was greater than the Bonferroni threshold, were classified as ‘moderately significant’.Whole-genome sequence resolution genotypes within a 1-Mbp window were annotated using the SnpEff software   and Ense. [p-values of the trait QTL and all eQTL within the interval of interest were computed. To account for regional differences in LD structure, Pearson correlation coefficients were evaluated across the entire 1-Mbp region of interest, and a smaller 500-kbp region, with the strongest correlation used to assess the relationship between the trait and expression QTL p-values. Trait QTL were filtered to those for which the Pearson correlation from either window was higher than 0.7.Wavenumber and predicted-trait QTL were scrutinized to identify co-localized eQTL, following the methodology of Lopdell et al. . This ap10 for the representative tag variant were compiled across FT-MIR wavenumbers, creating significance ‘profiles’ that allowed patterns of association across the mid-infrared region to be compared between loci. To facilitate these comparisons and account for differences in p-value magnitudes between loci, the –log10 were scaled to sum to unity. Differences between scaled significance profiles for loci were evaluated based on the Euclidean distance between corresponding points on the profiles for pairs of genes, and clustering of the distances based on the largest pairwise dissimilarity across elements was performed using the hclust function in R (v4.0.2) [After conducting GWAS across FT-MIR wavenumbers, wavenumber QTL that were in strong LD with a PIV, or had a co-localized eQTL (as described in detail above) were identified. In cases where there were multiple candidate genes implicated for a QTL, the gene with a PIV in highest LD with the QTL was selected as representative of the locus. Where multiple loci were implicated for the same gene, the variant in highest LD with either the corresponding PIV or the top variant of the eQTL was used. For the identified genes, the –log(v4.0.2)  with def. [DGAT1 gene that has been widely reported as impacting many milk composition traits [The first-round pre-iteration (base) GWAS, including 17,873,880 imputed sequence variants, resulted in significant associations for 37,779 variants for FP, 17,159 variants for LP, and 36,067 variants for PP. The number of significant associations for individual FT-MIR wavenumbers ranged from 50 to 60,242, with a mean and median of 24,505 and 25,895 variants, respectively. For 18 of the 895 individual wavenumber phenotypes, the Bolt-LMM GWAS did not converge, due to insufficient genetic variation in the trait. Among the remaining wavenumbers, 830 had at least one significant association in the base GWAS. The numbers of significant variants in the base GWAS for individual wavenumbers across the mid-infrared range are shown in Fig. . . Signifin traits , 57. ForIn the base GWAS, individual FT-MIR wavenumber QTL were observed on 27 of the 29 bovine autosomes Fig.  within 2p-values at previous iterations for the phenotype, and p-values for the corresponding top chromosomal SNP in that iteration are in Table S5  and PP phenotypes (ABCG2). For this cluster of genes, prominent peaks were observed in bands of the mid-infrared spectrum from ~ 1020 to 1180 cm−1, from ~ 1200 to 1470 cm−1, from ~ 2610 to 2840 cm−1 and from ~ 2870 to 2980 cm−1. The second cluster  and PP  phenotypes, with multiple peaks observed across the mid-infrared spectrum, with the most prominent of these being in the ranges from ~ 910 to 1010 cm−1, from ~ 1070 to 1560 cm−1, from ~ 1700 to 2450 cm−1, from ~ 2630 to 2980 cm−1 and from ~ 3620 to 3680 cm−1. The third cluster  and PP  phenotypes. For this cluster of genes, peaks were observed in many bands of the mid-infrared spectrum in common with peaks for ABCG2 and USP3  is the same Y581S variant that was previously reported to be associated with milk yield and composition in Holstein cattle [ABCG2 mutation in milk composition regulation can be assumed to derive from osmotic impacts due to its function as an efflux transporter [PAEP gene encodes the major whey protein β-lactoglobulin. The variant rs109625649 reported here (V134A) is one of the variants that distinguishes the ‘A’ and ‘B’ haplotypes of β-lactoglobulin [PAEP gene also exhibited an eQTL that was significantly correlated with wavenumber 2548 cm−1, which is concordant with previous reports of PAEP promotor variants associated with milk composition [DGAT1 encodes diacylglycerol O-acyltransferase 1, which catalyses the final step in triglyceride production and which, given the substantial quantities of fat secreted during milk production, makes DGAT1 a well-demonstrated and straightforward candidate gene for this effect. The variant rs109234250 (K232A) reported here has been widely ascribed to the effects of the DGAT1 gene on milk production, with a recent study showing that these effects may be due in part to an expression-based mechanism [In total, 31 wavenumber QTL were identified that we deemed to be ‘highly significant’  [p-values for the same variant for LP and PP were 9.0e-717 and 6.4e-115, respectively. Similarly, the p-value for the most significant wavenumber at the chr11:103304757 locus, the V134A PAEP mutation (rs109625649) was 1.2e-134, whereas the p-value for the same variant for FP was 4.3e-46; and the p-value for the most significant wavenumber at the chr14:1802265 locus, represented by the K232A DGAT1 mutation (rs109234250) [p-value for the same locus for PP was 1.2e-61.For the effects observed in the 3702337) , was 7.3n rs1096249 was 1.TGDS and DNAJB13), and genes previously reported in other studies of milk composition traits: GBA [MTX1 [SLC50A1 [CSF2RB [NCF4 [TBC1D22A [MROH1 [MTARC1 [FCGR2B [SCAMP3 [THBS3 [CSN1S1, CSN2 and CSN3 [ABO [CPSF1 [SPAG1 [RNF214 [KAT2A [STAT5A [CCDC57 [FCRLA, WDR97, KRT9, KRT16, KRT17, HID1, KCNK1 and NXF1.Multiple protein-coding mutations could be attributed to loci with QTL in both wavenumber and milk composition traits, highlighting genes that appear to be novel to the present study  or a co-localized eQTL (LTF). To our surprise, only the CSN3 eQTL was identified by analysis of the milk composition traits, with a p-value of 2.9e-45 for the PP phenotype, which was less significant than the p-value for the most significant wavenumber .Many wavenumber QTL with a co-localized eQTL also had a co-localized eQTL identified for a predicted milk composition trait. In these cases, a common pattern was observed whereby the wavenumber QTL had more highly significant CLDN8, CSTB, TALAPTM4A, CAPN5, PMP22, HID1 and THRB; and a number of genes previously reported as having an effect on bovine milk composition: SLC37A1 [NCF4 [SLC34A2 [TENT5A [RNF217 [MPC1 [XDH [PAEP [DGAT1 [RGL1 [LTF [MUS81 [Other wavenumber QTL where a co-localized eQTL was identified within FT-MIR wavenumbers, but not the predicted milk composition traits, included effects that highlighted a number of genes that appear novel to the present study:  SLC37A1 , 86, NCFA1 [NCF4 , 69, SLC[SLC34A2 , TENT5A  [TENT5A , RNF217  [RNF217 , MPC1 [817 [MPC1 , XDH [88PC1 [XDH , PAEP [6DH [PAEP , DGAT1 [P [DGAT1 , RGL1 [9T1 [RGL1 , LTF [91GL1 [LTF  and MUS8F [MUS81 . These rABCG2, PAEP and DGAT1), in addition to other genes that have previously been linked to bovine milk composition phenotypes . Of these, the ABO exon 5 splice donor mutation  is a particularly interesting and seemingly novel candidate causative variant identified through our GWAS of FT-MIR wavenumbers.Although we identified a large number of candidate causative variants for FT-MIR wavenumbers and predicted milk composition phenotypes, variants in perfect LD with a tag locus . In humans, ABO has a widely recognised role as encoding the glycosyltransferases that catalyse the synthesis of the oligosaccharide ABO blood group antigens [ABO generated by rs207688357 could be assumed to be non-functional , this mutation would be akin to the human O blood group in homozygotes, where analogous human null alleles generate a non-functional enzyme [ABO alleles change carbohydrate structures in milk, therefore presenting differing FT-MIR signals detected by GWAS.The rs207688357 variant was selected as the representative peak tag variant for 11 wavenumbers, with the most significant peak association observed for wavenumber 1462 cmantigens , 95. Sinl enzyme . These al enzyme . This fiABO locus [ABO p.Arg206Gln  amino acid substitution present on the Illumina BovineHD chip as a potential causative mutation for this effect [ABO coding sequence , in this case using imputed sequence-based genotypes [−1 wavenumber phenotype. These alternative candidates are less strongly associated than the rs207688357 splice donor mutation . While these findings might suggest that these variants are simply linked to the functionally more compelling rs207688357 splice donor mutation, LD between the variants and the splice donor mutation is moderate to low , which suggests that all three variants might contribute to the oligosaccharide content of milk. In support of this concept, we also note that the non-coding rs110534892 variant proposed by Liu et al. [ABO eQTL highlighted in our study , which suggests that multiple molecular mechanisms  might contribute to oligosaccharide modulation at this locus.It should also be noted that although we are unaware of other studies proposing the rs207688357 (chr11:104242578) mutation as underlying such effects, other studies have reported genetic associations for bovine milk oligosaccharides for the broader BO locus , 74. Oneenotypes . Both thu et al.  is in stAlthough FT-MIR spectroscopy is a valuable tool for predicting a range of milk composition traits, there are limitations to the approach, i.e. it is often unable to detect molecules that are present in small quantities, and does not discriminate well between compounds that are chemically similar. Nevertheless, we have demonstrated that individual FT-MIR wavenumber phenotypes can provide valuable insights for establishing causal links between the genome and milk composition. Having observed patterns of association across multiple FT-MIR wavenumbers for individual loci (i.e. genome positions that appeared to highlight specific subsets of wavenumbers), our aim was to formally detect these patterns of association through cluster analysis. We hypothesised that the identified clusters could be rationalised based on shared biology or the physico-chemical properties of the encoded molecules—given that these signatures would presumably reflect common functions and structures in milk.DGAT1, GPAT4, and MGST1  [−1) [2 and –CH3 (from ~ 1450 to 1500 cm−1) [−1) [−1) [−1) [The cluster with the largest number of individual attributed loci included genes with prominent roles in the regulation of fat synthesis such as ST1 Fig. . These tAT1 Fig. a was ver10 cm−1) , triglyc−1) [−1) , 100, C–00 cm−1) , C=O str−1) [−1) , carboxyABCG2 Y581S polymorphism  [−1) [2 and –CH3 (from ~ 1410 to 1470 cm−1) [2 and –CH3 (from ~ 2700 to 2980 cm−1) [ABCG2 and many of the other genes classified in the same cluster  have been previously associated with lactose phenotypes [ABCG2 Y581S polymorphism were in different bands of the mid-infrared spectrum to the DGAT1 K232A polymorphism, assumedly reflecting the different roles that these two genes play in altering milk composition.The cluster that included the −1) [−1) , 103, C–70 cm−1) , and C–Henotypes , 71. NotCSN3, PAEP and ANKH genes , PAEP (from ~ 1350 to 1650 cm−1) and ANKH (from ~ 1260 to 1620 cm−1). The CSN3 gene encodes κ casein, one of the most abundantly expressed proteins in milk. Bound at the aqueous-hydrophobic interface of casein micelles, κ casein content influences the size of these structures, thereby affecting various coagulation and cheese-making properties [CSN3 locus were in spectral regions related to amide III and phosphate bands (from ~ 1220 to 1320 cm−1), C–H stretching vibrations of CH2 and –CH3 (from ~ 1370 to 1480 cm−1), and N–H bending and C–N stretching in the amide II band (from ~ 1490 to 1590 cm−1) [CSN3 in similar bands of the mid-infrared spectrum, with specific wavenumbers coinciding with highly significant association effects observed in our study [ANKH gene encodes a transmembrane protein involved in pyrophosphate transport regulation, and is associated with lactose concentrations in milk [ANKH and PAEP shared a prominent peak for adjacent wavenumbers, 1391 cm−1 and 1395 cm−1, respectively. These wavenumbers were in a region related to carboxylic acid C = O bond stretching [−1 wavenumber, also in a region related to carboxylic acid C=O bond stretching [PAEP have been reported in previous studies [ANKH and PAEP shared peaks in their significance profiles, it is notable that they also had exclusive peaks. For ANKH, a distinct peak was observed in a region related to amide III and phosphate bands (from ~ 1270 to 1290 cm−1) [PAEP a distinct peak was observed in a region related to C–NH peptide bonds and N–H stretching and bending vibrations of NH2 (from ~ 1600 to 1640 cm−1) [Three other notable gene clusters were those represented by the nes Fig. , which hoperties , 106. Thoperties . The lar90 cm−1) . Previouur study , 43. The in milk , 71. Intretching . Anotherretching . Associa studies , 43. Alt90 cm−1) , 103, an40 cm−1) , 109, whIn this study, we demonstrated that GWAS conducted on individual FT-MIR wavenumbers can improve power for identifying QTL and candidate causal variants, compared to GWAS conducted on FT-MIR predicted milk composition traits. Although many QTL were successfully identified, several refinements to our approach could be expected to enable the identification of additional QTL. The first of these relates to the approach used in adjusting phenotypes prior to conducting the GWAS. The repeated measures model that we used for adjusting phenotypes included a random effect to capture individual animal variation, but did not use pedigree information to account for covariance between individuals. This means that genetic trend may have been captured in herd by test day effects. A more optimal, but computationally more expensive approach, would have been to fit a repeatability model including the additive relationship matrix, thereby ensuring more accurate partitioning of fixed and random effects. To assess the potential impact of this on the final GWAS results in our study, we generated adjusted phenotypes for FP, LP and PP using a full animal model with an additive relationship matrix, and compared these to the adjusted phenotypes evaluated from the simplified repeated measures model we report. The correlations between the adjusted phenotypes from the two models were all high: 0.983, 0.994 and 0.987 for FP, LP and PP respectively. This implies that although the model that we used may be considered suboptimal, it is likely that the use of this model would have only a very minor impact on the final GWAS results.p-value of the association effect, and fitted this as a covariate in subsequent rounds of GWAS. This approach does not take nonlinear interactions between variants into account, and can lead to the selection of multiple variants in high LD with a single QTL, if that QTL is not itself represented by a single biallelic variant. Alternatively, multiple QTL at a single locus might be best tagged by a single, non-causal variant that captures multiple signals. In both these instances, factors such as imputation or genotyping error may also further compound these issues. To address this, a modified approach could be adopted, whereby gene annotation information and other genomic and molecular data sources are used to assist with variant selection. Finally, although we tried to identify causal variants representing a variety of molecular mechanisms including coding variants (missense and nonsense) and regulatory effects (through integration of mammary eQTL data), these approaches are far from comprehensive, and will still miss many candidates. Improved variant prediction methods, and generation of other functional datasets (e.g. ChIP-seq) could be used to map additional molecular QTL, where integration of those data would enhance fine mapping and identification of candidate variants [Other potential refinements to our approach specifically relate to genomic information and our strategy for identifying QTL. First, our study relied on datasets that were mapped to the UMD3.1 genome, whereas a newer reference genome (ARS-UCD1.2) that has improved sequence continuity and per-base accuracy  is now avariants .We conducted a sequence-based GWAS on individual FT-MIR wavenumber phenotypes, and employed gene annotation and mammary tissue gene expression datasets to identify candidate causative genes and variants. Compared to GWAS on predicted milk composition traits, GWAS on individual FT-MIR wavenumbers resulted in stronger association effects, and improved power for identifying candidate causal variants. Although many of the genomic regions with significant associations that we identified in this work have previously been linked to milk composition traits, we report the discovery of several loci that have never previously been linked to milk phenotypes. Examining patterns of significance across wavenumbers in the mid-infrared range for loci of interest provided further insights into the relationships between specific genes and the underlying chemical structure of milk. Leveraging this information and incorporating the candidate causative mutations that we have identified into genomic prediction could result in improved selection of dairy cattle for the ever-growing range of traits of interest to the industry.Additional file 1: Figure S1. Sequence resolution effects for highly significant wavenumber QTL. Effects shown for 14 base GWAS wavenumber QTL in high LD (R2 > 0.9) with a putative impact variant. Putative impact variants are defined as a splice region variant, or a moderate or high impact variant according to the SnpEff classification. 1-Mbp regions centred on the wavenumber QTL are shown. The x-axis represents positions on the UMD 3.1 Bos taurus reference genome; the y-axis shows the strength of association signal, represented as the −log10 of the effect for each variant. Effects are coloured based on the predicted effect of the variant on genes, according to the SnpEff classification. The horizontal red line shows the Bonferroni significance threshold of −log10(6.2e-13).Additional file 2: Table S2. Peak variants of 27 protein-sequence association effects classified as moderately significant for FT-MIR wavenumber phenotypes. Moderately significant effects are those for which the −log10 of the effect was greater than 1x the Bonferroni threshold of −log10(6.2e-13) and the correlation between the tag variant and the protein-sequence variant was higher than 0.9, but the effect did not meet the criteria of a highly significant effect (see Table 1). Effects where the locus has been identified as highly significant based on the LD with one or more other genes  are shaded yellow. No. of hits is the number of wavenumbers for which the variant was selected as the representative (most significant) tag variant for a peak. Iterations are defined relative to the base GWAS, with the base GWAS represented as iteration 0. L = Low impact splice region variant; M = Moderate impact missense variant; H = High impact splice donor. Table S3. Minor allele frequencies and allele effects for WGS tag variants with a highly significant protein-sequence association effect in at least one FT-MIR wavenumber. Table S4. Association statistic profiles for 31 highly significant protein-sequence effects identified in FT-MIR wavenumber phenotypes. For each protein-sequence mutation, the proportion of phenotypic and genetic variance that it accounts for is shown for each of the 895 FT-MIR wavenumbers and three FT-MIR predicted milk composition phenotypes. The genetic variance for each phenotype is the SNP-based estimate evaluated by the Bolt-LMM software. Table S5. Chronological profiles across iterations for 17 highly significant protein-sequence association effects observed in FT-MIR wavenumbers, where the association is observed after fitting the top chromosomal variant(s) in previous GWAS iterations and/or the base GWAS as covariates. Iterations are defined relative to the base GWAS, with the base GWAS represented as iteration 0. P-values at previous iterations for the phenotype, and p-values for the corresponding top chromosomal SNP in that iteration are provided. Table S6. Peak variants of 14 protein-sequence association effects classified as moderately significant for FT-MIR predicted milk composition traits. Moderately significant effects are those where the −log10 of the effect was greater than 1x the Bonferroni threshold of −log10(6.2e-13) and the correlation between the tag variant and the protein-sequence variant was higher than 0.9, but the effect did not meet the criteria of a highly significant effect (see Table 2). Effects where the locus has been identified as highly significant based on the LD with one or more other genes  are shaded yellow. Iterations are defined relative to the base GWAS, with the base GWAS represented as iteration 0. FP = Fat %; LP = Lactose %; PP = Protein %; L = Low impact splice region variant; M = Moderate impact missense variant; H = High impact splice donor. Table S7. Minor allele frequencies and allele effects for WGS tag variants with a highly significant protein-sequence association effect in at least one FT-MIR predicted milk composition trait. FP = Fat %; LP = Lactose %; PP = Protein %. Table S8. Chronological profiles across iterations for highly significant protein-sequence association effects observed in FT-MIR predicted milk composition traits, where the association is observed after fitting the top chromosomal variant(s) in previous GWAS iterations and/or the base GWAS as covariates. Iterations are defined relative to the base GWAS, with the base GWAS represented as iteration 0. P-values at previous iterations for the phenotype, and p-values for the corresponding top chromosomal SNP in that iteration have been provided. FP = Fat %; LP = Lactose %; PP = Protein %.Additional file 3: Figure S9. Sequence resolution effects for 19 base GWAS wavenumber QTL with a co-localized expression QTL. 1-Mbp regions centred on the wavenumber QTL are shown. The x-axis represents positions on the UMD 3.1 Bos taurus reference genome; the y-axis shows the strength of association signal, represented as the −log10 of the effect for each variant. Effects are coloured based on the predicted effect of the variant on genes, according to the SnpEff classification. The horizontal red line shows the Bonferroni significance threshold of −log10(6.2e-13).Additional file 4: Table S10. Minor allele frequencies and allele effects for WGS tag variants with a significant association effect in FT-MIR wavenumbers and a co-localized eQTL. Table S11. Association statistic profiles for 38 loci with a co-localized eQTL for at least one FT-MIR wavenumber phenotype. The proportion of phenotypic and genetic variance accounted for by each locus is shown for each of the 895 FT-MIR wavenumber and three FT-MIR predicted milk composition phenotypes. The genetic variance for each phenotype is the SNP-based estimate evaluated by the Bolt-LMM software. Table S12. Chronological profiles across iterations for 19 significant association effects with a co-localized eQTL observed in FT-MIR wavenumbers, where the association is observed after fitting the top chromosomal variant(s) in previous GWAS iterations and/or the base GWAS as covariates. Iterations are defined relative to the base GWAS, with the base GWAS represented as iteration 0. P-values at previous iterations for the phenotype, and p-values for the corresponding top chromosomal SNP in that iteration are provided. Table S13. Minor allele frequencies and allele effects for WGS tag variants with a significant association effect in at least one FT-MIR predicted milk composition trait and a co-localized eQTL. FP = Fat %; LP = Lactose %; PP = Protein %. Table S14. Chronological profiles across iterations for 12 significant association effects with a co-localized eQTL observed in FT-MIR predicted milk composition traits, where the association is observed after fitting the top chromosomal variant(s) in previous GWAS iterations and/or the base GWAS as covariates. Iterations are defined relative to the base GWAS, with the base GWAS represented as iteration 0. P-values at previous iterations for the phenotype, and p-values for the corresponding top chromosomal SNP in that iteration have been provided. FP = Fat %; LP = Lactose %; PP = Protein %.Additional file 5: Figure S15. Significance profiles of associations between FT-MIR wavenumbers and loci/genes in high LD with a putative impact variant (PIV), or in high LD with the top variant of a co-localized eQTL. A PIV is defined as a splice region variant, or moderate or high impact variant, according to the SnpEff classification. Significance is expressed as the –log10 between each FT-MIR wavenumber and locus/gene of interest.


Acanthis spp.). We demonstrate that variation in redpoll phenotype is broadly controlled by a ~55-Mb chromosomal inversion. Within this inversion, we find multiple candidate genes related to melanogenesis, carotenoid coloration, and bill shape, suggesting the inversion acts as a supergene controlling multiple linked traits. A latitudinal gradient in ecotype distribution suggests supergene driven variation in color and bill morphology are likely under environmental selection, maintaining supergene haplotypes as a balanced polymorphism. Our results provide a mechanism for the maintenance of ecotype variation in redpolls despite a genome largely homogenized by gene flow.The genetic architecture of a phenotype can have considerable effects on the evolution of a trait or species. Characterizing genetic architecture provides insight into the complexity of a given phenotype and, potentially, the role of the phenotype in evolutionary processes like speciation. We use genome sequences to investigate the genetic basis of phenotypic variation in redpoll finches ( Trait genetic architecture influences how populations evolve and adapt. Genomic analysis finds that an inversion links genetic variation controlling redpoll finch color and bill shape, allowing the maintenance of latitudinal ecotypes despite a genome largely homogenized by gene flow. Understanding the genetic architecture of traits  may provide insight into the complexity of the phenotype, and its role in various evolutionary processes5. Speciose radiations, such as the Capuchino seedeaters (Sporophila spp.), demonstrate that traits under independent modular genetic architecture might readily generate novel phenotypes through genetic recombination, with the potential to lead to increased species diversity8. Alternatively, traits may become tightly linked by large structural variants, such as chromosomal inversions10. When chromosomal inversions link multiple genetic elements that control a suite of traits  they are commonly referred to as supergenes11. Because supergenes can maintain complex phenotypic differences within a population, supergenes may have unique evolutionary implications. For example, different evolutionary outcomes may depend on if (and how) incompatibilities arise between supergene haplotypes. Mutations that arise along one inversion haplotype might be locally advantageous in an isolated population, but incompatible with the alternative inversion haplotype, resulting in a classic model of lineage divergence and speciation through Bateson–Dobzhansky–Muller incompatibilities13. However, the immediate effects of an inversion  or subsequent point mutations within an inversion may result in an inversion genotype being lethal or highly deleterious to fitness, despite providing a fitness benefit to heterozygous individuals14. This latter model can generate a stable polymorphism that promotes intraspecific variation (such as different ecotypes) but not lineage divergence and subsequent speciation. Importantly, even in the absence of lethal genotypes, inversions may persist as stable polymorphisms if they affect traits involved in local adaptation across a heterogeneous environment15.Identifying the genetic basis of divergent traits has become a major goal in biology. Studies demonstrating associations between genotype and phenotype have provided evidence for key evolutionary processes, such as adaptive introgressionAcanthis spp.) are high-latitude Holarctic songbirds that have a long history of taxonomic controversy due to low levels of genetic divergence and overlapping geographic distributions despite variation in body size, bill morphology, and plumage coloration . Although these species co-occur in much of their ranges, environmental niche models demonstrate slight latitudinal differences between common and hoary redpolls during the breeding months18. Specifically, lighter-plumaged individuals with shorter and narrower bills  are more common at higher latitudes while lesser redpolls are restricted to western Europe and southern Scandinavia. This variation in redpoll morphology across latitude suggests phenotype may be playing a role in local adaptation; however, it is unclear the extent to which adaptation is contributing to reproductive isolation and divergence. While redpolls are commonly defined as three species, including the common redpoll (Acanthis flammea), the hoary redpoll (A. hornemanni), and the lesser redpoll (A. cabaret), we refer to the different redpoll groups described above as ecotypes based on phenotype and breeding distribution, given the lack of taxonomic consensus.Redpoll finches   reference genome and searched for local peaks of differentiation between PCA clusters by calculating FST and dXY in 25-kb windows across all chromosomes including all ecotypes. These scans identified a highly differentiated region across 55 Mb of chromosome 1 , bill size and shape, and body size. Transitioning from the AA, to AB, to BB genotype also broadly mirrors a transition in phenotype from dark to light plumage coloration, where the AA genotype is associated with dark plumage, BB is associated with light plumage, and AB is intermediate. Mason and TaylorFST peaks, and (2) by identifying SNPs significantly associated with species classification using a genome-wide efficient mixed model analysis (GEMMA)22. While species identity does not perfectly correlate with redpoll phenotype because they exhibit continuous phenotypic variation, the fact that species classification relies almost entirely on morphology makes it a reasonable proxy for total phenotypic variation. Finally, we annotated missense mutations within the identified genes based on a variant’s location with respect to open reading frames using SNPeff v4.323. Our results suggest that the vast majority of SNPs associated with phenotypic variation in redpolls are within or close to the inversion: 99% of 20,443 SNPs significantly associated with redpoll phenotype were located on chromosome 1, with only 167 located elsewhere in the genome  by compiling a list of genes that fell within the highest FST outlier analysis, resulting in 322 genes across 7 chromosomes . The proteins produced by these genes likely function in the recognition of the lipoproteins that transport the hydrophobic carotenoid pigments. We identified two genes  within the inversion region that may also be related to carotenoid pigmentation through their involvement in lipid transport. Specifically, STARD13 produces a stAR-related lipid transfer protein, which as a protein family, are involved in intracellular lipid transport, metabolism, and cell signaling events33. While further validation studies are required to understand the role of these genes in carotenoid variation, their functions appear to be in line with other recently reported genes associated with carotenoid pigmentation.Redpoll phenotype also varies in the amount of red feather coloration resulting from carotenoid pigmentation. Carotenoid pigments are unique in animals in that they cannot be synthesized endogenously and must instead be taken in through their diet before they can be deposited in feathers. Previous studies of genes involved in carotenoid pigmentation in birds highlight the role of two scavenger receptor genes (TSKU and FSTL1 are known antagonists of bone morphogenic protein (BMP) signaling26. However, the effects of BMP inhibition may influence phenotype in at least two disparate ways: through the regulation of melanogenesis, or by contributing to differences in bill morphology. BMPs are regulators with important roles in epidermal homeostasis and hair follicle growth and pigmentation34. Specifically, BMP4 and BMP6 products have both been demonstrated as inhibiting or stimulating melanogenesis, respectively34. However, other studies have also implicated BMP4 in the development of bird bill morphology36. For example, studies of BMP4 in Darwin’s Finches find strong correlations of BMP4 expression with both bill depth and width35, two traits known to vary in redpolls37. Similar to Frizzled, TSKU was also shown to be differentially expressed in redpolls18. We therefore emphasize the observed differences in TSKU and FSTL1 documented here could influence biologically important phenotypic variation in redpoll coloration, bill morphology, or both. Given the implication of BMP4 in multiple pathways affecting different phenotypes, there could be pleiotropic effects resulting from one or more loci altering BMP signaling. Taken together, these candidate loci provide evidence that multiple aspects of redpoll phenotype are likely affected by a single genomic region maintaining associated SNPs from numerous genes in tight physical linkage.Two additional genes within the chromosome 1 inversion region that could be affecting phenotype are well-characterized: FILIP1L (chromosome 1 but outside of the inversion region), and SFRP4 (chromosome 2)—act as regulators in the WNT pathway, suggesting they likely play roles in further modulating melanogenesis39. Similar to TSKU and FSTL1, SFRP4 has also been demonstrated to regulate BMP, further emphasizing the possibility of singular or joint effects on plumage coloration and bill morphology.While nearly all associated SNPs with gene annotations were within the chromosome 1 inversion region, three additional genes containing, or neighboring, associated SNPs may also have important phenotypic effects. Two of these—PKS15/1, its function in birds has yet to be fully validated. However, its synteny with RAB18, and YME1L1, suggests homology with a PKS described in budgerigars (Melopsittacus undulatus)40. Functional validation through yeast-based expression demonstrated that the budgerigar PKS plays a critical role in the accumulation of red/yellow, parrot-specific pigments known as psittacofulvins. The association of PKS with redpoll phenotype indicates that it might play a similar role for organisms that contain carotenoids instead of psittacofulvins. While this requires further investigation, PKSs have been demonstrated elsewhere as important in animal pigment biosynthesis41.A third locus outside of the inversion region near an associated SNP on chromosome 2 includes a polyketide synthase (PKS). While this gene was annotated based on similarity to Mycobacterium 11. As lesser redpolls form the darkest and smallest end of the redpoll phenotype distribution, the associated SNPs located outside the inversion may also be additive with respect to overall phenotype. Given the range restriction and more extreme phenotype of the lesser redpoll, there is less opportunity for disassortative mating, and its unclear how the derived SNPs outside of the inversion that further modulate phenotype interact with the B inversion haplotype. A previous study of an avian supergene in white-throated sparrows 10 demonstrated that one of the supergene haplotypes in sparrows had likely introgressed from a closely related species. However, topology weighting across windows of the redpoll supergene favored a topology that included a sister relationship between the two haplotypes, with a combined average weight of 54% among the three topologies that included this sister relationship  of recombination. This simple scenario could result in a balanced polymorphism stemming from associative overdominance, where inversion heterozygotes perform best because heterozygosity masks some of the deleterious mutations12. However, redpolls heterozygous for the inversion appear to occur in fewer numbers than homozygotes (7/73 samples in this study), suggesting an alternative mechanism may be responsible for maintaining the polymorphism. Given the presence of all three inversion genotypes in redpolls, no combination of the supergene appears to be lethal—a finding in contrast to other recently described supergenes of similar size45. Because there is no lethal inversion genotype, recombination likely occurs regularly in homozygotes (and possibly at low levels in heterozygotes), potentially allowing for some purging of deleterious mutations. This could have a considerable influence on the maintenance of the variation, and the evolutionary consequences of this supergene.Considerable theoretical attention has recently been given to the evolution and degradation of supergenes12. Even with some selection, high levels of migration (between inversion genotypes) would swamp out any loci contributing to local adaptation. The persistence of the redpoll supergene is therefore likely dependent on both selection and migration. One scenario that is supported by field data is that the supergene remains balanced through assortative mating. Redpolls often mate assortatively46, but, intermediates and mixed pairs have also been observed from multiple localities47. Thus, the strictness of assortative mating may vary depending on the locality or may relax during irruptive population years47. Relaxation of mate choice and mixed pairings would produce the intermediate number of inversion heterozygotes seen in our data, and ultimately maintain the supergene as a stable polymorphism. However, this scenario alone does not provide an explanation for the maintenance of latitudinal differences between ecotypes. Furthermore, no hybrid zone has ever been documented in redpolls, which would be expected under a strict assortative mating scenario. While regions of hybridization have been suggested in places like Iceland, where high color variation exists49, previous genetic studies have not recovered support for this hypothesis50.Understanding the effects of the redpoll supergene, and the forces responsible for its maintenance, is difficult. In the absence of selection , the supergene would function as a single locus with one of the haplotypes eventually becoming fixed or lost due to drift52. Despite including some individuals sampled during the non-breeding season (n = 27), we are able to detect differences in latitude by inversion genotype group, with B haplotypes significantly more common at higher latitudes . Gene flow among ecotypes would be expected to disrupt linkage between any latitude-associated loci and phenotype through recombination unless those loci were tightly linked as in an inversion. In light of the link between the redpoll supergene and phenotype and differences in breeding distribution between ecotypes18, the supergene may impart local adaptation to the environment. However, given the detection of inversion heterozygotes and the presence of gene flow, the inversion likely does not influence reproductive isolation. Thus, redpolls appear to function as a single species harboring ecotypic variation, rather than as three distinct species.The phenotypes produced by the supergene are likely subject to environmentally mediated selection: notably, the more northerly distributed redpoll ecotype demonstrates features associated with high-latitude adaptation in other bird species des Fig. . This pa53 to simulate data under two spatial models of evolution informed by the aspects described above  whether or not a simulation resulted in a stable polymorphism, and (2) the inversion genotype ratios that were produced. We compared these ratios to the inversion genotype ratio in redpolls captured by our sampling. These simulations revealed that the strength of assortative mating, or amount of migration, played a larger role in the balancing of the inversion polymorphism than selection did at the levels tested 55. The maintenance of redpoll ecotypes via an inversion across an environmental gradient places redpolls within this growing number of species. In some cases, such as monkeyflowers (Mimulus guttatus)14, inversion polymorphisms may confer sex-specific effects, and can be maintained within a population through a balance of positive and negative fitness interactions. In other cases, though not exclusive to sex-specific effects, inversions may affect phenotypes related to local adaptation, and species distributed across a heterogeneous environment may retain an inversion polymorphism through spatially varying selection, as suggested here for redpolls. This has recently been demonstrated in seaweed flies (Coelopa frigida)15 and deer mice (Peromyscus maniculatus)55. In addition, studies of Drosophila have reported clinal variation in multiple survival traits controlled by an inversion as a result of spatially varying selection across latitude56. These findings in Drosophila highlight the need for further investigation into the selection pressures and fitness effects of the inversion we report in redpolls.As whole-genome sequences proliferate, an emerging body of literature is providing empirical evidence of intraspecific variation maintained through inversion polymorphism57), we find no evidence of genome-wide population genetic structure consistent with current taxonomy. Instead, we provide evidence that the suite of morphological traits used to describe redpoll species differences are linked within the identified supergene. The presence of all possible inversion genotypes suggests there are no lethal supergene combinations and indicate that while these traits are likely involved in local adaptation, they are not involved in reproductive isolation. Though breeding distributions vary latitudinally, even minor levels of contemporary gene flow within broad areas of sympatry likely maintain these traits as stable polymorphisms. Manipulations involving common garden experiments, or aviary crosses will help elucidate the strength of selection and may reveal additional unknown genetic interactions with the supergene that are affecting the evolution of redpolls.We provide evidence from whole-genome sequence data of loci associated with redpoll plumage coloration and bill morphology contained within a ~55-Mb inversion supergene. While some authorities classify redpolls as three separate species , including common redpoll (n = 26), hoary redpoll (n = 33), and lesser redpoll . We extracted genomic DNA using a salt extraction protocol. Samples were first lysed using a homogenizing solution , and a 20% SDS solution. We added 2 μl of glycoblue dye to aid in the identification of the DNA pellet, and precipitated DNA using a 6 M NaCl solution and 100% EtOH. DNA pellets were resuspended in 100 μl of TE buffer . We prepared genomic libraries using the Nextera XT kit with half-reaction volumes. We pooled all 73 individuals, and sequenced whole genomes using two lanes of an S4 flow cell on an Illumina Novaseq . The collection and handling of all samples were done with approval and in accordance with the ethical guidelines set out by the University of Colorado Boulder Institutional Animal Care and Use Committee, the University of Iceland, Reykjavik Institution of Life and Environmental Science, the Czech Academy of Sciences Institute of Vertebrate Biology, the Greenland Home Rule Government, Danish Polar Center, and the Cornell University Institutional Animal Care and Use Committee.We sampled 73 individuals from across the three redpoll species currently recognized by many authorities  reference genome using the BWA mem algorithm with default settings60. We called variants using bcftools mpileup61, and filtered to keep only single nucleotide polymorphisms (SNPs) with a quality score higher than 80. We dropped one individual (R97) due to its sibling status with another individual. We removed all potentially paralogous loci by filtering SNPs with a depth lower than 2x and higher than 12x coverage, removed all SNPs with a minor allele frequency lower than 5%, and generated multiple datasets based on allowed missing data using VCFtools v 0.1.1662. We ran subsequent analyses on datasets allowing for no missing data (100p), and 25% missing data (75p) with concordant results between both datasets. We present results from the 75p dataset, unless noted otherwise. Scripts used in our bioinformatic pipeline are publicly available on Github (https://github.com/erikrfunk/whole_genome_bioinformatics)63.Raw reads were trimmed using TrimmomaticPE64 with default settings. Resulting bam alignment files were used to detect structural variants with the program SVIM v1.4.221. We adjusted the maximum detectable variant size to 60 Mb using the –max_sv_size argument.In addition, we selected two individuals to generate long-read whole genomes resequenced using Oxford Nanopore Technologies MinION sequencing platform. These individuals  were selected as representatives of two distinct inversion genotypes within redpolls. Library preparation and sequencing were carried out at Colorado State University using the SQK-LSK-109 Ligation Sequencing Kit , across 5 flow cells. Long reads were mapped using NGMLR v0.2.765. To further assess clustering of individuals by species designation, we ran the program conStruct v.1.0.466. We assessed models for all number of populations from K = 1 to K = 6 using both spatial and non-spatial models. Model performance was evaluated using a combination of cross validation and layer contribution scores. We selected the best value of K as the model that exhibited the largest gains in predictive accuracy, while maintaining observable layer contributions.To visualize population genomic structure, we ran principal component analyses using the R package SNPRelate v1.19.3FST, and dXY. All calculations were made using the python script popgenWindows.py . We conducted these genome scans as pairwise comparisons between named species, and distinct clusters of individuals identified in PCAs. After identification of the chromosome 1 inversion, we calculated heterozygosity of the inversion for each of the three PCA clusters using R package adegenet v.2.1.367.We assessed heterogeneity in divergence across the genomic landscape using windowed calculations of diversity statistics for variant sites, including Pi, r2 using plink v1.968. LD was calculated between pairwise SNPs across each chromosome for the entire genome. We also calculated LD separately along sections of chromosome 1 that were outside, and inside the inversion. LD for each region was averaged by combining all calculations of r2 for a given distance between SNPs, resulting in a plot of LD decay.To evaluate linkage across the chromosome 1 inversion, we calculated linkage disequilibrium (LD) as FST peaks, and a genome-wide mixed model analysis using GEMMA22. While continuous variation exists in redpolls, species classifications are based on morphological characters, including plumage coloration, and bill size and shape. We used species classification as a summary of phenotype to test for genetic associations in GEMMA and ran analyses using sex as a covariate, and without using any covariates. No differences were recovered between these two analyses and we report the results with sex as a covariate here. We included a matrix of relatedness, generated using the -gk 1 command within GEMMA. Positions of significant SNPs identified by GEMMA, and peak regions of FST were used to compile lists of genes that either encompassed or neighbored these SNPs (within 100-kb) from the annotated brown-capped rosy-finch reference genome. We numbered our chromosomes based on gene content and synteny with the zebra finch (Taeniopygia guttata). Significance for associated SNPs were drawn using a false discovery rate of p < 1e−5. To evaluate the degree to which the associated SNPs can be used to explain phenotype, we used GEMMA to performed a leave-one-out cross validation using a Bayesian sparse linear mixed model (BSLMM) and the -predict 1 argument. To generate a predicted phenotype, we systematically dropped the phenotype for a single individual, rerunning the model each time. This resulted in a separate model, and a predicted phenotype for each individual. The variance in predicted phenotype was quantified using a regression against observed phenotype.We used two approaches to identify regions of the genome associated with PCA clusters and phenotypic differences: 69. We tested for overrepresented GO categories and examined functional classification across three GO databases , as well as signaling and metabolic pathways. In addition, we compared our gene lists to the over- and under-expressed gene lists produced by Mason and Taylor18. Finally, we categorized each redpoll variant by comparing its chromosomal position to the gene model coordinates in our reference genome using SNPeff v4.323. Based on its position with respect to gene model reading frames, variants were classified as either intergenic, upstream/downstream, intronic, synonymous, or missense mutations.To evaluate how the genes identified by each approach may be playing a role in the generation of divergent phenotypes, we examined known gene ontologies using Panther v.1642. Results were congruent among the three different window sizes so we only present results from the 100 SNP window analyses. Trees were generated using 4 redpolls, 2 from each of the inversion homozygote groups, and 9 additional individuals from across 5 taxa at varying degrees of divergence from redpolls. We selected these taxa based on the most recently published phylogeny for the family Fringillidae70. These additional individuals included two species grouped as crossbills (Loxia leucoptera and Loxia curvirostra), two species grouped as rosy-finches (Leucosticte atrata and Leucosticte tephrocotis), and the tree was rooted using a Fringilla coelebs genome from the NCBI Sequence Read Archive (SRR11537170).To explore the possibility that one of the inversion haplotypes introgressed into redpolls from a closely related species, we used phylogenetic methods to test if the two inversion haplotypes were (1) sister, indicating an origin within the redpoll lineage, or (2) not sister, indicating an origin outside of the redpoll lineage followed by introgression. We generated phylogenies using 50, 100, and 200 SNP windows along the chromosome 1 inversion using TwisstLeucosticte australis) reference genome and the same bioinformatics pipeline described above for redpolls. We converted the resulting VCF file into a .geno file using the parseVCF.py python script from Simon Martin (https://github.com/simonhmartin) and generated rooted phylogenies using PhyML71. PhyML was run using the Twisst script phyml_sliding_windows.py with default settings. Topology weights were calculated and visualized in R using the plot_twisst.R script.All sequences were aligned using the same brown-capped rosy-finch , allowing for migration each generation. Each simulation was allowed to run for 10,000 generations and was iterated 50 times. Each simulation also varied in one of two parameters, including selection, strength of assortative mating (model 1), or amount of migration (model 2). We generated a custom output that tallied the total number of iterations that resulted in a balanced polymorphism  and extracted the average count of each inversion genotype, along with its spatial position. Eidos code for the models we used can be found on github at https://github.com/erikrfunk/redpoll_slim_models.The evolutionary processes that act on a population in order to maintain a balanced polymorphism are likely complex and numerous. As a first step in understanding the maintenance of the supergene polymorphism in redpolls, we simulated 100-Kb chromosomes with a 50-kb inversion in 1000 diploid individuals using the program SLiMFurther information on research design is available in the Supplementary InformationPeer Review FileDescription of Additional Supplementary FilesDataset 1Dataset 2Reporting Summary