Advances in high-throughput sequencing technologies have made it possible to access millions of measurements from thousands of people. Single nucleotide polymorphisms (SNPs), the most common type of mutation in the human genome, have been shown to play a significant role in the development of complex and multifactorial diseases. However, studying the synergistic interactions between different SNPs in explaining multifactorial diseases is challenging due to the high dimensionality of the data and methodological complexities. Existing solutions often use a multi-objective approach based on metaheuristic optimization algorithms such as harmony search. However, previous studies have shown that using a multi-objective approach is not sufficient to address complex disease models with no or low marginal effect. In this research, we introduce a locus-driven harmony search (LDHS), an improved harmony search algorithm that focuses on using SNP locus information and genetic inheritance patterns to initialize harmony memories. The proposed method integrates biological knowledge to improve harmony memory initialization by adding SNP combinations that are likely candidates for interaction and disease causation. Using a SNP grouping process, LDHS generates harmonies that include SNPs with a higher potential for interaction, resulting in greater power in detecting disease-causing SNP combinations. The performance of the proposed algorithm was evaluated on 200 synthesized datasets for disease models with and without marginal effect. The results show significant improvement in the power of the algorithm to find disease-related SNP sets while decreasing computational cost compared to state-of-the-art algorithms. The proposed algorithm also demonstrated notable performance on real breast cancer data, showing that integrating prior knowledge can significantly improve the process of detecting disease-related SNPs in both real and synthesized data. SNPs are the most common cause of genetic diversity in humans and can be identified as single nucleotide differences in the same location in the human genome. On average, there is one SNP per thousand nucleotides in the human genome, and each individual’s genome contains about 4 to 5 million SNPs. A major challenge in finding disease-related SNPs is identifying those that are synergistic or non-linearly related in causing a specific disease. While each SNP may have a relatively small or medium effect on a specific disease, the interaction of several SNPs can have a significant effect on that disease at the phenotype level. The study of the synergistic effect of SNPs on diseases is an important field of study in bioinformatics and computational biology. The main challenge in finding synergistic subsets of SNPs is a large number of possible solutions and a huge search space that is exponential concerning the number of SNPs. The problem of identifying SNP interactions can be defined as efficiently detecting multiple SNPs that are non-linearly related, significantly associated with phenotypes, and possibly influential in disease incidence. The search space for this problem contains all combinations of SNPs that may be related to a particular disease.Despite using filters to limit the search space, the number of possible combinations for these SNPs is so large, and existing methods have only reached a few hundred or at most a few thousand SNPs combinations to check, and also only interactions of at most a limited k-order are searched. The calculation of interactions between these SNPs grows exponentially as the number of SNPs increases . For exaGiven a dataset of m SNPs and n samples, each classified as a case (samples with the disease) or control (samples without the disease), the problem is to find one or more optimal sets of k SNPs (being k the epistasis order) that are influential on the disease state. For each SNP, there are three genotypes : the homozygous reference genotype, the heterozygous genotype, and the homozygous variant genotype. These genotypes are encoded into numeric labels .Given the genotype data of a set of samples, which are classified as cases and controls, the problem is to find a set of combinations of k SNPs (being k the epistasis size) that cause the disease. Since each SNP is represented with a number between 0 and N − 1 (being N the number of SNPs in the samples dataset), a solution is given by a list of k non-repeated values between 0 and N − 1.In recent years, most of the related researches are limited to those that examine the interaction between only a few SNPs which still needs lots of computation and time, particularly when we deal with several hundred thousand SNPs. Machine learning  methods 1-E2, the difference between classification error when the original dataset is used (E1), and the classification error for the permuted SNP pairs (E2). Pairs with the highest ΔE are assumed to be interacting SNP pairs most related to the disease state.Li et al.  proposedBoutorh and Guessoum  proposedA wide variety of other methods such as clustering and information theory-based searching methods –21, statSince the searching of all possible SNPs combinations is not computationally efficient, different heuristic techniques such as MCMC-based search , 36, swaIn this study, we focus on addressing this problem by introducing an improved harmony search. In the improved harmony search, we take advantage of biological prior knowledge to improve the chance of biologically relevant SNP combinations to be generated in the initial harmonies. The proposed approach, namely locus-driven based harmony search (LDHS), efficiently generates solutions (harmonies) that are better candidates than a complete randomly generated set of individual solutions. Experimental results confirm that the proposed method improves the efficiency (in terms of time and number of detected SNP interactions) compared to the previous algorithms, including the HS algorithm without the proposed initialization.In this study, we used genetic linkage, the pattern of simultaneous inheritance of parts of DNA, as biological evidence to guide the process of generating initial solutions. While the search algorithm may not be able to find the optimal SNP set in disease models with non-marginal effects, the proposed strategy for initializing harmony memories can instead compensate for this issue and generate better candidates that already guide the search algorithm to regions with higher scores. In the rest of this paper, first, the objective functions used in the previous research are introduced briefly in the methods section. After that, the biological background behind the new strategy used for generating individuals (besides random generation) is explained. We called this strategy SNP grouping which introduces groups of SNPs that biologically have a higher chance to interact and cause diseases. SNP grouping and weighting idea is explained after the biological background is provided. Finally, the results of applying the proposed method on synthesized and real datasets are reported and discussed.In order to successfully detect high-order SNPs, it is essential to efficiently search the very large space of all possible SNP combinations. As mentioned in the introduction section, we propose a harmony search (HS) based method that integrates biological knowledge for generating harmonies with a higher chance of having interactions from a biological perspective. In this section, we first explain the objective functions and then explain the integration of biological knowledge.In the present work, we used the same multi-population HS and objective functions as in Tuo et al. . They prDifferent improvements on the original HS algorithm has been suggested by researchers, to improve HS performance; such as proposing new operators, parameter adaptation, improving HS by hybridizing it with other heuristic algorithms, integrating multiple objective functions and constraints into the original HS structure, and adaptation of new harmony memory initialization methods . Multi-oAs mentioned, we used the same objective functions proposed by Tuo et al. . These si is the number of samples related to the genotype composition, and nij is the number of samples obtained for phenotype j and genotype number i. The lower the value of the K2-Score is, the greater the association between an SNP combination and disease status.BN K2-score is a score used in Bayesian network models and is applied to evaluate the association between nodes that are connected using directed edges in an acyclic graph. This objective function has a high power to detect SNP interactions and is defined in LR-score is defined to measure some kind of relation between the disease and a specific SNP set , 53. In ij is the number of samples related to phenotype j and genotype i, and the eij is the number of expected genotypes i having phenotype j. This function is well-compatible with the model of unknown diseases.In this formula, nJS-score  is defini is the number of samples related to genotype composition and nij is the number of samples obtained for phenotype j, and genotype number i.In this formula, ncontrol is a subset of X including only control samples; nsj,control and nsj,case indicate the number of samples with ‘case’ or ‘control’ state for jth SNP locus in which the SNP takes a value equal to s ; nicontrol and nicase denotes the number of control and case samples in which the SNP combination X takes its ith value from all possible SNP combination values. Finally, the number of control samples is denoted by nicontrol. d(xj) (th SNP combination. D(X) is the difference between the numbers of case and control records for all SNP values in a SNP-combination X. JE (X control) is used for normalization. The variable picontrol is the probability of observing a specific SNP combination with a value equal to i .The last objective function is the normalized distance with entropy (NDJE). This function, defined in Eqs l. d(xj)  is the dThe problem with existing score functions is that they are not fully capable of modeling marginal effects, hence cannot discriminate between SNP sets containing no correct SNP and SNP sets containing only a subset of correct SNPs. The score function is only increased when the SNP combination contains all (and not only a subset) of the correct disease-causing SNPs. As a result, the search algorithm will not be guided to optimal points . To compensate for this lack of ability, we propose a SNP grouping prior to initial population generation using which SNPs with a higher probability of interaction are placed in each harmony . The union of these SNPs naturally has a higher chance than random to be functional. This idea is explained in the next section.Genetic contents that are located close to each other on DNA sequence (on the same chromosome) have more tendency to be inherited together than independent genetic content. This phenomenon is called Genetic Linkage. Genetic Linkage has been so far known as a good source to detect genomic regions that affect diseases and as a result, genetic linkage studies have been so far used as one of the principal approaches to identify disease-causing genomic regions , 56. WhiThree categories of SNPs can be considered: SNPs that occur in coding regions, SNPs that occur in non-coding regions, and those in the promoter region. SNPs can have different functions depending on where on the genome they are located. Mutations or SNPs that occur in the coding regions of genes cause changes in the proteins produced by genes, and groups of SNPs that occur in these regions, by possibly generating a synergic effect, can change the function of the protein and cause new traits (i.e. disease-causing functions) in the cell. Any significant error in the process of gene expression also leads to a change  in the final product. The gene expression process is initiated by the binding of transcription factors to the promoter region. Mutations in the promoter region can also lead to expression disorders.The third category of SNPs, which are also more frequent on DNA than the first and second categories, are SNPs that occur in non-coding areas. Non-coding DNA has no instructions for making proteins and does not contain genetic information. Some non-coding regions of DNA, called introns, are located inside the genes but are removed, through RNA splicing, during the production of the final RNA strand.https://www.ncbi.nlm.nih.gov/snp/, Retrieved on November 3rd 2022).We introduce a SNP grouping method based on the mentioned SNP categories in this section , and also considering the location of SNPs and the genetic linkage. This grouping of the SNPs based on their location, considering genetic linkage and functionality, provides sets of SNPs that are good candidates to be considered as disease-causing SNP combinations; and considering these groups, in addition to considering random SNP groups, can group together the SNPs that are not recognized in the search process when the non-marginal effect holds on the search space. The SNP information (location and category) is available in the SNP database on NCBI website  are put in the same group. These groups, then are used in a method explained further, in generating the initial harmonies.After retrieving the SNP information and grouping them, the number of vectors  generated using each group is determined proportional to the number of functional or non-functional SNPs in each group. In the implementation, we considered two groups of SNPs. Group 1 includes SNPs that are located on genomic regions or gene upstream/downstream/promoter. Other SNPs are assigned to group 2. The number of generated harmonies from each group is proportional to the group size. In addition, we decreased the count of SNPs from group 2 by a factor of w, which we obtained using grid search and experiments on simulated data (w = 2). In the final population, the number of individuals that are generated using functional SNPs is more  since functional SNPs have more chance to cause disease. Detail of the data preparations and memory initialization is represented in the pseudocode available in As the outcome of this grouping and weighting scheme, the group of SNPs occurring on intron and intergenic regions take a smaller weight than genes on the promoter and also exon areas. Finally, in addition to random vectors, a set of vectors generated based on the proposed grouping strategy are placed into the initial harmony memories. The flowchart of the proposed method is represented in Co-occurrence of these SNPs that have biologically more chance to interact, increases the chance of a group of disease-causing SNPs to be placed in the same harmony in the harmony memory. This helps the search algorithm to initiate the HM with individuals that contain SNPs having more chance to interact with each other from a biological perspective, which is beneficial for discovering SNPs for disease models with no marginal effects. Also, because of the same biological reason, it increases the chance to detect SNPs for disease models with marginal effects.rd, 4th and 5th-order SNP data were also performed to obtain multiple interactions. To do this, as in the case of grouping double SNPs, we first group the SNPs according to their natural position as explained formerly. Then the different SNPs of each gene are weighed and higher weight is considered for the SNPs that are in functional regions of the gene. After grouping, we generate the initial harmonies using these groups. It is possible to generate vectors of gene SNPs when the number of SNPs on the gene is greater than the number of interactions we have considered. When we have to choose an SNP but the number of SNPs in the neighborhood is not enough, we use the random selection of other SNPs. As it is observed in the experiments, the grouping of higher order SNPs also improves the searchability of the algorithm.Grouping and weighting of 3Synthesized and real datasets are used to evaluate the effectiveness of the proposed method. The results reported in this section, are achieved on MATLAB software, Windows X operating system with 4 GB of RAM, and a dual-core Intel processor.We considered 8 other methods for comparison; the first one is a harmony search with similar objective functions but without the proposed initialization, MP-HS-DHSI . Other aWe considered two disease models for generating the synthesized dataset: with and without marginal effects. In the following subsections, for each of the two models, evaluation criteria including the number of successfully detected SNPs of order 2, 3, 4 and 5, the number of objective function evaluations, and execution time are provided.Four disease models with marginal effects (DME 1–4) are considered for evaluation in this section. For each model, 100 simulated data sets with a sample size of 4000 (2000 controls and 2000 cases) were generated using GAMETES 2.1 software. The parameter settings are the same parameter setting and datasets used in MP-HS-DHSI .Finally, The best performance of the proposed method can be observed in diseases with no marginal effect. For each DNME, there are 100 datasets with 1500 case samples and 1500 controls. The data of nonfunctional SNPs are generated randomly based on the Hardy-Weinberg equilibrium (HWE). The parameter setting related to eight DNME models is similar to the parameter setting used in Tuo et al. , in ordeIn Finally, in The dataset of breast cancer , 60 usedIn this work, we present an improved harmony search algorithm for detecting high-order interacting SNP combinations. LDHS is a method for improving metaheuristic search algorithms for detecting disease-causing SNPs. We demonstrate that in diseases with no marginal effect, where existing objective functions cannot effectively find optimal solutions, integrating biological knowledge can guide the search process to better candidates.In the present study, our main focus is on addressing the issue of current score functions not being able to discriminate SNP sets that only contain a subset of one or more members  of the true complete disease-causing SNPs. However, it is not straightforward to define or improve current objective functions to achieve this goal. As a result, we focus on initializing the harmony memories with SNP combinations that already have a higher chance of having interactions (in addition to random harmonies). This automatically increases the chance of putting together single SNPs that are parts of the final solution and therefore increases the chance of detecting disease-causing SNP combinations. The heuristic used in initializing the harmony memories is based on the biological fact that according to genetic linkage studies, SNPs located closer to each other on DNA strands have a greater tendency to have functional interactions and are a good source for detecting disease-causing genetic regions. In addition, we differentiate between SNPs located in coding or non-coding regions. Based on this knowledge, we propose a grouping strategy in advance of initializing harmony memories and propose a method based on this grouping to generate individual harmonies.The idea behind the proposed method is that while the score functions are not efficient to discriminate the SNP sets with a different number of correct disease-related SNPs, initializing the correlating SNPs in one harmony in disease with non-marginal effects can increase the chance of the search algorithm to reach the optimum SNP set. Experimental results on simulated and synthesized datasets approve the effectiveness of the proposed method. 96% of two-order SNP interactions and all five-order SNP interactions are detected by LDHS improved strategy, which shows a 31% and 33% improvement in the number of detected SNP combinations compared to MP-HS-DHSI algorithm which uses the same objective functions, but not benefit from biological knowledge integration in the harmony memory initialization. Three and four order SNP combinations are completely detected by the two algorithms. Also, the proposed method can perform close or equal to MTHSA-DHEI method which is a multitasking recent algorithm in disease models with no marginal effects, and better than MTHSA-DHEI in disease models with marginal effects. LDHS outperforms all other compared algorithms  in disease models with and without marginal effects.As reported in the results section, the number of required objective function evaluations to find the correct answer is reduced compared to the harmony search with the same objective functions, and also in cases that harmony search without the proposed initialization has not been able to find some of the disease-causing SNP combinations, the harmony search with the proposed memory initialization has successfully detected the regarding SNP sets. Compared to other methods, the LDHS has a performance very close or better than the state-of-the art algorithms under study. Our experiments however, shows that the lowest number of objective function evaluations corresponds to MTHSA-DHEI which is a multitasking algorithm. LDHS is the second-best algorithm considering the number of objective function evaluations in most of the experiments. However, the idea in LDHS can also be applied using a multitasking strategy.In this study, we consider the problem of discovering disease-causing SNP combinations. While there is a trend in using harmony search-based methods to detect high-order SNP combinations that cause a disease, studies show that these algorithms are not efficient in detecting SNP combinations with non-marginal effects. In diseases with non-marginal effects, common score functions cannot discriminate between SNP sets of size K that include different numbers of correct SNPs, and hence the search algorithm is not guided to optimal SNP sets. In this study, we propose a method for using biological knowledge to improve the memory initialization of harmony search. In addition to generating random harmonies, the proposed approach generates harmonies that include SNP combinations with a high tendency to interact considering the SNP locus information and the inheritance pattern of genomic regions. Experiments confirm that by adding these harmonies, the probability of finding optimal solutions in the presence of non-marginal effects increases. The experiments show that not only is the definition of objective functions important in finding disease-related SNPs, but also considering biological information can improve the performance of search algorithms. The authors suggest that this method can be applied to other metaheuristic algorithms for detecting SNP interactions.S1 Table(DOCX)Click here for additional data file.S2 Table(DOCX)Click here for additional data file. 26 Jun 2023 <div> PONE-D-23-13759 </div>  <div> Discovering SNP-disease relationships in genome-wide SNP data using an improved harmony search based on SNP locus and genetic inheritance patterns </div>  <div> PLOS ONEDear Dr. Narimani,Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.plosone@plos.org. 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Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented. Reviewer #1: YesReviewer #2: Partly********** <font color="black"> 2. Has the statistical analysis been performed appropriately and rigorously?  </font> Reviewer #1: YesReviewer #2: I Don't Know********** <font color="black"> 3. Have the authors made all data underlying the findings in their manuscript fully available?PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified. </font> The Reviewer #1: YesReviewer #2: Yes********** <font color="black"> 4. Is the manuscript presented in an intelligible fashion and written in standard English? </font> PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.Reviewer #1: YesReviewer #2: Yes********** <font color="black"> 5. Review Comments to the Author </font> Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. Reviewer #1: It appears that the paper successfully utilized harmony search in discovering SNP-disease relationships. However, it needs the following revisions:= There are some more harmony search approaches applied in SNP. Please survey them also in literature section, such as:- HS-MMGKG: A Fast Multi-objective Harmony Search Algorithm for Two-locus Model Detection in GWAS- A Secure High-Order Gene Interaction Detecting Method for Infectious Diseases= Section 2: Algorithm description is too short. Please provide algorithm pseudo-code and/or flow-chart. Also, provide the difference among algorithms in terms of algorithm structures by refering [1]:[1] Review of Harmony Search with Respect to Algorithm Structure,” Swarm and Evolutionary Computation, 48, 31-43, 2019.= Typos- Table 1: In "HMCR = 0.98 0.98". Delete "= 0.98". Same for "Tau0=1, eta=1, alpha=1, beta=1"Reviewer #2: The authors propose an algorithm (Discovering SNP-disease relationships in genome-wide SNP data using an improved harmony search based on SNP locus and genetic inheritance patterns) that claims to integrate biological knowledge to improve harmony memory, however, this is not reflected in the code, including the main contribution in the authors' paper  are also not specific enough.********** <font color="black"> 6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.If you choose “no”, your identity will remain anonymous but your review may still be made public.Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy. </font> Reviewer #1: NoReviewer #2: No**********https://pacev2.apexcovantage.com/. 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Please note that Supporting Information files do not need this step.While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool,  27 Aug 2023Dear Professor Sheng Du, Thanks for consideration and your comments on the submitted manuscript entitled “Discovering SNP-disease relationships in genome-wide SNP data using an improved harmony search based on SNP locus and genetic inheritance patterns”.The formatting requirements addressed in PLOSOne_formatting_sample_main_body.pdf and PLOSOne_formatting_sample_title_authors_affiliations.pdf are applied to the re-submitted version. Minimal dataset is uploaded as a supplementary file (S1 and S2 Table).https://github.com/BioLab-IASBS/LDHS. Real data is also accessible via http://bioinfo.kmu.edu.tw/brca-steroid-96SNP.xlsx. Data availability statement is updated on re-submission. Data  is made available at public github repository, accessible via Supporting information with missing file is corrected .Authors contribution is explained in detail and the pseudocode is added .The response to reviewer comments are provided in the following . For each comment, the answer is provided afterwards (beginning with a ‘++’ mark).Sincerely,Zahra NarimaniDepartment of Computer Science and Information TechnologyInstitute for Advanced Studies in Basic Sciences, Zanjan, Iran=============================================Dear Reviewers, Authors would like to thank you for reviewing our manuscript entitled “Discovering SNP-disease relationships in genome-wide SNP data using an improved harmony search based on SNP locus and genetic inheritance patterns”.The comments are addressed carefully and the answers are provided after each question (beginning with a ‘++’ mark). The most important comment was about missing detail of the algorithms. In addition to completing ‘section 3.2’ and adding the details of weighting and grouping method, the pseudocode of the proposed initialization is provided in Fig 1 of the revised manuscript. Sincerely,F Esmaeili, Z Narimani, M VasighiReview Comments to the AuthorPlease use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. Reviewer #1: It appears that the paper successfully utilized harmony search in discovering SNP-disease relationships. However, it needs the following revisions:= There are some more harmony search approaches applied in SNP. Please survey them also in literature section, such as:- HS-MMGKG: A Fast Multi-objective Harmony Search Algorithm for Two-locus Model Detection in GWAS- A Secure High-Order Gene Interaction Detecting Method for Infectious Diseases++ Thank you. The previous work section is updated in the manuscript (lines 86-90).= Section 2: Algorithm description is too short. Please provide algorithm pseudo-code and/or flow-chart. ++ Algorithm and flowchart are added , also section “3.2 Weighting SNPs” is updated to add the details (lines 284-292). Also, provide the difference among algorithms in terms of algorithm structures by refering [1]:[1] Review of Harmony Search with Respect to Algorithm Structure,” Swarm and Evolutionary Computation, 48, 31-43, 2019.++ Thank you. This is a very interesting paper to use and address for explaining what is done in the proposed method. The explanation is added and highlighted in “2 Materials and methods”. Corrections can be found in lines 132-145. = Typos- Table 1: In "HMCR = 0.98 0.98". Delete "= 0.98". Same for "Tau0=1, eta=1, alpha=1, beta=1"++ corrected.Reviewer #2:The authors propose an algorithm (Discovering SNP-disease relationships in genome-wide SNP data using an improved harmony search based on SNP locus and genetic inheritance patterns) that claims to integrate biological knowledge to improve harmony memory, however, this is not reflected in the code, including the main contribution in the authors' paper  are also not specific enough.++ Thank you. The description of the process is updated , and also the pseudocode of the proposed method is provided in Fig 1.AttachmentResponse to Reviewers.docxSubmitted filename: Click here for additional data file. 18 Sep 2023Discovering SNP-disease relationships in genome-wide SNP data using an improved harmony search based on SNP locus and genetic inheritance patternsPONE-D-23-13759R1Dear Dr. Narimani,We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.http://www.editorialmanager.com/pone/, click the 'Update My Information' link at the top of the page, and double check that your user information is up-to-date. 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The survival and fertility of heifers are critical factors for the success of dairy farms. The mortality of heifers poses a significant challenge to the management and profitability of the dairy industry. In dairy farming, achieving early first calving of heifers is also essential for optimal productivity and sustainability. Recently, Council on Dairy Cattle Breeding (CDCB) and USDA have developed new evaluations of heifer health and fertility traits. However, the genetic basis of these traits has yet to be thoroughly studied.Leveraging the extensive U.S dairy genomic database maintained at CDCB, we conducted large-scale GWAS analyses of two heifer traits, livability and early first calving. Despite the large sample size, we found no major QTL for heifer livability. However, we identified a major QTL in the bovine MHC region associated with early first calving. Our GO analysis based on nearby genes detected 91 significant GO terms with a large proportion related to the immune system. This QTL in the MHC region was also confirmed in the analysis of 27 K bull with imputed sequence variants. Since these traits have few major QTL, we evaluated the genome-wide distribution of GWAS signals across different functional genomics categories. For heifer livability, we observed significant enrichment in promotor and enhancer-related regions. For early calving, we found more associations in active TSS, active Elements, and Insulator. We also identified significant enrichment of CDS and conserved variants in the GWAS results of both traits. By linking GWAS results and transcriptome data from the CattleGTEx project via TWAS, we detected four and 23 significant gene-trait association pairs for heifer livability and early calving, respectively. Interestingly, we discovered six genes for early calving in the Bovine MHC region, including two genes in lymph node tissue and one gene each in blood, adipose, hypothalamus, and leukocyte.Our large-scale GWAS analyses of two heifer traits identified a major QTL in the bovine MHC region for early first calving. Additional functional enrichment and TWAS analyses confirmed the MHC QTL with relevant biological evidence. Our results revealed the complex genetic basis of heifer health and fertility traits and indicated a potential connection between the immune system and reproduction in cattle.The online version contains supplementary material available at 10.1186/s12864-023-09736-0. Heifers are young female cows that have not yet given birth to a calf and are the future of the dairy herd. Heifer health and fertility are crucial for the success of a dairy farm, as it directly affects milk production and the sustainability of a farm . HealthyABCC9 and GC genes have been associated with pregnancy rate [ARRDC3 was associated with growth and calving traits [The health and fertility of cows are complex issues that involve various factors, including nutrition, environment, physiology, and genetics –6. Compancy rate , while Ag traits . Heifer https://uscdcb.com/). Recently, they added heifer livability and early first calving to the evaluation system [Although the heritability of fertility and health traits tends to be relatively low, CDCB and the USDA Animal Genomics and Improvement Lab have been evaluating fertility and health-related traits using the large volume of data collected from the dairy industry  passed the Bonferroni-corrected threshold for early calving . After calculating deregressed predicted transmitting ability (PTA) as phenotype and editing, we included 510,318 and 768,645 animals for the GWAS of heifer livability and early first calving, respectively. All of the animals were imputed to 79 K SNPs, and we retained 73,554 SNPs after QC editing. We applied SLEMM  to perfoCHCHD7 and PLAG1, which are related to growth and development [LYN gene related to the regulation of innate and adaptive immune responses [P < 0.05) were found, with the top relevant terms being mineral absorption, homeostasis, metabolic process, and development (Table S2). According to existing studies and the cattle QTL database [Despite the few QTL regions detected in the initial GWAS, we evaluated all SNPs passing the suggestive significance levels for functional annotation analyses. For heifer livability, we obtained 118 genes located within or overlapping the vicinity of leading SNPs (< 1 Mb) using BioMart in the Ensembl database  with a large proportion associated with immune processes (Table S5). Finally, previously reported QTL within 1 Mb of associated SNPs were associated with milk production, reproduction, body type, and disease-related traits in cattle (Table S6).For early first calving, we identified 596 genes within or near the associated SNPs (Table S4). Notably, the top associated SNPs were located within or near the bovine MHC region on BTA 23, indicating potential connections between the immune system and early first calving . Many neMOG, OR12D2E, OR12D3, OR2H1, OR5V1, OR5V1C, OR5V2, TRIM10, TRIM15 (Table S7).To refine the GWAS results, we conducted additional GWAS analyses with imputed sequence data for heifer livability and early first calving in 27,235 bulls that have highly accurate phenotypes. We used 3,148,506 imputed sequence SNPs as genotype and de-regressed PTAs as phenotype. After editing and filtering on reliability, we included 11,562 and 10,700 bulls for heifer livability and early calving, respectively. The QTL regions discovered in the large-sample GWAS were validated for both traits at the nominal significance level  and genic annotations  inferred by SnpEff . As a reOR12D2 in adipose was significantly associated with early calving  were retained for downstream analyses.In this study, we conducted GWAS analyses with two datasets, a discovery dataset including 3,649,734 Holstein cattle  genotyped by various SNP chips and imputed to 79,060 SNPs and a fine-mapping dataset including 27,235 bulls genotyped by 50 K SNP chips and imputed to 3,148,506 sequence variants. The original SNP data of the discovery dataset were from multiple SNP chips with densities ranging from 3 to 50 K [The phenotype data were part of the December 2021 genomic evaluations from the U.S. Council on Dairy Cattle Breeding (CDCB), which routinely calculates predicted transmitting ability (PTA) values for dairy cattle of multiple breeds. We only included Holstein data for this study. We used deregressed PTA values as phenotype in the GWAS of two traits, heifer livability and early first calving . To ensuBos taurus ARS-UCD1.2 assembly [For the fine-mapping dataset, we obtained imputed sequence data of 27,235 bulls from previous studies . Brieflyassembly .r2-1, where r2 is the reliability of deregressed PTAs.We analyzed the discovery and fine-mapping datasets separately in the GWAS analysis. We performed the GWAS using a linear mixed model approach implemented in the SLEMM program . SLEMM cAfter GWAS analysis, we retrieved genes within 1 Mb of the significant SNPs using BioMart in the Ensembl database (Ensembl Genes 106). We carried out Gene Ontology (GO) and Pathway analysis using KOBAS . GO termhttps://github.com/jiang18/mph) with the annotations inferred by SnpEff [To evaluate the potential functions of the associated genomic regions, we explored the enrichment of GWAS results in different functional regions using the 27,235 bulls and imputed sequence variants. We performed enrichment analyses via MPH (MINQUE for Partitioning Heritability, y SnpEff  and 14 cP < 0.005 as suggestive significant.We performed TWAS analyses based on the 27 K bull data using S-PrediXcan  to link Below is the link to the electronic supplementary material.Supplementary Material 1


The adoption of dicamba-tolerant (DT) soybean in the United States resulted in extensive off-target dicamba damage to non-DT vegetation across soybean-producing states. Although soybeans are highly sensitive to dicamba, the intensity of observed symptoms and yield losses are affected by the genetic background of genotypes. Thus, the objective of this study was to detect novel marker-trait associations and expand on previously identified genomic regions related to soybean response to off-target dicamba. A total of 551 non-DT advanced breeding lines derived from 232 unique bi-parental populations were phenotyped for off-target dicamba across nine environments for three years. Breeding lines were genotyped using the Illumina Infinium BARCSoySNP6K BeadChip. Filtered SNPs were included as predictors in Random Forest (RF) and Support Vector Machine (SVM) models in a forward stepwise selection loop to identify the combination of SNPs yielding the highest classification accuracy. Both RF and SVM models yielded high classification accuracies  with minor extreme misclassifications . Eight genomic regions associated with off-target dicamba tolerance were identified on chromosomes 6 [Linkage Group (LG) C2], 8 (LG A2), 9 (LG K), 10 (LG O), and 19 (LG L). Although the genetic architecture of tolerance is complex, high classification accuracies were obtained when including the major effect SNP identified on chromosome 6 as the sole predictor. In addition, candidate genes with annotated functions associated with phases II (conjugation of hydroxylated herbicides to endogenous sugar molecules) and III (transportation of herbicide conjugates into the vacuole) of herbicide detoxification in plants were co-localized with significant markers within each genomic region. Genomic prediction models, as reported in this study, can greatly facilitate the identification of genotypes with superior tolerance to off-target dicamba. Genotypes were distributed in field trials based on MG. Each field trial was arranged in a three-replicate randomized complete block design where each plot consisted of four 3.66 m long rows spaced 0.76 m apart. The homogeneity of off-target dicamba exposure was assessed and confirmed using an inhomogeneous Poisson marked point process  based onSoybean genotypes were visually assessed for off-target dicamba damage on a 1 to 4 scale with 0.5 increments between R1 and R3 . As descls_means’ of the R   and the GAPIT” .2.4pls’ to fit the PLS model  and Support Vector Machine (SVM) models in a forward stepwise selection loop to identify the combination of SNPs yielding the highest classification accuracy. The selection loop started by fitting the SNP with the highest VIP, followed by adding each SNP one at a time. The SNP yielding the highest accuracy in the preceding iteration was retained in the subsequent loop, of which the classification accuracy was calculated with an additional SNP. The loop concluded when no further improvement in the classification accuracy was observed by the addition of another SNP, thereby identifying the optimal combination of predictors. To evaluate the impact of overfitting on the prediction accuracy of both models, the loop continued despite no additional gain in classification accuracy, and classification accuracy metrics were recorded for each iteration.Each iteration was analyzed with 5-fold cross-validation and classification accuracy metrics were recorded. The overall accuracy of each iteration was computed using eq. 1. Class accuracy is represented by the proportion of true positives (TP) and true negatives (TN) for individual classes , and false negative (FN)) (Eq. 2). Precision is described as the number of TP by the number of predicted positives (TP + FP) for individual classes (Eq. 3). Specificity is defined by the ratio of TN by TN and FP for individual classes (Eq. 4).where,TP = True Positive (correctly predicted as the positive class);TN = True Negative (correctly predicted as the negative class);FP = False Positive (incorrectly predicted as the positive class);FN = False Negative (incorrectly predicted as the negative class).RF and SVM machine learning models were used for the multi-class prediction problem. These were chosen based on their efficacy in handling data in which the number of predictors is larger than the number of observed samples, as well as a providing satisfactory balance between the variance-bias trade-off . RF is arandomForest’ (p predictors (number of predictors) randomly selected at each split. The SVM model was conducted using the R package ‘e1071’ , a total of 107 genotypes were classified as tolerant (19.4%), 341 as moderate (61.9%), and 103 as susceptible (18.7%) Figure 23.2Wm82.a2, www.soybase.org). In chromosome 6, three separate genomic regions were detected at 10,891,060 bp, 20,739,900 bp, and 47,550,354 bp. The genomic region on chromosome 6  represented by the SNP ss715592728  of 0.33) resulted in LOD scores of 5.4 and 12.3 for the FarmCPU and BLINK models, respectively  had the highest LOD scores in both FarmCPU and BLINK models  across the entire set of SNPs. A Universal Stress Protein (Glyma.06g209600) has been reported within 50 kb of ss715593866 . Lastly, ss715594836  is co-localized with a glycosyltransferase protein (Glyma.06g286500) and resulted in LOD scores of 6.0 and 7.5 for the FarmCPU and BLINK models, respectively. In chromosome 8, a genomic region at 22,622,648 bp  resulted in LOD scores of 6.1 and 4.3 for the FarmCPU and BLINK models, respectively. A gene (Glyma.08g255800) expressing an S-adenosylmethionine decarboxylase is located within 50 kb of ss715600920. In chromosome 9, ss715604850  had LOD scores of 4.9 and 6.4 for the FarmCPU and BLINK models, respectively. Interestingly, an additional glycosyltransferase protein (Glyma.09g224800) is located within 50 kb of ss715604850. The genomic region identified on chromosome 10  is co-localized with the region previously reported by ss715608720 (MAF of 0.40) had LOD scores of 4.6 and 6.3 for the FarmCPU and BLINK models, respectively. Two genes with plant herbicide detoxification functions were detected within 50 kb of ss715608720, including Glyma.10g010000 (glycosyltransferase protein) and Glyma.10g010700 (oxidoreductase activity). Lastly, a novel genomic region in chromosome 19 was identified at 1,656,743 bp. The SNP ss715633252 (MAF of 0.47) had LOD scores of 7.5 and 10.0 for the FarmCPU and BLINK models, respectively. Two ATP-binding cassette (ABC) transporter family proteins (Glyma.19g016400 and Glyma.19g016600) were identified within 50kb of this SNP. A second genomic region at 45,152,186 bp of chromosome 19 was also detected. This region was previously reported by ss715635454 (MAF of 0.33) had LOD scores of 6.3 and 13.9 for the FarmCPU and BLINK models, respectively. Across all significant marker-trait associations, the reported candidate genes have biological functions directly associated with the multi-phase herbicide detoxification model (Significant marker-trait associations (logarithm of the odds (LOD) > 4.0) were identified using both FarmCPU and BLINK models across chromosomes 6 (LG C2), 8 (LG A2), 9 (LG K), 10 (LG O), and 19 (LG L) Figure 3on model . The gen3.3ss715598194) to 3.16 (ss715593866) (eD). Given the average of squared VIP scores are equal to 1.0, a threshold higher than 1.0 is employed to select features that make the most substantial contribution to eD  to 327 SNPs (chromosome 8). The average VIP score across 4,970 SNPs was 0.82, ranging from 0.01 (5593866) Figure 4n to De . In scenn to De . A totalss715593866, ss715600920, ss715594836, ss715592728, ss715635403, ss715627948, ss715579081, ss715588076, ss715582179, ss715608720, ss715586851, ss715634898, and ss715616396. The model including the 12 SNPs as predictors outperformed both model including only the highest VIP SNP (ss715593866) and the model including all 41 selected SNPs by approximately 11% (0.71 to 0.79)  including 12 SNPs as predictors, with a noticeable reduction in overall classification accuracy with the inclusion of more SNPs Table 2.ss715593866, ss715635403, ss715588076, ss715592728, ss715600920, ss715582179, ss715633252, ss715626266, ss715583058, ss715582533, ss715610029, ss715605561, ss715605251, ss715599209, ss715627948, ss715616396, ss715595654, and ss715580115  was observed between the baseline model including only ss715593866 (0.65) and the model including 17 SNPs (0.76). Substantial improvements in class accuracy, precision, and specificity were also observed between the two models. The RF model also demonstrated high suitability to be implemented in real-world prediction problems. Out of all tolerant predictions, 86% were observed as tolerant and 14% as moderate, while out of all susceptible predictions, 78% were observed as susceptible and 22% as moderate  in the RF model was achieved using 17 SNPs as predictors, including 15580115 Table 3.4Gossypium hirsutum L.) was a major biotechnology breakthrough grounded on diversifying strategies of herbicide-based weed management as well as overcoming weeds resistant to glyphosate at a time when GT was the only genetically-engineered herbicide tolerance system available (dicamba monooxygenase (DMO) from Pseudomonas maltophilia (Strain DI-6)  . Geneticc levels . In the c levels .The goal of this study was to detect genomic regions related to various responses to prolonged off-target dicamba exposure in a population consisting of advanced soybean breeding lines. A total of 551 non-DT advanced breeding lines derived from 232 unique bi-parental populations were grown in environments surrounded by DT soybean and cotton growing systems, thus being exposed to prolonged unintentional off-target dicamba. Although each testing environment showed homogenous off-target dicamba distribution , one limGlyma.06g209600 is located within 50 kb of ss715593866 . This gene has been reported to be a Universal Stress Protein with adenine nucleotide alpha hydrolase function. Phase I of herbicide detoxification usually introduces a reactive functional group for the subsequent metabolism and detoxification through oxidation or hydrolysis by cytochrome P450s or carboxylesterases, respectively , 8 (1), 9 (1), 10 (1), and 19 (2). Interestingly, several candidate genes co-localized with significant SNPs have been reported to have biological functions directly related to proteins participating in the three phases of herbicide detoxification in plants . Thus, iectively . AlthougGlyma.06g286500 is a candidate gene located within 50 kb of ss715594836  with glycosyltransferase-related functions. Phase II of herbicide detoxification involves conjugation reactions of herbicides with reduced glutathione [catalyzed by glutathione S-transferases (GST)] or glucose   expresses an S-adenosylmethionine decarboxylase. This enzyme is key in the biosynthesis of polyamines  . In chrolyamines . Althouging salt , droughting salt , temperaing salt , and oxiing salt . A conseing salt . This reing salt .Glyma.06g286500, the candidate genes Glyma.09g224800  and Glyma.10g010000  have glycosyltransferase-related functions which are associated with conjugation reactions of phase II of herbicide detoxification , was co-localized with the significant SNP ss715605561  harbors two candidate genes (Glyma.19g016400 and Glyma.19g016600) that belong to the ABC transporter family. Herbicide conjugates from phase II are transported into the vacuole of plant cells by transporters, concluding phase III of herbicide detoxification (Similar to fication . Within fication . This ge15605561 . On chrofication . Anotherfication .eD). This was followed by a pair-wise correlation filtering step, resulting in a subset of important, uncorrelated SNPs. In both RF and SVM models, a pronounced decrease in prediction accuracy was observed with the increment of SNPs as predictors. Therefore, identifying fewer but relevant predictors (i.e. feature selection) yielded higher prediction accuracies as compared to fitting the model with the highest number of predictors available. Equivalent results were observed by Meloidogyne incognita (Kofold & White) Chitwood). In their study, a more pronounced decrease in prediction accuracy as a consequence of overfitting was observed. In addition, a lower number of predictors was needed to achieve the highest prediction accuracy, which could be explained by the qualitative nature of the phenotype. In this study, although the tolerance to off-target dicamba is substantially more complex and quantitative than resistance to southern root-knot nematode, less than 0.5% of total predictors were needed to achieve the highest prediction accuracy in both RF  and SVM  models. One of the main challenges in analyzing high-dimensional genomic data is the presence of multicollinearity and excessive noise among predictors, which often leads to a substantial detection of false-positive associations in GWAS . Given tBoth RF and SVM models yielded high classification accuracies using the best combination of predictors . Both prediction models resulted in high precision, meaning that minimal extreme misclassifications  were observed. Using a nearly identical panel of soybean breeding lines, 5ss715593866 is a major effect SNP and resulted in high classification accuracies in both RF and SVM when included as the sole predictor. Candidate genes with biological functions associated with herbicide detoxification in plants were co-localized with significant minor and major effect SNPs. These genes need to be further confirmed through gene-editing and controlled-environment experiments. Non-DT genotypes with tolerance were previously shown to yield significantly more than non-DT susceptible genotypes under prolonged off-target dicamba exposure. Accurate genomic prediction models have been proposed and can be implemented in soybean breeding programs to speed up the identification and development of non-DT genotypes tolerant to off-target dicamba. In addition, the negative impacts of overfitting toward model performance were reported and may guide the application of genomic prediction models.The widespread adoption of DT crops resulted in numerous events involving off-target dicamba damage to non-DT vegetation. Environmental conditions that exacerbate the likelihood of off-target movement are often observed in soybean-producing regions during the growing season, hence the reports of damage in most states where the over-the-top use of dicamba is authorized. Soybean is highly sensitive to dicamba exposure, critically compromising the yield and quality of non-DT genetically engineered and non-GMO growing systems. In this study, two genomic regions conferring tolerance to off-target dicamba were confirmed from previous studies, and six novel regions were identified. The genetic architecture of tolerance is complex and regulated by multiple small and large effect loci. However, The original contributions presented in the study are included in the article/supplementary files, further inquiries can be directed to the corresponding author.CV, DJ, JFZ, BD, DR, HN, and GS contributed to the conception and design of the study. CV, BD, DR, and GS contributed to the funding resources of the study. CV contributed to the collection of data used in this study. CV and JZ contributed to the statistical analysis of this study. CV wrote the first draft of the manuscript. All authors contributed to the article and approved the submitted version.


SNPs were selected to be: i) evenly distributed according to physical position ii) selected to minimise the linkage disequilibrium between adjacent SNPs or iii) randomly selected. Imputation was performed with three different software packages . The results revealed that FImpute v.3 was faster and achieved higher imputation accuracies. Imputation accuracy increased with increasing panel density for both SNP selection methods, reaching correlations greater than 0.95 in the three fish species and 0.80 in Pacific oyster. In terms of genomic prediction accuracy, the LD and the imputed panels performed similarly, reaching values very close to the HD panels, except in the pacific oyster dataset, where the LD panel performed better than the imputed panel. In the fish species, when LD panels were used for genomic prediction without imputation, selection of markers based on either physical or genetic distance (instead of randomly) resulted in a high prediction accuracy, whereas imputation achieved near maximal prediction accuracy independently of the LD panel, showing higher reliability. Our results suggests that, in fish species, well-selected LD panels may achieve near maximal genomic selection prediction accuracy, and that the addition of imputation will result in maximal accuracy independently of the LD panel. These strategies represent effective and affordable methods to incorporate genomic selection into most aquaculture settings.Genomic selection can accelerate genetic progress in aquaculture breeding programmes, particularly for traits measured on siblings of selection candidates. However, it is not widely implemented in most aquaculture species, and remains expensive due to high genotyping costs. Genotype imputation is a promising strategy that can reduce genotyping costs and facilitate the broader uptake of genomic selection in aquaculture breeding programmes. Genotype imputation can predict ungenotyped SNPs in populations genotyped at a low-density (LD), using a reference population genotyped at a high-density (HD). In this study, we used datasets of four aquaculture species , phenotyped for different traits, to investigate the efficacy of genotype imputation for cost-effective genomic selection. The four datasets had been genotyped at HD, and eight LD panels  were generated  Aquaculture has been the fastest-growing food production sector in recent decades, with a 609% rise in the total annual output from 1990 to 2020 . This grIn 2016 over 95% of the global aquaculture output originated from low and middle-income countries . The rapGenomic selection uses genetic markers to more accurately predict the breeding values of individuals compared to pedigree-based approaches, leading to higher rates of genetic gain and better management of inbreeding . DespiteSeveral studies have looked into the use of low-density (LD) SNP panels as a cost-effective alternative, with only a few thousands or even hundreds of SNPs used for genomic selection, in contrast to high-density (HD) panels, usually containing tens of thousands SNPs. Generally, studies on aquaculture species have reported that SNP densities can be reduced from tens of thousands to thousands without a significant loss of prediction accuracy . AdditioGenotype imputation is a method that can be used to predict missing genotypes in an individual based on the genotypes of other individuals of the same species. A common imputation strategy is to use a group of individuals genotyped with a HD panel (reference population) to infer the missing genotypes of other individuals (target population) genotyped with a LD panel, which is composed of a subset of markers from the HD panel . The refImputation algorithms can use a combination of population and pedigree-based methods . FImputeIn addition to the imputation method, there are several other factors affecting genotype imputation accuracy, namely, SNP minor allele frequency (MAF), the selection of SNPs for the LD panel , the number of individuals in the reference population and the population structure. MAF significantly impacts imputation accuracy for all imputation methods; as MAF increases, the accuracy of imputation of the minor allele increases . ImputatSeveral studies have compared the performance of imputation software and the different parameters affecting genotype imputation in human, plant and livestock populations. However, aquaculture broodstock populations are typically comprised of relatively few (but large) full and half sib families, with limited population structure and, as such, might be expected to show a different response to imputation strategies. Despite this, the number of studies testing imputation performance in aquaculture species is limited and they mainly use either FImpute or AlphaImpute software in Atlantic salmon , rainbowThe objectives of this study were to i) evaluate the performance of three imputation software packages, FImpute v.3, AlphaImpute2 and findhap v.4 in breeding populations from four diverse aquaculture species; ii) investigate the impact of the number of markers in the LD panel and their selection method on imputation accuracy; and iii) evaluate the genomic prediction accuracy of imputed vs. LD genotypes for different traits in the four species. Our results contribute towards the definition of best practices for the broader application of genotype imputation and cost-effective genomic selection in aquaculture.Salmo salar) population of 624 individuals (90 parents and 534 offspring), belonging to 61 full-sib families as described in  population of 1,445 fish , distributed across 36 full-sib families as described in (Philasterides dicentrarchi). Individuals were genotyped using RAD-seq and after quality control 11,069 SNPs were successfully mapped to the 22 pairs of chromosomes.• A turbot (ribed in . The gonCyprinus carpio) population of 1,319 individuals , comprising 195 full-sib families. This population was challenged with koi herpesvirus as described in • A common carp (Crassostrea gigas) population of 762 individuals (44 parents and 718 offspring), belonging to 30 full-sib families. Individuals in this study were challenged with ostreid herpesvirus (OsHV-1), measured for time to death, and genotyped using a SNP array with ∼27 K informative Pacific oyster SNPs ; MAF <0.05; or Mendelian error rates >10% were also excluded from subsequent imputation analyses. A summary of the data for the different species before and after quality control can be found in All datasets were filtered using PLINK v.1.9 . Individin silico by selecting 300, 500, 700, 1,000, 2,000, 3,000, 5,000 and 6,000 SNPs using the two methods described below. The LD panels were created by masking  all the SNPs not selected by each method.The LD SNP panels were generated https://github.com/Roslin-Aquaculture/Select-SNPs-to-generate-low-density-panels), considering the total number of SNPs and the length of each chromosome. For each density, a single panel was created with the number of markers selected being proportional to chromosome length and evenly distributed across the chromosomes according to position . For this SNP selection method, the first and the last SNP on each chromosome were always selected and included in the LD panel. When no SNPs were available in the required position to achieve an even distribution, the closest available SNP was selected to obtain a LD panel with the desired number of markers. If a chromosome did not have enough SNPs , all of the SNPs on that chromosome were selected and the final panel density was allowed to be slightly lower than expected .The selection of SNPs for the LD panels was implemented with a custom R script (available in 2) threshold values, to achieve the desired number of SNPs for each density. SNP pruning was performed using the “--indep-pairwise” command. In brief, at each step, squared correlation was calculated between each pair of SNPs within a genomic window, specified using SNP count (“variant ct”). All SNPs with squared correlation greater than the given r2 threshold were removed from the window until there were no such pairs. At the end of each step, the window was shifted forward by a “step size (variant ct),” and the procedure was repeated. A single LD panel was created for each target density.For the SNP selection method based on linkage disequilibrium, PLINK 1.9  was usedAdditionally, four LD panels were generated by randomly choosing 300, 500, 700 and 1,000 SNPs throughout the genome to test prediction accuracy before and after imputation with FImpute v.3.Imputation of the offspring’s LD genotypes was performed using their parents as reference population (genotyped for the HD panels) with three software packages: AlphaImpute2 , FImputeAlphaImpute2  imputatiFImpute v.3  uses a sFor Findhap v.4 , the maxFor all three methods, imputation accuracy was measured as the average Pearson correlation between the original and the imputed genotypes for each test individual. To test the effect of MAF on imputation accuracy, we calculated minor allele frequencies with PLINK v.1.9 and divided the SNPs into five MAF bins:  body weight in Atlantic salmon, ii) factorial-cross group (four levels) in carp, iii) box (36 levels) in turbot, and iv) tank (two levels) in oyster.gjk) was calculated using the GCTA software . The phenotypes in the validation set were masked, and genomic best linear unbiased prediction (GBLUP) was applied to predict the breeding values of the validation set individuals in ASReml 4.2 , available at Reml 4.2 , using tA different phenotype was used in each dataset : i) In AImputation accuracy increased with increasing panel density for all software . OverallRegarding computing time, FImpute v.3 was faster than the other two software tested. Running time results of the three software when imputing the 300 SNPs panel density for each species are shown in In There is a visible pattern of slightly decreased imputation accuracy at the ends of the chromosomes of the four species , but thiThe HD panel was used to estimate the genomic heritability and obtain genomic prediction accuracies for each species , which wSince these results were unexpected according to previous reports, which showed that the accuracy of genomic prediction post imputation was higher than using the LD panels, we wanted to further investigate whether the SNP selection methods were responsible for the high prediction accuracy of the LD panels without imputation. Therefore, we randomly sampled SNPs throughout the genome to generate LD panels and perform imputation to compare their prediction accuracy with the other SNP selection methods. Genotype imputation is a powerful tool that has the potential to reduce the genotyping cost of genomic selection in aquaculture breeding programmes without a dramatic loss of prediction accuracy. In this study, we investigated some of the main factors affecting the accuracy of imputation and genomic prediction to contribute towards the establishment of best practices for the wider application of this method in the aquaculture sector.Three genotype imputation software were tested for their performance and compared between four populations of different aquatic species. All three software packages used a combination of population and pedigree-based imputation methods, and both parents’ genotypes were present for all individuals in the datasets. The existence of pedigree information and close relatives in the dataset becomes more important as the number of markers in the LD panels decreases, as it becomes difficult to find the truly shared haplotypes between the reference and the target individuals.FImpute showed the best performance across the four species in our study, with highest imputation accuracies for most LD panels and a shorter running time. FImpute shows extremely fast computational times when compared to other imputation software  for populations where pedigree information was available . CompareThe number of SNPs in the LD panel and the linkage disequilibrium between adjacent SNPs was found to substantially affect imputation accuracy; by increasing the number of SNPs in the LD panels, we observed an increase in imputation accuracy . As prevde novo mutations during meiosis or larval development, which contribute to unusual segregation patterns and deviations from Mendelian inheritance patterns , and therefore their effects can be captured even with a small number of markers. Further, the number of families in a standard aquaculture breeding programme is small (100–200 families). The small effective population size and the degree of relatedness between individuals can explain the good performance of extremely low-density SNP panels.Other studies have shown that a small number of markers and imputation are sufficient for accurate genomic prediction. For example, Our findings demonstrate that for three out of the four species tested, the accuracy of genomic prediction is heavily dependent on the choice of SNPs when using the LD panels without imputation. The selection of evenly distributed SNPs in the LD panels resulted in markedly higher prediction accuracies when compared to that obtained with randomly selected SNPs. Whilst evenly distributed SNPs did not benefit from imputation, since the accuracy was already similar to that obtained with HD panels, imputation significantly increased the accuracy of randomly selected LD panels, bringing it in line with HD genotypes. In conclusion, the choice of SNPs in the LD panel is crucial when they are used without imputation for genomic selection; however, if imputation is used the choice of SNPs in the panel is irrelevant. Considering that the LD panel would have to be designed specifically for the target population, and that its performance might decrease as the genetic makeup of the population changes with each generation of selection, imputation is an exceptional tool to ensure that near-maximum prediction accuracies are obtained in every scenario.Imputation accuracy did not affect prediction accuracy in the three fish species tested, with imputation accuracies of 0.76–0.98 depending on the number of SNPs in the LD panel resulting in similar prediction accuracies. However, this is not true in oysters, where the prediction accuracy of the imputed LD panel was significantly lower than that achieved with the LD panel alone, even when the number of SNPs in the LD panel was increased to 6,000 . In thisA significant cost reduction can be achieved by sequencing the target population with a very low-density panel (300–500 SNPs), which should still provide maximal prediction accuracy when combined with imputation to HD, using a reference population containing relatives of the target population. While using the LD panels alone could result in a further reduction of the cost of genomic selection, we consider that the potential risk is not worth it since the number of animals that have to be genotyped at HD for imputation is low . In any case, if we estimate the cost of HD genotyping at $15 and the cost of LD genotyping at $12, for a relatively small population of 5,000 animals, the use of LD panels would result in a reduction of the cost in the application of genomic selection of 20% . Considering that the cost of HD genotyping is usually higher for most aquaculture species and that most species require the use of genetic tools to reconstruct the pedigree, LD panels and imputation can play an important role in the incorporation of genomic selection into aquaculture breeding programmes worldwide.In this study, we explored the use of LD panels and imputation to reduce the cost of genomic selection in aquaculture breeding programmes, exploring different imputation software and SNP selection methods. Imputation accuracies were very high for the three fish species tested, while the performance of imputation was markedly lower in our oyster dataset. FImpute v.3 was the fastest and most accurate imputation method in almost all scenarios tested. When the LD panels were used without imputation, LD panels with the SNPs evenly distributed across the chromosomes achieved prediction accuracies very similar to the HD panel in the three fish species, even with just 300 SNPs, while randomly selected LD panels resulted in markedly lower prediction accuracies. However, imputation significantly increased the prediction accuracy of the randomly selected LD panels, reaching values similar to those of the HD panel in the fish species. Our results indicate that genotyping cost for the implementation of genomic selection can be reduced by the use of LD panels or a combination of LD panels and imputation. While the use of appropriately selected LD SNP panels would be more cost-effective, we suggest the use of imputation to eliminate the risk from potential changes in performance of the LD panels. This manuscript will help facilitate the widespread adoption of genomic selection in commercial aquaculture, leading to increased production and stability.