Additionally, complex correlation patterns are present among variables. As a consequence, reliable variable selection techniques play a pivotal role in predictive analysis, generalization capability, and robustness in clustering, as well as interpretability of the derived models.High-throughput sequencing technology has revolutionized both medical and biological research by generating exceedingly large numbers of genetic variants. The resulting datasets share a number of common characteristics that might lead to poor generalization capacity. Concerns include noise accumulated due to the large number of predictors, sparse information regarding the K-dominating set, a parameterized graph-theoretic generalization model, was used to model SNP (single nucleotide polymorphism) data as a similarity network and searched for representative SNP variables. In particular, each SNP was represented as a vertex in the graph, (dis)similarity measures such as correlation coefficients or pairwise linkage disequilibrium were estimated to describe the relationship between each pair of SNPs; a pair of vertices are adjacent, i.e. joined by an edge, if the pairwise similarity measure exceeds a user-specified threshold. A minimum k-dominating set in the SNP graph was then made as the smallest subset such that every SNP that is excluded from the subset has at least k neighbors in the selected ones. The strength of k-dominating set selection in identifying independent variables, and in culling representative variables that are highly correlated with others, was demonstrated by a simulated dataset. The advantages of k-dominating set variable selection were also illustrated in two applications: pedigree reconstruction using SNP profiles of 1,372 Douglas-fir trees, and species delineation for 226 grasshopper mouse samples. A C++ source code that implements SNP-SELECT and uses Gurobi optimization solver for the k-dominating set variable selection is available (https://github.com/transgenomicsosu/SNP-SELECT). Note that v∉N(v) and the closed neighborhood of vertex v is denoted by N[v] = {v}∪N(v).Let V]2 , a subset of vertices D is said to be k-dominating if |N(v)∩D|≥k for every vertex v∉D.D is a k-dominating set, then every vertex in V−D is said to be k-dominated. A minimum k-dominating set is one of smallest cardinality in the graph and this cardinality is called the k-domination number of the graph, denoted as γk(G). Note that the k-domination number of a graph increases as parameter k increases and the model becomes more restrictive as more neighbors are needed for each vertex outside the set to be k-dominated. Hence, every 2-dominating set is also a 1-dominating set, but the converse is not true. Intuitively, as the parameter k increases, we expect the k-dominating set to be a more reliable representation of the dataset as each point has at least k similar points in the k-dominating set. Hence, the choice of k must balance two conflicting criteria: solution fidelity (how well the dataset is represented) and solution size (how many data points are selected). To illustrate, graphic presentations of k-dominating sets for k = 1 and k = 2 were showed in C. elegans  forms a cluster that altogether cover V. Since by definition, every vertex not in the 1-dominating set has a neighbor in it and hence, is assigned to at least one cluster. Since the problem of finding a minimum k-dominating set is NP-hard . The randomly chosen edge weights, denoted by al, where wi,j<wi,j+1 and wi,j<wi+1,j.To demonstrate the capacity of the Step 1: Initialize l←1;i = 1Step 2: for  to n−1j = i+1Step 3:        for  to nwij←alStep 3:                ;l←l+1Step 4:                ;Step 5:        end-forStep 6: end-forA correlative relationship among SNP variables, or linkage disequilibrium (LD), is the non-random association between SNP alleles. The distribution of these relationships among SNPs in a given genome tends to be greater when SNPs are closely located; this correlation diminishes quickly as genomic distance between SNPs gets larger, e.g. LD decay . As a rei that has all neighbors with wij<0.1, where j∈V and j≠i, was defined as an independent variable. The subset generated by SNP-SELECT has to include all the independent variables to confirm that the k-dominating set based approach is able to identify independent variables. Highly correlated variables were defined as a subset (P) of the variables where P⊂V, and the edge weights  of the DF dataset is known due to the structured pedigree, and was used as a baseline for comparison. We calculated the genomic estimated relatedness (G-matrix) using R package “rrBLUP” [k-dominating SNP subsets. The comparison of the pedigree-based relatedness (A-matrix) elements with those of the G-matrices of the selected SNP subsets was performed to validate that SNP-SELECT is able to minimize the deviation of diagonal elements while obtaining comparable genetic covariance among individuals .The average numerator relationship matrix (“rrBLUP”  using thOnychomys) are cricetid rodents that inhabit prairies, deserts and desert grasslands throughout the western United States, northern Mexico, and south-central Canada [O. leucogaster is readily distinguished based on body size, the two smaller species, O. arenicola and O. torridus, are morphologically cryptic and were treated as a single species until 1979 [O. leucogaster is sympatric with O. arenicola and O. torridus, respectively. SNPs were called using a reference-free SNP discovery protocol , and fik ∈ {1,2,3,4,5}, all the k-dominating sets found included the predefined independent variables. The performance of the k-dominating set model in the selection of proxy variables is presented in λ∈{0.8,0.7,0.6,0.5,0.4,0.3}. As shown in k or λ was encouraged. Also shown in k and λ to capture all relationships. By varying on k and λ, we demonstrate the flexibility and strength of SNP-SELECT in choosing proxy variables from highly correlated variables.When the SNP-SELECT algorithm was applied to the synthetic network with k-dominating sets  with k = 1, and λ∈{0.7,0.5,0.3,0.2} were generated. Among the four 1-dominating sets, DF103 has the best performance as shown in k on variable selection, another k-dominating set, DF203, with k = 2 and λ = 0.3 was generated to compare with DF103. The number of selected SNPs in DF107, DF105, DF103, DF102 and DF203 is 80,735, 67,062, 51,415, 41,539, and 68,188, respectively.The SNP-SELECT algorithm was applied to select the influential SNPs to reconstruct the known pedigree for a Douglas-fir (DF) breeding population. Four k-dominating subsets was showed in the reduced diagonal differences from the genomic relationship matrix (G-matrix) to the traditional pedigree-based average numerator relationship matrix (A-matrix)  . Comparid subset .A- and G-matrices resulted from using correlation coefficient of 0.3 and λ = 0.3 was listed in The effectiveness of SNP-SELECT was also examined by the conventional approach that filters for SNP variables by pairwise correlation coefficients, as well as the LRTag algorithm that applies minimum set covering for SNP selection . The disO. arenicola (n = 76), O. leucogaster (n = 67), and O. torridus (n = 83), collected at 12 geographic locations  demonstrated the greatest agreement among all selected subsets  was performed using samples’ dissimilarity matrix of each species. To describe the dissimilarity matrix, we first define the G-matrix as To confirm that the performance of SNP-SELECT was not the result of a specific clustering algorithm, the partitioning around medoids (PAM) algorithm  with k =i.e. only a small subset of variables is associated with the phenotypic variation [Owing to technological advancement in DNA sequencing methods, life scientists are grappling with exceedingly large data sets . The mosariation .In genetic analyses using high dimensional data sets where there are more parameters than observations, penalized regression techniques are often required to ensure stable estimates , 83. Thecorr|) is less than a predefined threshold λ; or if |corr| is no less than the given threshold, only the second variable will be selected |≥λ, SNP j will be selected). Here, we demonstrate the superior performance of the proposed k-dominating set variable selection over the conventional method of pairwise correlation coefficients . In prificients , COR03. ficients , suggestG-matrix), which can be used as a substitute for the traditional pedigree-based average numerator relationship matrix (A- matrix) in Henderson’s animal model [A-matrix and the G-matrix into a single genetic relationship matrix (H-matrix) has proven to be an effective approach to improve the relationship coefficients for better genetic parameter estimation [G- and A-matrices should be compatible [G-matrix need to be consistent with the A-matrix diagonal elements; therefore rescaling A- and G-matrices would reflect the mean difference between these matrices [The use of genomic markers to uncover hidden relationships and potential pedigree in open-pollinated progeny has been effective in tree breeding programs , 96. Sucal model –103. Alstimation , 105 andtimation , and to mpatible , and diamatrices , a contek-dominating set model provides a flexible and effective method for selecting informative SNPs; a C++ source code (SNP-SELECT) that uses GurobiTM Optimization solver is also released with the manuscript. This approach is scalable through the use of integer programming solvers and graph preprocessing, and can be extended to other genomic applications.The Using pedigree reconstruction and cluster analysis, the capacity of SNP-SELECT was demonstrated for solving the variable selection conundrum of large datasets without any significant runtime considerations. Furthermore, SNP-SELECT does not depend on the use of LD to define threshold for edges; other similarity/distance measure would broaden its applicability beyond breeding science and ecological genetics. Future work on the algorithmic aspects of this approach could focus on the development of graph and model decomposition techniques, as well as preprocessing techniques to improve scalability in practice.


Triticum aestivum L.) production is required to feed a growing human population. In order to accomplish this task a deeper understanding of the genetic structure of cultivated wheats and the detection of genomic regions significantly associated with the regulation of important agronomic traits are necessary steps. To better understand the genetic basis and relationships of adaptation and yield related traits, we used a collection of 102 Argentinean hexaploid wheat cultivars genotyped with the 35k SNPs array, grown from two to six years in three different locations. Based on SNPs data and gene-related molecular markers, we performed a haplotype block characterization of the germplasm and a genome-wide association study (GWAS).Increasing wheat . In particular FEh stands out as a promising trait to raise yield potential in Argentinean wheats; we detected fifteen haplotypes/markers associated with increased FEh values, eleven of which showed significant effects in all three evaluated locations. In the case of adaptation, the This work reveals the genetic structure of the Argentinean hexaploid wheat germplasm using a wide set of molecular markers anchored to the Ref Seq v1.0. Additionally GWAS detects chromosomal regions (haplotypes) associated with important yield and adaptation components that will allow improvement of these traits through marker-assisted selection. World population is projected to grow to nearly 10 billion by 2050 and more than 11 billion by 2100 and, on a global scale, agriculture expansion has slowed down and production increases have been achieved mainly through agricultural intensification . This scIn Argentina, with 4.46 Mha, wheat is the third most important crop in terms of planted area after soybean and corn, average 2012-2016 , spanninQuantitative trait locus (QTL) mapping is currently key for understanding the genetic basis of complex traits , includiThe recently released wheat reference genome assembly (IWGSC Ref. Seq. v1.0), developed by the International Wheat Genome Sequencing Consortium (IWGSC) , allows In this study, 102 Argentinean wheat cultivars were genotyped by using the 35k Axiom Wheat Breeder’s Genotyping Array . The polThe genotyping of the 102 Argentinean hexaploid wheat cultivars collection yielded a total of 7972 polymorphic SNPs with MAF ≥ 10%. A set of 6486 polymorphic SNPs was genetically anchored to specific wheat chromosomes based on mapping information from five biparental populations described previously . A seconA detailed information about the haplotype-based map construction for the Argentinean wheat collection is found in the Table All evaluated traits showed high heritability: the crop adaptation traits HD and PH showed broad sense heritability values higher than 0.95 and the yield related traits FEh, TGW and GNS displayed values in all cases higher than 0.80 Table .Table 3Regarding correlations between traits across the tested locations, the most consistent pattern was observed for FEh vs GNS, with positive correlations in most years at the Southern locations, Azul and Balcarce, and in all years at the Northern location Marcos Juárez Table . The relThe PH showed a positive correlation with TGW in Azul (one year) and in all years in Marcos Juárez with higher significant values. On the other hand, the PH showed negative correlations with GNS in most years at the Southern locations, contrasting with Marcos Juárez with no significant correlation in most tested years. A similar pattern can be described for PH vs FEh, with negative correlations in most years at the Southern locations, contrasting with Marcos Juárez with no significant correlations in all years Table .The HD showed a positive correlation with GNS in the Southern locations (2 years), contrasting with Marcos Juárez with negative correlations in three years. The HD also showed negative and highly significant correlations with TGW in Azul (1 year) and Marcos Juárez (2 years). A positive correlation between HD and FEh was observed in Azul (2 years), differing from Marcos Juárez with no significant correlations in most tested years. The HD vs PH showed contrasting correlations at the Southern locations and no significant correlations in most years in Marcos Juárez. The TGW vs GNS correlation showed positive values in Marcos Juárez (3 years), with no significant correlations in most Southern environments Table .Contrasting correlations observed across the Southern and Northern locations for PH vs GNS, PH vs FEh, HD vs GNS, HD vs FEh and, to a lesser extent, PH vs TGW, might suggest different strategies are involved in building site-specific yield components performance: genotypes adapted to the Northern latitudes would be favored by taller plants improving TGW, but affected by late flowering penalyzing TGW and GNS, whereas genotypes adapted to Southern latitudes would be favored by late flowering improving GNS and FEh, but affected by taller plants penalyzing FEh. Interestingly, independently of the environment, genotypes with high FEh would favor GNS, one of the most important yield components.We identified 17 haplotypes/markers associated with FEh of which one belongs to chromosome 1A, seven to 2A, one to 3B, two to 4A, two to 5A, three to 6A and one to 7A  Fig. a. The HBThree haplotypes significantly associated with FEh were detected as colocating with additional traits: haplotype Chr2A-B49-Hap2 on 2A 704.8-705.8 Mb) was colocated with GNS, haplotype Chr5A-B33-Hap4 on chromosome 5A (445.2-445.2 Mb) with PH and Chr6A-B24-Hap2 on chromosome 6A (205.1-233.3 Mb) with TGW. The correlations for the first two haplotypes were significant only in Southern locations , while the third was significant in all locations. In the case of Chr2A-B49-Hap2, the correlation with GNS was positive, as shown in Table .8 Mb wasWe identified 11 haplotypes/markers associated with TGW, of which one belongs to chromosome 2D, two to 3A, one to 3B, four to 6A and three to 7B Table . The SNPTwo haplotypes significantly associated with TGW and colocating with other traits were detected. The Chr3B-B111-246 Hap4 on chromosome 3B (817.4-817.8 Mb) colocated with PH, with the previously described Chr6A-B24-247 Hap2 on chromosome 6A (205.1-233.3Mb) colocating with FEh. In the case of Chr3B-B111-Hap4, the correlation with PH was positive, as cultivars carrying the haplotype for higher TGW also expressed higher PH . Cultivars carrying the Ppd-D1 sensitive allele (42 of the 102 cultivars tested) delayed flowering in all environments. Also it is important to mention that all haplotypes affecting HD showed significant associations at the Northern location in two or more years, contrasting with Southern locations Azul, showing three haplotypes with no significant effects on HD, and Balcarce, with nine haplotypes in the same situation. Additionally, we identified one haplotype colocated with PH, Chr6B-B26-Hap3 (157.6-157.8Mb), that increased HD values and negatively affected PH  that associates with both traits, but in opposite directions.TaGW2-A1, which is located at 237.75Mb on chromosome 6A and has been shown to be related to grain weight [TaGW2-A1 into a promising candidate gene for Chr6A-B24-Hap2. On the other hand, the gene TaGS5-3A located at 176.55Mb on chromosome 3A has also been associated with larger grain size and higher thousand grain weight [TaGS5-3A  to be considered as a gene candidate. In the opposite direction to that observed for FEh, the strongest genetic associations for TGW were detected in the Northern location Marcos Juárez, promoting TGW as an interesting trait to increase yield for those latitudes.Another relevant trait in the determination of yield potential is grain weight. We detected six significant haplotypes/markers with positive effects and five with negative effects on TGW Table . This lin weight . Non-funn weight . Shared n weight . We founFor GNS,  used GWAPpd-D1 gene marker [Ppd-D1 gene was found to be the main determinant of life cycle in Argentinean wheat cultivars.For HD, we found that the e marker  is the se marker , where tTaFT-B3 (581.4Mb) as a HD modifier for short days on this chromosome. Our nearest significant haplotype, Chr1B-B76-Hap2  gene, located at 740.1Mb on chromosome 3A, were associated with extra-early flowering time. We detected four haplotypes on chromosome 3A associated with HD. Our nearest significant haplotype, Chr3A-B-Hap4  [Vrn-B1 (5B), Vrn-D1 (5D) [Ppd-B1 (2B) [Finally, no significant associations were detected for HD with the genes -A1 (5A) , Vrn-B1 -D1 (5D)  and Ppd--B1 (2B) , indicatRht-B1 and Rht-D1, described by [Rht-B1 and Rht-D1 genes are balanced.In the case of PH, we did not find significant associations between the trait and the molecular markers for the “green revolution” dwarfism genes ribed by . AlthougWithin the 51 significant associations detected, the chromosome 1B haplotype Chr1B-B17-Hap4 and the chromosome 6B SNP AX-94943227 (234.8 Mb) were particularly noteworthy, since they were significant across the three locations in all analyzed years. To our knowledge, there are no plant height related genes described on these chromosomes, which suggest these consistent PH-HB/SNP associations are promising targets for further gene cloning projects.Rht genes Rht9 and Rht12 on chromosome arm 5AL, where Rht9 was linked to the SSR barc151 (558.34 Mb) and Rht12 was located 5.4cM from the SSR Xgwm291 (698.19 Mb). Our haplotype Chr5A-B54-Hap3 mapped at 516.1-527.9 Mb might be associated with Rht9 linked to SSR barc151 at 558.34Mb. However, such an association with Rht12 has to be discarded in our study, since additional PH haplotypes are placed in genetic regions distant to this PH gene.We detected four haplotypes on chromosome 5A associated with PH. In a mapping work  located Rht25 (144.0-148.3 Mb) detected by [Rht18/Rht14/Rht24(413.73 Mb) described previously [On chromosome 6A, we detected six haplotypes associated with PH; in particular, the haplotype Chr6A-B54-Hap5 (610.0 Mb) was significantly associated with PH in the three locations and in all evaluation years, except Balcarce 2015. However, none of the associated haplotypes was located in physical positions close to any of the known PH genes on 6A, namely ected by  and Rht1eviously .It is important to highlight that small association panels have been shown to increase both type 1 and type 2 error rates, failing to detect true associations while also generating a higher rate of false positive associations . In thisPpd-D1 gene on chromosome 2D, being the main determinant in the variations in the life cycle of the Argentinean wheats. The use of the IWGSC Ref Seq v1.0 allowed us to precisely compare all detected associated regions with genes and QTLs reported in previous studies.The genetic structure of the Argentinean hexaploid wheat collection was determined by the use of SNP markers, in which a strong relationship was displayed between the subpopulations obtained and the germplasm origin used by the main breeding programs in the country. Based on SNP and gene-related markers physically anchored to the IWGSC Ref Seq v1.0, a haplotype map was constructed, allowing the detection of highly conserved and selected regions like the 1BL/1RS translocation. A GWAS detected ninety-seven chromosome region associated with yield components and adaptation. In the case of yield components, we highlight regions on chromosomes 1A, 2A, 3B, 4A, 5A, 6A and 7A associated with FEh, particularly at higher yield potential locations. For adaptation, the most relevant effect on HD was the A previously described  set of 1P ≤ 0.0001 to a chromosome were assigned to it  Genotyping Laboratory, La Plata, Argentina, using the 35k Axiom Wheat Breeder’s Genotyping Array . Informa, Rht-D1 , Vrn-A1  [Vrn-A1 , Vrn-B1,, Vrn-D1 , Elf3-D1[Elf3-D1 , Ppd-B1  [Ppd-B1  and Ppd- [Ppd-D1 . RegardiD1 [Lr10 , Lr34 [610 [Lr34  and Lr24, Ppo-D1 , R-A1, RB1, R-D1 , Glu-B1aGlu-B1al , Wx-A1, 1, Wx-B1 , Vp1-B3  [Vp1-B3 , Glu-A3  [Glu-A3 , PinA-D1 PinB-D1  were incribed by .The SNP-based haplotype structure for each wheat chromosome was evaluated using the Haploview 4.2 software package . The pac∘ 42 ′ S, 62∘ 07 ′ W, 114 m.a.s.l.). In Azul, the field experiments were carried out during 2013 and 2014 at the Experimental Field of the Faculty of Agronomy, Universidad Nacional del Centro de la Provincia de Buenos Aires, Azul . In Balcarce, the field experiments were carried out during crop seasons 2013, 2014 and 2015 at INTA Experimental Station Balcarce . In all experiments except Marcos Juárez 2011 and Balcarce 2013 a Randomized Complete Block Design (RCBD) with two replications was used. More detailed information of the field experiments carried out for GWAS is described in Table In Marcos Juárez, the field experiments were carried out during 2011 to 2016 (6 years) at INTA Experimental Station Marcos Juárez (32H2) was estimated using the formulaThe best linear unbiased predictors (BLUPs) of traits in each environment were obtained  and were used for Pearson’s correlation analyses and broad sense heritability estimates. Broad sense heritability  at four environments, with at least one environment with highly significant differences (P <0.001). All the haplotypes/markers that satisfied these criteria are presented in Table 5011 = 0.00063 (per trait).GWAS were performed using 4516 haplotypes (from 1268 HB) and 495 informative SNP/gene markers anchored to the wheat genome and the SUPER method  implemenAdditional file 1Table S1. Polymorphic SNPs and gene-related molecular markers genetically and physically anchored to IWGSC Ref Seq v1.0. based on 102 Argentinean hexaploid wheats.Additional file 2Table S2. STRUCTURE Q matrix of the 102 Argentinean hexaploid wheats cultivars.Additional file 3Figure S1. Graphical representation of STRUCTURE Q matrix in the 102 Argentinean hexaploid wheats cultivars.Additional file 4Table S3. Haplotype-based map used for HB characterization and GWAS in the Argentinean hexaploid wheat collection.Additional file 5Table S4. Phenotypic data from Balcarce (2013-2015), Azul (2013-2014) and Marcos Juárez (2011-2016) for FEh, GNS, TGW, HD and PH used in GWAS.Additional file 6Table S5. Detailed information of the significant associated Haplotypes/markes detected by GWAS for FEh, TGW, GNS, PH and HD using the 102 Argetninean hexaploid wheat collection including all the SNPs/markers ID.


The important property of the quantitative traits of model organisms is time-dependent. However, the methodology for investigating the genetic interaction network over time is still lacking. Our study aims to provide insights into the mechanistic basis of epistatic interactions affecting the phenotypes of model organisms.n = 475) at multiple time points (day of hatch (BW0) and 1, 3, 5, and 7 weeks ). Statistical analysis detected 67, four, and two significant SNP pairs associated with BW0, BW1, and BW3, respectively, with a significance threshold at 8.67 × 10− 12 (Bonferroni-adjusted: 1%). Meanwhile, no significant SNP pairs associated with BW5 and BW7 were found. The SNP-SNP interaction networks of BW0, BW1, and BW3 were built and annotated.We performed an exhaustive genome-wide search for significant SNP-SNP interactions associated with male birds’ body weight (BW) (With strong annotated information and a strict significant threshold, SNP-SNP interactions underpinned the gene-gene interactions that might occur between chromosomes or within the same chromosome. Comparing and combing the networks, the results indicated that the genetic network for chicken body weight was dynamic and time-dependent. Drosophila melanogaster), yeast (Saccharomyces cerevisiae), mouse (Mus musculus), thale cress , maize (Zea mays), and human (Homo sapiens) demonstrate that epistasis is pervasive and is an important factor in determining the variation of quantitative phenotypes [Epistatic interactions (non-linear interactions between segregating loci) are gaining attention in contemporary biology, yet their role in the genetic architecture of quantitative traits is still obscure and controversial. Studies on fruit fly  were important for quantitative traits in chicken . FurtherIn the current study, we focused on the body weight of chickens whose phenotypic data could be analyzed as a series of data points (i.e. time series). The chickens’ lifespan was divided into four equal periods of 2 weeks. The body weight at five time points was selected as a phenotypic value. Significant SNP-SNP interactions associated with the body weights at different weeks  were detected with an exhaustive genome-wide test. Next, the SNP-SNP interaction networks were built and annotated. Our results provide further insight into the genetic network that controls body weight in chickens.After quality control, the following was included in this study: a total of 48,152 SNPs on 28 autosomes, the Z chromosome, linkage groups, and 672 SNPs not assigned to any chromosomes in chickens (Table Phenotypic descriptive statistics for body weight are listed in Table − 12 (Bonferroni-adjusted: 1%), 67  on the Z chromosome interacting with the gene set on the chromosome 19 . Furthermore, SubNet_2 claimed the gene set  on the Z chromosome interacting with the gene set  near the hub SNP on the chromosome 2. All the inferred gene set interactions are shown in Table The interaction network feature analysis was applied to the BW0 network, because the interaction network size and topology structure of BW1 and BW3 were small and apparent. The significant interaction SNP-SNP pairs contain 80 single SNPs in which 30 SNPs are located in the Z chromosome. Observing the annotation information indicated something interesting. Many SNPs from the same subnet are neighbors, concentrating in the same region. Therefore, we adjusted the spatial position of SNPs in Fig. The interaction effects could be detected in the same or different chromosomes. SubNet_3 and SubNet_4 indicated that the interaction effect could happen within the same chromosome. Furthermore, SNPs in SubNet_4 were all in the same region, neighborhood genes interacting with each other. Other SubNets all illustrated that the interaction effects were present in different chromosomes.Eight gene ontology terms were significantly enriched, including chromosome, nucleus, phosphoprotein, acetylation, DNA-binding, nucleosome, nucleosome core, and histone H5  is a vertebrate, a model organism, and agricultural species, and its body weight is a typical quantitative trait that can be easily measured. Broiler body weight’s heritability in males ranges from 0.29 to 0.37 [Chicken  was far smaller than 1%. The significant test results heavily depended on the arbitrary significance threshold. Although some effects were thus ignored, the strict threshold enhanced the confidence of our results. With the strict threshold, the detection results showed that the interaction effect was completely different at different time points. This suggests that the time point is an important factor in the quantitative trait interaction test. It is easy to determine the interaction effect on the day of hatch, whereas it is difficulty at 5 and 7 weeks. This demonstrates that the cooperation between genes is closer in the early weeks than later weeks. From the perspective of data driving, the correlations between the body weight at BW0 and other weeks were relatively small, which can partially explain the different results. Furthermore, the results indicate that the genetic regulation networks are different at different time points. Carlborg et al. [Testing multiple hypotheses caused that the significance threshold g et al.  have fouMany SNP positions on the chromosome are neighboring in the SNP-SNP interaction network. We suggest it should be the signal of gene-gene interactions in the corresponding regions.IGFBP1 is associated with body weight in the Jinghai Yellow chicken [MuSK was abundantly expressed in the muscle of early-stage fowl embryos [ADCY5 is related to obesity in men and mice [PHKG1 is important in pig skeletal muscle [ATP2A3 [ITGA1 [THBS4 [In this study, we detected 55 regions on 17 chromosomes. Based on the literature, some genes are associated with body weight; for example,  chicken . MuSK wa embryos . ADCY5 iand mice . PHKG1 il muscle . We idenl muscle . The focl muscle . In addi [ATP2A3 , ITGA1 [3 [ITGA1 , and THB1 [THBS4 .Linkage disequilibrium and quantitative trait locus information were not introduced in this study, because linkage disequilibrium testing is not correlated with epistatic interaction tests and gene-gene results are usually more accurate than quantitative trait locus interactions. In fact, gene-gene interaction results were based on the gene sets, and the actual gene-gene interactions could be verified by biological experiments.In the future, more research will be needed to better understand the genetic network of quantitative traits.The interaction effect is most active on the day of hatch, after which the effects decline, and by 5–7 weeks the effects are hardly detected. No significant SNP pairs recurred at different time points. Our study demonstrated that the genetic interaction network of chicken body weight is time-dependent and the epistatic interaction effect is dynamic. For the first three time points, the interaction networks indicated that SNP-SNP interactions were concentrated in some special regions on the chromosomes, which were the results of gene-gene interactions. To our knowledge, we are the first to describe and summarize the significant interaction effects that affect chicken body weight variation.A total of 475 male chickens derived from the 11th generation population of the Northeast Agricultural University broiler lines divergently selected for abdominal fat content (NEAUHLF) were used in the study.The G0 generation was selected in 1996 and came from the same grandsire line, which originated from the Arbor Acres broiler. According to their plasma very low-density lipoprotein (VLDL) concentration at 7 weeks of age, the G0 birds were divided into two lines, the lean line and the fat line. For each line, 25 half-sib families, with an average of 70 G1 offspring per family in two hatches, were produced by mating the G0 birds (one sire: four dams). From G1 to G11, the birds were raised in two hatches. Abdominal fat percentage  of the male birds in the first hatch was used as the artificial selection criterion for NEAUHLF. The families’ sib birds, with lower (lean line) or higher (fat line) AFP than the population’s average value, were selected as candidates for breeding, taking into consideration the plasma VLDL concentration, the body weights of male birds in the second hatch, and the egg production of female birds in both hatches. G11 contained 203 chickens in the lean line and 272 chickens in the fat line.All the birds were fed with a corn-soybean-based diet that met all National Research Council (NRC) requirements and were raised under the same environmental conditions with free access to feed and water. From hatch to 3 weeks of age, the birds received a starter feed . From 4 weeks of age to slaughter, the birds were fed a grower diet . The birds were weighed at day of hatch and at 1, 3, 5, and 7 weeks of age , 12.Genotyping was carried out using chicken 60 K SNP chip  manufactured by the Illumina Inc. . Monomorphic or minor allele frequencies (< 5%) loci were filtered out. Individuals whose missing SNP genotypes were ≥ 5% were removed. After quality control, SNPs with chromosome position information were selected for the interaction analysis. Phenotypic values were analyzed with descriptive statistics. The correlation coefficients of body weight among different weeks age were calculated in the combined population.https://github.com/fanglab/MatrixEpistasis. The statistical model was:The method for detecting the interaction effect was implemented in R and is available at α is the overall mean of the quantitative phenotype; β1 / β2, β3 and γv are the regression coefficients for the main genetic additive effect, interaction effect, and covariates, respectively, and ε is a normal variable with zero mean and ξ2 variance [β3. Therefore, the hypotheses are H0: β3 = 0 and H1: β3 ≠ 0; the tests of interaction correspond to testing whether the regression coefficient β3 equals zero or not.Where variance . In this− 12 (Bonferroni-adjusted: 1%).MatrixEpistasis  was usedThe plots illustrating the SNP-SNP interaction networks with the significant epistatic effects for chicken body weight were drawn with the Cytoscape 3.7.0 software package . The dethttps://genome.ucsc.edu/) . Genes in the same region were put together . Gene interactions in gene sets were deduced if the significant SNP pairs were located in the corresponding regions.For annotating genes to the interaction networks, a 1 Mb length region was designated for each SNP, 0.5 Mb upstream and 0.5 Mb downstream. The regions were merged if the distance between SNPs was < 1 Mb. Genes overlapping the regions were retrieved from UCSC (https://david.ncifcrf.gov/home.jsp) for gene ontology terms. KOBAS2.0 [p-value < 0.05.Functional annotation of genes was performed by DAVID bioinformatics resources 6.8 (KOBAS2.0  was usedAdditional file 1: Table S1. Annotation information of BW0.Additional file 2: Table S2. Annotation information of BW1.Additional file 3: Table S3. Annotation information of BW3.Additional file 4: Table S4. Functional annotation of genes.Additional file 5: Table S5. KEGG pathway analysis.


Fertility is among the most important economic traits in dairy cattle. Genomic prediction for cow fertility has received much attention in the last decade, while bull fertility has been largely overlooked. The goal of this study was to assess genomic prediction of dairy bull fertility using markers with large effect and functional annotation data. Sire conception rate (SCR) was used as a measure of service sire fertility. Dataset consisted of 11.5 k U.S. Holstein bulls with SCR records and about 300 k single nucleotide polymorphism (SNP) markers. The analyses included the use of both single-kernel and multi-kernel predictive models fitting either all SNPs, markers with large effect, or markers with presumed functional roles, such as non-synonymous, synonymous, or non-coding regulatory variants.The entire set of SNPs yielded predictive correlations of 0.340. Five markers located on chromosomes BTA8, BTA9, BTA13, BTA17, and BTA27 showed marked dominance effects. Interestingly, the inclusion of these five major markers as fixed effects in the predictive models increased predictive correlations to 0.403, representing an increase in accuracy of about 19% compared with the standard model. Single-kernel models fitting functional SNP classes outperformed their counterparts using random sets of SNPs, suggesting that the predictive power of these functional variants is driven in part by their biological roles. Multi-kernel models fitting all the functional SNP classes together with the five major markers exhibited predictive correlations around 0.405.The inclusion of markers with large effect markedly improved the prediction of dairy sire fertility. Functional variants exhibited higher predictive ability than random variants, but did not outperform the standard whole-genome approach. This research is the foundation for the development of novel strategies that could help the dairy industry make accurate genome-guided selection decisions on service sire fertility. Suboptimal reproductive performance in dairy cattle, specifically in Holstein purebred, is still a concerning problem in today’s dairy industry. Reproduction inefficiency in dairy cattle has a direct impact on the overall herd profitability by leading the system to reduced incomes  and additional expenditures  , 2.Causes of poor fertility in dairy cows have been well studied  and effoEstablishing a successful pregnancy in dairy cattle is a complex process and there is strong evidence that service sire fertility has an important role. Relevant links between bull fertility and reproductive success have been observed not only in the fertilization process through differences in semen quality , but alsGenome wide association studies have been successful in using dense genetic markers such as single nucleotide polymorphism (SNP) markers to identify genomic regions affecting relevant phenotypes. Often, very stringent significant thresholds must be used in order to avoid multiple-testing problems, leading in general to lose both variants with small effect and rare variants . In addiThe accuracy of genomic prediction can be improved by either increasing the number of markers or the size of the reference population. The rationale behind increasing marker density or even using whole-genome sequence data is that the linkage disequilibrium between SNP makers and causative mutations is somehow maximized. However, incorporating high-density markers or even imputing SNP to sequence level may not result in higher prediction accuracies, as genomic prediction is affected not only by the reference population and the imputation process , 12, butGenerally, genomic prediction models assume that all markers in the genome have an effect in the trait of interest and that the marker effects have all the same magnitude . HoweverFunctional annotation information can be used to prioritize groups of markers by assigning them different weights in the predictive models. Markers located near genes, affecting gene function or known to be causal mutations have been used to improve the accuracy of genomic predictions. A study by Wiggans et al.  reportedWe recently reported promising results regarding the prediction of service sire fertility using 7.4 k US Holsteins bulls and 55 k SNP markers . We concThe bull fertility phenotype evaluated in this study is sire conception rate (SCR), which represents the US national dairy bull fertility evaluation based on cow field data (pregnancy records). This is a phenotypic rather than a genetic evaluation because the fertility estimates include both genetic and non-genetic effects. The current model for SCR evaluation considers not only factors related to the sire under evaluation, but also factors, also known as nuisance variables, related to the cow that receives the unit of semen. These nuisance variables, such as cow age, parity and milk yield, could distort the measurements of bull fertility, and therefore, should be accounted for in the model , 27. Thehttps://www.uscdcb.com/) with the corresponding reliabilities calculated as a function of the number of breedings. Since there are sires with more than one SCR record from different evaluations, the most reliable SCR value, i.e. the record with most breedings was kept for the analyses. The Cooperative Dairy DNA Repository provided 312 k SNP data for all the 11,539 bulls with SCR records. SNP markers that either mapped to the sex chromosomes, presented a minor allele frequency below 5% or a call rate below 95% were removed. After quality control, a total of 295,159 SNP markers remained for subsequent analyses.A total of 11,539 Holstein sires with SCR records were used in this study. These SCR records belong to 29 consecutive evaluations released from August 2008 to April 2018. All records are freely available in the Council on Dairy Cattle Breeding (CDCB) website (‘Base’ model), assuming that all markers have the same contribution to the phenotype. For the second objective, where the goal was to evaluate the benefits of including markers with large effect, dominance genetic effects were evaluated across the entire genome following the study by Nicolini et al. [y = Xb + Zu + e, without including SNP was fitted. The random effects were assumed multivariate normal with y = Xβ + XSNPβSNP + ε, assuming that SNP, genotypes were coded as 0 for the AA and 1 for either AB or BB in order to test if a single copy of the B allele  has the same effect on the phenotype as two copies. The significance of the SNP effect was tested using the following test statistic:R package MixABEL [R package GenABEL [‘Base + 5 SNP’ model, i.e., the base model plus five 0/1 markers fitted as fixed effects.For the first objective, the predictive power of the entire high-density SNP dataset was evaluated using a whole-genome prediction model  were downloaded and used to map and retrieve functional roles of the entire SNP dataset based on Bos taurus UMD3.1 genome assembly. Sequence Ontology terms are used in the UCSC database to describe the effect of each genetic variant on the structure of the gene transcripts. The SNPs were grouped into five functional classes  class are grouped genetic variants in the sequence of non-coding RNA genes, including tRNAs, ribosomal RNAs, and small RNAs. Finally, the set of SNPs that did not map to any of these five SNP classes were labeled as intergenic.For the third objective, different SNP classes were evaluated based on the functional roles of the genetic variants. Gene annotations from the University of California Santa Cruz (UCSC) database  were evaluated using Bayesian reproducing kernel Hilbert spaces regression models (RKHS) , 31. Kery is the vector of phenotypic records ; b is the vector of fixed effects including a general intercept (μ) and the SCR evaluation class effect; X is the design matrix relating fixed effects to SCR records; K is an n × n kernel matrix indexed by the SNP genotype matrix and takes the form K = SST/p, where S is a matrix of centered and standardized SNP genotypes and p represents the number of SNPs, which is equivalent to the well-known additive genomic relationship matrix formulated by VanRaden [α is the vector of RKHS regression coefficients estimated as the solution that minimizes l(α| λ) = (y − Kα)′(y − Kα) + λα′Kα, where λ is the regularization parameter; and e is the error term. The random effects α and e were distributed as R is an identity matrix.Single-kernel models were fitted for either all the SNPs or each of the functional SNP subsets. Phenotypes were analyzed using the following model:VanRaden  and YangVanRaden ; α is th‘Intergenic + Functional’ and ‘Intergenic + 5 SNP + Functional’, were evaluated. These models included six different kernels representing the five functional SNP classes and the intergenic SNPs. These multi-kernel models were evaluated using the following equation:i = 6 is the number of SNP classes and Kj, with j = 1, 2, .., 6, is the linear kernel linking SCR records with each of the SNP classes. The random genomic and residual effects were assumed to be independent and normally distributed as In this predictive model, multiple kernels were fitted simultaneously in order to evaluate the different functional SNP classes. The use of multiple kernels in one model allows to differentially weight one or more kernels that largely contribute to the trait of interest, overcoming at the same time possible loss in predictive ability due to the use of a single kernel . Two altR package Bayesian Generalized Linear Regression (BGLR) [All the RKHS models were run using Gibbs sampling. For each model, a Markov chain Monte Carlo (MCMC) with 100,000 samples (iterations) was run and the first 30,000 samples were discarded as burn-in. The remaining 70,000 samples were thinned at a rate of 5 resulting in 14,000 samples for computing features of the posterior distribution. Convergence of the chain was checked by visual inspection of trace plots of some key parameters, such as variance components. In addition, the converge of the multi-kernel models, arguably the most complex models used in this study, was also evaluated using Geweke. All these analyses were performed using the n (BGLR) .n is the number of animals in each fold (f), and y and The predictive ability of the different RKHS regression models was assessed by 5-fold cross-validation. In this scenario, the entire data set  was divided at random into five sets. Four out of the five subsets were combined to create the training population while the remaining subset was used as testing set. Phenotypes in the testing set where set to unknown and the training population was used to train the model in order to predict phenotypes for the testing set. Each of the five subsets was used as testing population one time. The entire five-fold cross-validation process was repeated ten times, therefore, each analysis resulted in 50 estimations. The predictive performance of each model was assessed using the Pearson product moment correlation (CORR) between observed phenotypes and predicted phenotypes in the testing population. Additionally, the mean-squared error of prediction (MSEP) was calculated as a measure of prediction bias and variability, using the following formula,Service sire has an important role in establishing a successful pregnancy in dairy cattle. Semen from a single sire can be used to inseminate hundreds of cows, and therefore, the fertility of the service sire should not be overlooked. The accurate prediction of yet-to-be observed fertility phenotypes is very challenging, and the incorporation of different sources of information can help to improve model predictive performance. This study was specially conducted to investigate the feasibility of predicting dairy bull fertility using either markers with large effect and functional annotation data. We first evaluated model predictive ability using 300 k SNP markers and the entire U.S. Holsteins SCR dataset. Second, we investigated the impact of including non-additive markers with large effect on model predictive performance. Third, we assessed the predictive ability of different sets of functional SNP variants.‘Base’ model using the entire SNP dataset in a single linear kernel, which is mathematically equivalent to the genomic-BLUP [‘Base + 5 SNP’ model that includes five significant non-additive markers fitted as fixed effects. The ‘Base’ model exhibited an average correlation between observed and predicted SCR values of 0.340, and a mean-squared error of prediction equal to 3.973. The predictive ability of this model is in concordance with our previous study [‘Base + 5 SNP’ model delivered CORR = 0.403 and MSEP = 3.761, representing an increase in predictive correlation of about 19% and a decrease in prediction bias by more than 5% compared with the standard model. The whole-genome scan for dominance effects showed that these five markers have a major impact on sire conception rate with extreme significance values  we obtain a predictive accuracy equal to 0.735. This value is higher than the selection accuracies obtained for some health traits currently evaluated in U.S., such as ketosis and metritis, as well as higher than the accuracies reported for some calving ability traits, such as sire calving ease or sire stillbirth rate [If we divide the average predictive correlation (0.403) by the square root of the heritability  and synonymous variants explained the highest proportion of variance compared with the rest of the SNP classes. Morota et al. [The prediction ability of each of the five functional SNP classes described in Table s et al.  investiga et al.  and Abdoa et al.  also evaa et al. .Fig. 3Pr‘Intergenic + Functional’ model (CORR = 0.342 and MSEP = 3.967) showed similar predictive ability than the single-kernel ‘Base’ model (CORR = 0.340 and MSEP = 3.973). Similarly, the multi-kernel ‘Intergenic + 5 SNP + Functional’ model (CORR = 0.405 and MSEP = 3.753) did not outperform the single-kernel ‘Base + 5 SNP’ model (CORR = 0.403 and MSEP = 3.761). Overall, each functional SNP class delivered higher predictive ability than its counterpart using random SNPs, however, multi-kernel models fitting all functional variants together did not outperform the standard whole-genome approach. It should be emphasized that in dairy cattle, linkage disequilibrium interferes with the use of biological information in prediction because irrelevant markers  capture part of the information encoded by relevant markers, causing that the intergenic and the functional SNP classes exhibit similar predictive abilities.Figure The genomic prediction of service sire fertility is possible, and this could have a great impact on the dairy industry worldwide. Compared to our previous study , the inc


P < 0.05, and the MFVW of the Asian accessions (0.65) was significantly higher than that of the European accessions (0.48) at P < 0.01. The GWAS performed using the general linear model (GLM) and mixed linear model (MLM) identified 137 and 14 SNP loci related to WT, respectively, and 11 associations were commonly predicted. By calculating the phenotypic effect values for 11 common SNP loci, six highly favorable SNP alleles that explained 12.85—21.85% of the phenotypic variations were identified. Furthermore, the dosage-pyramiding effects of the favorable alleles and the significant linear correlations between the numbers of highly favorable alleles and phenotypic values were identified . A major SNP locus (Marker6619-75) was converted into a derived cleaved amplified polymorphic sequence (dCAPS) marker that cosegregated with WT with an average efficiency of 78.9%. Finally, four putative candidate genes in the WT were identified via quantitative real-time PCR (qRT-PCR). The results presented in this study provide insights for further research on WT mechanisms and the application of molecular marker-assisted selection (MAS) in chrysanthemum WT breeding programs.Chrysanthemums are sensitive to waterlogging stress, and the development of screening methods for tolerant germplasms or genes and the breeding of tolerant new varieties are of great importance in chrysanthemum breeding. To understand the genetic basis of waterlogging tolerance (WT) in chrysanthemums, we performed a genome-wide association study (GWAS) using 92,811 single nucleotide polymorphisms (SNPs) in a panel of 88 chrysanthemum accessions, including 64 spray cut and 24 disbud chrysanthemums. The results showed that the average MFVW  of the disbud type (0.65) was significantly higher than that of the spray type (0.55) at  Researchers in China have identified several genes that help chrysanthemum plants withstand waterlogging. Fadi Chen’s team at Nanjing Agricultural University used high-throughput sequencing to search for correlations between genetic mutations and waterlogging tolerance in 88 chrysanthemum varieties. One analysis method identified 137 mutations linked to waterlogging tolerance, while a second uncovered 14 mutations. Comparing the two lists revealed 11 mutations common to both. Six of these mutations could improve waterlogging response by 25%, and the team found that the mutations could be combined to improve performance even further. The team developed and tested a genetic marker to identify one of the high-tolerance mutations, demonstrating how this information may help breeders. They also identified four genes linked with the 137 mutations. Altogether, these findings point the way towards breeding chrysanthemums with greater waterlogging tolerance. Chrysanthemum morifolium Ramat.) is the second-most important ornamental species in the world, and it accounts for a large proportion of the total commercial production of these plants1. Cut chrysanthemums can be divided into the following two types depending on the flower diameter: spray cut type and disbud-cut type. The disbud type bears a large flower of greater than 6 cm and a single flower per stem, and the spray type bears several small flowers of less than 6 cm per stem.The chrysanthemum , the possible mechanisms underlying water stress and the genetic variations associated with WT within a species must be investigated. Previous studies have revealed considerable variations in WT traits in maize3, soybeans4, barley5, and dry beans6. Recently, we evaluated the WT of 100 chrysanthemum germplasm resources through two greenhouse experiments and one field experiment, and we screened out 7 accessions that exhibited high WT7. However, the traditional screen is gruelling and time-consuming work, and it is also readily affected by environmental factors. Therefore, the breeding of tolerant varieties tends to focus on identifying and exploiting molecular markers that are closely linked to the genes that control the WT trait.Waterlogging stress is a common constraint in the chrysanthemum industry around the world, particularly in the southern production regions of China8. SNP markers belong to the third generation of DNA molecular marker technology and have several advantages, including abundance, stability, high-throughput genotyping, and relatively low mutation rates. A large number of SNPs can be identified within a species via high-throughput next generation sequencing (NGS) technologies, such as restriction-site-associated DNA sequencing (RAD-seq)9, genotyping-by-sequencing (GBS)10, specific-locus amplified fragment sequencing (SLAF-seq)11, and double digest RAD-seq12. Thus, SNP markers have been widely used in genetic diversity assessments, molecular evolution studies, and genetic mapping for traits of interest in crop species13.Single nucleotide polymorphisms (SNPs) are defined as single-base changes at a specific nucleotide position, and they are widely distributed throughout genomes in both the coding and noncoding regions of all organisms14, Arabidopsis thaliana15, and maize16 and the unsequenced genomes of wheat17 and roses18. In chrysanthemums, GWASs have been used to identify favorable alleles and to explore the pattern of inheritance for a number of horticultural and WT traits based on gel-based markers20. However, the low marker density exhibited in the traditional molecular marker system limits the detection power of GWASs. Recently, Chong et al.21 first attempted to assess the genetic diversity and evolutionary relationships and conducted a GWAS analysis for a set of 199 accessions using > 90,000 SNPs amplified via SLAF-seq, which provides a more efficient method for high-density, sequence-based, and genome-wide polymorphism screening in the chrysanthemum population.In recent years, genome-wide association studies (GWASs) based on linkage disequilibrium have been shown to represent a powerful tool for detecting important QTLs or genes underlying complex traits in the sequenced genomes of rice22, high resolution melting (HRM)23, allele-specific PCR (ASP)24, nucleotide-amplified polymorphisms (SNAPs)25, competitive allele-specific PCR (KASP)26, and cleaved amplified polymorphic sequences (CAPSs) or derived CAPSs (dCAPSs). Among these options, the CAPS and dCAPS methods have been demonstrated as superior techniques for SNP detection because of their simplicity, efficiency, and economy25. The CAPS/dCAPS method, which is also known as the PCR-RFLP marker, is a technique that combines PCR and restriction enzyme digestion to detect restriction fragment length polymorphisms (RFLPs). In detail, CAPSs are based on restriction enzyme site polymorphisms that are detected after the amplification of a locus by PCR. When these restriction sites are not available within the SNP locus, restriction sites can be created during PCR amplification by using primer design to introduce one or more mismatches adjacent to the SNPs of interest, thus creating a synthetic restriction site in the amplified product allele; this method is called dCAPS27. For both methods, the PCR products are then subjected to restriction enzyme digestion, and the presence or absence of the SNP is determined by the resulting restriction pattern that is resolved on an agarose or polyacrylamide gel. To date, successfully developed CAPS or dCAPS markers have been linked to different traits in various crops, such as a waxy character in wheat28, yellow leaf curl disease resistance in tomatoes29, eating quality in rice25, head smut resistance in maize30, and fiber quality traits in cotton31. However, the use of CAPS/dCAPS markers in chrysanthemums has not been reported.However, SNP assays require expensive equipment or reagents, which has limited the application of SNPs. SNPs can be employed through conversion to other available markers, including single-strand conformation polymorphisms (SSCPs)21. The objectives of this study were to (1) detect SNP loci associated with WT chrysanthemums, (2) mine favorable alleles underlying the WT and assess their pyramiding effects, (3) develop dCAPS markers that cosegregated with WT, and (4) identify potential candidate genes for WT. The results of this study will provide insights into the genetic determination of WT and benefit marker-assisted selection in chrysanthemum breeding.In the present study, a GWAS for the WT of chrysanthemums was performed using an association panel with 88 chrysanthemum accessions, which were genotyped by SLAF-seq20. All the materials were maintained at the Chrysanthemum Germplasm Resource Preserving Centre of Nanjing Agricultural University, China.A total of 88 representative chrysanthemum accessions were used in the present study, including 30 entries developed in Europe, 17 in China, 23 in Japan, 2 in South Korea, and 16 entries of unknown provenance (Supplementary Table 7. Another pot experiment (EXP.3) was performed to reduce the environmental factor influence in this study. The experimental design and WT evaluation were described in our earlier report7. In brief, the pot experiments followed a randomized complete block design with three replications for the waterlogging treatment and two with normal water management. Three seedlings per entry were included in each replicate. The waterlogging treatments were conducted at the 10–12-leaf stage, and each pot was filled with 3 cm of water above the soil surface. After 3 d of waterlogging stress, the wilting index (WI) was recorded based on a symptom severity scale from 1 to 5, with 1 indicating no symptoms. After 10 d of treatment, the ratio of the dead leaf area (DLR) to the chlorosis score (Score) was recorded. A membership function value of waterlogging (MFVW), which integrated these three measurements, was calculated for each entry and was employed for the subsequent GWAS analysis. The range of the MFVWs was from 0 to 1.0, and a higher MFVW was indicative of enhanced WT. For additional details on the WI, DLR, Score, and MFVW calculation criteria, please refer to Su et al.7. Significant correlations (P < 0.01) with r values ranging from 0.61 to 0.74 and no significant differences (P > 0.05) were observed among the three pot experiments . The data for EXP.1 and EXP.2 have been previously reported in Su et al.21. The SNPs were filtered using a minor allele frequency (MAF) > 0.05 and an integrity of each SNP > 0.5. As a result, 92,811 SNPs were identified from 468,521 SNPs and were used for further analysis.The SNP genotyping of the association panel was performed using the SLAF-seq approach reported by Chong et al.32 in MEGA533. The population structure was assessed using the ADMIXTURE software package according to the minimum cross-validation error value34. The kinship matrix was calculated with SPAGeDi software35. A principal component analysis (PCA) was performed using Cluster software36.A phylogenetic tree of the chrysanthemum accessions based on the informative SNPs was constructed using the neighbor-joining algorithm37 with two models, the general linear model (GLM) considering Q and the mixed linear model (MLM) considering Q and K. The mean values of the three pot experiments were used for the GWAS. The significance threshold for a trait marker association was set at P ≤ 0.001. Moreover, the P values were also adjusted using the Bonferroni threshold  to reduce false positive associations38. The identified SNP loci were named with the SLAF tag followed by a hyphen (-) and the position . The proportion of the phenotypic variation explained (PVE) by each marker was estimated by the relevant R2. Because a higher MFVW is indicative of an enhanced WT, a phenotypic effect (ai) > 0 indicates a favorable allele. The ai of the SNP loci that was simultaneously detected under two models was estimated by comparing the average phenotypic value of panel accessions harboring favorable alleles with that of accessions harboring unfavorable alleles.Based on the filtered SNP data, the GWAS analysis was conducted using TASSEL v4.0 software1 lines showing an extreme WT derived from‘Nannong Xuefeng’ and ‘Monalisa’ were used to verify the dCAPS markers .Thirteen waterlogging-tolerant cultivars and thirteen waterlogging-sensitive cultivars were used to convert the SNPs into dCAPS markers and to identify the WT mechanisms. Additionally, 26 F2+ plus), 2.0 µL of dNTP (2.5 mM each), 1 µL of each primer, 1 U of Taq DNA polymerase, 1 µL of template DNA, and 17.3 µL of ddH2O. The PCR protocol consisted of an initial denaturation at 94 °C/3 min followed by 35 cycles of 94 °C/30 s, 57 °C/30 s, and 72 °C/30 s and finally an elongation step of 72 °C/7 min. The amplified PCR products were sequenced and digested at 37 °C for 3 h in a final volume of 50 µL, including 5 µL of 10 × NEBuffer, 10 µL of the PCR product, 34 µL of ddH2O, and 1 µL of restriction endonuclease that was then heat-deactivated according to the manufacturer’s instructions . The digestion products were separated via 10% native polyacrylamide gel electrophoresis and visualized by silver staining.The PCR reactions were conducted in a total volume of 25 µL, including 2.5 µL of 10 × Buffer . Root samples from the waterlogging-tolerant cultivar ‘Nannong Xuefeng’ and the waterlogging-sensitive cultivar ‘Monalisa’ were collected after 12 h of waterlogging stress treatment and normal watering treatment, with three plants in each group. The total RNA was extracted using a Plant RNA Extraction Kit  according to the manufacturer’s protocol. The primers used for qRT-PCR amplification are listed in Supplementary Table SThe genotype data of 92,811 high-quality SNPs were used for the population stratification. The testing accessions could be largely separated into three subpopulations according to the minimum cross-validation error value , and the MFVW of the Asia chrysanthemum accessions (0.65) was significantly higher than that of the European chrysanthemum accessions .The phenotypic data on the WT across the three experiments for the panel are summarized in Supplementary Figure P ≤ 1E-3, and they explained 9.39–21.76% of the phenotypic variance; 14 associations were detected based on the MLM at the same threshold value, and they explained 12.68–23.60% of the phenotypic variance. Among these associations, 11 SNPs were found in both models  in the GLM and 16.90% of the PVE in the MLM. The marker was also the only association that remained significant after applying the Bonferroni correction (P ≤ 1.08E-5). A summary of the favorable SNP alleles is shown in Table ai) of the eleven SNPs that were consistently associated with WT ranged from 0.04 to 0.33, and all the ai values reached the P < 0.05 or P < 0.01 significance level except for Marker6288-117, Marker9771-143, and Marker6288-36. The alleles Marker6619-75 and Marker 5022-204 expressed the greatest ai values, and both could increase the WT by 33.0%.In total, 137 SNPs were identified as being significantly associated with the WT based on the GLM at a threshold of ai values of greater than 0.25), Marker6619-75, Marker18364-144, Marker12711-95, Marker3678-87, Marker99922-41, and Marker5022-204, were selected for further analysis, and the favorable alleles of these loci were C, A, A, T, G, and C, respectively (Table P < 0.05). Similarly, the MFVW of the accessions that held two favorable alleles increased by 15.09% compared with those that held only one favorable allele (P > 0.05). When the number of favorable alleles reached three, the MFVW of the accessions (0.61) could exceed the mean values of the entire panel (0.58).To determine whether the WT-favorable SNP alleles had pyramiding effects, the following six SNP loci exhibiting significant phenotypic effects . The detailed primer designation and sequence information for SLAF tag Marker6619 are shown in Supplementary Table 1 population derived from the tolerant cultivar Nannong Xuefeng and the sensitive cultivar Monalisa, with each containing 13 waterlogging-tolerant lines and 13 waterlogging-sensitive lines  tolerant lines that generated a single undigested 170 bp band, whereas 11 (84.6%) susceptible lines showed two bands of 170 bp and 149 bp  encoding betaine aldehyde dehydrogenase (BADH). Three identified SLAF sequences lay within genes  encoding three protein kinases, namely APK1B (Arabidopsis protein kinase 1), SnRK2.6 (SNF1-related protein kinase 2), and BAM1, respectively. The primer design failed for Unigene33415_All as annotated to SnRK2.6 because of the short sequence. The SLAF tag Marker6619 lay within a gene homologous to Cynara cardunculus var. scolymus (CL17968.Contig2_All) that encodes the hypothetical protein Ccrd_010998; however, little is known about its function in plants. Because of the importance of SNP locus Marker6619-75, all four selected candidate genes along with CL17968.Contig2_All were preliminarily verified using qRT-PCR, and the relative expression levels are demonstrated in Supplementary Figure Unigene6108_All in the susceptible ‘Monalisa’ cultivar showed a significant increase after exposure to waterlogging stress (70.15%), while no significant increase was found in the tolerant cultivar ‘Nannong Xuefeng’ (14.40%). The expression of Unigene21682 decreased in the tolerant variety ‘Nannong Xuefeng’ (51.93%), whereas it increased in the susceptible variety ‘Monalisa’ (45.60%). In addition, a similarly decreased expression was found for CL5639.Contig3_All and CL17968.Contig2_All but did not reach statistical significance.All SLAF sequences harboring one or more of the 140 SNPs detected under the GLM or MLM models were aligned with the available chrysanthemum transcriptome databases, and only four candidate genes were implicated for their involvement in abiotic stress responses according to the gene annotation  were used, and more than 700 loci were identified using the same model and threshold value (data not shown). Long and Langley (1999) showed that increases in the population size have a greater impact on the power of QTL detection than increases in the marker density49. Zhu et al.50 also indicated that using a larger population would facilitate the exploration of smaller-effect QTLs. Population sizes ranging from 100 to 300 have been frequently documented in GWAS53; however, this selection also depends on many factors, including the plant species, estimated cost, analysis platform, and objective traits. A large population is not always practicable for GWASs, especially for certain tolerance traits, which often require complicated treatments and the simultaneous measurements of all the lines to obtain accurate phenotypic data. In our study, although an association population with only 88 accessions was not large enough, a moderately large phenotypic variation coefficient (30.74%) was calculated for the MFVW . Among these SNPs, 11 were found in both models, which validates the efficiency of GWASs when using an MLM model based on abundant SNP markers compared with gel-based markers. Of particular interest, the SNP locus Marker6619-75 exhibited the minimum P-value under both models and presented a comparatively large PVE of 20.67% in the GLM and 16.90% in the MLM. Thus, this locus was selected as an example for developing a PCR marker to assist in breeding.Repeating experiments during different years or in different places is critical for GWASs, especially for certain complex quantitative traits that are controlled by multiple genes and environmental factors, such as the WT. The stable associations for target traits are more useful in breeding programs with broad adaptability to different environments. Our previous study found that the MFVWs derived from field data were generally lower than those derived from greenhouse-based data, and the two greenhouse experiments exhibited a closer correlation55. Wu et al. set the heterozygous SNP to missing and only used the homozygous SNPs for a GWAS study in Brassica napus56. The chrysanthemum is a highly heterozygous ornamental species with a complex background, and the heterozygous loci are too common to be neglected. A locus was considered to be in a heterozygous state if the depth of the minor allele was larger than one-third of the total sample depth during SNP calling21. The 11 significant SNP loci associated with WT were all heterozygous, and the average MFVW of entries harboring heterozygous alleles was closer to or even lower than the entries harboring unfavorable homozygous alleles for all the associations except for Marker9771-143 (Supplementary Table P < 0.05). As a result, SNP alleles with higher MFVWs that increase the WT were defined as “favorable alleles”, whereas SNP alleles with lower MFVWs, including heterozygous sites, were defined as “unfavorable alleles” in our study. This classification may enlarge the phenotypic effect (ai) of the favorable alleles for WT.Associations with higher phenotypic effects for target traits are usually more useful in breeding programs. The favorable alleles and unfavorable alleles are easily determined without considering the heterozygous SNPs in certain species with simple genetic backgrounds57, stigma traits in rice52, and clubroot resistance in rapeseed58. In our study, six elite alleles that could significantly improve the WT by 25% were mined from the 11 associated loci. Among these alleles, 54.39% were carried by accessions collected from Asia, which presented ~3.1 alleles on average, per entry; 26.36% were carried by accessions from Europe, which presented ~2.1 alleles on average, per entry; and the remaining 20.50% were carried by accessions of unknown provenance. These results suggested that during the chrysanthemum evolution process from Asia to Europe, changes in certain SNP alleles likely resulted in changes in the WT traits. For example, all the unfavorable alleles of Marker6619-75 and Marker 5022-204 were common among the European accessions but were not found in the Asian accessions. Moreover, dosage-pyramiding effects were found in the highly favorable alleles, and the results revealed that the genetic control of WT exhibits a largely additive effect in chrysanthemums  marker63. A simple and low-cost marker is more promising and practical, especially for the selection of early breeding work; therefore, the most prominent SNP locus Marker6619-75 was transformed into a dCAPS marker, which is codominant, locus-specific, and feasible for use in a typical molecular biology laboratory. The WT-dCAPS1 was coassociated with WT at an average efficiency of 78.9%, which is lower than the values reported in other traits and crops65. The inconsistent conditions may be caused by the complexity of the chrysanthemum’s genetic background and WT. Nevertheless, to our knowledge, this study presents the first report of a dCAPS marker linked to WT in plants, and the developed marker validates the method for screening for tolerant germplasm resources and provides a powerful MAS tool. Developing additional dCAPS markers linked to WT and validating them in a larger population are necessary in further studies.The availability of molecular markers linked specifically to the target trait can facilitate the shortening of the breeding process. Although many molecular marker loci have been identified as being associated with horticultural and tolerances traits in chrysanthemums66. BADH is one of the two enzymes that catalyze glycine betaine synthesis in chloroplasts from choline, and several studies have reported that BADH gene-transgenic plants could enhance tolerance by accumulating glycine betaine, which is an important osmoprotectant that is widely distributed in higher plants and provides protection against various types of abiotic stress by stabilizing the quaternary structure of complex proteins67, thereby maintaining the osmotic potential balance with the environment68 and stabilizing the oxygen-evolving photosystem II67. With respect to WT, Yan et al. observed stimulated BADH expression after 1 d of waterlogging stress but the inhibition of the BADH expression at 2 d and 4 d in wheat69. Similar results were obtained in cotton70. APK1 (Arabidopsis protein kinase 1) purified from an overproducing E. coli strain showed serine/threonine kinase activity and has been shown to be important in mediating stomatal responses to environmental stimuli, including the light intensity, atmospheric carbon dioxide concentration, and the drought hormone abscisic acid71. A study showed that the Arabidopsis APK1b gene is predominantly expressed in guard cells, and it has an enhanced ability to increase water use efficiency and tolerance to drought conditions72. The SnRK2 (SNF1-related protein kinase 2) protein kinase family is unique in plants and consists of 10 members (SnRK2.1 to −2.10) in Arabidopsis73. Several SnRK2s have been reported to be major kinases in osmotic stress and ABA signaling, which regulates various environmental stresses and developmental and physiological processes. SRK2E/OST1/SnRK2.6 encodes an Arabidopsis SnRK2 protein kinase and has been found to act as a positive regulator in water stress signaling and ABA-induced stomatal closure74. BAM1 is a plastid-targeted β-amylase of Arabidopsis thaliana that is specifically activated by its reducing conditions, and it plays a role in starch degradation in guard cells to sustain stomatal opening during the day. Several studies in different plant species have indicated that BAM1 regulates a wide variety of developmental75 and abiotic stress-related processes, particularly those relating to drought76, cold77, salt78, osmotic79, and heat stress80. To date, no reports have directly addressed the function of three other candidate genes in waterlogging stress. However, the regulatory networks of various abiotic stresses are fairly complex, and different types of stresses have certain cross interactions. A preliminary qRT-PCR verification experiment was performed in the present study; however, further validation with additional genotypes with contrasting WT traits and additional waterlogging stresses would be required to identify the function of these candidate genes in chrysanthemums.Finally, four candidate genes that encode BADH and the three protein kinases SnRK2, APK1B, and BAM1, as well as one gene with unknown function were predicted via an alignment with the transcriptome library. Plants can activate their signal transduction system when adverse environmental stress occurs. Plant signal transduction can perceive and transduce different stress signals and activate a variety of physiological and biochemical reactions to survive. Plant protein kinases play important roles in signal transduction, growth, development, and gene expression regulationA substantial number of SNP markers were used in a GWAS to investigate the genetic control of WT in chrysanthemums. Eleven significant associations and four candidate genes were detected for WT. The dosage-pyramiding effects of the six highly favorable SNP alleles strongly suggests that the WT is largely controlled by quantitative genes with additive effects. Moreover, a major SNP locus (Marker6619-75) was converted into a dCAPS marker, which would be beneficial for future MAS for WT. The results of this study demonstrate that GWASs based on high-density SNP markers represent a powerful approach for dissecting complex WT traits and identifying candidate genes in chrysanthemums.Table S1Table S2Table S3Table S4Table S5Table S6Table S7Figure S1Figure S2Figure S3Figure S4Figure S5


Populus trichocarpa, each providing a layer of information which can be represented as a density signal across a chromosome. We make use of genome sequence data, variants data across a population as well as methylation data across 10 different tissues, combined with wavelet-based signal processing to perform a comprehensive analysis of the signature of the centromere in these different data signals, and successfully identify putative centromeric regions in P. trichocarpa from these signals. Furthermore, using SNP (single nucleotide polymorphism) correlations across a natural population of P. trichocarpa, we find evidence for the co-evolution of the centromeric histone CENH3 with the sequence of the newly identified centromeric regions, and identify a new CENH3 candidate in P. trichocarpa.Various ‘omics data types have been generated for  Populus trichocarpa, several heterogenous datasets have been generated. The full genome sequence is available and is currently in its third version , which were derived from the resequenced genomes of ~1,000 P. trichocarpa genotypes propagated in common gardens  which can be represented as vectors of numbers, with each vector representing a signal which varies across a chromosome, for example, the gene density across a chromosome, or the methylation profile of a chromosome. Once represented as a signal, these data types are amenable to signal processing techniques. This study aims to make use of signal processing techniques of these multiple data types in order to attempt to identify chromosome structural features in The centromere is an important chromosomal structure which controls the segregation of chromosomes during cell division, and is the location for the assembly for the kinetochore protein complex  (Equation 1), for every scale s and translation  τ  peaks and low-frequency (broad) peaks. These different scales of peaks contain different information. Thus, techniques to analyse these signals at different scales are valuable  in characterizing chromosomal gene density, SNP density and methylation density signals in Populus trichocarpa  was obtained from https://doi.ccs.ornl.434gov/ui/doi/55. This dataset consists of SNP 28,342,758 SNPs called across 882 P. trichocarpa genotypes and is derived the whole genome resequencing of a Genome Wide Association Study (GWAS) population clonally replicated in common gardens  was used to determine the minor allele frequency (MAF) and the call rate  for each SNP, and removed all SNPs with MAF ≤ 0.01 and call rate ≤ 0.5.The most reliable SNPs within the dataset were selected, consisting of the 90% tranche (the tranche recovering 90% of the “true” SNPs). VCFtools   at A SNP density profile was created for each chromosome using the filtered set of SNPs by counting the number of these SNPs in non-overlapping 10 kb windows across the chromosome.P. trichocarpa tissues generated from the study by Vining et al.  data from 10 g et al.  re-alignSamtools , and identified the scale p (row of M) at which this maximum coefficient was found. This identified the general pericentromeric scale. The borders of the approximate pericentromeric regions b1 and b2 were identified as the zeroes of the methylation wavelet coefficient vector at scale p  at which this minimum occurs was considered the centromeric scale. The methylation pericentromeric scale vector Mp (row p in matrix M) and the SNP centromeric scale vector Sc (row c of matrix S) were extracted, and scaled to have mean 0 and standard deviation 1. The approximate centromere locations were then identified as the position x at which the maximumPutative centromeres were located for each chromosome by computationally identifying the “tooth-X-ray” signature in the wavelet landscapes. Let the matrix  scale p . The minxth entry in the scaled vectors of Mp and Sc, respectively.is obtained, where See http://pgsb.helmholtz-muenchen.de/plant/recat/index.jsp. The repeat sequences were then BLASTed  with a plant centromeric repeat sequence. We obtained putative P. trichocarpa centromeric repeat sequences from Cossu et al.  RNA-seq dataset from JGI Plant Gene Atlas project . This dataset consists of samples for standard tissues  and libraries generated from nitrogen source study. A list of sample descriptions was accessed from Phytozome at https://phytozome.jgi.doe.gov/phytomine/aspect.do?name=Expression. Networks were visualized in Cytoscape  was obtained from Phytozome  to such density signals results in a coefficient landscape for each signal, represented as a heatmap  as BLAST  in P. trichocarpa genotypes using the CCC metric -Seq. We also found evidence for the co-evolution of the sequence of the centromere-specific histone CENH3 with the sequences of the centromere on many chromosomes. In particular, we found that the previously unannotated gene Potri.002G169000 is the most likely candidate for an active, centromere-co-evolving CENH3 gene in P. trichocarpa, involving information from multiple ‘omics data layers and providing information about centromeric signatures derived from multiple sources. In order to extend these analyses to produce an automated centromere prediction approach applicable to other species, further testing and validation will be required. The wavelet-based approach would need to be applied to multiple species, and validated against exact centromeric locations determined using ChIP-seq.This study illustrates how through integrating multiple sources of data, one can arrive at a more comprehensive understanding of the system one is investigating. In this case, we have produced at a more reliable and detailed characterization of centromere location in This study illustrated the utility of wavelet-based signal processing of genomic signals to identify structural characteristics of chromosomes. While this study made primary use of the larger-scale wavelet coefficients, we would recommend the use of the smaller scale wavelet coefficients to investigate smaller-scale structural characteristics, such as nucleosome occupancy.Populus genotypes. SD and DM-S performed the SNP calling. JS and AS contributed the genome sequence and transcriptome expression analysis. MS mapped gene expression atlas reads and calculated gene expression TPM values. WJ developed the parallel GPU CCC metric code. DW, DJ, GT, DM-S, and AS edited the manuscript.DW and DJ conceived of and designed the study. DW performed the analysis, developed the wavelet centromere identification strategy, interpreted the results, and wrote the manuscript. GT lead the sequencing of 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.