Genomic selection method and its application in breeding of homoeologous polyploid species

Abstract

The present application relates to the technical field of bioinformatics, and particularly relates to a genome selection method and application thereof in breeding of homologous polyploids. The method comprises the following steps: constructing an additive genomic kinship matrix; constructing a genomic selection model based on the additive genomic kinship matrix; and estimating breeding values of individuals of a species according to the genomic selection model. The genotype matrix used in the additive genomic kinship matrix of the homologous polyploids is a polyploid genotype matrix, and the value of the genotype in the polyploid genotype matrix is determined by the copy number of any one allele. The present application proposes a genome selection method based on the homologous polyploid genomic kinship matrix for the species with the characteristics of homologous polyploids, which can accurately predict the genomic breeding values of individuals of the homologous polyploid species and improve the accuracy of genome selection, and has important significance in the field of genome selection breeding.

Description

Technical Field

[0001] This invention relates to the field of bioinformatics, and in particular to a genome selection method and its application in the breeding of autopolyploid species. Background Technology

[0002] Genomic selection (GS) has developed rapidly since its inception and has become a key research focus and hot topic in the genetics and breeding of animals, plants, and aquatic animals. Theory and breeding practice show that GS is more accurate than traditional breeding values, accelerating breeding progress and improving breeding efficiency. The principle of GS is to estimate the effect value of each SNP marker using SNP (single nucleotide polymorphism) marker information and phenotypic information from the entire genome. The estimated breeding value for an individual is obtained by summing all effect values; this estimated breeding value is called the genomic estimated breeding value (GEBV). Currently, the methods for calculating GEBV are quite mature. Among them, the genomic best linear unbiased prediction (GBLUP) method is a standard method for genomic selection in animals and plants and is widely used in the genetic evaluation of different livestock and poultry breeds. The core of the GBLUP method is to construct additive (G), dominance (D), and epistatic (E) genomic phylogenetic relationship matrices using molecular markers covering the entire genome. These matrices are then fed into mixed model equations (MMEs) to directly obtain an individual's GEBV. However, currently, the GBLUP method primarily targets diploid species, and other similar methods or prediction methods derived from GBLUP struggle to perform genomic selection based on autopolyploid characteristics.

[0003] Polyploidy refers to organisms whose somatic cells contain two or more complete sets of chromosomes. Most polyploids have an even number of chromosomes, with four sets being the most common (tetraploid). Polyploids are common in plants, amphibians, and fish, and usually exhibit good adaptability. Based on the origin of the chromosome sets, polyploids can be divided into autopolyploids and allopolyploids: in autopolyploids, the added chromosome sets originate from the same species and are generally produced by the direct doubling of chromosomes from a diploid organism; allopolyploids are produced by the doubling of chromosomes from the offspring of hybrids between different species. To date, data on autopolyploid species have typically been analyzed using diploid genomic selection methods. For example, Gouy et al. [Gouy, M., Y. Rousselle, D. Bastianelli, P. Lecomte, et al., Experimental assessment of the accuracy of genomic selection in sugarcane, Theoretical and Applied Genetics, 2013, 126(10):2575-2586] and Annicchiarico et al. [Annicchiarico, P., N. Nazzicari, XHLi, YLWei, et al., Accuracy of genomic selection for alfalfa biomass yield in different reference populations, BMC Genomics, 2015, 16:1020] simplified the construction of the genomic kinship matrix in autopolyploid genomic selection by using a diploid G-matrix construction method. However, autopolyploids can affect phenotype accuracy through additive effects of multiple copies of the same allele, or through more complex interactions (such as dominance or epistasis) between loci or alleles. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention provides a genomic selection method and its application in the breeding of autopolyploids. By establishing a genomic kinship matrix of autopolyploids and constructing a genomic selection model, the genomic breeding value of individual autopolyploid species can be accurately predicted, exhibiting high accuracy in genomic selection.

[0005] Firstly, the present invention provides a genome selection method.

[0006] Construct a homologous polyploid additive genomic kinship matrix; construct a genomic selection model based on the homologous polyploid additive genomic kinship matrix;

[0007] Genome selection is performed based on the described genome selection model;

[0008] The genotype matrix used in the homologous polyploid additive genomic kinship matrix is ​​a polyploid genotype matrix; the genotype value in the polyploid genotype matrix is ​​determined by the copy number of any allele.

[0009] Furthermore, the homologous polyploid additive genomic kinship matrix includes the following:

[0010]

[0011] Where W is the centered polyploid genotype matrix, W = X - ploidyP, and P is the allele frequency p. i Matrix, p i is the frequency of the second allele at the i-th locus; ploidy is the polyploidy level value; X is the polyploidy genotype matrix.

[0012] Furthermore, the genome selection model is constructed based on the autopolyploid dominant genome kinship matrix and / or the autopolyploid epistatic genome kinship matrix.

[0013] Furthermore, the homologous polyploid dominant genomic phylogenetic relationship matrix includes the following:

[0014]

[0015]

[0016] Where P is the allele frequency p i Matrix, p i Let M be the frequency of the second allele at the i-th locus, and M be an m×m diagonal matrix with m elements on the diagonal. i C represents the ploidy level value; C is an m×m diagonal matrix, with diagonal elements... ⊙ represents the Hadamard product; X represents the polyploid genotype matrix;

[0017] And / or,

[0018] The homologous polyploid epistatic genomic kinship matrix includes one or more of the following: a homologous polyploid plus epistatic genomic kinship matrix, a homologous polyploid plus phasic epistatic genomic kinship matrix, or a homologous polyploid phasic epistatic genomic kinship matrix;

[0019] The added hypergenomic kinship matrix includes:

[0020]

[0021] The epistatic genomic kinship matrix includes:

[0022]

[0023] The epistatic genomic kinship matrix includes:

[0024]

[0025] Where polyG is the homologous polyploid additive genomic kinship matrix, polyD is the homologous polyploid dominant genomic kinship matrix; ⊙ is the Hadamard product; tr is the trace of the matrix; and m is the number of loci.

[0026] Furthermore, the genomic selection model includes:

[0027] y = Xb + Za + Zd + Zr + e

[0028] Where y is the phenotypic value vector, b is the fixed effect, and a is the additive genetic effect vector, following a normal distribution N(0, polyGσ). a 2 ), σ a 2 The variance is additive genetic; d is the dominant effect vector, which follows a normal distribution N(0, polyDσ). d 2 ), σ d 2 σ is the variance of the dominant effect; r is the vector of the epistatic effect, which follows a normal distribution N(0, polyEσr). r 2 ),σ r 2 Here, σ represents the variance of the upper-level effect; e is the random residual, following a normal distribution: e ~ N(0,R)=N(0,Iσ) e 2 ), where I is the identity matrix, σ e 2 Let X be the variance of the random residuals; and Z be the corresponding incidence matrices.

[0029] The genomic selection model above considers additive, dominant, and epistatic effects simultaneously. In practical applications, only additive effects can be considered, or only additive and dominant effects can be considered.

[0030] For example:

[0031] y = Xb + Za + e

[0032] or,

[0033] y = Xb + Za + Zd + e

[0034] The parameters are the same as those in the aforementioned genome selection model.

[0035] Furthermore, the estimation of the breeding value of an individual species based on the genomic selection model includes:

[0036] Based on the genomic selection model, a hybrid model equation system was established, and the breeding value of individual species was estimated using the conjugate gradient iteration method.

[0037] Furthermore, the hybrid model equation set includes:

[0038]

[0039] Where X is the correlation matrix of fixed effects; X′ is the transpose of X; Z is the correlation matrix of random effects; Z′ is the transpose of Z; R -1 Let R be the inverse matrix of R, and R = Iσ e 2 I is the identity matrix, σ e 2 The variance is the random residual. These are estimates of fixed effects; σ represents the additive effect estimate; polyG is the additive genomic kinship matrix for homologous polyploids; σ a 2 It represents additive genetic variance.

[0040] Furthermore, if the genomic selection model is also based on a homologous polyploid dominant genomic kinship matrix, then the mixed model equations include:

[0041]

[0042] Where PolyE is the phylogenetic relationship matrix of autopolyploid dominant genomes; σ d 2 Variance of the dominant effect; This is an estimate of the explicit effect.

[0043] Furthermore, if the genomic selection model is also based on a homologous polyploid epigenomic phylogenetic matrix, then the hybrid model equation set includes:

[0044]

[0045] Where, σ r 2 The variance of the upper-level effect. This is the estimate of the upper-level effect.

[0046] The present invention further provides the application of the described genome selection method in the breeding of autopolyploid species; or in improving the breeding accuracy of autopolyploid species.

[0047] The present invention has the following beneficial effects:

[0048] This invention constructs a genome selection model by establishing a phylogenetic relationship matrix of homologous polyploid genomes. Compared with the existing GBLUP model, it can make fuller use of the additive, dominant and epistatic effects of the same allele in homologous polyploids, and has higher predictive power, thus achieving genome selection more accurately. Attached Figure Description

[0049] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0050] Figure 1 This is a schematic diagram illustrating the accuracy of genome prediction based on simulated data from polyGBLUP and GBLUP under two different ploidies and two different heritability, as provided in Embodiment 2 of the present invention.

[0051] Figure 2 This is a schematic diagram illustrating the genomic prediction bias of simulated data from polyGBLUP and GBLUP under two different ploidies and two different heritability, provided in Embodiment 2 of the present invention.

[0052] Figure 3 This is a schematic diagram illustrating the comparison of the genome prediction accuracy of polyGBLUP and GBLUP under three different traits in homotetraploid blueberries provided in Example 3 of the present invention.

[0053] Figure 4 This is a schematic diagram illustrating the difference in genome prediction bias between polyGBLUP and GBLUP under three different traits in the homotetraploid blueberry genome, as provided in Example 3 of the present invention. Detailed Implementation

[0054] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0055] Example 1

[0056] This invention provides a genome selection method, comprising the following steps:

[0057] 1. Establish a statistical model

[0058] The prediction of Genomic Breeding Value (GEBV) can be carried out from multiple dimensions. In the traditional GBLUP, additive effects can be used to construct a complete genomic selection model. On this basis, different genomic selection models can be constructed by taking into account dominance effects and epistatic effects.

[0059] Therefore, this invention takes the additive effect, dominant effect and epistatic effect as an example, but in practice, the genomic selection model can be constructed by using the additive effect.

[0060] The matrix form of the genomic selection model provided by this invention can be represented as follows:

[0061] y = Xb + Za + Zd + Zr + e

[0062] Where y is the phenotypic value vector, b is the fixed effect, and a is the additive genetic effect vector, following a normal distribution N(0, polyGσ). a 2 ), where polyG is the additive genomic kinship matrix, σ a 2 The variance is additive genetic; d is the dominant effect vector, which follows a normal distribution N(0, polyDσ). d 2 ), where polyD is the dominant genomic kinship matrix, σ d 2 Here, r is the variance of the dominant effect; r is the vector of the epistatic effect, which follows a normal distribution N(0, polyEσ). r 2 ), where polyE is the epigenomic kinship matrix, σ r 2 Here, σ represents the variance of the upper-level effect; e is the random residual, following a normal distribution: e ~ N(0,R)=N(0,Iσ) e 2 ), where I is the identity matrix, σ e 2 Let X be the variance of the random residuals; and Z be the corresponding incidence matrices.

[0063] 2. SNP genotype coding

[0064] This invention employs a specific encoding method to confirm the genotype values ​​of the genotype matrix used in establishing the genomic kinship matrix. Specifically, the genotype value is determined by the copy number of any given allele; that is, for any given allele, the genotype value is equal to the copy number of that allele.

[0065] For example, the octoploid SNP genotype codes are 0 (AAAAAAAA), 1 (AAAAAAAB), 2 (AAAAAABB), 3 (AAAAABBB), 4 (AAAABBBB), 5 (AAABBBBB), 6 (AABBBBBB), 7 (ABBBBBBB), and 8 (BBBBBBBB). Other ploidies follow the same pattern, and the number of any allele can be used as the coding basis. Taking octoploid as an example, the resulting polyploid genotype matrix is ​​as follows:

[0066] 3 3 3 4 5 8 6 2 2 7 1 2 3 2 3 1…

[0067] 3 2 4 4 4 7 5 2 1 7 2 2 3 2 3 2…

[0068] 3 3 3 4 4 7 5 3 1 7 1 2 3 2 3 1…

[0069] 2 5 4 6 5 8 6 3 1 6 2 1 3 2 2 1…

[0070] 1 4 4 5 4 8 5 3 0 7 2 1 3 2 2 1…

[0071] …

[0072] Each row represents an individual, each column represents a SNP locus, and the numbers represent different SNP genotypes.

[0073] 3. Establishment of a phylogenetic relationship matrix for homologous polyploid genomes

[0074] (1) Construction of the additive genomic kinship matrix (polyG) of homologous polyploids

[0075]

[0076] Where W is the centered polyploid genotype matrix, W = X - ploidyP, and P is the allele frequency p. i Matrix, p i is the frequency of the second allele at the i-th locus; X is the polyploid genotype matrix; ploidy is the polyploidy level value, such as ploidy = 8 for octoploid species.

[0077] (2) Construction of the homologous polyploid dominant genomic kinship matrix (polyD)

[0078]

[0079]

[0080] Where P is the allele frequency p i Matrix, p i Let M be the frequency of the second allele at the i-th locus, and M be an m×m diagonal matrix with m elements on the diagonal. i C represents the ploidy level value; C is an m×m diagonal matrix, with diagonal elements... ⊙ represents the Hadamard product; X represents the polyploid genotype matrix;

[0081] So, let's take octoploid as an example:

[0082]

[0083]

[0084] The value of each element of the Q matrix is:

[0085] and

[0086] (3) Construction of the epigenomic phylogenetic relationship matrix (polyE) of homologous polyploids

[0087] For polyE, including the addition of the superposition (polyE) AA ), add upper position (polyE AD ) and explicit superposition (polyE) DD The formula for constructing a genome kinship matrix is ​​as follows:

[0088]

[0089]

[0090]

[0091] Where polyG is the homologous polyploid additive genomic kinship matrix, polyD is the homologous polyploid dominant genomic kinship matrix; ⊙ is the Hadamard product; tr is the trace of the matrix; and m is the number of loci.

[0092] 4. Estimation of genomic breeding value

[0093] A system of mixed model equations is established, and the individual genome breeding value is estimated using the conjugate gradient iterative method. The system of mixed model equations can be expressed as:

[0094] (1) If only additive effects are considered in the statistical model

[0095]

[0096] Where X is the correlation matrix of fixed effects; X′ is the transpose of X; Z is the correlation matrix of random effects; Z′ is the transpose of Z; R -1 Let R be the inverse matrix of R, and R = I e 2 I is the identity matrix, σ e 2 The variance is the random residual. These are estimates of fixed effects; σ represents the additive effect estimate; polyG is the additive genomic kinship matrix for homologous polyploids; σ a 2 It represents additive genetic variance.

[0097] (2) If the statistical model considers both additive and explicit effects

[0098]

[0099] Where PolyE is the phylogenetic relationship matrix of autopolyploid dominant genomes; σ d 2 Variance of the dominant effect; The values ​​are estimates of the dominant effect, and the other parameters are the same as those in the mixed model equations of (1).

[0100] (3) If the statistical model simultaneously considers additive effects, dominant effects, and epistatic effects

[0101]

[0102] Where, σ r 2 The variance of the upper-level effect. The values ​​are estimates of the superordinate effects, and the remaining parameters are the same as those in the mixed model equations of (1) and (2).

[0103] Example 2

[0104] This invention utilizes simulated data to verify the advantages of the genome selection method provided by this invention in genome selection for autopolyploid species. The specific process is as follows:

[0105] This invention utilizes the simulation software simDiseq to simulate autopolyploid genotype data. The number of SNP markers is set to 100,000, the ploidy levels are set to 4 and 8 respectively, and the number of individuals is set to 600 as the base population to obtain autotetraploid and autooctoploid genotype data. Then, pSBVB software is used to simulate phenotype and pedigree data using the simulated genotype data. Two traits with heritability of 0.1 and 0.3 are simulated respectively, and the QTL number is randomly set to 1000. Using the base population of 600 individuals (300 males and 300 females), completely random mating is performed, with each pair producing two offspring (1 male and 1 female). This process continues for 1000 non-overlapping generations, labeled from generation -999 to generation 0, as the historical population. After 1000 historical generations, three more generations are simulated, labeled from generation 1 to generation 3. Each generation consists of 50 males and 100 females, who mate randomly. Each female produces 40 offspring (20 males and 20 females), resulting in 4000 individuals (2000 males and 2000 females) in the second generation. From these, 50 males are randomly selected as fathers and 100 females as mothers for the next two generations of mating, yielding a total of 12600 individuals. Each simulation scenario is repeated 20 times.

[0106] For the genomic selection reference population, 4000 individuals from the second generation were selected as the reference population. For the genomic selection candidate population, 1000 individuals from the third generation were randomly selected as the candidate population. The genomic prediction accuracy and prediction bias of the polyGBLUP model and the GBLUP model of this invention were compared (both genomic selection models were constructed based on additive effects, dominant effects, and additive contingency effects). Prediction accuracy was evaluated by the correlation r(GEBV, TBV) between the estimated genomic breeding value (GEBV) and the actual breeding value (TBV) (higher prediction accuracy indicates a better model). For prediction bias, it was evaluated by subtracting the absolute value of the regression of GEBV and EBV, |1-b(TBV, GEBV)|, from 1 (smaller prediction bias indicates a better model).

[0107] The results are as follows Figure 1 As shown, based on different genetic hypotheses for complex traits, the four graphs correspond to four different ploidy and different types of simulated traits, namely, autotetraploid heritability of 0.1, autotetraploid heritability of 0.3, autooctoploid heritability of 0.1, and autooctoploid heritability of 0.3. The horizontal axis of each graph represents the GBLUP model and the ployGBLUP model proposed in this invention, respectively, while the vertical axis represents the prediction accuracy. Simulation results show that the prediction accuracy of the ployGBLUP model is higher than that of the GBLUP model in all cases.

[0108] like Figure 2 As shown, the distribution of the four graphs is similar to... Figure 1The results are consistent, but the horizontal axis of each graph represents the GBLUP model and the ployGBLUP model proposed in this invention, respectively, while the vertical axis represents the prediction bias. Simulation results show that the prediction bias of the ployGBLUP model is lower than that of the GBLUP model in all cases.

[0109] Example 3

[0110] This invention further utilizes real data to verify the advantages of the genome selection method provided by this invention in genome selection for autopolyploid species. The specific process is as follows:

[0111] Data were selected from a homologous tetraploid blueberry population from the University of Florida Blueberry Breeding Program. This population comprised 1804 genotypes, derived from 117 crosses between 146 parents, including data from 2014 and 2015. The population included three phenotypes, total yield (grades 1-5), fruit weight (g), and fruit firmness (g mm). -1 (Compression intensity). Least squares mean (LSMeans) analysis was performed on each trait, with the year considered a fixed effect. Subsequently, the corrected phenotypes after adjusting for fixed effects were used as phenotypic values ​​for genomic selection. For genotypic data, autotetraploid genotypes were obtained using FreeBayes software. After quality control processing, a total of 86,930 SNPs per individual were used for genomic selection analysis (average sequencing depth per sample was 76X).

[0112] The genomic prediction accuracy and prediction bias of the polyGBLUP model and the GBLUP model (both genomic selection models were constructed simultaneously based on additive effects, dominant effects, and additive concurrency effects) were compared using a 5-fold cross-validation method with 5 replicates. Prediction accuracy was assessed by the correlation r(GEBV, TBV) between the estimated genomic breeding value (GEBV) and the actual breeding value (TBV) (higher prediction accuracy indicates a better model). Prediction bias was assessed by subtracting the absolute value of the regression between GEBV and EBV, |1-b(TBV, GEBV)|, from 1 (smaller prediction bias indicates a better model).

[0113] like Figure 3 As shown, the three graphs correspond to the genome prediction accuracy of total yield, fruit weight, and fruit firmness in autotetraploid blueberries, respectively. The horizontal axis of each graph represents the GBLUP model and the ployGBLUP model proposed in this invention, respectively, while the vertical axis represents prediction accuracy. Real data results show that for all traits, the ployGBLUP model has higher prediction accuracy than the GBLUP model.

[0114] like Figure 4As shown, the three graphs correspond to the genomic prediction biases for total yield, fruit weight, and fruit firmness in autotetraploid blueberries, respectively. The horizontal axis of each graph represents the GBLUP model and the ployGBLUP model proposed in this invention, respectively, while the vertical axis represents the prediction bias. Real data results show that for all traits, the prediction bias of the ployGBLUP model is lower than that of the GBLUP model.

[0115] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A genomic selection method, characterized by, The method comprises the following steps: constructing a homoeologous polyploid additive genomic kinship matrix, a homoeologous polyploid dominant genomic kinship matrix and a homoeologous polyploid epistatic genomic kinship matrix; constructing a genomic selection model based on the homoeologous polyploid additive genomic kinship matrix, the homoeologous polyploid dominant genomic kinship matrix and the homoeologous polyploid epistatic genomic kinship matrix; performing genomic selection according to the genomic selection model; establishing a mixed model equation set based on the genomic selection model, and estimating the breeding value of the individual of the species by using a conjugate gradient iteration method; the genotype matrix used in the homoeologous polyploid additive genomic kinship matrix is a polyploid genotype matrix; the value of the genotype in the polyploid genotype matrix is determined by the copy number of any one allele; the homoeologous polyploid additive genomic kinship matrix comprises the following: where W is the centered ploidy genotype matrix, W = X - ploidyP, P is the allele frequency p i matrix, p i is the second allele frequency at the ith locus; ploidy is the ploidy level value; X is the ploidy genotype matrix; the homoeologous polyploid dominant genomic kinship matrix comprises the following: where P is the allele frequency p i matrix, p i is the second allele frequency at the ith locus, M is an mxm diagonal matrix with diagonal elements m i is the ploidy level value (ploidy); C is an mxm diagonal matrix with diagonal elements is the Hadamard product; X is the ploidy genotype matrix; the homoeologous polyploid epistatic genomic kinship matrix comprises one or more of a homoeologous polyploid additive-additive epistatic genomic kinship matrix, a homoeologous polyploid additive-dominant epistatic genomic kinship matrix or a homoeologous polyploid dominant-dominant epistatic genomic kinship matrix; the additive-additive epistatic genomic kinship matrix comprises: the additive-dominant epistatic genomic kinship matrix comprises: the dominant-dominant epistatic genomic kinship matrix comprises: wherein, polyG is the homoeologous polyploid additive genomic kinship matrix, polyD is the homoeologous polyploid dominant genomic kinship matrix; is the Hadamard product; tr is the trace of the matrix; m is the number of loci; the genomic selection model comprises: y=Xb+Za+Zd+Zr+e where y is the vector of phenotypic values, b is the fixed effect; a is the vector of additive genetic effects, which follows a normal distribution N(0, polyGσ a 2 ), σ a 2 is the additive genetic variance; d is the vector of dominance effects, which follows a normal distribution N(0, polyDσ d 2 ), σ d 2 is the dominance variance; r is the vector of epistatic effects, which follows a normal distribution N(0, polyEσ r 2 ), σ r 2 is the epistatic variance; e is the random residual, which follows a normal distribution e ~ N(0, R) = N(0, Iσ e 2 ), where I is the identity matrix, σ e 2 is the random residual variance; X, Z are the corresponding incidence matrices; the mixed model equation set comprises: where X is the correlation matrix of fixed effects; X ′ is the transpose of X; Z is the correlation matrix of random effects; Z ′ is the transpose of Z; R -1 is the inverse matrix of R, R = Iσ e 2 , I is the identity matrix, σ e 2 is the variance of random residuals; is the estimate of fixed effects; is the estimate of additive effects; polyG is the additive genomic relationship matrix of polyploids; σ a 2 is the additive genetic variance; if the genomic selection model is also based on the homoeologous polyploid dominant genomic kinship matrix, the mixed model equation set comprises: where PolyE is the homozygous polyploid dominance genetic relationship matrix; σ d 2 is the dominance effect variance; is the dominance effect estimate. if the genomic selection model is also based on the homoeologous polyploid epistatic genomic kinship matrix, the mixed model equation set comprises: where σ2 r 2 is the variance of the epistatic effects, is the estimate of the epistatic effect.

2. The genomic selection method of claim 1 is applied to the breeding of a homoeologous polyploid species, or to improving the breeding accuracy of a homoeologous polyploid species.

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