A method for determining heterologous hexaploid imbalance coefficient

Abstract

The application relates to the technical field of biology, and in particular to a method for determining a heterologous hexaploid imbalance coefficient. The method comprises the following steps: constructing a parent gamete frequency calculation model comprising an HWD coefficient and an LD coefficient; inputting the parent gamete frequency calculation model into a progeny zygote frequency distribution model to obtain a progeny zygote frequency calculation model; constructing a determination model; obtaining actual values of the heterologous hexaploid progeny zygote frequency in a natural population, inputting the actual values of the progeny zygote frequency into the determination model, and determining estimated values of the parent gamete frequency; and performing parameter estimation on the determination model by using a numerical optimization algorithm to obtain determined values of the HWD coefficient and the LD coefficient. The HWD coefficient and the LD coefficient are used to reflect the complex LD network between heterologous hexaploid genomic markers, and the problems that current general polyploid LD estimation does not consider the complex LD network between two-site multiple alleles and that a heterologous hexaploid LD network model is lacking are solved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of biotechnology, and particularly relates to a method for determining a heterogenic hexaploid imbalance coefficient. BACKGROUND

[0002] Linkage disequilibrium (LD) refers to a phenomenon of non-random association between alleles at different loci in a genome. The degree and distribution of LD in a genome provide an important reference for inferring population differences and evolutionary events of a natural population. Considering the relationship between LD and recombination rate, LD provides strong support for whole-genome association studies of complex traits and high-resolution positioning. Heterogenic hexaploids exist widely in animals and plants, such as important food crops like wheat, and therefore, accurate measurement of LD of heterogenic hexaploids has important application value.

[0003] Although LD is widely used in genetic studies of diploid animal and plant populations, considering the complex gamete combinations formed by alleles at the same locus and non-alleles at different loci of homogenic and heterogenic hexaploids and the special meiotic mechanism of allopolyploids, a suitable LD model needs to be developed for heterogenic hexaploids, and the existing diploid LD model cannot accurately measure the degree of complex gamete LD of heterogenic hexaploids.

[0004] At present, the LD model for heterogenic hexaploids has the following deficiencies: first, the general polyploid LD composite model only uses one linkage disequilibrium parameter to measure the association degree of two loci with multiple alleles, without considering the complex LD network between two loci with multiple alleles; second, the existing technology estimates the complex LD network between two loci in the genome of a natural population of heterogenic tetraploids, but cannot be used for heterogenic hexaploids, and the composite network LD model of heterogenic hexaploids is more complex than that of tetraploids. SUMMARY

[0005] The present application provides a method for determining a heterogenic hexaploid imbalance coefficient, which can solve the problems that the current general polyploid LD estimation does not consider the complex LD network between two loci with multiple alleles and the problem that the LD network model of heterogenic hexaploids is lacking.

[0006] The technical scheme of the present application is a method for determining a heterogenic hexaploid imbalance coefficient, comprising:

[0007] S1: based on Hardy-Weinberg disequilibrium, constructing a heterogenic hexaploid parent gamete frequency calculation model comprising a plurality of HWD coefficients and LD coefficients;

[0008] S2: confirming a heterogenic hexaploid offspring zygote frequency distribution model, substituting the parent gamete frequency calculation model into the offspring zygote frequency distribution model, and accordingly obtaining an offspring zygote frequency calculation model.

[0009] S3: Based on the log-likelihood function, and according to the progeny zygote frequency calculation model, a determination model is constructed with the parental gamete frequency as the parameter and the progeny zygote frequency as the variable.

[0010] S4: Obtain the actual values ​​of the progeny zygote frequency of allohexaploid progeny in the natural population, input the actual values ​​of the progeny zygote frequency into the measurement model, and determine the estimated values ​​of the parental gamete frequency based on the EM algorithm;

[0011] S5: Based on the estimated values ​​of parental gamete frequencies, parameter estimation is performed on the measurement model using a numerical optimization algorithm, resulting in the measurement values ​​of several HWD coefficients and LD coefficients.

[0012] Optionally, the HWD coefficient is the HWD coefficient between alleles within the marker;

[0013] Furthermore, the LD coefficients include: HWD coefficients between alleles within a marker, LD coefficients between diallelic genes of different markers, LD coefficients between triallelic genes of different markers, LD coefficients between tetraallelic genes of different markers, LD coefficients between pentaallelic genes of different markers, and LD coefficients between hexaallelic genes of different markers.

[0014] Optionally, the offspring zygote frequency calculation model is as follows:

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[0017]

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[0020]

[0021]

[0022]

[0023]

[0024]

[0025]

[0026] In the formula, Indicates the frequency of double-marked parental gametes;

[0027] m1, m2 and m3 represent the single marker parent gamete for marker SNP1, n1, n2 and n3 represent the single marker parent gamete for marker SNP2; m1 = m2 = m3 = n1 = n2 = n3 = A, a;

[0028] k1, k2 and k3 represent the indicator variable for the allelic composition in the single marker parent gamete for SNP1;

[0029] l1, l2 and l3 represent the indicator variable for the allelic composition in the single marker parent gamete for SNP2;

[0030] Q1 represents the calculation formula for the linkage disequilibrium coefficient of two alleles;

[0031] Q2 represents the calculation formula for the linkage disequilibrium coefficient of three alleles;

[0032] Q3 represents the calculation formula for the linkage disequilibrium coefficient of four alleles;

[0033] Q4 represents the calculation formula for the linkage disequilibrium coefficient of five alleles;

[0034] Q5 represents the calculation formula for the linkage disequilibrium coefficient of six alleles;

[0035] Q6 represents the calculation formula for the linkage disequilibrium coefficient of two alleles interacting with two alleles;

[0036] Q7 represents the calculation formula for the linkage disequilibrium coefficient of two alleles interacting with three alleles;

[0037] Q8 represents the calculation formula for the linkage disequilibrium coefficient of two alleles interacting with four alleles;

[0038] Q9 represents the calculation formula for the linkage disequilibrium coefficient of three alleles interacting with three alleles;

[0039] Q 10 represents the calculation formula for the linkage disequilibrium coefficient of three alleles interacting with three alleles;

[0040] D A2 represents the HWD coefficient of two alleles of SNP1;

[0041] D A3 represents the HWD coefficient of three alleles of SNP1;

[0042] D B2 represents the HWD coefficient of two alleles of SNP2;

[0043] D B3 represents the HWD coefficient of three alleles of SNP2;

[0044] Dab represents the LD coefficient of two alleles of the same gamete between two SNPs;

[0045] D a / b represents the LD coefficient of two alleles of different gametes between two SNPs;

[0046] D Ab represents the LD coefficient of two alleles of SNP1 and one allele of SNP2;

[0047] D aB represents the LD coefficient of one allele of SNP1 and two alleles of SNP2;

[0048] D AB represents the LD coefficient of two alleles of SNP1 and two alleles of SNP2;

[0049] D AAb represents the LD coefficient of three alleles of SNP1 and one allele of SNP2;

[0050] D aBB represents the LD coefficient of one allele of SNP1 and three alleles of SNP2;

[0051] D AAB represents the LD coefficient of three alleles of SNP1 and two alleles of SNP2;

[0052] D ABB represents the LD coefficient of two alleles of SNP1 and three alleles of SNP2;

[0053] D AABB represents the LD coefficient of three alleles of SNP1 and three alleles of SNP2.

[0054] Optionally, the determination model is as follows:

[0055]

[0056] wherein, represents the number of 49 offspring zygotes formed by the parental gamete marked SNP1 and the parental gamete marked SNP2; represents the frequency of 49 offspring zygotes formed by the parental gamete marked SNP1 and the parental gamete marked SNP2;

[0057] j A = 1, 2,..., 7, respectively representing the genotypes of SNP1 AAAAAA, AAAAa,..., aaaaaa;

[0058] j B= 1, 2, …, 7, respectively representing the genotype BBBBBB, BBBBb, …, bbbbbb of SNP2;

[0059] c represents a constant.

[0060] Optionally, further comprising:

[0061] S6: performing a test on the linkage disequilibrium coefficient of the HWD coefficient of the offspring zygote, and obtaining a likelihood ratio accordingly;

[0062] According to the likelihood ratio, the significance of the linkage disequilibrium coefficient is determined.

[0063] Optionally, the step S6 comprises:

[0064] S61: performing a hypothesis test on the HWD coefficient and the linkage disequilibrium coefficient of the offspring zygote, and obtaining a plurality of likelihood ratios accordingly;

[0065] The test formula includes but is not limited to the following formula:

[0066] H0: D AAb = 0; H1: D AAb ≠ 0;

[0067] S62: comparing the plurality of likelihood ratios with the critical value respectively, and obtaining a plurality of comparison results accordingly;

[0068] According to the plurality of comparison results, the significance of the measured value of the HWD coefficient or the measured value of the linkage disequilibrium coefficient is determined accordingly.

[0069] Optionally, further comprising:

[0070] S7: performing a standardization operation on the measured value of the LD coefficient, and obtaining the interval range of the LD coefficient in the interval [0, 1].

[0071] Optionally, the step S7 comprises:

[0072] S71: according to the allele frequency, screening the maximum value less than 0 as the minimum value of the interval and the minimum value greater than 0 as the maximum value of the interval for the measured value of the LD coefficient, and determining the interval range of the LD coefficient in the interval [0, 1] accordingly;

[0073] S72: repeating the step S71 until the interval range of all LD coefficients in the interval [0, 1] is determined.

[0074] Optionally, further comprising:

[0075] S8: Perform simulation evaluation on several measured values ​​of LD coefficients, and determine the accuracy of the measured values ​​of several LD ​​coefficients accordingly based on the sample size and standard deviation.

[0076] Beneficial effects:

[0077] This application constructs a disequilibrium analysis model for natural allohexaploid populations, using several HWD coefficients and several LD ​​coefficients to reflect the complex LD network between allohexaploid genomic markers. The LD network involves Hardy-Weinberg disequilibrium at a single point, linkage disequilibrium of multiple alleles at two points, and the interaction strength between disequilibriums. Furthermore, a measurement model is constructed to estimate several HWD coefficients and several LD ​​coefficients, thereby obtaining several measurement values.

[0078] In summary, this application can solve the problems of current general polyploid LD estimation not considering the complex LD network between two alleles and the lack of LD network models for allohexaploids. It also makes up for the defects of the results bias caused by applying diploid methods in current allohexaploid linkage disequilibrium analysis and improves the accuracy of allopolyploid linkage disequilibrium analysis. Attached Figure Description

[0079] To more clearly illustrate the technical solution of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0080] Figure 1 This is a flowchart illustrating the method for determining the disequilibrium coefficient of allohexaploids in this application. Detailed Implementation

[0081] The embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described below do not represent all embodiments consistent with this application. They are merely examples of systems and methods consistent with some aspects of this application as detailed in the claims.

[0082] (I) Example 1

[0083] This application provides a method for determining the disequilibrium coefficient of allohexaploids, such as... Figure 1 As shown, Figure 1 This is a flowchart illustrating the method for determining the disequilibrium coefficient of allohexaploids in this application, including:

[0084] S1: Construct the calculation model of the gamete frequency of the allohexaploid parent based on the Hardy-Weinberg disequilibrium, which includes several HWD coefficients and LD coefficients.

[0085] wherein the HWD coefficient is the HWD coefficient between alleles within a marker;

[0086] The LD coefficients include: the HWD coefficient between alleles within a marker, the LD coefficient between di-allelic genes of different markers, the LD coefficient between tri-allelic genes of different markers, the LD coefficient between tetra-allelic genes of different markers, the LD coefficient between penta-allelic genes of different markers, and the LD coefficient between hexa-allelic genes of different markers.

[0087] The combination AB|AB|ab and AB|Ab|aB represent the same genotype AAaBBb, and the frequency is represented as The combination Ab|AB|ab and Ab|Ab|aB, …, ab|AB|ab and ab|Ab|aB, etc. can also represent the same genotype.

[0088] S2: Confirm the zygote frequency distribution model of the allohexaploid offspring, and substitute the calculation model of the parent gamete frequency into the zygote frequency distribution model, to obtain the calculation model of the offspring zygote frequency accordingly.

[0089] wherein the calculation model of the offspring zygote frequency is as follows:

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[0101] wherein, Diploid gamete frequency of two markers, i.e. the frequency of the parental gamete including both markers.

[0102] m1, m2 and m3 represent the single marker parental gamete of marker SNP1, n1, n2 and n3 represent the single marker parental gamete of marker SNP2; m1 = m2 = m3 = n1 = n2 = n3 = A, a; single marker means only a certain marker is represented;

[0103] k1, k2 and k3 represent the indicator variable of allele composition in the single marker parental gamete of SNP1;

[0104] l1, l2 and l3 represent the indicator variable of allele composition in the single marker parental gamete of SNP2;

[0105] Q1 represents the calculation formula of linkage disequilibrium coefficient of two alleles;

[0106] Q2 represents the calculation formula of linkage disequilibrium coefficient of three alleles;

[0107] Q3 represents the calculation formula of linkage disequilibrium coefficient of four alleles;

[0108] Q4 represents the calculation formula of linkage disequilibrium coefficient of five alleles;

[0109] Q5 represents the calculation formula of linkage disequilibrium coefficient of six alleles;

[0110] Q6 represents the calculation formula of linkage disequilibrium coefficient of two alleles and two alleles interaction;

[0111] Q7 represents the calculation formula of linkage disequilibrium coefficient of two alleles and three alleles interaction;

[0112] Q8 represents the calculation formula of linkage disequilibrium coefficient of two alleles and four alleles interaction;

[0113] Q9 represents the calculation formula of linkage disequilibrium coefficient of three alleles and three alleles interaction;

[0114] Q 10 represents the calculation formula of linkage disequilibrium coefficient of three two alleles interaction;

[0115] D A2 represents the HWD coefficient of two alleles of SNP1;

[0116] D A3 represents the HWD coefficient of three alleles of SNP1;

[0117] D B2 represents the HWD coefficient of two alleles of SNP2;

[0118] D B3HWD coefficient representing three alleles of SNP2;

[0119] D ab LD coefficient representing two non-allelic genes of the same gamete between two SNPs;

[0120] D a / b LD coefficient representing two non-allelic genes of different gametes between two SNPs;

[0121] D Ab LD coefficient representing two alleles of SNP1 and one allele of SNP2;

[0122] D aB LD coefficient representing one allele of SNP1 and two alleles of SNP2;

[0123] D AB LD coefficient representing two alleles of SNP1 and two alleles of SNP2;

[0124] D AAb LD coefficient representing three alleles of SNP1 and one allele of SNP2;

[0125] D aBB LD coefficient representing one allele of SNP1 and three alleles of SNP2;

[0126] D AAB LD coefficient representing three alleles of SNP1 and two alleles of SNP2;

[0127] D ABB LD coefficient representing two alleles of SNP1 and three alleles of SNP2;

[0128] D AABB LD coefficient representing three alleles of SNP1 and three alleles of SNP2.

[0129] Specifically, it is assumed that there are two co-segregating markers SNP1 and SNP2 in a natural population, SNP1 contains alleles A and a, the frequencies of the two alleles are p and 1-p, respectively, SNP2 contains alleles B and b, the frequencies of the two alleles are q and 1-q, respectively. The non-allelic genes on the two SNPs are located on a chromosome, which can form four haplotypes (gametes), which are AB, Ab, aB and ab; based on the above diploid haplotype, we establish the gamete and zygote combination and frequency of allohexaploid.

[0130] The gametic combinations of the above diploid haplotypes combined to obtain allohexaploid are AB|AB|AB, AB|AB|Ab, AB|AB|aB, AB|AB|ab, AB|Ab|Ab, AB|Ab|aB, AB|Ab|ab, AB|aB|aB, AB|aB|ab, AB|ab|ab, …, ab|ab|ab, and their frequencies are represented as Where | is used to split two chromosomes.

[0131] Suppose in a natural population of allohexaploid, SNP1 may have seven genotypes, namely AAAAAA, AAAAAa, AAAAaa, AAAaaa, AAaaaa, Aaaaaa and aaaaaa, and SNP2 may have seven genotypes, namely BBBBBB, BBBBBb, BBBBBbb, BBBbbb, BBbbbb, Bbbbbb and bbbbbb, and the two markers form 49 zygotic genotypes, which are the zygotic frequency distribution model of offspring.

[0132] Suppose these zygotic genotypes are obtained by random combination of allohexaploid gametes, then the frequency of zygotic genotypes can be represented as the product of the frequency of hexaploid gametes, as shown in Table 1.

[0133] Table 1 Calculation model of zygotic frequency of allohexaploid offspring

[0134]

[0135] The above imbalance coefficients can be divided into: 1) Hardy-Weinberg imbalance coefficients (D A2 , D A3 , D B2 and D B3 ), 2) imbalance coefficients between two alleles (D ab and D a / b ), 3) imbalance coefficients between three alleles (D Ab and D aB ), 4) imbalance coefficients between four alleles (D AB , D AAb and D aBB ), 5) imbalance coefficients between five alleles (D AAB and D ABB ), 6) imbalance coefficients between six alleles (D AABB ).

[0136] Let m1m2m3 and n1n2n3 represent the gametes formed by SNP1 and SNP2, respectively, where alleles m1=m2=m3=n1=n2=n3=A, a;

[0137] Let k1k2k3 and l1l2l3 represent the indicator variables of the SNP1 and SNP2 gamete alleles, respectively, where k1=k2=k3=l1=l2=l3=1, 2, m1=A if k1=1, m1=a if k1=2, and so on. The correspondence between m and k, n and l can be obtained.

[0138] Let P m1 represent the frequency of allele m1, P m1 =p if m1=A, P m1 =1-p if m1=a, and so on. The frequencies of SNP1 alleles m1 and m2, and the frequencies of SNP2 alleles can be obtained.

[0139] Based on the above settings and 14 disequilibrium parameters, the expression of the gamete genotype frequency of the alien hexaploid can be derived as follows:

[0140] = = allele frequency under linkage equilibrium + Q1 represents the LD of 15 two-allele genes + Q2 represents the LD of 20 three-allele genes + Q3 represents the LD of 15 four-allele genes + Q4 represents the linkage LD of 6 five-allele genes + Q5 represents the linkage LD of 1 six-allele gene + Q6 represents the LD of 45 two-allele genes interacting with two-allele genes + Q7 represents the LD of 60 two-allele genes interacting with two-allele genes + Q8 represents the LD of 15 two-allele genes interacting with four-allele genes + Q9 represents the LD of 10 three-allele genes interacting with three-allele genes + Q10 represents the LD of 15 three two-allele genes interacting with each other. 10 .

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[0150] The above gamete frequencies are substituted into Table 1 to obtain the zygote frequencies of the allohexaploid.

[0151] S3: Based on the log-likelihood function, a measurement model is constructed according to the model of the offspring zygote frequencies, which takes the parental gamete frequencies as parameters and the offspring zygote frequencies as variables.

[0152] The measurement model is as follows:

[0153]

[0154] In the formula, represents the number of 49 offspring zygotes formed by the parental gamete of marker SNP1 and the parental gamete of marker SNP2; represents the frequency of 49 offspring zygotes formed by the parental gamete of marker SNP1 and the parental gamete of marker SNP2;

[0155] j A = 1, 2, …, 7, respectively representing the genotypes of SNP1 AAAA AA, AAAAa, …, aaaaaa;

[0156] j B = 1, 2, …, 7, respectively representing the genotypes of SNP2 BBBB BB, BBBBb, …, bbbbbb;

[0157] c represents a constant.

[0158] Specifically, The zygote frequencies can be obtained from Table 1.

[0159] S4: Obtain the actual values of the allohexaploid offspring zygote frequencies in the natural population, input the actual values of the offspring zygote frequencies into the measurement model, and determine the estimated values of the parental gamete frequencies based on the EM algorithm.

[0160] Specifically, since the frequencies of some zygotes contain different components, the current sequencing technology cannot distinguish these components, and the EM algorithm without gradient is used to complete the estimation of the gamete frequencies, which is a simplified version of the traditional EM algorithm.

[0161] S5: According to the estimated values of the parental gamete frequencies, parameter estimation is performed on the measurement model by using a numerical optimization algorithm, and the measurement values of a plurality of linkage disequilibrium coefficients are obtained accordingly.

[0162] Specifically, based on the above likelihood function, a quasi-Newton method or other numerical optimization algorithm is used for parameter estimation.

[0163] S6: Test the linkage disequilibrium coefficients of the HWD coefficients of the offspring zygotes, and obtain the likelihood ratio accordingly.

[0164] According to the likelihood ratio, the significance of the linkage disequilibrium coefficient is judged.

[0165] The step S6 comprises:

[0166] S61: Hypothesis testing of the HWD coefficient and the linkage disequilibrium coefficient is performed for the offspring zygote, and a plurality of likelihood ratios are obtained accordingly; the test formula includes but is not limited to the following formula:

[0167] H0: D AAb = 0; H1: D AAb ≠ 0;

[0168] S62: The plurality of likelihood ratios are compared with the critical value in size respectively, and a plurality of comparison results are obtained accordingly;

[0169] According to the plurality of comparison results, the significance of the measured value of the HWD coefficient or the measured value of the linkage disequilibrium coefficient is judged accordingly.

[0170] Specifically, actual marker data is obtained for an allohexaploid natural population, and in order to better evaluate the significance of the linkage disequilibrium parameters, the following hypothesis test is established: taking the parameter D AAb as an example, the following hypothesis test can be performed,

[0171] H0: D AAb = 0; H1: D AAb ≠ 0;

[0172] The likelihood ratio can be obtained through the likelihood values of the two hypotheses, and the significance of the D parameter can be judged by comparing the LR value with the critical value . Similarly, the significance of the remaining 13 linkage disequilibrium parameters can also be detected. When the number of marker pairs to be detected is large, the bonferroni method is used to correct the significance level. Considering that the LR value approximately obeys the chi-square distribution requires a large sample size and the complexity of the composite model, the critical value can also be determined by the permutation test method which does not depend on the data distribution. This strategy does not require correction of the P value.

[0173] S7: The measured value of the LD coefficient is standardized to obtain the interval range of the LD coefficient in [0, 1].

[0174] The step S7 comprises:

[0175] S71: For the measured value of the LD coefficient, the maximum value less than 0 is screened as the minimum value of the interval according to the allele frequency, and the minimum value greater than 0 is screened as the maximum value of the interval, to determine the interval range of the LD coefficient in [0, 1];

[0176] S72: Repeat step S71 until the interval range of all LD coefficients is determined in the interval [0, 1].

[0177] Specifically, the estimated LD parameter is a relative value, and the LD parameters obtained under different marker combinations, different populations and different experimental designs cannot be directly compared, so it is necessary to standardize all the estimated LD parameters.

[0178] By referring to the standardization method of diploid LD parameters, first, the interval range of each LD parameter is determined, and the minimum value less than 0 is selected as the minimum value of the interval and the minimum value greater than 0 is selected as the maximum value of the interval based on the allele frequency, so as to determine the interval of each LD parameter. If the LD parameter is less than 0, the parameter is divided by the minimum value of the interval; if the LD parameter is greater than 0, the parameter is divided by the maximum value of the interval, so as to complete the standardization of the LD parameter. After regularization, the LD is in the interval [0, 1].

[0179] S8: Simulate and evaluate the measured values of a plurality of LD coefficients, and determine the accuracy of the measured values of a plurality of LD coefficients based on the sample size and the standard deviation.

[0180] Specifically, to determine the accuracy and applicable sample size of the model estimation parameters, we carried out computer simulation research for evaluation, setting p = 0.35 and q = 0.45. Table 2 lists the accuracy and statistical power of the constructed model linkage disequilibrium parameter estimation, and the true value in the parentheses of each parameter. From the table, it can be found that the composite model has more parameters, leading to the increase of parameter estimation difficulty. In small samples, the accuracy of part of the parameter estimation is higher, but a part of the parameter has a large standard deviation, which is reflected in the power level, leading to the decrease of the power of part of the parameter estimation. With the increase of sample size, the accuracy and power of the parameter estimation of the composite model are continuously improved. When the sample size is 400, the power of parameters D B3 and D AB is 0.675, and the power of other parameters is above 93%, and the power of 6 parameters reaches 1.00.

[0181] Table 2 Accuracy and power of linkage disequilibrium parameter estimation of two models under full information markers

[0182]

[0183] Note: MLE: maximum likelihood estimation; Power: power; Δ ab = D ab + 2D a / b .

[0184] The above detailed description of the embodiments of the application has been given for the purposes of illustration only. It is not intended to be exhaustive or to limit the application to the precise forms described, and many modifications and variations are possible in light of the falling disclosure. It is intended that the scope of the application be defined by the claims appended hereto.

Claims

1. A method for determining the disequilibrium coefficient of allohexaploids, characterized in that, include: S1: Based on Hardy-Weinberg imbalance, a calculation model for the frequency of allohexaploid parental gametes is constructed, including several HWD coefficients and LD coefficients. S2: Confirm the offspring zygote frequency distribution model of the allohexaploid, substitute it into the parental gamete frequency calculation model to obtain the offspring zygote frequency distribution model, and obtain the corresponding offspring zygote frequency calculation model. S3: Based on the log-likelihood function, and according to the progeny zygote frequency calculation model, a determination model is constructed with the parental gamete frequency as the parameter and the progeny zygote frequency as the variable. S4: Obtain the actual values ​​of the progeny zygote frequency of allohexaploid progeny in the natural population, input the actual values ​​of the progeny zygote frequency into the measurement model, and determine the estimated values ​​of the parental gamete frequency based on the EM algorithm; S5: Based on the estimated values ​​of parental gamete frequencies, parameter estimation is performed on the measurement model using a numerical optimization algorithm, resulting in the measurement values ​​of several HWD coefficients and LD coefficients.

2. The method for determining the disequilibrium coefficient of allohexaploids according to claim 1, characterized in that, The HWD coefficient is the HWD coefficient between alleles within the marker; Furthermore, the LD coefficients include: HWD coefficients between alleles within a marker, LD coefficients between diallelic genes of different markers, LD coefficients between triallelic genes of different markers, LD coefficients between tetraallelic genes of different markers, LD coefficients between pentaallelic genes of different markers, and LD coefficients between hexaallelic genes of different markers.

3. The method for determining the disequilibrium coefficient of allohexaploids according to claim 2, characterized in that, The offspring zygote frequency calculation model is shown below: In the formula, Indicates the frequency of double-marked parental gametes; m1, m2, and m3 represent single-marked parental gametes labeled SNP1, and n1, n2, and n3 represent single-marked parental gametes labeled SNP2; m1 = m2 = m3 = n1 = n2 = n3 = A, a; k1, k2, and k3 represent indicator variables for the allele composition of single-marker parental gametes of SNP1; l1, l2, and l3 represent indicator variables of allele composition in single-marker parental gametes of SNP2; Q1 represents the formula for calculating the linkage disequilibrium coefficient of diallelic genes; Q2 represents the formula for calculating the linkage disequilibrium coefficient of trieles; Q3 represents the formula for calculating the linkage disequilibrium coefficient of tetraelements; Q4 represents the formula for calculating the linkage disequilibrium coefficient of the pentele; Q5 represents the formula for calculating the linkage disequilibrium coefficient of the six alleles; Q6 represents the formula for calculating the linkage disequilibrium coefficient of bisele interactions; Q7 represents the formula for calculating the linkage disequilibrium coefficient of the interaction between dieles and trieles; Q8 represents the formula for calculating the linkage disequilibrium coefficient of the interaction between dieleries and tetraeleries; Q9 represents the formula for calculating the linkage disequilibrium coefficient of triele interactions; Q 10 Formula for calculating the linkage disequilibrium coefficient of three diallele interactions; D A2 The HWD coefficients of the two alleles of SNP1 are represented. D A3 HWD coefficients representing the three alleles of SNP1; D B2 The HWD coefficients of the two alleles of SNP2 are represented. D B3 The HWD coefficients represent the three alleles of SNP2; D ab The LD coefficient represents the two non-allelic genes in the same gamete between two SNPs; D a / b The LD coefficient represents the two non-allelic genes in different gametes between two SNPs; D Ab This represents the LD coefficient between two alleles of SNP1 and one allele of SNP2; D aB This represents the LD coefficient between one allele of SNP1 and two alleles of SNP2. D AB This represents the LD coefficients between the two alleles of SNP1 and the two alleles of SNP2; D AAb This represents the LD coefficient between the three alleles of SNP1 and the one allele of SNP2; D aBB This represents the LD coefficient between one allele of SNP1 and three alleles of SNP2; D AAB This represents the LD coefficient between the three alleles of SNP1 and the two alleles of SNP2; D ABB This represents the LD coefficient between the two alleles of SNP1 and the three alleles of SNP2; D AABB This represents the LD coefficients of the three alleles of SNP1 and the three alleles of SNP2.

4. The method for determining the disequilibrium coefficient of allohexaploids according to claim 1, characterized in that, The measurement model is shown below: In the formula, This indicates the number of 49 progeny zygotes formed by the parental gametes marked SNP1 and SNP2; This represents the frequency of the 49 progeny zygotes formed by the parental gametes labeled SNP1 and SNP2; j A =1,2,……,7, corresponding to the SNP1 genotypes AAAAAA, AAAAAa,……,aaaaaa; j B =1,2,……,7, corresponding to the SNP2 genotypes BBBBBB,BBBBBB,……,bbbbbb; c represents a constant.

5. The method for determining the disequilibrium coefficient of allohexaploids according to claim 1, characterized in that, Also includes: S6: Test the linkage disequilibrium coefficient of the HWD coefficient of the offspring zygotes and obtain the likelihood ratio accordingly; The significance of the linkage disequilibrium coefficient is determined based on the likelihood ratio.

6. The method for determining the disequilibrium coefficient of allohexaploids according to claim 5, characterized in that, Step S6 includes: S61: Perform hypothesis testing on the HWD coefficient and linkage disequilibrium coefficient for the progeny zygotes, and obtain several likelihood ratios accordingly; The test formulas include, but are not limited to, the following formulas: H0:D AAb <0; H1:D AAb ≠0; S62: For several likelihood ratios and critical values ​​respectively The sizes are compared, and several comparison results are obtained accordingly; Based on several comparison results, the significance of the measured values ​​of the HWD coefficient or the linkage disequilibrium coefficient is determined accordingly.

7. The method for determining the disequilibrium coefficient of allohexaploids according to claim 1, characterized in that, Also includes: S7: Standardize the measured values ​​of the LD coefficient to obtain the range of the LD coefficient in the interval [0,1].

8. The method for determining the disequilibrium coefficient of allohexaploids according to claim 7, characterized in that, Step S7 includes: S71: For the measured LD coefficient, the maximum value less than 0 is selected as the minimum value of the interval based on the allele frequency, and the minimum value greater than 0 is selected as the maximum value of the interval, thus determining the range of the LD coefficient in the interval [0,1]. S72: Repeat step S71 until the range of all LD coefficients in the interval [0,1] is determined.

9. The method for determining the disequilibrium coefficient of allohexaploids according to claim 1, characterized in that, Also includes: S8: Perform simulation evaluation on the measured values ​​of several LD ​​coefficients, and determine the accuracy of the measured values ​​of several LD ​​coefficients based on the sample size and standard deviation.

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