A method for combined determination of homologous tetraploid double-reduction parameter and HWD coefficient

Abstract

The application relates to the field of homologous tetraploid organisms, in particular to a combined determination method of homologous tetraploid double-reduction parameters and HWD coefficients. The method comprises the following steps: constructing a homologous tetraploid natural population double-reduction and linkage disequilibrium combined model; constructing a combined calculation model; inputting actual values of double-marker offspring zygote frequencies into the combined calculation model to determine estimated values of double-marker direct parent gamete frequencies; calculating estimated values of single-marker direct parent gamete frequencies according to the estimated values of the double-marker direct parent gamete frequencies; inputting the estimated values of the single-marker direct parent gamete frequencies into a single-marker direct parent gamete frequency calculation model to obtain a nonlinear equation; and determining the measured values of the double-reduction parameters and the Hardy-Weinberg disequilibrium coefficients according to the nonlinear equation. The application simultaneously completes the determination of double-reduction frequency estimation, Hardy-Weinberg disequilibrium and linkage disequilibrium between markers by constructing a combined model, and improves the precision of parameter estimation.

Description

Technical Field

[0001] This application relates to the field of autotetraploid biology, and more particularly to a method for the joint determination of autotetraploid double meiotic parameters and HWD coefficients. Background Technology

[0002] Double Reduction (DR) is a unique phenomenon in meiosis in homologous polyploids. It is mainly characterized by the crossing of two sets of sister chromatids on the same chromosome during the first meiotic division and their subsequent migration to the same pole.

[0003] In autotetraploids, the main characteristic is the multivalent pairing of four homologous chromosomes with similar genetic backgrounds during meiosis. The occurrence of DR affects the segregation rate of genotypes, leading to biases in the estimation of recombination rate in linkage analysis of mapped populations; while in natural populations, DR affects Hardy-Weinberg equilibrium, thereby affecting the frequency of alleles.

[0004] Currently, some methods have considered the influence of DR in the calculation of recombination rate in mapping populations (artificially calculated populations), but there is little research on DR frequency estimation methods in natural populations, especially the lack of a method for joint detection of DR frequency, Hardy-Weinberg equilibrium, and inter-marker linkage disequilibrium.

[0005] Most existing methods are single-function, leading to insufficient accuracy in parameter estimation. The main shortcomings are as follows: First, existing double meiosis frequency detection methods only estimate the double meiosis frequency individually or under limited equilibrium conditions, and more importantly, they do not consider linkage disequilibrium between markers. Second, the newly developed polyploid LD complex model simply uses a linkage disequilibrium parameter to measure the degree of association between multiple alleles at two loci, without considering the complex LD network between multiple alleles at two loci. Third, the patent "A method for constructing a linkage disequilibrium analysis model for a natural population of homotetraploids" does not consider the limitations of current sequencing technology; it develops a linkage disequilibrium analysis model for tetraelements, which is not applicable to current nucleotide polymorphism marker data for diallelic genes. More importantly, existing linkage disequilibrium analysis frameworks for homotetraploids do not consider the influence of double meiosis. Summary of the Invention

[0006] This application provides a method for the joint determination of autotetraploid double meiosis parameters and HWD coefficients, which can solve the problems that existing double meiosis frequency determination methods do not consider the inter-marker linkage disequilibrium phenomenon and existing linkage disequilibrium determination methods do not consider the double meiosis phenomenon.

[0007] The technical solution of this application is a method for the combined determination of autotetraploid double meiotic parameters and HWD coefficients, including:

[0008] S1: Based on the Hardy-Weinberg imbalance of autotetraploids, a single-marker direct parental gamete frequency calculation model is determined, taking into account double meiosis parameters and HWD coefficients.

[0009] Based on the single-marker direct parental gamete frequency calculation model, a joint model of double meiosis and linkage disequilibrium in natural populations of autotetraploids was constructed.

[0010] S2: Based on the log-likelihood function, a joint computational model is constructed for the joint model, with the frequency of gametes from the direct parent generation of the double-labeled generation as the parameter and the frequency of zygotes from the offspring generation of the double-labeled generation as the variable;

[0011] S3: Obtain the actual values ​​of the frequency of zygotes of the two-marked progeny in the natural population, and input the actual values ​​of the frequency of zygotes of the two-marked progeny into the joint calculation model. Based on the EM algorithm, determine the estimated values ​​of the frequency of gametes of the two-marked direct parents in the joint calculation model.

[0012] Based on the estimated values ​​of the gamete frequency of the double-marked direct parent, calculate the estimated value of the gamete frequency of the single-marked direct parent;

[0013] S4: Substitute the estimated value of the single-marked direct parent gamete frequency into the single-marked direct parent gamete frequency calculation model to obtain the nonlinear equations about the double meiosis parameter and the Hardy-Weinberg imbalance coefficient;

[0014] S5: For the nonlinear equation, optimization based on the Barzilai-Borwein step size and Gaussian elimination are performed in sequence to obtain the measured values ​​of the double subtraction parameter and HWD coefficient.

[0015] Optionally, step S1 includes:

[0016] S11: Based on Hardy-Weinberg imbalance, construct a formula for the distribution of single-marker distant parent gamete frequencies in natural populations, including the HWD coefficient;

[0017] S12: Determine the formula for the frequency distribution of single-marker direct-parent zygotes based on the formula for the frequency distribution of single-marker distant-parent gametes;

[0018] S13: Construct a formula for the frequency distribution of single-marker direct parental gametes, including double meiotic parameters;

[0019] Substituting the formula for the frequency distribution of single-marked orthogonal zygotes into the formula for the frequency distribution of single-marked orthogonal gametes, a calculation model for the frequency of single-marked orthogonal gametes is obtained accordingly.

[0020] S14: Based on the linkage disequilibrium between markers in autotetraploids, a joint model of double meiosis and linkage disequilibrium in the natural population of autotetraploids is constructed according to the single-marker direct parental gamete frequency calculation model.

[0021] Optionally, the formula for the frequency distribution of single-marked distant parent gametes is as follows:

[0022] P AA =p 2 +D A ;P Aa =2p(1-p)-2D A ;P aa =(1-p) 2 +D A ;

[0023] P BB =q 2 +D B ;P Bb =2q(1-q)-2D B ;P bb =(1-q) 2 +D B ;

[0024] In the formula, A and a represent a pair of alleles marking SNP1, and B and b represent a pair of alleles marking SNP2.

[0025] D A D represents the HWD coefficient of SNP1; B This represents the HWD coefficient of the SNP2 marker;

[0026] p represents the frequency of gene A, and 1-p represents the frequency of gene a;

[0027] q represents the frequency of gene B, and 1-q represents the frequency of gene b;

[0028] P AA P Aa and P aa This indicates the frequency of gametes from distant parents of the single marker SNP1.

[0029] P BB P Bb and P bb This indicates the frequency of gametes from distant parents of the single-marker SNP2.

[0030] Furthermore, the formula for the frequency distribution of the single-marker orthotopic zygote is as follows:

[0031] P AAAa =2P AA P Aa ; P Aaaa =2P Aa P aa ;

[0032] P BBBb =2P BB P Bb ; P Bbbb =2P Bb P bb ;

[0033] In the formula, P AAAA P AAAa P AAaa P Aaaa and P aaaa P represents the frequency of single-marker orthotopic zygotes of marker SNP1; BBBB P BBBb P BBbb P Bbbb and P bbbb This represents the frequency of the single-marked orthogonal zygote of the SNP2 marker.

[0034] Optionally, the formula for the frequency distribution of single-marked orthotopic gametes is as follows:

[0035]

[0036]

[0037]

[0038]

[0039]

[0040]

[0041] In the formula, Q AA Q Aa and Q aa This indicates the frequency of gametes from the first parent generation of the marker SNP1;

[0042] Q BB Q Bb and Q bb This represents the frequency of single-marker orthotopic gametes of marker SNP2;

[0043] Furthermore, the calculation model for the single-marker orthotopic gamete frequency is as follows:

[0044]

[0045]

[0046]

[0047]

[0048]

[0049]

[0050] Optionally, the combined model of double meiosis and linkage disequilibrium in the natural population of autotetraploids is as follows:

[0051]

[0052]

[0053]

[0054]

[0055]

[0056]

[0057]

[0058]

[0059]

[0060] Δ ab =D AB -D ab D a / b ;Δ ab =D ab +D a / b ;

[0061] In the formula, and Indicates the frequency of double-labeled progeny zygotes;

[0062] D ab It represents the linkage disequilibrium coefficient of two non-allelic genes with the same haplotype at two loci;

[0063] D ab It represents the linkage disequilibrium coefficient of two non-allelic genes with different haplotypes at two loci;

[0064] D Ab The linkage disequilibrium coefficient represents the linkage disequilibrium coefficient between two alleles of marker SNP1 and one allele of marker SNP2;

[0065] D aBThe linkage disequilibrium coefficient represents the linkage disequilibrium coefficient between one allele of marker SNP1 and two alleles of marker SNP2.

[0066] D AB The linkage disequilibrium coefficient represents the two alleles of marker SNP1 and the two alleles of marker SNP2.

[0067] Optionally, the joint computation model is as follows:

[0068]

[0069] In the formula, Λ=(Q l ) indicates the frequency of gametes from the first generation of the double-marked parent;

[0070] l = 1, 2, ..., 9, corresponding to the double-labeled orthoparental gametes AABB, AABb, ..., aabb;

[0071] Q ij Indicates the frequency of double-labeled progeny zygotes;

[0072] i = 1, 2, ..., 5, where i represents the single-marked orthotopic gametes of SNP1, AAAA, AAAa, ..., aaaa;

[0073] j = 1, 2, ..., 5, where j represents the single-marker orthotopic gametes BBBB, BBBB, ..., bbbb of the SNP2 marker.

[0074] Optionally, step S3 includes:

[0075] S31: Obtain the actual numerical value of the frequency of double-labeled progeny zygotes in a natural population;

[0076] S32: Based on the E-step of the EM algorithm, determine the conditional probability of the gametes of the direct parent generation of two-marked children given a progeny zygote;

[0077] The formula for calculating conditional probability is as follows:

[0078]

[0079] In the formula, Q l|ij This represents the conditional probability of the gametes of the bilabeled parent given a bilabeled progeny zygote;

[0080] S33: Based on the M step of the EM algorithm, calculate the estimated value of the gametes of the double-marked progeny based on the actual value of the frequency of the double-marked progeny zygotes and the conditional probability;

[0081] The formula for calculating double-marked orthotopic gametes is shown below:

[0082]

[0083] In the formula, n ij Indicates the number of double-labeled progeny zygotes;

[0084] S34: Calculate the estimated value of the single-marked parental gamete based on the estimated value of the double-marked parental gamete;

[0085] The formula for calculating the frequency of gametes from the direct parent generation is shown below:

[0086]

[0087]

[0088] In the formula, Q AA| Q Aa| and Q aa| This represents the estimated value of the first-parent gamete of the single-marker SNP1;

[0089] Q BB| Q Bb| and Q bb| This represents the estimated value of the single-marked orthoparental gamete of marker SNP2.

[0090] Optionally, it also includes:

[0091] S6: Tests are performed on the dual-labeled progeny zygotes to determine whether double meiosis exists, whether Hardy-Weinberg equilibrium exists, and the degree of linkage disequilibrium, and the likelihood ratios are obtained accordingly.

[0092] The significance of the measured values ​​of the double subtraction parameter and the Hardy-Weinberg imbalance coefficient is determined based on the likelihood ratio.

[0093] Optionally, step S6 includes:

[0094] S61: Perform a hypothesis test on the existence of double subtraction for the double-labeled progeny zygote to obtain several first likelihood ratios;

[0095] The test formulas include, but are not limited to, the following formulas:

[0096] H0: α = 0; H1: α ≠ 0;

[0097] S62: Perform a hypothesis test on the existence of linkage disequilibrium for the double-labeled progeny zygotes to obtain several second likelihood ratios;

[0098] The test formulas include, but are not limited to, the following formulas:

[0099] H2:D A =0; H3:D A ≠0;

[0100] S63: Perform hypothesis testing on the degree of linkage disequilibrium for double-labeled progeny zygotes to obtain several third likelihood ratios;

[0101] The test formulas include, but are not limited to, the following formulas:

[0102] H4:D Ab =0; H5:D Ab ≠0

[0103] S64: For several first likelihood ratios, several second likelihood ratios, and several third likelihood ratios, and the critical value respectively. The sizes are compared, and several comparison results are obtained accordingly;

[0104] Based on several comparison results, the significance of the measured values ​​of the double subtraction parameter or the Hardy-Weinberg imbalance coefficient is determined accordingly.

[0105] Beneficial effects:

[0106] This application establishes a model integrating double meiosis frequency estimation, Hardy-Weinberg equilibrium, and joint detection of linkage disequilibrium between markers. The EM algorithm is developed to estimate the frequencies of different gamete genotypes between two markers. Gaussian elimination is used to solve the linear system equations composed of the frequencies of different gamete genotypes between the two markers and all unknown parameters, simultaneously estimating the frequency of double meiosis and linkage disequilibrium parameters. Computer simulation validation shows that, with a certain sample size, the constructed model can accurately estimate the parameters.

[0107] In summary, this application can solve the problems of existing double meiosis frequency determination methods not considering the linkage disequilibrium phenomenon between markers and existing linkage disequilibrium determination methods not considering the double meiosis phenomenon, thus making up for the shortcomings of current genetic detection technology for autotetraploid populations. Attached Figure Description

[0108] 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.

[0109] Figure 1 This is a flowchart illustrating the method for jointly determining the double meiotic parameter and HWD coefficient of autotetraploids in this application.

[0110] Figure 2 This is a formula logic diagram for distant relatives, direct relatives, and offspring in the embodiments of this application. Detailed Implementation

[0111] 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.

[0112] (I) Example 1

[0113] This application provides a method for the joint determination of autotetraploid double meiotic parameters and HWD coefficients, such as... Figure 1 As shown, Figure 1 This is a schematic flowchart illustrating the method for jointly determining the autotetraploid double meiotic parameter and HWD coefficient in an embodiment of this application, including:

[0114] S1: Based on the Hardy-Weinberg imbalance of autotetraploids, a single-marker direct parental gamete frequency calculation model is determined, taking into account double meiosis parameters and HWD coefficients.

[0115] Based on the single-marker direct parental gamete frequency calculation model, a joint model of double meiosis and linkage disequilibrium in the natural population of autotetraploids was constructed.

[0116] Step S1 includes:

[0117] S11: Based on Hardy-Weinberg disequilibrium, construct a formula for the distribution of single-marker distant parent gamete frequencies in natural populations, including the HWD coefficient.

[0118] The formula for the frequency distribution of gametes from single-marked distant parents is shown below:

[0119] P AA =p 2 +D A ;P Aa =2p(1-p)-2D A ;P aa =(1-p) 2 +D A ;

[0120] P BB =q 2 +D B ;P Bb =2q(1-q)-2D B ;P bb =(1-q) 2 +D B ;

[0121] In the formula, A and a represent a pair of alleles marking SNP1, and B and b represent a pair of alleles marking SNP2.

[0122] D A D represents the HWD coefficient of SNP1; B This represents the HWD coefficient of the SNP2 marker;

[0123] p represents the frequency of gene A, and 1-p represents the frequency of gene a;

[0124] q represents the frequency of gene B, and 1-q represents the frequency of gene b;

[0125] P AA P Aa and P aa This indicates the frequency of gametes from distant parents of the single marker SNP1.

[0126] P BB P Bb and P bb This represents the gamete frequency of the single-marker distant parent of the SNP2 marker.

[0127] S12: Determine the formula for the frequency distribution of single-marker direct-parent zygotes based on the formula for the frequency distribution of single-marker distant-parent gametes.

[0128] The formula for the frequency distribution of single-marked orthotopic zygotes is shown below:

[0129] P AAAa =2P AA P Aa ; P Aaaa =2P Aa P aa ;

[0130] P BBBb =2P BB P Bb ; P Bbbb =2P Bb P bb ;

[0131] In the formula, P AAAA P AAAa、 P AAaa P Aaaa and P aaaa This represents the frequency of the single-marker orthogonal zygote of the SNP1 marker;

[0132] P BBBB P BBBb P BBbb P Bbbband P bbbb This represents the frequency of the single-marked orthogonal zygote of the SNP2 marker.

[0133] S13: Construct a formula for the frequency distribution of single-marker direct parental gametes, including double meiotic parameters;

[0134] Substituting the formula for the frequency distribution of single-marked orthogonal zygotes into the formula for the frequency distribution of single-marked orthogonal gametes, a corresponding calculation model for the frequency of single-marked orthogonal gametes is obtained.

[0135] The formula for the frequency distribution of gametes from single-marked orthotopic offspring is shown below:

[0136]

[0137]

[0138]

[0139]

[0140]

[0141]

[0142] In the formula, Q AA Q Aa and Q aa This indicates the frequency of gametes from the first parent generation of the marker SNP1;

[0143] Q BB Q Bb and Q bb This represents the frequency of single-marker orthotopic gametes of marker SNP2;

[0144] The model for calculating the gamete frequency of a single-marked orthotopic offspring is shown below:

[0145]

[0146]

[0147]

[0148]

[0149]

[0150]

[0151] S14: Based on the linkage disequilibrium between markers in autotetraploids, a joint model of double meiosis and linkage disequilibrium in the natural population of autotetraploids is constructed according to the single-marker direct parental gamete frequency calculation model.

[0152] The combined model of double meiosis and linkage disequilibrium in the natural population of autotetraploids is shown below:

[0153]

[0154]

[0155]

[0156]

[0157]

[0158]

[0159]

[0160]

[0161]

[0162] Δ ab =D AB -D ab D a / b ;Δ ab =D ab +D a / b ;

[0163] In the formula, and Indicates the frequency of double-labeled progeny zygotes;

[0164] D ab It represents the linkage disequilibrium coefficient of two non-allelic genes with the same haplotype at two loci;

[0165] D ab It represents the linkage disequilibrium coefficient of two non-allelic genes with different haplotypes at two loci;

[0166] D Ab The linkage disequilibrium coefficient represents the linkage disequilibrium coefficient between two alleles of marker SNP1 and one allele of marker SNP2;

[0167] D aB The linkage disequilibrium coefficient represents the linkage disequilibrium coefficient between one allele of marker SNP1 and two alleles of marker SNP2.

[0168] D ABThe linkage disequilibrium coefficient represents the two alleles of marker SNP1 and the two alleles of marker SNP2.

[0169] Specifically, it is assumed that double meiosis exists in a natural population of autotetraploids.

[0170] Considering that the marker SNP1 on the homologous tetraploid genome has two alleles, denoted as A and a, it can form three possible diploid gametes: AA, Aa, and aa.

[0171] The marker SNP2 also has two alleles, denoted as B and b, which can form three possible diploid gametes: BB, Bb, and bb.

[0172] For SNP1, three gamete combinations can form five different genotypes (progeny zygotes) including AAAA, AAAa, Aaaa, Aaaa, and aaaa; according to Mendel's first law and the frequency of double meiosis, the frequencies of the five genotypes producing three gametes are shown in Table 1; α represents the double meiosis frequency of the marker SNP1.

[0173] Table 1. Frequency of gametes in SNP1

[0174] AA Aa aa AAAA 1 0 0 AAAa 1 / 2+α / 4 1 / 2-α / 2 α / 4 AAaa 1 / 6+α / 3 2 / 3-2α / 3 1 / 6+α / 3 Aaaa α / 4 1 / 2-α / 2 1 / 2+α / 4 aaaa 0 0 1

[0175] Similarly, the frequencies at which the five genotypes of SNP2, BBBB, BBBb, BBbb, Bbbb, and bbbb, produce the three gametes BB, Bb, and bb, can be obtained, as shown in Table 2; β represents the double subtraction frequency of the marker SNP2.

[0176] Table 2 Frequency of gametes in SNP2

[0177] BB Bb bb BBBB 1 0 0 BBBb 1 / 2+β / 4 1 / 2-β / 2 β / 4 BBbb 1 / 6+β / 3 2 / 3-2β / 3 1 / 6+β / 3 Bbbb β / 4 1 / 2-β / 2 1 / 2+β / 4 bbbb 0 0 1

[0178] like Figure 2 As shown, Figure 2 This is the formula logic diagram for distant relatives, direct relatives, and offspring in the embodiments of this application. For the marker SNP1, it is obtained through Q. AA Q Aa and Q aa The frequency of the three types of gametes (parental gametes) produced by the direct parents in the population is represented by the formula for the frequency distribution of single-marker direct parental gametes labeled SNP1, as shown below:

[0179]

[0180]

[0181]

[0182]

[0183]

[0184]

[0185] In the formula, P AAAA P AAAa P AAaa P Aaaa and P aaaa This represents the frequency of the single-marker orthogonal zygote of the SNP1 marker;

[0186] P BBBB P BBBb P BBbb P Bbbb and P bbbb This represents the frequency of the single-marked orthogonal zygote of the SNP2 marker.

[0187] Similarly, the formula for the frequency distribution of single-marker orthotopic gametes of marker SNP2 can also be obtained.

[0188] The frequencies of the five genotypes in the direct parents of marker SNP1 / SNP2 can be obtained from the gamete frequencies of the distant parents (the generation before the direct parents). The formula for the zygotic frequency distribution of single-marker direct parents is shown below:

[0189] P AAAa =2P AA P Aa ; P Aaaa =2P Aa P aa ;

[0190] P BBBb =2P BB P Bb ; P Bbbb =2P Bb P bb ;

[0191] In marker SNP1 / marker SNP2, regarding the gamete frequency of distant parents, assuming the natural population is in a high-density wing (HWD) state, the two alleles A and a / B and b in SNP1 are not independent. The formula for the gamete frequency distribution of single-marker distant parents is as follows:

[0192] P AA =p 2 +D A ;P Aa=2p(1-p)-2D A ;P aa =(1-p) 2 +D A ;

[0193] P BB =q 2 +D B ;P Bb =2q(1-q)-2D B ;P bb =(1-q) 2 +D B ;

[0194] In the formula, A and a represent a pair of alleles marking SNP1, and B and b represent a pair of alleles marking SNP2;

[0195] p represents the frequency of gene A, and 1-p represents the frequency of gene a;

[0196] q represents the frequency of gene B, and 1-q represents the frequency of gene b;

[0197] P AA P Aa and P aa This indicates the frequency of gametes from distant parents of the single marker SNP1.

[0198] P BB P Bb and P bb This indicates the frequency of gametes from distant parents of the single-marker SNP2.

[0199] D A D represents the HWD coefficient of SNP1; B This represents the HWD coefficient of the SNP2 label.

[0200] By substituting the formulas for the frequency distribution of gametes from distant parents and zygotes from direct parents into the formula for the frequency distribution of gametes from direct parents, we can obtain the general formulas for the frequencies of the three gametes of marker SNP1, including the double meiotic division frequency and the HWD coefficient. The formula for the frequency distribution of gametes from direct parents is shown below:

[0201]

[0202]

[0203]

[0204]

[0205]

[0206]

[0207] Considering the linkage disequilibrium between SNP1 and SNP2, and drawing on the definition of linkage disequilibrium in allotetraploids, this application defines the frequency representation of different gamete genotypes between two markers in autotetraploids as a joint model of double meiosis and linkage disequilibrium in a natural autotetraploid population. The joint model is shown below:

[0208]

[0209]

[0210]

[0211]

[0212]

[0213]

[0214]

[0215]

[0216]

[0217] Δ ab =D AB -D ab D a / b ;Δ ab =D ab +D a / b ;

[0218] In the formula, and Indicates the frequency of double-labeled progeny zygotes;

[0219] D ab It represents the linkage disequilibrium coefficient of two non-allelic genes with the same haplotype at two loci;

[0220] D ab It represents the linkage disequilibrium coefficient of two non-allelic genes with different haplotypes at two loci;

[0221] D Ab The linkage disequilibrium coefficient represents the linkage disequilibrium coefficient between two alleles of marker SNP1 and one allele of marker SNP2;

[0222] D aB The linkage disequilibrium coefficient represents the linkage disequilibrium coefficient between one allele of marker SNP1 and two alleles of marker SNP2.

[0223] D AB The linkage disequilibrium coefficient represents the two alleles of marker SNP1 and the two alleles of marker SNP2.

[0224] S2: Based on the log-likelihood function, a joint computational model is constructed for the joint model, with the frequency of gametes from the direct parent generation of the double-labeled generation as the parameter and the frequency of zygotes from the offspring generation of the double-labeled generation as the variable.

[0225] The joint computation model is shown below:

[0226]

[0227] In the formula, Λ=(Q l ) indicates the frequency of gametes from the first generation of the double-marked parent;

[0228] l = 1, 2, ..., 9, corresponding to the double-labeled orthoparental gametes AABB, AABb, ..., aabb;

[0229] Q ij Indicates the frequency of double-labeled progeny zygotes;

[0230] i = 1, 2, ..., 5, where i represents the single-marked orthotopic gametes of SNP1, AAAA, AAAa, ..., aaaa;

[0231] j = 1, 2, ..., 5, where j represents the single-marker orthotopic gametes BBBB, BBBB, ..., bbbb of the SNP2 marker.

[0232] S3: Obtain the actual values ​​of the frequency of zygotes of the two-marked progeny in the natural population, and input the actual values ​​of the frequency of zygotes of the two-marked progeny into the joint calculation model. Based on the EM algorithm, determine the estimated values ​​of the frequency of gametes of the two-marked direct parents in the joint calculation model.

[0233] Based on the estimated values ​​of the gamete frequency of the double-marked orthotopic generation, the estimated values ​​of the gamete frequency of the single-marked orthotopic generation are calculated.

[0234] Step S3 includes:

[0235] S31: Obtain the actual numerical value of the frequency of double-labeled progeny zygotes in a natural population.

[0236] Specifically, the frequency of the double-labeled progeny zygotes was determined according to Table 3.

[0237] Table 3. Frequency of double-marked progeny zygotes

[0238]

[0239] S32: Based on the E-step of the EM algorithm, determine the conditional probability of the gametes of the direct parent generation of two-marked children given a progeny zygote;

[0240] The formula for calculating conditional probability is as follows:

[0241]

[0242] In the formula, Q l|ij This represents the conditional probability of the gametes of the bilabeled parent given a bilabeled progeny zygote;

[0243] S33: Based on the M step of the EM algorithm, calculate the estimated value of the gametes of the double-marked progeny based on the actual value of the frequency of the double-marked progeny zygotes and the conditional probability;

[0244] The formula for calculating double-marked orthotopic gametes is shown below:

[0245]

[0246] In the formula, n ij Indicates the number of double-labeled progeny zygotes;

[0247] S34: Calculate the estimated value of the single-marked parental gamete based on the estimated value of the double-marked parental gamete;

[0248] The formula for calculating the frequency of gametes from the direct parent generation is shown below:

[0249]

[0250]

[0251] In the formula, Q AA| Q Aa| and Q aa| This represents an estimated value for the single-marked orthoparental gamete of marker SNP1;

[0252] Q BB| Q Bb| and Q bb| This represents the estimated value of the single-marked orthoparental gamete of marker SNP2.

[0253] S4: Substitute the estimated value of the single-marked orthoparent gamete frequency into the single-marked orthoparent gamete frequency calculation model to obtain the nonlinear equations regarding the double meiosis parameter and the Hardy-Weinberg imbalance coefficient.

[0254] S5: For the nonlinear equation, optimization based on the Barzilai-Borwein step size and Gaussian elimination are performed in sequence to obtain the measured values ​​of the double subtraction parameter and HWD coefficient.

[0255] S6: Tests are performed on the dual-labeled progeny zygotes to determine whether double meiosis exists, whether Hardy-Weinberg equilibrium exists, and the degree of linkage disequilibrium, and the likelihood ratios are obtained accordingly.

[0256] The significance of the measured values ​​of the double subtraction parameter and the Hardy-Weinberg imbalance coefficient is determined based on the likelihood ratio.

[0257] Step S6 includes:

[0258] S61: Perform a hypothesis test on the existence of double subtraction for the double-labeled progeny zygote to obtain several first likelihood ratios;

[0259] The test formulas include, but are not limited to, the following formulas:

[0260] H0: α = 0; H1: α ≠ 0;

[0261] S62: Perform a hypothesis test on the existence of linkage disequilibrium for the double-labeled progeny zygotes to obtain several second likelihood ratios;

[0262] The test formulas include, but are not limited to, the following formulas:

[0263] H2:D A =0; H3:D A ≠0;

[0264] S63: Perform hypothesis testing on the degree of linkage disequilibrium for double-labeled progeny zygotes to obtain several third likelihood ratios;

[0265] The test formulas include, but are not limited to, the following formulas:

[0266] H4:D Ab =0; H5:D Ab ≠0

[0267] S64: For several first likelihood ratios, several second likelihood ratios, and several third likelihood ratios, and the critical value respectively. The sizes are compared, and several comparison results are obtained accordingly;

[0268] Based on several comparison results, the significance of the measured values ​​of the double subtraction parameter or the Hardy-Weinberg imbalance coefficient is determined accordingly.

[0269] Specifically, within the framework of maximum likelihood, the significance of the parameters of the joint model is tested using the maximum likelihood ratio test, the linkage disequilibrium parameters are standardized, and the accuracy of the parameter estimation of the joint model is tested through computer simulation, thereby determining the power and false positives of the detection method.

[0270] (II) Experimental Verification

[0271] To verify the accuracy of parameter estimation of the joint model under different samples, computer simulation was used for evaluation, with the allele frequencies of A and B for SNP1 and SNP2 set as p = 0.5 and q = 0.55, respectively.

[0272] Table 4 lists the accuracy and statistical power of the parameter estimation for the constructed joint detection method, with the true value in parentheses for each parameter. Table 4 shows that as the sample size increases, the standard deviation of the estimated parameters decreases continuously, and the accuracy of the parameter estimation continuously improves. The power of the double subtraction frequency parameter is relatively small with a sample size of 100, not reaching above 30%, but the power of other parameters is above 60%.

[0273] When the sample size reaches 400, the estimation power of the double subtraction frequency parameter is above 85%, and the power of the Hardy Weinberg parameter and the linkage disequilibrium parameter of the two labels is above 90%. This indicates that the power of the joint detection model can be guaranteed when the sample size is 400.

[0274] Table 4. Accuracy and power of parameter estimation for the joint detection model

[0275]

[0276] Notes: MLE: Maximum Likelihood Estimation; Power: Efficacy; Δ ab＝ D ab +2D a / b .

[0277] The embodiments of this application have been described in detail above, but the content is only a preferred embodiment of this application and should not be considered as limiting the scope of this application. All equivalent changes and improvements made within the scope of this application should still fall within the patent coverage of this application.

Claims

1. A method for jointly determining the double meiotic parameter and HWD coefficient of autotetraploids, characterized in that, include: S1: Based on the Hardy-Weinberg imbalance of autotetraploids, a single-marker direct parental gamete frequency calculation model is determined, taking into account double meiosis parameters and HWD coefficients. Based on the single-marker direct parental gamete frequency calculation model, a joint model of double meiosis and linkage disequilibrium in natural populations of autotetraploids was constructed. S2: Based on the log-likelihood function, a joint computational model is constructed for the joint model, with the frequency of gametes from the direct parent generation of the double-labeled generation as the parameter and the frequency of zygotes from the offspring generation of the double-labeled generation as the variable; S3: Obtain the actual values ​​of the frequency of zygotes of the two-marked progeny in the natural population, and input the actual values ​​of the frequency of zygotes of the two-marked progeny into the joint calculation model. Based on the EM algorithm, determine the estimated values ​​of the frequency of gametes of the two-marked direct parents in the joint calculation model. Based on the estimated values ​​of the gamete frequency of the double-marked direct parent, calculate the estimated value of the gamete frequency of the single-marked direct parent; S4: Substitute the estimated value of the single-marked direct parent gamete frequency into the single-marked direct parent gamete frequency calculation model to obtain the nonlinear equations about the double meiosis parameter and the Hardy-Weinberg imbalance coefficient; S5: For the nonlinear equation, optimization based on the Barzilai-Borwein step size and Gaussian elimination are performed in sequence to obtain the measured values ​​of the double subtraction parameter and HWD coefficient. Step S1 includes: S11: Based on Hardy-Weinberg imbalance, construct a formula for the distribution of single-marker distant parent gamete frequencies in natural populations, including the HWD coefficient; S12: Determine the formula for the frequency distribution of single-marker direct-parent zygotes based on the formula for the frequency distribution of single-marker distant-parent gametes; S13: Construct a formula for the frequency distribution of single-marker direct parental gametes, including double meiotic parameters; Substituting the formula for the frequency distribution of single-marked orthogonal zygotes into the formula for the frequency distribution of single-marked orthogonal gametes, a calculation model for the frequency of single-marked orthogonal gametes is obtained accordingly. S14: Based on the linkage disequilibrium between markers in autotetraploids, a joint model of double meiosis and linkage disequilibrium in the natural population of autotetraploids is constructed according to the single-marker direct parental gamete frequency calculation model. The joint computation model is shown below: ; In the formula, Indicates the frequency of gametes from the first parent generation of the double-marked parent; Correspondingly, this indicates the double-marked direct parental gametes. AABB , AABb , ..., aabb ; Indicates the frequency of double-labeled progeny zygotes; , This indicates a single-marked orthotopic gamete of marker SNP1. AAAA , AAAa , ..., aaaa ; , This indicates a single-marked orthotopic gamete of marker SNP2. BBBB , BBBb , ..., bbbb .

2. The method for jointly determining the double meiotic parameter and HWD coefficient of autotetraploids according to claim 1, characterized in that, The formula for the frequency distribution of single-marker distant parent gametes is as follows: ； ； ； ； ； ； In the formula, and This represents a pair of alleles that mark SNP1. and This represents a pair of alleles that mark SNP2; This represents the HWD coefficient of the SNP1 marker; This represents the HWD coefficient of the SNP2 marker; Indicates gene frequency, Indicates gene The frequency; Indicates gene frequency, Indicates gene The frequency; , and This indicates the frequency of gametes from distant parents of the single marker SNP1. , and This indicates the frequency of gametes from the distant parent of the marker SNP2; Furthermore, the formula for the frequency distribution of the single-marker orthotopic zygote is as follows: ； ； ； ； ； ； ； ； ； ； In the formula, , , , and This represents the frequency of the single-marker orthogonal zygote of the SNP1 marker; , , , and This represents the frequency of the single-marked orthogonal zygote of the SNP2 marker.

3. The method for jointly determining the double meiotic parameter and HWD coefficient of autotetraploids according to claim 2, characterized in that, The formula for the frequency distribution of single-marked orthotopic gametes is shown below: ； ； ； ； ； ； In the formula, , and This indicates the frequency of gametes from the first parent generation of the marker SNP1; , and This represents the frequency of single-marker orthotopic gametes of marker SNP2; Furthermore, the calculation model for the single-marker orthotopic gamete frequency is as follows: ； ； ； ； ； 。 4. The method for jointly determining the double meiotic parameter and HWD coefficient of autotetraploids according to claim 3, characterized in that, The combined model of double meiosis and linkage disequilibrium in the natural population of autotetraploids is shown below: ； ； ； ； ； ； ； ； ； ； In the formula, , , , , , , and Indicates the frequency of double-labeled progeny zygotes; D ab It represents the linkage disequilibrium coefficient of two non-allelic genes with the same haplotype at two loci; D ab It represents the linkage disequilibrium coefficient of two non-allelic genes with different haplotypes at two loci; D Ab The linkage disequilibrium coefficient represents the linkage disequilibrium coefficient between two alleles of marker SNP1 and one allele of marker SNP2; D aB The linkage disequilibrium coefficient represents the linkage disequilibrium coefficient between one allele of marker SNP1 and two alleles of marker SNP2. D AB The linkage disequilibrium coefficient represents the two alleles of marker SNP1 and the two alleles of marker SNP2.

5. The method for jointly determining the double meiotic parameter and HWD coefficient of autotetraploids according to claim 1, characterized in that, Step S3 includes: S31: Obtain the actual numerical value of the frequency of double-labeled progeny zygotes in a natural population; S32: Based on the E-step of the EM algorithm, determine the conditional probability of the gametes of the direct parent generation of two-marked children given a progeny zygote; The formula for calculating conditional probability is as follows: ; In the formula, This represents the conditional probability of the gametes of the bilabeled parent given a bilabeled progeny zygote; S33: Based on the M step of the EM algorithm, calculate the estimated value of the gametes of the double-marked progeny based on the actual value of the frequency of the double-marked progeny zygotes and the conditional probability; The formula for calculating double-marked orthotopic gametes is shown below: ; In the formula, Indicates the number of double-labeled progeny zygotes; S34: Calculate the estimated value of the single-marked parental gamete based on the estimated value of the double-marked parental gamete; The formula for calculating the frequency of gametes from the direct parent generation is shown below: ； ； ； ； ； ； , and This represents the estimated value of the single-marked orthoparental gamete of marker SNP2.

6. The method for jointly determining the double meiotic parameter and HWD coefficient of autotetraploids according to claim 1, characterized in that, Also includes: S6: Tests are performed on the dual-labeled progeny zygotes to determine whether double meiosis exists, whether Hardy-Weinberg equilibrium exists, and the degree of linkage disequilibrium, and the likelihood ratios are obtained accordingly. The significance of the measured values ​​of the double subtraction parameter and the Hardy-Weinberg imbalance coefficient is determined based on the likelihood ratio.

7. The method for jointly determining the double meiotic parameter and HWD coefficient of autotetraploids according to claim 6, characterized in that, Step S6 includes: S61: Perform a hypothesis test on the existence of double subtraction for the double-labeled progeny zygote to obtain several first likelihood ratios; The test formulas include, but are not limited to, the following formulas: ； ； S62: Perform a hypothesis test on the existence of linkage disequilibrium for the double-labeled progeny zygotes to obtain several second likelihood ratios; The test formulas include, but are not limited to, the following formulas: ； ； S63: Perform hypothesis testing on the degree of linkage disequilibrium for double-labeled progeny zygotes to obtain several third likelihood ratios; The test formulas include, but are not limited to, the following formulas: ； ； S64: For several first likelihood ratios, several second likelihood ratios, and several third likelihood ratios, and the critical value 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 double subtraction parameter or the Hardy-Weinberg imbalance coefficient is determined accordingly.

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