CN108197435A - Localization method between a kind of multiple characters multi-region for containing error based on marker site genotype - Google Patents
Localization method between a kind of multiple characters multi-region for containing error based on marker site genotype Download PDFInfo
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Abstract
The present invention provides localization method between a kind of multiple characters multi-region for containing error based on marker site genotype, including：Obtain molecular genetic linkage map；Determine the recombination fraction γ between i-th of marker interval both sides labeliAnd the recombination fraction γ in i-th of marker interval between QTL and upper marker sitei1；Recombination fraction γ between being marked according to i-th of marker interval both sidesiAnd the recombination fraction γ in i-th of marker interval between QTL and upper marker sitei1Generate marker genetype and QTL genotype；Marker genetype containing error is obtained according to the error rate of configuration；Parameter true value is configured；Phenotypic character observed value is obtained by model；Initial parameter values are configured；The parameter expression that EM algorithmic derivations go out is iterating through until convergence；Repetitive cycling n times obtain parameter Estimation average value and mean square error as desired value.The present invention can solve marker gene information and contain error this problem, and can estimate the error rate of marker gene information.
Description
Technical field
The invention belongs to technical field of molecular biology, contain error based on marker site genotype more particularly to one kind
Multiple characters multi-region between localization method.
Background technology
The genetic disease and crops phenotypic character of the mankind is nearly all related with gene, for a long time, in order to study
Convenient, most of research ignore-tag genotype contain the situation of error.But due to measure of precision of instrument etc., base is marked
Because of information, often there are errors.In order to prevent the generation of genetic disease, and also to preferably utilize having in germ plasm resource
Niche is because of a kind of, it is proposed that new QTL localization methods.The analysis method can be very good solution marker genetype and contain error
Multiple characters assignment of genes gene mapping problem.
Invention content
The present invention can solve marker gene information and contain error this problem, and can estimate marker gene information
Error rate.So that people, under known phenotypic number and marker gene information condition containing error, estimation influences phenotypic character
QTL numbers, position and effect it is more accurate.
Following method may be used to realize in the present invention：
Localization method between a kind of multiple characters multi-region for containing error based on marker site genotype, including：
Step 1: obtain molecular genetic linkage map；
Step 2: determine the recombination fraction γ between i-th of marker interval both sides labeliWith QTL in i-th of marker interval
Recombination fraction γ between upper marker sitei1；
Step 3: according to the recombination fraction γ between the label of i-th of marker interval both sidesiIn i-th of marker interval
Recombination fraction γ between QTL and upper marker sitei1Generate marker genetype and QTL genotype；
Step 4: the marker genetype containing error is obtained according to the error rate of configuration；
Step 5: configuration parameter true value；
Step 6: phenotypic character observed value is obtained by model；
Step 7: configuration initial parameter values；
Step 8: the parameter expression that EM algorithmic derivations go out is iterating through until convergence；
Step 9: repetitive cycling n times obtain parameter Estimation average value and mean square error as desired value.
Further, it is described that phenotypic character observed value is obtained by model, specifically by statistical modelPhenotypic character observed value is obtained, wherein,It is phenotypic character matrix, q is the q of close linkage
A section,WithRepresent i-th of the QTL genotype property shown vector of n individual respectively, then,
ξji=1, ηji=-1/2, when
ξji=0, ηji=1/2, when
ξji=-1, ηji=-1/2, when
ai=(ai1,ai2...ait) and di=(di1,di2...dit) represent that i-th of QTL adds t phenotypic character respectively
Property effect and dominant effect vector；E={ eji}n×tFor residual matrix, e herejiBe j-th of individual, i-th phenotypic characteristic with
Chance error is poor, mean value 0, cov (eji,ejl)=σil=ρ σiσl, i, l=1 ..., t.
Further, the QTL that i-th of QTL forms the additive effect and dominant effect vector of t phenotypic character is imitated
The matrix is answered to be
To sum up, following method may be used to realize in the present invention：
Localization method between a kind of multiple characters multi-region for containing error based on marker site genotype, including：Step 1: it obtains
Molecular genetic linkage map；Step 2: determine the recombination fraction γ between i-th of marker interval both sides labeliWith i-th of marker interval
Recombination fraction γ between interior QTL and upper marker sitei1；Step 3: according to the weight between the label of i-th of marker interval both sides
Group rate γiAnd the recombination fraction γ in i-th of marker interval between QTL and upper marker sitei1Generate marker genetype and QTL genes
Type；Step 4: the marker genetype containing error is obtained according to the error rate of configuration；Step 5: configuration parameter true value；Step
6th, phenotypic character observed value is obtained by model；Step 7: configuration initial parameter values；Go out Step 8: being iterating through EM algorithmic derivations
Parameter expression until convergence；Step 9: repetitive cycling n times obtain parameter Estimation average value and mean square error as target
Value.
It has the beneficial effect that：
1. considering marker site genotype contains error, positioning is more accurate.
2. the instrument precision degree of label information is obtained without preferably, saving cost.
3. give the parameter Estimation of marker site genotype error rate.
Description of the drawings
Fig. 1 localization methods between the multiple characters multi-region provided by the invention for containing error based on marker site genotype are random
Model configuration figure；
Fig. 2 is the valuation of QTL effects and square mean error amount schematic diagram under different genetic force；
Fig. 3 is recombination fraction and covariance matrix evaluation schematic diagram under different genetic force；
Fig. 4 is the QTL positioning results that gall stone is formed.
Specific embodiment
The present invention gives localization methods between a kind of multiple characters multi-region for containing error based on marker site genotype to implement
Example, in order to which those skilled in the art is made to more fully understand the technical solution in the embodiment of the present invention, and make the present invention it is above-mentioned
Objects, features and advantages can be more obvious understandable, technical solution in the present invention is made below in conjunction with the accompanying drawings further details of
Explanation：
Present invention firstly provides localization method between a kind of multiple characters multi-region for containing error based on marker site genotype,
As shown in Figure 1, including：
S101, Step 1: obtain molecular genetic linkage map；
Data in the present embodiment come from the works of Wittenburg et al.2003, this data set includes 305
F2 filial generations.Phenotypic data selects gall stone (gallstone) weight and high-density lipoprotein (High-density
Lipoprotein), label D4Mit31 and D4Mit126 is located at No. 4 chromosomes 51.3cM, 71cM respectively, marks D10Mit66
It is located at No. 10 chromosomes 49cM, 62cM respectively with D10Mit34,4 marker sites form two marker intervals.
S102, Step 2: determining the recombination fraction γ between the label of i-th marker interval both sidesiWith i-th of marker interval
Recombination fraction γ between interior QTL and upper marker sitei1；
Where it is assumed that F2At most there are one QTL, j-th of individual i-th of marker intervals for each marker interval of group
When known, QTL genotype in marker intervalConditional probabilityIt is shown in Table 1.
The conditional probability of QTL genotype under 1 marker genetype known case of table
ri=γi1/γi
S103, Step 3: configuration initial parameter values；
Step 4: the parameter expression that EM algorithmic derivations go out is iterating through until convergence, obtains estimates of parameters as most
Result afterwards.
Preferably, the statistical model isWherein,It is phenotypic character matrix, q
For q section of close linkage,WithRepresent i-th of the QTL genotype property shown vector of n individual respectively, then,
ξji=1, ηji=-1/2, when
ξji=0, ηji=1/2, when
ξji=-1, ηji=-1/2, when
ai=(ai1,ai2...ait) and di=(di1,di2...dit) represent that i-th of QTL adds t phenotypic character respectively
Property effect and dominant effect vector；E={ eji}n×tFor residual matrix, e herejiBe j-th of individual, i-th phenotypic characteristic with
Chance error is poor, mean value 0, cov (eji,ejl)=σil=ρ σiσl, i, l=1 ..., t.
Preferably, the QTL effects that i-th of QTL forms the additive effect and dominant effect vector of t phenotypic character
Matrix is
Wherein, based on EM algorithms, detailed deduction is given for parameter Ω=(C, Σ, γ, θ) in the present embodiment.Tool
Body is as follows：
Deduction in relation to likelihood function, the complete likelihood function about parameter vector Ω can be expressed as form
Its complete log-likelihood function is
Here Yj=(Yj1,...,Yjt), Xj=(Xj1,...,Xj(q+1)),
Wherein Yji(j-th of individual i-th of phenotypic character value of j=1 ..., n, i=1 ..., t) expression, Xji(j=1 ..., n, i=
1 ..., q+1) andThe marker genetype of j-th of individual, i-th of label is represented respectively and is contained
The marker genetype of error,Represent the QTL genotype in j-th of individual i-th of marker interval.
Further it is calculated as in relation to Q functions,
Further it is calculated as in relation to posterior probability,
Further enable
HereRepresent Xj,Yj,Ω(s)Under the conditions ofK-th of value conditional probability.It enables
It represents genotype error rate, further enablesRepresent the joint error rate of j-th of individual.In every single-step iteration, when true
Genotype XjA given value is compared to genotypeWrong gene code number k in q+1 marker sitejIt is that can calculate
's.
By the iteration expression formula for being derived from QTL effect Matrix Cs：
Here R(s)And M(s)Expression formula be
Here # represents two vectorial Hadamard products.The iterative formula of Σ is：
It is n × 3qMatrix, D=(D1,D2,D3,...,Dcq), consider additive effect and dominant effect
When c=2.
As c=2
The indicative function of marker interval where enabling QTL genotype and genotypeWith following formula
Here j=1 ..., n, i=1 ..., q.The dominant of recombination fraction γ can be obtained by indicative function above and Q functions
Expression formula
Error rate θ Explicit functions can be derived by Q functions
The testing result that Fig. 4 is provided is shown at No. 10 chromosome 56cM and there is influence courage knot at No. 4 chromosome 62cM
The QTL of stone weight and high-density lipoprotein (HDL).QTL is formed with inhibiting effect to gall stone at 56cM, to high-density lipoprotein
(HDL) there is facilitation.QTL is formed with facilitation to gall stone at 62cM, has inhibition to make to high-density lipoprotein (HDL)
With.
Localization method between a kind of multiple characters multi-region for containing error based on marker site genotype of the present invention, including：Step
First, molecular genetic linkage map is obtained；Step 2: determine the recombination fraction γ between i-th of marker interval both sides labeliWith i-th
Recombination fraction γ in marker interval between QTL and upper marker sitei1；Step 3: it is marked according to i-th of marker interval both sides
Between recombination fraction γiAnd the recombination fraction γ in i-th of marker interval between QTL and upper marker sitei1Generate marker genetype
With QTL genotype；Step 4: the marker genetype containing error is obtained according to the error rate of configuration；Step 5: configuration parameter is true
Value；Step 6: phenotypic character observed value is obtained by model；Step 7: configuration initial parameter values；Step 8: it is iterating through EM calculations
The parameter expression that method is derived is until convergence；Step 9: repetitive cycling n times obtain the average value and mean square error of parameter Estimation
As desired value.
The present invention can solve marker gene information and contain error this problem, and can estimate marker gene information
Error rate.So that people's estimation under known phenotypic number and marker gene information condition containing error influences phenotypic character
QTL (quantitative trait locus) number, position and effect are more accurate, and the present invention utilizes F2 group expansions using QTL plotting techniques
Quantitative Trait Genes position, and create a kind of new method of QTL Position Research when containing error based on marker genetype, enrich
QTL Position Research improves accuracy, the reliability of QTL Position Research when marker genetype contains error, will accelerate QTL
Position Research process.
It is localization method between a kind of multiple characters multi-region for containing error based on marker site provided by the present invention above
One specific example, example are merely used to help understand the method and its core concept of the present invention, and the content of the present specification should not manage
It solves as limitation of the present invention.Those skilled in the art goes out or associates from present disclosure direct derivation and is all
Flexible situation, is considered protection scope of the present invention.
Claims (3)
1. a kind of localization method between multiple characters multi-region for containing error based on marker site genotype, which is characterized in that including：
Step 1: obtain molecular genetic linkage map；
Step 2: determine the recombination fraction γ between i-th of marker interval both sides labeliWith QTL in i-th of marker interval with it is upper
Recombination fraction γ between marker sitei1；
Step 3: according to the recombination fraction γ between the label of i-th of marker interval both sidesiWith QTL in i-th of marker interval with
Recombination fraction γ between upper marker sitei1Generate marker genetype and QTL genotype；
Step 4: the marker genetype containing error is obtained according to the error rate of configuration；
Step 5: configuration parameter true value；
Step 6: phenotypic character observed value is obtained by model；
Step 7: configuration initial parameter values；
Step 8: the parameter expression that EM algorithmic derivations go out is iterating through until convergence；
Step 9: repetitive cycling n times obtain parameter Estimation average value and mean square error as desired value.
2. contain localization method between the multiple characters multi-region of error, feature based on marker site genotype as described in claim 1
It is, it is described that phenotypic character observed value is obtained by model, specifically by statistical model
Phenotypic character observed value is obtained, wherein,It is phenotypic character matrix, q is q section of close linkage,WithN is represented respectively
Individual i-th of QTL genotype property shown vector, then,
When
When
When
ai=(ai1,ai2...ait) and di=(di1,di2...dit) represent that i-th of QTL imitates the additivity of t phenotypic character respectively
It should be with dominant effect vector；E={ eji}n×tFor residual matrix, ejiIt is the random error of j-th of individual i-th of phenotypic characteristic,
It is worth for 0, cov (eji,ejl)=σil=ρ σiσl, i, l=1 ..., t.
3. contain localization method between the multiple characters multi-region of error based on marker site genotype as claimed in claim 3, it is special
Sign is, the QTL effect matrixes that i-th of QTL forms the additive effect and dominant effect vector of t phenotypic character are
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Cited By (3)
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| CN109326322A (en) * | 2018-08-17 | 2019-02-12 | 华中科技大学 | The method and system that QTL compares between a kind of crop difference segregating population |
| CN109493919A (en) * | 2018-10-31 | 2019-03-19 | 中国石油大学(华东) | Genotype assigning method based on conditional probability |
| CN113779502A (en) * | 2021-08-20 | 2021-12-10 | 绥化学院 | Image processing evidence function estimation method based on correlation vector machine |
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| CN113779502B (en) * | 2021-08-20 | 2023-08-29 | 绥化学院 | Image processing evidence function estimation method based on correlation vector machine |
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