CN105104306A - Animal apolegamy method - Google Patents

Abstract

The invention discloses an animal apolegamy method. A filial generation inbreeding coefficient matrix is built according to a herd pedigree, a pairing matrix is built according to the number of female breeding stocks and the number of male breeding stocks, inbreeding coefficient minimization is taken as an optimization objective, a constraint condition is built from a female stock heredity angle and a male stock heredity angle, and a linear programming equation is obtained and solved to obtain an optimal pairing combination and the breeding stocks. Accordingly, the problems that through an existing apolegamy method, the inbreeding coefficient changes of a herd cannot be predicted, and the breed conservation practice cannot be precisely guided are solved, continuous heredity monitoring can be performed on an animal breed conservation group, deviations in the breed conservation practice can be found in time, and a basis is supplied for taking improvement measures in time and continuously improving the breed conservation effect.

Description

A kind of animal matching method

Technical field

The present invention relates to animal breeding field, particularly relate to a kind of animal matching method.

Background technology

The optimization of animal varieties is the important foundation maintaining bio-diversity and the ecological balance, also can be animal breeding in the future and provides material, the gene of the specific trait needed for laying in the future.Consider from genetics angle, the optimization of animal varieties is exactly the optimization to animal gene.Because gene is the basic function unit of genetic variation, any proterties is all by gene-determined, so the extinction of kind is exactly the forfeiture of gene in fact.Existing animal varieties protected mode major part is live population, and be microcommunity live population, it is subject to Natural selection pressure is inevitable, so require that the colony of live population is large, prevent inbreeding, otherwise easily cause genetic drift, gene is lost, inbreeding coefficient increases, and causes inbreeding depression, and even colony degenerates or extinction; Therefore, on the basis of certain population size, how to control inbreeding coefficient and just seem particularly important.

In the colony that a locking is bred, the increase of inbreeding coefficient is inevitable, controls and reduces the average inbreeding coefficient of colony mainly through having matched; Existing common practice is: random mating, avoids full sibs, half sibs to match in conservation group, or adopt non-near hand over to the collective or the state poultry samsara breeding.Even if but adopt above-mentioned existing common practice, or can not the average inbreeding coefficient increment of next generation population of Accurate Prediction, and the average inbreeding coefficient of colony after some generations, also conservation just can not be instructed to put into practice, introduce outer blood as to when, so a practicable animal matingplan must be set up, lasting genetic monitoring is carried out to animal conservation group, deviation in the practice of Timeliness coverage conservation, provides foundation for taking corrective measure in time and improving constantly effect of breeds conservation.

The technical problem that the invention mainly solves has: according to different matingplans, the average inbreeding coefficient of next generation population of Accurate Prediction; According to existing population size, structure and inbreeding coefficient, according to existing general mode of reserving seed for planting, namely each family equivalent is reserved seed for planting, when each is reserved seed for planting from generation to generation, and a male animal of selecting and remain in each male animal offspring, the number dam such as to select and remain in each dam offspring, adopt Zero-one integer programming method, determine optimum matingplan, namely determine each male animal with join dam, each dam with join male animal, thus average for next generation population inbreeding coefficient is controlled at floor level; After next generation population is reserved seed for planting and determined, adopt said method, work out next generation population matching method, predict the average inbreeding coefficient of next generation population, by that analogy, the average inbreeding coefficient of locking breeding populations after some generations can be predicted.

Summary of the invention

Goal of the invention: in order to overcome the deficiencies in the prior art, the invention provides a kind of animal matching method, reduces the average inbreeding coefficient of colony, realizes the optimization of kind.

Technical scheme: for achieving the above object, animal matching method of the present invention, comprises the following steps:

(1) set up colony's additive inheritance correlation matrix according to drove pedigree, described entry of a matrix element is the inbreeding coefficient of corresponding row or column domestic animals;

(2) according to kind dam number k and the sire number n of setting, filial generation inbreeding coefficient matrix is set up according to described additive inheritance correlation matrix;

(3) pairing matrix is set up according to described kind of dam number and described sire number;

(4) according to described filial generation inbreeding coefficient matrix and described pairing matrix, minimum as optimization aim using the filial generation inbreeding coefficient F of combinations of pairs, set up constraints from the angle of dam heredity, obtain the first linear programming equation and carry out solving obtaining optimum male and female poultry combinations of pairs and filial generation kind dam.

Further, according to described filial generation inbreeding coefficient matrix and described pairing matrix, minimum as optimization aim using the filial generation inbreeding coefficient F of combinations of pairs, set up constraints from the angle of male animal heredity, obtain the second linear programming equation and carry out solving obtaining filial generation sire.

Wherein, described in step (4), the first linear programming equation is:

Object function: $F=\underset{i=1}{\overset{k}{\Σ}}\underset{j=1}{\overset{n}{\Σ}}{F}_{ij}{A}_{ij}$

Constraints:

$\underset{j=1}{\overset{n}{\Σ}}{A}_{ij}=1,1\≤i\≤k$

$\underset{i=1}{\overset{k}{\Σ}}{A}_{ij}=k/n,1\≤j\≤n$

F _ijfor the element in filial generation inbreeding coefficient matrix, A _ijfor the element in pairing matrix, i represents i-th dam, and j represents a jth male animal.

Wherein, described in step (5), the second linear programming equation is:

Object function: $F=\underset{i=1}{\overset{k}{\Σ}}\underset{j=1}{\overset{n}{\Σ}}{F}_{ij}{A}_{ij}$

Constraints:

$\underset{j=1}{\overset{n}{\Σ}}{A}_{ij}\≤1,1\≤i\≤k$

$\underset{i=1}{\overset{k}{\Σ}}{A}_{ij}=1,1\≤j\≤n$

F _ijfor the element in inbreeding coefficient matrix, A _ijfor the element in pairing matrix, i represents i-th dam, and j represents a jth male animal.

Beneficial effect: animal matching method of the present invention, the pairing of energy efficient combination male and female poultry, the average inbreeding coefficient of offspring is controlled at floor level, the average inbreeding coefficient of domestic animal progeny population and individual inbreeding coefficient can be predicted simultaneously, the genetic diversity of energy accurate evaluation domestic animal.

Embodiment

Below in conjunction with embodiment, the present invention is further described.

Animal matching method in the present invention comprises the following steps:

1, according to drove pedigree, colony's additive inheritance correlation matrix is set up.

(1) adopt horizontal type pedigree, filial generation is on a left side, and parental generation is on the right side, and male animal is upper, and dam is upper;

(2) matrix form is arranged in from the previous generation to lower generation, from left to right;

(3) parental generation as each individuality is known, then mark, and is convenient to the correlation calculating filial generation;

(4) value on diagonal is calculated

$a_{ii}=\frac{a_{s_1{d}_i}}{2}+1$

In formula, a _ijrepresent i-th individuality and the correlation of self, be relevant between i-th individual father and mother.If only know father s _ior mother d _i, or father and mother are all unclear, so

(5) value above additive inheritance correlation matrix diagonal is calculated

$a_{ij}=\frac{a_{{\mathrm{is}}_j}+a_{{\mathrm{id}}_j}}{2}$

In formula, a _ijrepresent the correlation between i-th individuality and a jth individuality, i is the code name of row; J is the code name of row; s _jfor the father number of jth row; d _jfor mother number of jth row; it is the individual correlation arranging the father of individuality with jth of the i-th row; it is the individual correlation arranging mother of individuality with jth of the i-th row;

(6) value below additive inheritance correlation matrix diagonal be by diagonal above value transposition.

a _ij＝a _ji

(7) computing formula of inbreeding coefficient is:

F _i＝a _ii-1，

Pass in inbreeding coefficient matrix between matrix element and colony's additive inheritance correlation matrix elements is:

F _i＝a _ii-1； $a_{ii}=\frac{a_{s_i{d}_i}}{2}+1$

:

$F_i=a_{s_i{d}_i}/2$

Therefore, i-th individuality and a jth individual filial generation inbreeding coefficient are: the half of correlation between i.e. individual inbreeding coefficient=individual father and mother.

2, establish every generation to select k head dam, n head male animal (k/n=integer) carries out mating as breeding stock, and the male and female combinations of pairs setting up all breeding stocks obtains filial generation inbreeding coefficient matrix.

(1) all male animals of reserving seed for planting are positioned at first row, and all dams are positioned at the first row; Or all male animals of reserving seed for planting are positioned at the first row, and all dams are positioned at first row;

(2) in filial generation inbreeding coefficient matrix, matrix element is F _ij, i.e. the inbreeding coefficient in the i-th row place dam and jth row place male animal post-coitum generation;

(3) F _ijfor by dam corresponding in colony's additive inheritance correlation matrix be expert at (or row) and in the column (or row) cross unit lattice of male animal place numerical value 1/2.

3, set up the pairing matrix identical with filial generation inbreeding coefficient matrix ranks, pairing matrix is variable matrix

Numerical value very A in variable matrix _ij, A _ij=1 or 0; Get " 0 " expression and do not accept this combination, the animal namely in corresponding row or column does not carry out male and female pairing; Get " 1 " expression and accept this combination, the animal namely carrying out corresponding row or column carries out male and female pairing.

4, object function is set up

Minimum as optimization aim using the filial generation inbreeding coefficient F of combinations of pairs, formula is:

$F=\underset{i=1}{\overset{k}{\Σ}}\underset{j=1}{\overset{n}{\Σ}}{F}_{ij}{A}_{ij}$

5, consider from the hereditary angle of dam gene, set up constraints (asking dam of reserving seed for planting)

In animal conservation, in order to effectively control the increase of inbreeding coefficient, generally all carrying out each family equivalent and reserving seed for planting, namely when each is reserved seed for planting from generation to generation, carry out in each male animal offspring 1 male animal of selecting and remain, 1 dam of selecting and remain in each dam offspring, the male and female number of each family is suitable.Therefore, when setting up constraints:

Require that in father and mother's generation, every dam can only breed with 1 male animal, 1 dam of selecting and remain in the offspring of every dam, namely have k male and female breeding combination, k head dam of selecting and remain in offspring, then obtain constraints 1:

$\underset{j=1}{\overset{n}{\Σ}}{A}_{1j}=1,\underset{j=1}{\overset{n}{\Σ}}{A}_{2j}=1,...,\underset{j=1}{\overset{n}{\Σ}}{A}_{kj}=1$

In requirement father and mother generation, every male animal is equal with joining dam number, and namely every male animal is k/n head with joining dam number, obtains constraints 2:

$\underset{i=1}{\overset{k}{\Σ}}{A}_{i1}=k/n,\underset{i=1}{\overset{k}{\Σ}}{A}_{i2}=k/n,...,\underset{i=1}{\overset{k}{\Σ}}{A}_{in}=k/n$

Requirement object function is minimum, and the average inbreeding coefficient of k head dam namely selected and remain in offspring is minimum.

6, solve linear programming problem to obtain reserving seed for planting the optimum male and female combinations of pairs of dam

Utilize the above-mentioned optimum target of linear programming for solution, obtain optimum male and female poultry combinations of pairs, i.e. each A _ijvalue, this combination comprises k and raises male and female; From the angle of breeding, after the combinations of pairs of the male and female poultry of these optimums is bred, it is also minimum that the average inbreeding coefficient of filial generation give birth to by institute, and therefore, in the filial generation of these combinations, chooser is for kind dam.

According to breeding selective rule, the dam number that filial generation is reserved seed for planting is k, then in order to reduce the inbreeding coefficient that filial generation is reserved seed for planting between dam, from the filial generation that above-mentioned k male and female poultry combination breeding obtains, the dam in each combination in each selection filial generation is as the kind dam of filial generation.

7, consider from the hereditary angle of male animal gene, set up constraints, solve the sire of filial generation

Require that in father and mother's generation, every dam can only breed with 1 male animal at most, because male animal number is much smaller than dam number, then obtains constraints 3:

$\underset{j=1}{\overset{n}{\Σ}}{A}_{1j}\≤1,\underset{j=1}{\overset{n}{\Σ}}{A}_{2j}\≤1,...,\underset{j=1}{\overset{n}{\Σ}}{A}_{kj}\≤1$

Require to select and remain in every male animal offspring in father and mother's generation 1 male animal, total n breeding combination, n head male animal of selecting and remain, then obtain constraints 4:

$\underset{i=1}{\overset{k}{\Σ}}{A}_{i1}=1,\underset{i=1}{\overset{k}{\Σ}}{A}_{i2}=1,...,\underset{i=1}{\overset{k}{\Σ}}{A}_{in}=1$

Requirement object function is minimum, and the average inbreeding coefficient of n head male animal namely selected and remain in offspring is minimum.

8, the sire that linear programming problem is had combinations of pairs and filial generation is most solved

Utilize the above-mentioned optimum target of linear programming for solution, obtain optimum male and female poultry combinations of pairs, i.e. each A _ijvalue, this combination comprises n and raises male and female; From breeding angle, these optimums male and female poultry combinations of pairs breed after because the kind of low the obtained filial generation of inbreeding coefficient is also more excellent, therefore, these combination filial generation in chooser for sire.

According to breeding selective rule, the male animal number that filial generation is reserved seed for planting is n, coefficient is closed in the inbreeding of then reserving seed for planting between dam to reduce filial generation, from a said n filial generation that male and female poultry combination breeding obtains, respectively selects the male animal in a filial generation as the sire of filial generation in each combination.

9, in integration step 7 and 8 the breeding stock selected and best breeding combination.

Because the inbreeding coefficient of the parent breeding stock of breeding stock is known, then the breeding stock inbreeding coefficient of filial generation is also to calculate out, select breeding stock according to every generation of the breeding stock selection mode introduced in above-mentioned steps 2 to 9 to this drove, be handed down from age to age like this, effectively reduce the inbreeding coefficient of drove.

Embodiment 1:

There is a goat locking breeding populations, stuck ewe 9 (even number overbit), ram 3 (odd number overbit) of reserving seed for planting, work out best conservation matingplan according to colony's pedigree.

The first step: according to colony's pedigree, set up colony's additive inheritance correlation matrix, as shown in table 1.1, wherein, the 1st row the 1st arranges, for being numbered 136 individualities, represent the 1st individuality and the correlation of self, the element representation that 1st row the 10th arranges is numbered the correlation between 136 and 453, and the numeral in matrix on diagonal is the inbreeding coefficient+1 of each individuality, then this average inbreeding coefficient of colony of reserving seed for planting is 0.01525.

Table 1.1 Goat Population in Yangtse additive inheritance correlation matrix

Second step: set up reserve seed for planting ram and stuck ewe all combinations offspring inbreeding coefficient matrix, as shown in table 1.2.First behavior ram, first is classified as ewe, and the data of correspondence position in table 1.1 are multiplied by 1/2, obtains offspring's inbreeding coefficient F of respective combination _ij, form inbreeding coefficient matrix, in table 1.2, numerical value is the inbreeding coefficient of each ram and ewe combination offspring.

Table 1.2 inbreeding coefficient matrix

	453	455	459
				136	0.104	0.104	0.094
148	0.156	0.156	0.137
				156	0.156	0.156	0.137
182	0.093	0.093	0.066
				194	0.048	0.048	0.023
202	0.079	0.079	0.051
				204	0.154	0.154	0.148
206	0.064	0.064	0.043
				368	0.137	0.137	0.133

3rd step: set up the variable matrix identical with inbreeding coefficient matrix ranks, as shown in table 1.3.The variable matrix elements A of the i-th row place dam and the male animal mating of jth row place in table _ijget 0 or 1.

Table 1.3 variable matrix (ewe programming evaluation result)

4th step: set up object function, the inbreeding coefficient that requiring finally selects and remain combines offspring is minimum.

5th step: set up constraints (asking stuck ewe), each ewe joins a ram, and each ram joins 3 ewes, and each combination stays an ewe to plant, and solving result is as shown in table 1.3.

6th step: programming evaluation (asking stuck ewe), result is as shown in table 1.4.Select and remain 9 and combine, each combination is selected and remain an ewe, and total inbreeding coefficient of 9 ewes is 0.913.

Table 1.4 programming evaluation result (asking stuck ewe)

	453	455	459	Add up to
					136	0.104	0.000	0.000	0.104
148	0.156	0.000	0.000	0.156
					156	0.000	0.156	0.000	0.156
182	0.000	0.000	0.066	0.066
					194	0.000	0.000	0.023	0.023
202	0.000	0.000	0.051	0.051
					204	0.000	0.154	0.000	0.154
206	0.000	0.064	0.000	0.064
					368	0.137	0.000	0.000	0.137
Add up to				0.913

7th step: set up constraints (asking ram of reserving seed for planting), every ram joins an ewe, every ewe with join ram number and be less than or equal to 1.

Table 1.5 variable matrix (ram programming evaluation result)

8th step: programming evaluation (asking ram of reserving seed for planting), result is as shown in table 1.6.Select and remain 3 and combine, each combination is selected and remain 1 ram.Total inbreeding coefficient of 3 rams is 0.167.

Table 1.6 programming evaluation (asking ram of reserving seed for planting)

	453	455	459	Add up to
					136	0.000	0.000	0.000	0.000
148	0.000	0.000	0.000	0.000
					156	0.000	0.000	0.000	0.000
182	0.000	0.000	0.000	0.000
					194	0.000	0.000	0.023	0.023
202	0.079	0.000	0.000	0.079
					204	0.000	0.000	0.000	0.000
206	0.000	0.064	0.000	0.064
					368	0.000	0.000	0.000	0.000
Add up to				0.167

9th step: the matingplan working out male and female sheep of reserving seed for planting, result is as shown in table 1.7.

Result matched by table 1.7

Tenth step: predict next inbreeding coefficient from generation to generation, the total inbreeding coefficient of next generation population (9 ewes and 3 rams) is 1.080, and average inbreeding coefficient is 0.09, and comparatively going up one increases by 0.07475 from generation to generation.

Embodiment 2:

There is a locking to breed swinery, sow 20 (even number overbit) of reserving seed for planting, boar 5 (odd number overbit) of reserving seed for planting, work out best conservation matingplan according to colony's pedigree.

The first step: according to colony's pedigree, sets up colony's additive inheritance correlation matrix.In matrix, diagonal numeral is the inbreeding coefficient+1 of each individuality.This average inbreeding coefficient of colony of reserving seed for planting is 0.0186.

Second step: set up reserve seed for planting boar and sow all combinations offspring inbreeding coefficient matrix of reserving seed for planting, as shown in table 2.1.First behavior boar, first is classified as sow.In table, numerical value is the inbreeding coefficient of each boar and sow combination offspring.

Table 1.2 inbreeding coefficient matrix

3rd step: set up the variable matrix identical with inbreeding coefficient matrix ranks, as shown in table 2.2.In table, each male and female combined value gets 0 or 1.

Table 2.2 variable matrix (sow programming evaluation result)

	487	489	515	517	625	Add up to
							468	0.000	0.000	0.000	0.000	1.000	1.000
486	0.000	1.000	0.000	0.000	0.000	1.000
							488	0.000	1.000	0.000	0.000	0.000	1.000
570	0.000	0.000	0.000	1.000	0.000	1.000
							572	1.000	0.000	0.000	0.000	0.000	1.000
574	0.000	0.000	0.000	1.000	0.000	1.000
							600	0.000	0.000	0.000	1.000	0.000	1.000
602	0.000	0.000	1.000	0.000	0.000	1.000
							604	0.000	0.000	0.000	1.000	0.000	1.000
606	0.000	0.000	1.000	0.000	0.000	1.000
							614	0.000	0.000	0.000	0.000	1.000	1.000
616	0.000	1.000	0.000	0.000	0.000	1.000
							618	1.000	0.000	0.000	0.000	0.000	1.000
628	1.000	0.000	0.000	0.000	0.000	1.000
							630	0.000	0.000	0.000	0.000	1.000	1.000
632	0.000	1.000	0.000	0.000	0.000	1.000
							634	1.000	0.000	0.000	0.000	0.000	1.000
646	0.000	0.000	0.000	0.000	1.000	1.000
							648	0.000	0.000	1.000	0.000	0.000	1.000
650	0.000	0.000	1.000	0.000	0.000	1.000
							Add up to	4.000	4.000	4.000	4.000	4.000	20.000

4th step: set up object function, the inbreeding coefficient that requiring finally selects and remain combines offspring is minimum.

5th step: set up constraints (asking sow of reserving seed for planting), each sow joins a boar, and each boar joins 4 sows, and each sow stays a sow to plant.

6th step: programming evaluation (asking sow of reserving seed for planting), result is as shown in table 2.3.Select and remain 20 and combine, each combination is selected and remain a sow, and total inbreeding coefficient of 20 sows is 0.687.

Table 2.3 programming evaluation result (asking sow of reserving seed for planting)

	487	489	515	517	625	Add up to
							468	0.000	0.000	0.000	0.000	0.056	0.056
486	0.000	0.026	0.000	0.000	0.000	0.026
							488	0.000	0.026	0.000	0.000	0.000	0.026
570	0.000	0.000	0.000	0.025	0.000	0.025
							572	0.049	0.000	0.000	0.000	0.000	0.049
574	0.000	0.000	0.000	0.038	0.000	0.038
							600	0.000	0.000	0.000	0.018	0.000	0.018
602	0.000	0.000	0.030	0.000	0.000	0.030
							604	0.000	0.000	0.000	0.032	0.000	0.032
606	0.000	0.000	0.030	0.000	0.000	0.030
							614	0.000	0.000	0.000	0.000	0.042	0.042
616	0.000	0.026	0.000	0.000	0.000	0.026
							618	0.026	0.000	0.000	0.000	0.000	0.026
628	0.049	0.000	0.000	0.000	0.000	0.049
							630	0.000	0.000	0.000	0.000	0.043	0.043
632	0.000	0.015	0.000	0.000	0.000	0.015
							634	0.049	0.000	0.000	0.000	0.000	0.049
646	0.000	0.000	0.000	0.000	0.047	0.047
							648	0.000	0.000	0.033	0.000	0.000	0.033
650	0.000	0.000	0.025	0.000	0.000	0.025
							Add up to						0.687

7th step: set up constraints (asking boar of reserving seed for planting), every boar joins a sow, every sow with join boar number and be less than or equal to 1.

Table 2.4 variable matrix (boar programming evaluation result)

8th step: programming evaluation (asking boar of reserving seed for planting), result is as shown in table 2.5.Select and remain 5 and combine, each combination is selected and remain 1 boar.Total inbreeding coefficient of 5 boars is 0.126.

Table 2.5 programming evaluation (asking boar of reserving seed for planting)

9th step: work out the matingplan staying raw sow, result is as shown in table 2.6.

Result matched by table 2.6

Tenth step: predict next inbreeding coefficient from generation to generation, the total inbreeding coefficient of next generation population (20 sows and 5 boars) is 0.813, and average inbreeding coefficient is 0.03252, and comparatively going up one increases by 0.01392 from generation to generation.

More than describe the preferred embodiment of the present invention in detail; but the present invention is not limited to the detail in above-mentioned embodiment, within the scope of technical conceive of the present invention; can carry out multiple equivalents to technical scheme of the present invention, these equivalents all belong to protection scope of the present invention.

Claims (4)

1. an animal matching method, is characterized in that, comprises the following steps:

(1) set up colony's additive inheritance correlation matrix according to drove pedigree, the element of described additive inheritance correlation matrix is the inbreeding coefficient of domestic animals on correspondence position;

(2) according to the kind dam number k preset and sire number n, filial generation inbreeding coefficient matrix is set up according to described additive inheritance correlation matrix;

(3) pairing matrix is set up according to described kind of dam number k and described sire number n;

(4) according to described filial generation inbreeding coefficient matrix and described pairing matrix, minimum as optimization aim using filial generation inbreeding coefficient, set up constraints from the angle of dam heredity, obtain the first linear programming equation and carry out solving obtaining the first optimum male and female poultry combinations of pairs and filial generation kind dam;

(5) according to described filial generation inbreeding coefficient matrix and described pairing matrix, minimum as optimization aim using filial generation inbreeding coefficient, set up constraints from the angle of male animal heredity, obtain the second linear programming equation and carry out solving obtaining the second optimum male and female poultry combinations of pairs and filial generation sire.

2. animal matching method according to claim 1, is characterized in that, described in step (4), the first linear programming equation is:

Object function: $F=\underset{i=1}{\overset{k}{\Σ}}\underset{j=1}{\overset{n}{\Σ}}{F}_{ij}{A}_{ij}$

Constraints:

$\underset{j=1}{\overset{n}{\Σ}}{A}_{ij}=1,1\≤i\≤k$

$\underset{i=1}{\overset{k}{\Σ}}{A}_{ij}=k/n,1\≤j\≤n$

F _ijfor the element in filial generation inbreeding coefficient matrix, A _ijfor the element in pairing matrix, i represents i-th dam, and j represents a jth male animal.

3. animal matching method according to claim 1, is characterized in that, described in step (5), the second linear programming equation is:

Object function: $F=\underset{i=1}{\overset{k}{\Σ}}\underset{j=1}{\overset{n}{\Σ}}{F}_{ij}{A}_{ij}$

Constraints:

$\underset{j=1}{\overset{n}{\Σ}}{A}_{kj}\≤1,1\≤i\≤k$

$\underset{i=1}{\overset{k}{\Σ}}{A}_{ij}=1,1\≤j\≤n$

F _ijfor the element in filial generation inbreeding coefficient matrix, A _ijfor the element in pairing matrix, i represents i-th dam, and j represents a jth male animal.

4. animal matching method as claimed in any of claims 1 to 3, is characterized in that, the element F in described filial generation inbreeding coefficient matrix _ijfor 1/2 of corresponding element in described additive inheritance correlation matrix.