A method for calculating optimal contribution breeding stock and selective mating for endangered and rare cattle and sheep species.

Abstract

This invention discloses a method for calculating optimal contribution for breeding and mating selection in endangered and rare cattle and sheep populations. The method includes: acquiring pedigree data and genomic information of the rare cattle and sheep; constructing a pedigree matrix based on the pedigree data; constructing a genomic kinship matrix based on the genomic information; minimizing the average kinship of the population using a genetic algorithm based on the pedigree matrix or genomic kinship matrix to determine the set of individuals to be culled; calculating the optimal contribution value of each individual using a simulated annealing algorithm for the set of individuals to be retained; and minimizing the average kinship between all pairs using a simulated annealing algorithm based on the optimal contribution values ​​of all individuals to obtain the target mating scheme. This invention balances constraints such as sex ratio and population size with kinship control, aiming to minimize the average kinship coefficient of the next generation population, greatly reducing the risk of inbreeding and ensuring population genetic diversity.

Description

Technical Field

[0001] This invention belongs to the field of animal husbandry germplasm resource protection and bioinformatics technology, and in particular relates to a method for calculating the optimal contribution of breeding stock and selection for endangered and rare cattle and sheep. Background Technology

[0002] my country possesses abundant cattle and sheep germplasm resources, which are a crucial foundation for the sustainable development of animal husbandry. However, with the over-reliance on a few bred breeds in livestock production and the deterioration of their living environment, the population size of some local cattle and sheep breeds is shrinking and they are on the verge of extinction. Although various conservation measures have been established, there is still a lack of efficient and intelligent breeding strategies. Especially in the context of big data, it is difficult to balance the maintenance of genetic diversity and inbreeding control when formulating breeding plans based on human experience.

[0003] The goal of conservation programs is to maximize the survival probability of a population. The best approach is to maintain genetic diversity as much as possible while controlling inbreeding. Decline in genetic diversity is a major problem in conservation and evolutionary biology because natural selection acts directly on genetic diversity and allows populations to adapt to changes in the environment. Populations requiring protection are often small and therefore at risk of high inbreeding rates, which can negatively impact their adaptation and potentially lead to extinction. The optimal strategy for maintaining maximum genetic diversity and minimizing inbreeding is to use optimal contribution—the optimal number of offspring each individual should contribute to the next generation—to minimize the overall kinship of the population.

[0004] These methods were initially developed based on pedigree matrices, which do not account for variations caused by Mendelian sampling. While effective in managing genetic diversity, they also have limitations. For example, full siblings may inherit different alleles, yet they show the same correlation in the pedigree matrix. In response, genome-wide kinship matrices, constructed based on high-density SNP information across the entire genome, can replace pedigree matrices and are widely used in genetic assessment and breeding decisions. Furthermore, they have been shown to manage population genetic diversity more effectively.

[0005] Currently, the calculation of individual selection and mating combinations in breeding conservation still lacks a systematic method, relying heavily on human experience, which makes it difficult to maintain genetic diversity and control inbreeding in the long term. While optimization algorithms such as genetic algorithms and simulated annealing algorithms show promise in solving complex problems, their integration and specificity in practical applications of endangered cattle and sheep conservation are insufficient, failing to effectively combine with the specific needs of the population. Therefore, how to optimize cattle and sheep conservation strategies based on genomic or pedigree information to improve the scientific rigor and effectiveness of conservation remains an urgent problem to be solved. This invention addresses this weakness by proposing an optimal contribution method for breeding conservation and mating calculation in endangered and rare cattle and sheep, aiming to fill the gap in existing technologies. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention proposes an optimal contribution breeding and selection calculation method for endangered and rare cattle and sheep. This method takes into account constraints such as sex ratio and population size as well as kinship control, aiming to minimize the average kinship coefficient of the next generation population, thereby greatly reducing the risk of inbreeding and ensuring the genetic diversity of the population.

[0007] To achieve the above objectives, this invention provides a method for calculating the optimal contribution for breeding and selection of endangered and rare cattle and sheep, comprising:

[0008] To obtain pedigree data and genomic information of rare cattle and sheep;

[0009] Based on the pedigree data, construct a pedigree relationship matrix;

[0010] Based on the genomic information, construct a genomic kinship matrix;

[0011] Based on the pedigree matrix or genomic kinship matrix, a genetic algorithm is used to minimize the average kinship of the population to determine the set of individuals to be eliminated.

[0012] For the set of retained individuals, the optimal contribution value of each individual is calculated using the simulated annealing algorithm;

[0013] Based on the optimal contribution values ​​of all individuals, the average kinship among all pairs is minimized using the simulated annealing algorithm to obtain the target mating scheme.

[0014] Optionally, the pedigree data includes: individual ID, sex, parents, date of birth, and family number for all individuals in the population.

[0015] Optionally, constructing a phylogenetic relationship matrix based on the phylogenetic data includes:

[0016] Based on the pedigree data, the pedigree relationship matrix is ​​constructed using a recursive method:

[0017] ;

[0018] ;

[0019] in, For individuals Father For individuals Mother For individuals Father For individuals Mother Let be the inbreeding coefficient of individual i. Let be the kinship coefficient between individual i and individual j and ≠ , for Parental kinship coefficient Let be the kinship coefficient between the fathers of individual i and individual j. Let be the kinship coefficient between the fathers of individual i and individual j.

[0020] Optionally, constructing a genomic kinship matrix based on the genomic information includes:

[0021] Based on the genomic information, construct a genomic kinship matrix based on allele sharing status:

[0022] ;

[0023] in, As an indicator variable for allele sharing status, the value is 1 when the allele 'a' of the first individual is identical to the allele 'b' of the second individual, and 0 otherwise. Each SNP locus contains two alleles, a1, b1, a2, and b2. Four pairing comparisons are performed at the corresponding SNP locus, and the average of these four comparisons is taken as the degree of allele sharing at the corresponding SNP locus. The average of all SNP loci is taken as the kinship value between two individuals based on allele sharing. By calculating the kinship values ​​between all pairs of individuals in sequence, the genomic kinship matrix between individuals is finally constructed.

[0024] Optionally, based on the pedigree matrix or genomic kinship matrix, a genetic algorithm is used to determine the set of individuals to be eliminated, with the objective function of minimizing the average kinship of the population:

[0025] The genetic algorithm uses the pedigree matrix or genomic kinship matrix as the optimization object and minimizes the average kinship of the population as the objective function to determine the set of individuals to be eliminated.

[0026] The pedigree matrix represents the expected kinship between individuals, while the genomic kinship matrix reflects the actual kinship.

[0027] Optionally, for the set of retained individuals, the method for calculating the optimal contribution value is as follows:

[0028] ;

[0029] in, To predict the average kinship of the next generation, It is the kinship relationship between individuals i and j. and Let i represent the number of offspring contributed by individual i of male animal and individual j of female animal to the next generation, respectively, and C be the sum of all contributions.

[0030] Compared with the prior art, the present invention has the following advantages and technical effects:

[0031] This invention, based on an optimal contribution algorithm, significantly reduces the risk of inbreeding and effectively protects the genetic diversity of the population. Under multiple constraints such as population size and sex ratio, this method effectively selects superior breeding individuals through optimization algorithms, further improving the efficiency and quality of breeding stock preservation. By using genetic algorithms and simulated annealing algorithms, the method automatically calculates and optimizes the number of individuals retained for breeding, mating ratios, and pairing combinations, reducing manual intervention and improving operational efficiency and reliability. It is not only applicable to the genetic resource protection of livestock such as cattle and sheep but can also be applied to the population management of other species, demonstrating strong versatility and adaptability. Attached Figure Description

[0032] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

[0033] Figure 1 This is a flowchart of an embodiment of the present invention for calculating the optimal contribution for breeding and selection of endangered and rare cattle and sheep;

[0034] Figure 2 This is a diagram showing the preservation effect of using the genomic kinship matrix and pedigree kinship matrix in the long-term preservation simulation of this invention. (a) shows the trend of heterozygosity in the long-term preservation simulation, (b) shows the trend of pedigree inbreeding coefficient in the long-term preservation simulation, and (c) shows the trend of inbreeding coefficient calculated based on ROH in the long-term preservation simulation. Detailed Implementation

[0035] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0036] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0037] This invention proposes a method for calculating the optimal contribution for breeding and selection of endangered and rare cattle and sheep, such as... Figure 1 As shown, the specific steps include:

[0038] Based on the pedigree data, construct a pedigree relationship matrix;

[0039] Based on the genomic information, construct a genomic kinship matrix;

[0040] Based on the pedigree matrix or genomic kinship matrix, a genetic algorithm is used to minimize the average kinship of the population to determine the set of individuals to be eliminated.

[0041] For the set of retained individuals, the optimal contribution value of each individual is calculated using the simulated annealing algorithm;

[0042] Based on the optimal contribution values ​​of all individuals, the average kinship among all pairs is minimized using the simulated annealing algorithm to obtain the target mating scheme.

[0043] Specifically, in step S1, organize the pedigree information, including the individual ID, gender, parents, date of birth, and family number of all individuals in the population, with omissions allowed.

[0044] Step S2: Construct a pedigree matrix based on the pedigree data using a recursive method. Each element of the pedigree matrix can be calculated using the following recursive formula:

[0045] ;

[0046] ;

[0047] in, For individuals Father For individuals Mother For individuals Father For individuals Mother Let be the inbreeding coefficient of individual i. Let be the kinship coefficient between individual i and individual j and ≠ , for Parental kinship coefficient Let be the kinship coefficient between the fathers of i and j. Let be the kinship coefficient between the fathers of i and j.

[0048] Step S3: Using high-density SNP data, a genome kinship matrix is ​​constructed. The genome kinship matrix is ​​calculated using a large number of biallelic markers (SNPs) and the allelic similarity method proposed by Nejati-Javaremi et al. is used for calculation.

[0049] ;

[0050] in, As an indicator variable for allele sharing status, the value is 1 when the allele 'a' of the first individual is identical to the allele 'b' of the second individual, and 0 otherwise. Each SNP locus contains two alleles, a1, b1, a2, and b2. Four pairing comparisons are performed at the corresponding SNP locus, and the average of these four comparisons is taken as the degree of allele sharing at the corresponding SNP locus. The average of all SNP loci is taken as the kinship value between two individuals based on allele sharing. By calculating the kinship values ​​between all pairs of individuals in sequence, the genomic kinship matrix between individuals is finally constructed.

[0051] It should be noted that although the kinship calculated based on SNP data is more accurate than that of traditional pedigree kinship, it is still an estimate of the true genetic relationship unless all SNPs in the whole genome are used to calculate the kinship.

[0052] Step S4, elimination optimization: The genetic algorithm from the Scikit-opt open-source optimization library is used to minimize the total kinship between individual pairings. Under constraints such as population size and sex ratio, the set of individuals to be eliminated is determined, and the preferred individuals for breeding are retained.

[0053] ;

[0054] Where F_1 represents the sum of kinship relationships in the population, c is a vector of length equal to the number of individuals, where a value of 1 indicates retention for breeding and a value of 0 indicates culling. G is a kinship matrix. Constraints are set on c to determine the number of male and female animals to retain. The set of culled individuals is determined by minimizing F.

[0055] Step S5, Optimal Contribution Calculation: Based on the retained individuals in the population, the optimal contribution ratio of each individual is iteratively calculated according to the formula to minimize the average kinship of the next generation.

[0056] ;

[0057] in, To predict the average kinship of the next generation, It is the kinship relationship between individuals i and j. and Let represent the number of offspring contributed by individual i of the male animal and individual j of the female animal, respectively, and C be the sum of all contributions. This embodiment uses the simulated annealing algorithm for solving the problem. Simulated annealing is a probabilistic method used to find an approximate solution close to the global optimum in a large-scale solution space. At each step of the annealing process, the current solution is perturbed to generate a new candidate solution. Whether this new solution is accepted depends on the difference in the corresponding function values ​​and a parameter called the "temperature" T. Therefore, if exp(−∆D / T) > r, where ∆D is the difference in function values ​​and r is a random number between [0,1], then the new solution will be accepted. If T is large, almost all new solutions will be accepted; conversely, if T is small, most solutions will be rejected, and only improved solutions will be accepted. Therefore, a major component of simulated annealing is reducing the temperature T. As ∆D begins to decrease slowly, the temperature T is reduced, thus limiting the chance of accepting worse solutions. The temperature can be reduced multiple times, and the process may subsequently "quench" by accepting only "good" changes to find a local minimum of the function. The variable that changes during the optimization process is a vector c, where each element represents the number of offspring contributed by each individual in the population. Since the endangered cattle and sheep used for the calculation mostly produce one offspring per litter, a constraint is set that each female animal produces one offspring. Furthermore, the sum of the contributions of all fathers equals the sum of the contributions of all mothers, and this sum equals C. This embodiment starts with a random vector c, substitutes it into the formula for simulated annealing optimization calculations, iterates and continuously perturbs to generate new solutions until the optimal solution is finally generated.

[0058] Step S6: Generate mating schemes, use simulated annealing to arrange pairings between individuals, and optimize the following formula to minimize the average affinity between pairings.

[0059] ;

[0060] in, The total kinship between the pairs. The value is 0 when male animal individual i and female animal individual j are not paired, and 1 otherwise. To ensure kinship between pairs, each female animal can only mate with one male animal.

[0061] The following embodiment uses the protection of Luxi cattle as an example for detailed explanation:

[0062] (1) Data collection of Luxi cattle:

[0063] In this embodiment, a herd of 186 purebred Luxi cattle (65 males and 121 females), born between 2004 and 2012, was selected as the research subject. All cattle underwent second-generation whole-genome resequencing, variant detection, and data editing. 150,000 SNPs were evenly selected for analysis, and genotypic data were provided in standard VCF format. Parent IDs, dates of birth, and pedigree numbers of the Luxi cattle in the herd were collected as pedigree data files and used to calculate pedigree relationship matrices.

[0064] (2) Construct a pedigree matrix:

[0065] Based on pedigree information, a pedigree relationship matrix is ​​constructed using a recursive method. This matrix represents the additive genetic correlation matrix among all animal individuals. The additive genetic correlation between individuals i and j refers to the proportion of homologous genes in their genomes, or the probability that a randomly selected gene from individual i's genome is homologous to a randomly selected gene from individual j's genome. Each element of the pedigree relationship matrix can be calculated using the following recursive formula:

[0066] ;

[0067] ;

[0068] in and ( ) for individuals His father and mother.

[0069] The pedigree consists of individuals listed in a five-part table by individual number, father number, mother number, age, and pedigree number, with a header. Missing values ​​for individual number, father number, and mother number are set to 0, while missing values ​​for age and pedigree number are set to 99.

[0070] A genomic kinship matrix was constructed based on genomic information. The matrix was calculated using SNP data from 186 Luxi cattle, employing the allelic similarity method proposed by Nejati-Javaremi et al.

[0071] ;

[0072] In this example, both the pedigree matrix and the genomic kinship matrix can be used to calculate the breeding and selection strategies for Luxi cattle. The pedigree matrix reflects theoretical kinship based on pedigree information, while the genomic kinship matrix, based on actual genotype data, more accurately reflects the true kinship among the population. The genomic kinship matrix will be used subsequently to calculate the breeding and selection strategies. See also... Figure 2 (a)-(c) In long-term breeding iteration simulations, using a genome kinship matrix during breeding will achieve better breeding results, but it requires sequencing of each generation of cattle, resulting in long-term sequencing costs.

[0073] (3) Selection of breeding bulls:

[0074] This embodiment first uses the Genetic Algorithm (GA) in the Scikit-opt open-source optimization library to minimize the kinship among all individuals in the population. In order to improve breeding efficiency and save costs, it is planned to retain 20 bulls and 121 cows. Under the set conditions, the set of individuals to be culled is determined, and the individuals to be retained for breeding are kept.

[0075] ;

[0076] in, Let G be the sum of the kinship relationships of the population, G be the genomic kinship matrix, and c be a vector of length equal to the number of individuals, consisting of 0s and 1s. For each individual, a value of 1 indicates that the individual is retained for breeding, while a value of 0 indicates that the individual is culled. The sum of the values ​​for males in c represents the set number of males to be retained, and the sum of the values ​​for females represents the set number of females to be retained. In this example, 20 males and all 121 females are retained, and c' is the transpose of c. First, a random initial c that meets the requirements is set. A genetic algorithm is used to iterate through the formula with c, minimizing the objective function F. Finally, this embodiment can obtain the optimal solution c, culling unsuitable individuals while meeting the required number of males and females to be retained. The following are the numbers of the 20 breeding bulls selected using this method: 140073, 160163, 160209, 180035, 180041, 190024, 190030, 190032, 190037, 200005, 200013, 200014, 200019, 200030, 210032, 210039, 210043, 210045, and 210047.

[0077] (4) The number of bulls retained for breeding:

[0078] Among the remaining individuals after elimination optimization, further optimization based on contribution ratio is performed using simulated annealing. This embodiment uses the following formula to calculate the optimal contribution ratio for each individual:

[0079] ;

[0080] Simulated annealing plays a central role in this process, finding new candidate solutions by perturbing the current solution at each step. At higher temperatures, most new solutions are accepted, helping the algorithm escape local optima; however, as the temperature gradually decreases, only perturbations that significantly improve the solution are accepted, eventually stopping near local optima. This embodiment uses the individuals retained in the previous step to generate a new population, and finds the corresponding rows and columns of the new population from the genomic kinship matrix to generate a new genomic kinship matrix. First, this embodiment sets a random initial solution c, where the male portion of c equals the female portion, and the constraint for each female is a fixed value of 1. The simulated annealing optimization calculation is performed using the formula, iterating and continuously perturbing to generate new solutions until the optimal solution is finally generated. The male portion of the optimal solution is the optimal number of bulls retained for breeding (Table 1).

[0081] Table 1

[0082]

[0083] (5) Generate pairing schemes:

[0084] Simulated annealing is used to arrange pairings between individuals, and the following formula is optimized to minimize the average affinity between pairings.

[0085]

[0086] in, The total kinship between the pairs. The value is 0 when male animal individual i and female animal individual j are not paired, and 1 otherwise. To ensure kinship between pairs, each female animal can only mate with one male animal. First, an initial male animal vector is generated. and female animal vector In each iteration, simulated annealing is used to perturb the pairing of male and female animals, generating new male and female animal vectors. The total kinship relationship F3 between the new pairings is calculated, and it is determined whether to accept the new pairing scheme, until the optimal solution is found. The final pairing scheme corresponding to the male and female animal vectors is the obtained optimal pairing scheme. (Table 2):

[0087] Table 2

[0088]

[0089] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for calculating the optimal contribution for breeding and selection of endangered and rare cattle and sheep, characterized in that, include: To obtain pedigree data and genomic information of rare cattle and sheep; Based on the pedigree data, construct a pedigree relationship matrix; Based on the genomic information, construct a genomic kinship matrix; Based on the pedigree matrix or genomic kinship matrix, a genetic algorithm is used to minimize the average kinship of the population to determine the set of individuals to be eliminated. For the set of retained individuals, the optimal contribution value of each individual is calculated using the simulated annealing algorithm; Based on the optimal contribution values ​​of all individuals, the average kinship among all pairs is minimized using the simulated annealing algorithm to obtain the target mating scheme.

2. The method for calculating the optimal contribution for breeding and selection of endangered and rare cattle and sheep according to claim 1, characterized in that, The pedigree data includes: individual ID, sex, parents, date of birth, and family number for all individuals in the population.

3. The method for calculating the optimal contribution for breeding and selection of endangered and rare cattle and sheep according to claim 1, characterized in that, Based on the pedigree data, constructing a pedigree relationship matrix includes: Based on the pedigree data, the pedigree relationship matrix is ​​constructed using a recursive method: ; ; in, For individuals Father For individuals Mother For individuals Father For individuals Mother Let be the inbreeding coefficient of individual i. Let be the kinship coefficient between individual i and individual j and ≠ , for Parental kinship coefficient Let be the kinship coefficient between the fathers of individual i and individual j. Let be the kinship coefficient between the fathers of individual i and individual j.

4. The method for calculating the optimal contribution for breeding and selection of endangered and rare cattle and sheep according to claim 1, characterized in that, Based on the genomic information, constructing a genomic kinship matrix includes: Based on the genomic information, construct a genomic kinship matrix based on allele sharing status: ； in, As an indicator variable for allele sharing status, the value is 1 when the allele 'a' of the first individual is identical to the allele 'b' of the second individual, and 0 otherwise. Each SNP locus contains two alleles, a1, b1, a2, and b2. Four pairing comparisons are performed at the corresponding SNP locus, and the average of these four comparisons is taken as the degree of allele sharing at the corresponding SNP locus. The average of all SNP loci is taken as the kinship value between two individuals based on allele sharing. By calculating the kinship values ​​between all pairs of individuals in sequence, the genomic kinship matrix between individuals is finally constructed.

5. The method for calculating the optimal contribution for breeding and selection of endangered and rare cattle and sheep according to claim 1, characterized in that, Based on the aforementioned pedigree matrix or genomic kinship matrix, a genetic algorithm is used to determine the set of individuals to be eliminated, with the objective function of minimizing the average kinship of the population: The genetic algorithm uses the pedigree matrix or genomic kinship matrix as the optimization object and minimizes the average kinship of the population as the objective function to determine the set of individuals to be eliminated. The pedigree matrix represents the expected kinship between individuals, while the genomic kinship matrix reflects the actual kinship.

6. The method for calculating the optimal contribution for breeding and selection of endangered and rare cattle and sheep according to claim 1, characterized in that, The method for calculating the optimal contribution value for the set of retained individuals is as follows: ； in, To predict the average kinship of the next generation, It is the kinship relationship between individuals i and j. and Let i represent the number of offspring contributed by individual i of male animal and individual j of female animal to the next generation, respectively, and C be the sum of all contributions.

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