Single-plant Similarity-difference Selection in Wheat Breeding

A new method of single-plant selection was proposed using the principle of similarity-difference analysis to overcome the limitation of traditional breeding by means of experiences. The method is considered as the method of single-plant similarity-difference selection. Its principle and steps were introduced. By means of the breeding data of Yumai 35, Anmai No.1 and Anmai No.7, the analysis of single-plant similarity-difference selection was made in the process of single-plant selection. The results show that the method is feasible and efficient in the practice of breeding. Based on this, the superiorities of the method were discussed. It is pointed that combining the method with the technique of molecule marker assisted selection will is a very meaning study direction.


INTRODUCTION
Single-plant selection is a key link during the course of crop breeding.Therefore, the breeding workers extreme emphasize its technique and method for years.Early in 1936, Smith (1936) advanced the method of selection index on the basis of the conception of discrimination function proposed by Fisher (1936) to raise the selection effect of singleplant.Afterwards, Kempthome and Nordskog (1959) and Tallis (1962) put forward the method of restrictive selection index.Lin improved the method of selection index given by Smith (1936) to bring it to completion in Lin (1978).Nevertheless, the methods require the particular test design and more repetitions in test and it is very difficult to put them into practice in the breeding course, its application range has a certain restriction.For this reason, Wang and Guo (1991) advanced the improved contingency table method with the merits of being easy to compute and convenient for application.To set up the contingency table requires a lot of breeding information and data; it can not apply to breeding practice for the unit of shorter breeding history.Consequently, the principle and method of single-plant grey selection was born at the right moment (Guo et al., 1992;Guo, 1992;Xue et al., 1994), thus causing the single-plant selection to make considerable headway.On the basis of this, this study put forward a new method of single-plant selection using the principle of similarity-difference analysis (Zhao, 2000;Guo, 2004) to expect to supply an effective method for breeding workers.

MATERIALS AND METHODS
Observations of traits of new wheat (Triticum aestivum L.) cultivar yumai 35 each generation were from the test data of Neixiang County Institute of Agricultural Sciences, Henan province from1988 to 1990; observations of traits of new wheat (Triticum aestivum L.) cultivars wheat (Triticum aestivum L.) Anmai 1 and Anmai 7 from the test data of Anyang Institute of Agricultural Sciences, Henan province from 1990 to 1992 (Table 1).Anmai 1 and Anmai 7 came from the same cross combination (Yumai 13/Zhou 8826), which are sibling lines with different traits.Each singleplant in Table 1 was obtained by breeding worker visually selected in accordance with the breeding objectives, using pedigree method in the test field.
In the background of single-plant selection (suppose it is W), given 2 sets A and B. Among them, A stands for a certain single-plant and B ideal singleplant.They constitute the set pair H = (A, B).Define the connection degree of A, B 2 sets as: where, i is an uncertain value among interval [-1, 1] in accordance with concrete conditions, a means the identical degree between the single-plant A and ideal single-plant B, namely, similarity degree and b, difference degree.a, b satisfy the normalization conditions: The difference between a and b reflects the similarity-difference connection trend of 2 sets in the background of single-plant selection.Generally, the bigger a is, the higher the degree that some single-plant A is close to the ideal single-plant B, the better A is. Thus, draw some definitions as follows: Definition 1: In the connection degree µ (W) = a+bi, when b≠0, a/b is the connection trend in the set pair H which can be expressed as: where, S(H) M means that the identical and different trend between 2 sets are in equilibrium.The degree of the single-plant A closed to the ideal single-plant is 1/2.
Definition 3: In the connection degree µ (W) =a+bi, if a/b>1, the connection trend at present is known as the connection similarity trend in the set pair H under the similarity-difference relationship which can be indicated as: where, S(H) I shows that the identical trend between 2 sets has an advantage.
Definition 4: In the connection degree µ(W) = a+bi, if a/b<1, the connection trend now is known as the connection difference trend in the set pair H under the similarity-difference relationship which can be expressed as: where, S(H) D indicates that the difference trend between 2 sets has an advantage.On the grounds of the principle of golden section, the connection identical trend can be divided into 4 grades: a quasi-similarity trend, a strong identical trend, a weaker identical trend and a mini-identical trend and the connection difference trend can be divided into 4 grades: a mini-different trend, a weak different trend, a strong different trend and a quasi-different trend (Table 1).
According to Table 1, the rules of test of significance of connection trend can be gained: if the single-plants to be evaluated are in the same trend grade, there are no significant difference among them; if they are in the different trend grade of the same tendency, there are significant difference among them; if they are in the different tendency, there are remarkable significance among them.
By the analysis of similarity-difference, if the single-plant A and the ideal single-plant B are in the same trend, the single-plant A belongs to the first grade single-plant; if they are in the mean trend grade, the single-plant A second grade one; if they are in the difference trend grade, the single-plant A the third grade one.Generally, the first and second grade singleplant should be retained to be planted continuously; the third grade single-plant should be eliminated.
Thus it can be seen that the principles mentioned above is essentially to ascertain good or bad of the single-plant by the analysis of the identical or different degree.Hence, we call the method the similaritydifference selection method.
Let x gk (g = 1, 2, …, n; k = 1, 2,…, m) be the observation value of the gth single-plant, the kth character.Thus, steps of the method of single-plant similarity-difference selection as follows: Set the ideal value of various characters which is the best value in a certain character, the ideal singleplant character set B can be gained.The ideal value of the kth characters can be expressed as x 0k .
Find out the identical degree between the character value and ideal character value for single-plants which constitute the matrix P of similarity-difference degree: The element a gk of the matrix is known as the identical degree between the single-plant character value x gk and the ideal single-plant character value x0k.By further spreading the Eq. ( 1), there are: , When x 0k is moderate (10) Ascertain the weight matrix vector W = (w 1 , w 2 , …, w m ) of various characters using the method of grey relational degree (Guo, 1995).
Construct the comprehensive identical degree matrix U between the evaluated single-plant and the ideal single-plant: The element Ag in U is a comprehensive identical degree between the gth single-plant character and the ideal single-plant character set: According to the Eq. ( 1) and ( 2), write out the connection formulas among the various single-plant characters and the ideal single-plant character set.From this, we can make out the ratio relationship of the identical degree to difference degree.
On the grounds of Eq. ( 4), ( 5) and ( 6), calculate the mean connection trend of various single-plants.
In the right of the relation between the identical degree a and the difference degree b in Table 1, fix the connection trend and single-plant grades of various single-plants.
The single-plant evaluated as the first or the second grade should be planted continuously and the singleplant evaluated the third grade should be eliminated.

RESULTS AND DISCUSSION
The breeding observation data (Table 2) of wheat variety Yumai 35, Anmai 1 and Anmai 7 were analyzed during the course of single-plant selection by adopting the principle method above mentioned.Among them, Anmai 1 and Anmai 2 came from the same cross combination, which are sibling lines with different characters.
The ideal single-plant is the best single-plant for various characters which consist of the best values in single-plants evaluated.The breeding experiences for years show that the height of single-plant belongs to the moderate character, its suitable range is among 65-80 cm in conditions of breeding test field and other characters are upper limit characters, their ideal values are all the maximum value (Table 2).
In accordance with the Eq. ( 8)-( 10), the identical degree of single-plant gained in various characters in generations as shown in Table 3.For instance, the identical degree between the observation value (Table 2) and the ideal value of pedigree No. 87C29-66 is a 12 = x12/x02 = 7.5/13 = 0.5769 in the ears per plant.The calculation of other characters is similar to this.
To evaluate the good or bad of the single-plant comprehensively, each character's importance is clearly not alike.With a progressive increase in cross generations, the heritability for various characters has a certain change (Borojevic, 1990;Pan, 1994;Zhang, 2006).Consequently, the weight for various characters is inconsistent in generations.For this reason, the weights for various characters are determined by breeding expert's experience or by adopting the method of grey relational degree (Guo, 1995), according to the observation values of various characters for single-plant in generations.Using breeding expert's experience, the weights for various characters have been determined in this example, which is as shown in Table 4.
Generally, the bigger the comprehensive identical degree of the single-plant is, the nearer the single-plant is to the ideal single-plant, the better the single-plant shows.According to the Eq. ( 1) and ( 2), write out the connection formula for various single-plants (Table 5).From the expression formulas of connection degree, we can see that the bigger the identical degree of singleplant or the smaller the difference degree of single-plant is, the bigger the connection degree of single-plant is.For example, the identical degree of single-plant 87C29-66-1-25 for Yumai 35 is 0.9904; its difference degree is 1-0.9904= 0.0096, this show that the coincidence degree of breeding target character of the single-plant with the ideal single-plant character is 99.04% which is the definite part.Other 0.96% is difference to the ideal single-plant and is indefinite, its indefinite degree depends on i value.That is to say that identical degree and difference degree are two aspects of a contradiction, they are coexistence in a unitary body of single-plant which takes i as a link.If i is positive value, the part can be transformed into the identical degree; if i is negative value, the part can be transformed into the difference degree.Generally speaking, because the relationship between the identical degree and the difference degree is relatively complemented, i is -1 in the analysis of similaritydifference of single-plant.Thus, the connection degree between the single-plant and the ideal single-plant is 0.9904-0.0096= 0.9808, which shows that the singleplant has a higher connection degree; its comprehensive characters have attained the ideal status on the whole.The analysis of other single-plants is the same as this.
Calculate the connection trends of various singleplants by the Eq. ( 4), ( 5) and ( 6).In accordance with the relation between the identical degree and the difference degree in Table 1, determine the grades and connection trends of various single-plants.For instance, the connection trend value of 87C29-66 is a/b = 0.7454/0.2546= 0.9277.The calculation of other single-plants is similar to this.
From Table 5, we can see that the connection trend values of various single-plants are all bigger than 1.The connection trends among the various single-plants and the ideal single-plant are in the status of identical trend from the definition 3 above mentioned.Hence, the single-plants for Yumai 35, Anmai 1 and Anma 7 having been selected are all the first grade single-plant.After that, those good single-plants all climbed into the good strains and manifested excellent in the wheat region test in Henan province which were examined and approved by the Henan Province Agricultural Crop Variety Examination and Approval Committee (Table 6).
In recent years, varieties mentioned above show some prominent traits with high yield, stable yield and disease resistance in the promotion course, their cumulative promotion area have reached 1.35 million ha, having a tremendous economic and social benefits and by the farmer welcome.
Thus, using the principle and method of single plant similarity-difference selection to direct the wheat breeding is practical and effective.
The method of single-plant similarity-difference selection applying in the course of wheat single-plant selection has overcame the limitations of traditional breeding by subjective experiences making one's choice and has made a valuable try and exploration in the quantization of single-plant selection, making the single-plant selection more objective and science, being an important significance to speeding up the selection progress, to raising the selection efficiency and to realizing the intellectuality of crop breeding.
The method of single-plant similarity-difference selection can consider many characters simultaneously and can make the multiple breeding goals being an unity harmoniously each other, avoiding the phenomenon of caring for this and losing that in tradition breeding, being an unique decision-making method of multi-target single-plant selection.
The method of single-plant similarity-difference selection is simple in computing, mastered easily, disseminated conveniently.If it is programmed the computer system, the method shall be faster and more handy.Consequently, the method has a vast application prospect.
Application the method to the breeding course of Yumai 35, Anmai 1 and Anmai 7 has proved the feasibility of the method from the angle of breeding practice.Because the process of crop breeding has a similarity, the method can apply to the process of single-plant of other crop breeding simultaneously.Therefore, we have reason to think the method being an effective tool and means of breeding workers.
Owing to the method of the single-plant similaritydifference selection based on the phenotype of singleplant which observed characters are the results of interaction of genotype and environment, it could not describe and solve the problems from the angle of molecules.For this reason, Combining the method with the molecule marker assisted selection technique will be a meaning research direction in crop breeding.

CONCLUSION
It was concluded that similarity-difference selection method could be used as an effective tool and means for crop breeders.
Owing to the method of the single-plant similaritydifference selection based on the phenotype of singleplant, it could not solve the problems from the angle of molecules.For this reason, Combining the method with the molecule marker assisted selection technique will be a meaning research direction in crop breeding.

S
In the connection degree µ(W) = a+bi, if a/b = 1, or a = b = 0.5, the connection trend right now is known as the connection mean trend in the set pair H under the similarity-difference relationship which can be

Table 1 :
The trend and single-plant grades under the identical-difference relationship

Table 2 :
Observation values of characters in different generations

Table 4 :
Weighted coefficients of characters in different generations

Table 6 :
The regional test yield and their registration states of Yumai 35, Anmai 1 and Anmai 7