Results of the development of the integrated evaluation of the winter barley breeding identifiers

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Introduction
Currently, one of the main tasks of the agribusiness both in Russia and around the world is to increase food production, primarily through the creation of highly productive varieties and hybrids [1][2][3][4][5].This is very important for our country, since under the conditions of severe foreign sanctions there was an acute shortage of breeding material coming from abroad.So, its share, in particular, for vegetable growing reaches 90%.
Today, Russia is sufficiently provided with seeds of the main cereal crops, however, the decoding of the wheat genome by transnational corporations Monsanto and Sengenta may create additional difficulties.
Therefore, a possible shortage in supplying the sowing company in our country can and should be eliminated by creating new promising domestic varieties and hybrids in the shortest possible time and, if possible, with a minimum of costs with their objective assessment.These promises are solved through innovative methods of selection, [6], as well as when using relatively low-cost and affordable methods for evaluating selection results.
In essence, the task of evaluating the created varieties and hybrids of agricultural plants is a multicriteria one.
Unlike the multicriteria task of optimizing processes and phenomena, for which a sufficient number of methods, methods and techniques have been developed [7][8][9], this task has neither a theoretical nor an experimental solution.By the way, in [10], an attempt was made to develop a method of multi-criteria selection at the final stage of plant breeding, based on the use of a weighted sum of normalized deviations from the optimum set by the breeder for the set of breeding traits.However, the method has two significant drawbacks.So, the number of features used for the integral assessment and their contribution to the total assessment are not substantiated in any way and are not confirmed by anything.This prevents an objective assessment of breeding efforts.
The solution of the indicated problem is possible when using the method of expert evaluation.
The purpose of the research was to develop a methodology for a comprehensive assessment of winter barley breeding identifiers.

Methodology
In this paper, an attempt was made to develop a methodology for comparative evaluation of the results of crop breeding based on the method of expert assessments using the example of winter barley.
The idea of developing the methodology and its implementation was (Figure 1) as follows.
Based on the results of an expert assessment of the traits taken into account in the selection of winter barley in this case, they are ranked and the significant (most significant), insignificant and insignificant traits are distinguished from them.Considering separately significant (option I) and a set of significant and unimportant features (option II), determine the contribution (share) of each feature relative to the sums of the rank assessment for each of the above options.Taking into account this contribution and the ratio of the digitized value of each feature of the compared sample and the selected reference sample, the value of the complex indicator in conditional scores of the compared sample is determined as the sum in points for all features.The calculation results are implemented for several varieties.
Before the start of the research, 27 factors (characteristics) were selected, which, as a rule, are used when compiling a variety passport and in accordance with the International classifier of the genus HORDEUM.Next, we prepared a questionnaire and randomized the sequence of recording features in it using a table of random numbers [11] in order to exclude a hint of a programmed decision-making by an expert.During the survey (psychological experiment), the expert (specialist) was asked to indicate the place of each factor from 1 (the most significant) to 27 (the least significant of all).The rank assessment was carried out using the principle of "inverted scale", that is, the most significant feature of the j-th expert was assigned a rank score of 27, decreasing to 1 for the most insignificant.The rank assessment of each i-th factor was the sum of the assessments for all experts.
Breeding scientists from leading specialized scientific and educational institutions of Moscow, Voronezh, Krasnoyarsk, Krasnodar, Stavropol, Simferopol acted as experts.Their scientific work experience ranges from 15 to 40 years, the number of varieties and hybrids of barley bred is from 10 to 40.

Ranking of traits taken into account in the selection of winter barley, based on the results of an expert assessment
Assessment of the reliability of the results of an expert assessment Isolation of significant, less significant and non-significant features

Development of a general methodology for the comparative evaluation of the results of winter barley breeding
The choice of an assessment scale, the determination of the weight in points of the characteristics of the reference variety for significant, the totality of significant and unimportant characteristics

Analysis of the results and conclusion
Determination of a complex indicator (the sum of the weight of traits in points according to the selected assessment scale) for the compared variety Determination of the weight in points of each characteristic of the compared variety according to the selected evaluation scale Determination of the relative weight of the digitized values of the characteristics of the compared and reference varieties

Results and discussion
The results obtained (Table 1) were checked for reliability according to two criteria: the consistency of the opinions of experts and the non-randomness of their consistency.
To establish the consistency of the opinions of experts, we calculated [11] the Kendall criterion (coefficient of concordance) where m -number of experts, 7 чел.;K -number of factors (features) in the matrix, 27; tj -количество одинаковых рангов у jого эксперта, 2. S -the sum of squared deviations of the rank assessment of all factors for all experts is defined as (2) where yij -the sum of the rank assessment of the i-th factor for all experts; L -the arithmetic mean value of the sum of the rank score for all factors for all experts, defined as As a result, the calculated value of the concordance coefficient was Wр=0,6257, which indicates a fairly high degree of agreement among experts (upon request 0⩽ Wр⩽1,0).
Next, we checked the condition of non-randomness of the consistency of the opinions of experts.It is necessary [11] that, according to the Pearson criterion (χ2), the condition obs. ( The calculated value of the Pearson criterion was determined by the formula which amounted to 113,8800, and table value [11] at 0,01 significance χ 2 tab.=45,6420. Thus, the consistency of expert opinions is more than accidental.Taking into account the reliability check, the diagram of the rank evaluation of features was obtained in the following form (Figure 2).
To solve the issue of identifying significant, unimportant and insignificant features, in accordance with [13 -15], their totality was considered in the form of a multidimensional variable -an identifier.Having considered the sum of the rank assessment in this capacity, we obtained the integral empirical distribution function yi = F(xi) of the accumulated frequencies of the share of the value of each feature in their total set (Figure 3).The form of this function characterizes the increase in the probability of considering a feature with an increase in their number.
Since the rank estimation was carried out in accordance with the frequency of accumulation, the sharp increase in F(x) in the initial period turned into a relatively smooth flow, asymptotically approaching 1 at the final stage.Here (Figure 3) it was possible to identify three characteristic areas of change in the function F(x): -the first area is the area where the growth rate of the volume of features F(x) is greater than the growth rate of the features that form this volume -the second area is the area where the growth rate of F(x) is approximately proportional to the growth rate of features -the third area is the area where the rate of increase F(x) is less than the rate of increase in features According to these areas, the features of the effectiveness of winter barley breeding can be classified as significant, insignificant and non-significant.Using formulas (6)(7)(8), one can single out the ranks of those signs that satisfy these conditions.Thus, the fuzzy set described by the function F(x) can be structured.
Applying this method to the studied array, we obtained a graph of the accumulated frequencies δaf (Figure 3).
In this figure, a straight line characterizes the average rate of formation of the array, assuming that each value makes the same contribution to the total population.
The broken line highlights three areas: KS -significant, KLS -less significant, KNSnon-significant features for evaluating the effectiveness of winter barley breeding.
As a result of the implementation of the algorithm according to this method, it was found that the hypothetical rate of formation of the array (Δ1) =0,037.The condition δi>Δ1 is satisfied by the first 14 elements of the array in question.That is KS =14.
Thus, the first KS = 14 features of assessing the effectiveness of winter barley breeding form 69% of the rank weight of the total flow of requirements (51,85% from all 27 traits by number).
According to the algorithm, Δ2=0,0769.Of the remaining 13 elements of the array, the condition δk>Δ2 satisfy the following 8 criteria for evaluating the effectiveness of winter barley breeding.That is KLS =8.
Thus, the following KLS = 8 features form 25% of the requirements (but 29,63% of the 27 features by number).
Next, we determined the scale of points for significant and the totality of significant and unimportant features on the assumption that the weight of each feature in percent was: -for significant features where RiS -rank assessment of the i-th significant feature; KS -the number of significant features (values-identifiers), numerically equal to 14.
-for a set of significant and non-significant features where RiSLS -rank assessment of the i-th by the totality of significant and unimportant features; KSLS -the number of a set of significant and non-significant features, numerically equal to 22.
For convenience, a 100-point rating scale was adopted, corresponding to the percentage distribution of the weight of features.Such a scale of 100 points corresponds to the sum of the points of the reference variety.
The calculation results are summarized in Table 2.
The calculation of a complex indicator for the compared variety (hybrid) is carried out according to the formulas, respectively, based on the score for significant and the totality of significant and unimportant features where  ∑ С ,  ∑ С -the value, respectively, of the complex indicator of the compared variety (hybrid) for significant and the totality of significant and unimportant traits of winter barley breeding; δi -the weight of the compared trait relative to the corresponding trait of the reference variety (hybrid), calculated as ВiCV, BiE -respectively, the value in absolute digitized expression of the value of the trait of the compared variety (hybrid) and the corresponding trait of the reference variety (hybrid).For example, this value was calculated (Table 3) for the varieties of winter barley Zhiguli, Timofey, Vivat, Yerema and Marusya of the ARC "Donskoy" breeding.
As a result of calculating the complex indicator, a diagram (Figure 4) was obtained for assessing winter barley varieties for the winter barley varieties under consideration.Based on the method of expert assessments, the ranking of signs (identifiers) of winter barley was carried out.Using a mathematical algorithm for structuring a stylistic array, significant, insignificant and insignificant estimated identifiers of the selection of the agricultural crop in question were identified.Together with the established ranking list of each trait, this served as the basis for the development of a methodology for comparative evaluation of the results of winter barley breeding according to a complex (integral) indicator, which was implemented in the analysis of varieties of breeding ARC "Donskoy" At the same time, it was found that the nature of the change in the indicator of a comprehensive assessment of the results of winter barley breeding when using an evaluation scale that takes into account both essential and a complex of essential and unimportant features are similar and equidistant.Therefore, for practical use, it is quite sufficient to use data on a significant part of winter barley traits, whose contribution, according to experts, is up to 69% by rank estimate.
The reliability of the result obtained is confirmed by a sufficient degree of agreement between the opinions of experts [the concordance coefficient is 0.6257 and the nonrandomness of this agreement (the calculated value of the Pearson criterion exceeds its tabular value at a significance of 0.01 by 2.5 times)].
The signs that significantly determine (up to 69%) the results of the evaluation of the selection work of winter barley in the amount of 14 have been established.
The methodology can be diversified in relation to other selectable agricultural crops.

Fig. 1 .
Fig. 1.The structure of the idea and its implementation in the development of a method for comparative evaluation of the results of winter barley breeding

Fig. 2 .Fi. 3 .
Fig. 2. Diagram of rank evaluation of traits taken into account when analyzing the results of winter barley breeding

Fig. 4 .
Fig. 4. Diagram of assessment of varieties of winter barley by a complex indicator

Table 1 .
Input data for calculating the Kendall and Pearson criteria

Table 2 .
The results of determining the scoring scale for the characteristics of the reference variety of winter barley

Table 3 .
The results of the calculation of the weight of the characteristics of the compared varieties of winter barley