Selection of New Barley Advanced Lines Considering Several Agricultural Traits Simultaneously: Comparison of Two Mathematical Procedures

Plant breeders often handle large number of plants in a segregating population using limited resources. Therefore, the sooner they can reduce the number of plants to the barest minimum, but more importantly, to the most desirable and promising individuals, the better. The present short report deals with the selection of new advanced barley lines considering several agricultural traits simultaneously. We exemplify two new alternative uses of the Euclidean distance to identify the best 20% plant materials from a gamma radiation-mutant population. Plant height; days to flowering; plant lodging; coefficient of infection with leaf rust (Puccinia hordei), with powdery mildew (Blumeria graminis f. sp. hordei), with spot blotch (Cochliobolus sativus); yield; test weight; grain protein content and 1000 kernel weight were recorded and considered in the simultaneous selections described here. Essentially, selection indexes are proposed to calculate an overall value to a breeders' germplasm based on a number of traits. In reality, for many of the traits listed above, breeders are aiming for acceptable values such as for disease resistance and perhaps some morphological traits. For other traits, such as yield, the breeders are looking for the highest possible value. Therefore, each breeder will have different selection indexes; however, the mathematically defined indexes shown here would be particularly practical for plant breeders.


Introduction
For each crop there are a number of characters which considered together defining the overall desirability of the cultivar from the combined perspective of the producer and the consumer.These characters may range between about a dozen to several dozens and constitute the primary pool of characters that the breeder may target for improvement.These characters differ in economic and agronomic importance as well as easy with which they can be manipulated through breeding.Moreover, plant breeders often handle large number of plants in a segregating population using limited resources, e.g.time, space, labor and money.Therefore, the sooner they can reduce the number of plants to the barest minimum, but more importantly, to the most desirable and promising individuals, the better (Acquaah, 2007).
The present short report deals with the selection of new advanced lines considering several agricultural traits simultaneously.Various procedures have been described by Rodríguez-Fuentes, Pérez-Ponce and Fuchs (1987) and Acquaah (2007).It has been recommended to do one-trait-at-atime selection, and selection based on independent trait criteria (e.g.not more than 7 shoots per rice plant and not less than 180 grains per panicle).The scoring method based on an arbitrary scale designed by the breeder to score the plant traits has also been suggested.In the coefficient method, plant traits are scored according to the rate: trait value in the plant / trait average in the population.
Although this report only shows data of 55 plant materials to describe the new mathematical method, the complete breeding program developed at the National Agricultural University La Molina (Peru) involved more than 665 mutants and the parental material (control).Plant height; days to flowering; plant lodging; coefficient of infection with leaf rust (Puccinia hordei), with powdery mildew (Blumeria graminis f. sp.hordei), with spot blotch (Cochliobolus sativus); yield; test weight; grain protein content and 1000 kernel weight were recorded.To the best of our knowledge, the comparison shown in this paper has not been published to date.
Ten characters were recorded and each one was standardized to vary from 0 to 1 according to Kantardzic (2003).Two alternatives were compared, in the first one all agricultural traits had the same importance for the breeder, while in the second, yield and grain protein content were more relevant.In both strategies, the breeder searched for: maximum values of yield, mass of 1000 grains and hectoliter mass (test weight); minimum values of plant height and lodging, number of days to flowering, and coefficients of fungal infections; and 12% of grain protein content.~ 3 ~ Table 1 shows the quantitative data of 54 mutants and the original plant material.Figure 1 shows the selection of new plant materials considering several agricultural traits simultaneously.Following the first alternative, where all characters had the same relevance, the following materials should be selected for further evaluation in the next generation: 8, 23, 24, 19, 30, 42, original, 20, 48, 13 and 45 (11 out of 55, 20%).

Results
Results obtained following the second alternative, where yield and grain protein content had increased relevance over the other traits, identified 24, 8, 23, 19, 30, 16, 18, 13, 9, 49 and original as the best materials.Results of both alternatives were quite similar but materials were sorted differently.The breeder's experience is essential to increase the relative relevance of some traits, as shown in the second alternative.

Discussion
We have previously used the Euclidean distance to identify the best treatment in plant biotechnology experiments (Lorenzo et al., 2013).Moreover, in our plant breeding research, we have employed the Euclidean distance to recognize the best field performance of new in vitro androgenesis-derived double haploids of barley (Gomez-Pando et al., 2009).This paper shows a novel mathematical procedure useful for plant breeders that handle thousands plants in the field.

Table 1 .
Original data.The complete experimental program involved evaluation of more than 600 potential new plant genetic materials