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Article Excerpt
LENTIL is an annual legume best adapted to cool climate conditions and is traditionally grown as a rainfed crop in the Middle East. Legumes and especially lentil are the most important food crops in developing countries such as Iran. Lentil seed is a rich source of good protein (up to 28%) in human diets in arid and semiarid areas of west Asia (Sarker et al., 2003). Iranian farmers currently use landraces (e.g., Kermanshah) and pure lines (e.g., Gachsaran), which have good seed size and are adapted to local rainfed conditions. The yield performance of these varieties is very low (typically about 475 kg [ha.sup.-1]) compared with the highest global yields (1306 kg [ha.sup.-1], produced in Canada; FAO, 2001). Iran has had an important lentil-breeding program in recent years, supported by the International Center for Agricultural Research in Dry Areas (ICARDA). Increasing the genetic potential of yield is an important objective of lentil breeding programs in Iran and other countries. The improved lentil genotypes are evaluated in METs to test their performance across different environments and to select the best genotypes in specific environments. In most cases, G x E interaction is observed, complicating selection for improved yield.
Interpretation of G x E interaction can be aided by statistical modeling. Models can be linear formulations such as joint-regression (Yates and Cochran, 1938; Eberhart and Russell, 1966), multivariate clustering techniques (Lin and Butler, 1990), multiplicative formulations such as additive main effects and multiplicative interaction (AMMI; Zobel et al., 1988; Gauch, 1992), or nonparametric methods (Huehn, 1979). Modeling G x E interaction in METs helps to determine phenotypic stability of genotypes, but this concept has been defined in different ways and increasing numbers of stability parameters has been developed (Gauch and Zobel, 1996).
Huehn (1996) indicated that there are two major approaches to studying G x E interaction and determining adaptation of genotypes. The first and most common approach is parametric, which relies on distributional assumptions about genotypic, environmental, and G x E effects. The second major approach is the nonparametric or analytical clustering approach, which relates environments and phenotypes relative to biotic and abiotic environmental factors without making specific modeling assumptions. For practical applications, however, most breeding programs incorporate some elements of both approaches (Becker and Leon, 1988).
The parametric stability methods have good properties under certain statistical assumptions, like normal distribution of errors and interaction effects; however, they may not perform well if these assumptions are violated (Huehn, 1990). That means parametric tests for significance of variances and variance-related measures could be very sensitive to the underlying assumptions. Thus, it is wise to search for alternative approaches that are more robust to departures from common assumptions, such as nonparametric measures (Nassar and Huehn, 1987; Huehn and Nassar, 1989).
Several nonparametric procedures proposed by Huehn (1979), Nassar and Huehn (1987), Kang (1988), Fox et al. (1990), and Thennarasu (1995) are based on the ranks of genotypes in each environment and genotypes with similar ranking across environments are classified as stable. Huehn (1979) and Nassar and Huehn (1987) proposed four nonparametric measures of phenotypic stability (1) [S.sup.(1).sub.i] is the mean of the absolute rank differences of a genotype over the n environments, (2) [S.sup.(2).sub.i] is the variance among the ranks over the n environments, (3) [S.sup.(3).sub.i] and [S.sup.(6).sub.i] are the sum of the absolute deviations and sum of squares of rank for each genotype relative to the mean of ranks, respectively. Kang (1988) assigned ranks for mean yield, with the genotype with the highest yield receiving the rank of 1, and ranks for the stability variance of Shukla (1972), with the lowest estimated value receiving the rank of 1. The sum of these two ranks provides a final index, in which the genotype with lowest rank-sum is regarded as the most desirable. Fox et al. (1990) suggested a nonparametric superiority measure for general adaptability. They used stratified ranking of the cultivars and ranking was done at each environment separately; the proportion of sites at which the cultivar occurred in the top, middle, and bottom third of the ranks was computed to form the nonparametric measures TOP, MID, and LOW, respectively. A genotype that occurred mostly in the top third (high value of TOP) was considered as a widely adapted genotype. Thennarasu (1995) proposed as stability measures the nonparametric statistics N[P.sup.(1).sub.i], N[P.sup.(2).sub.i], N[P.sup.(3).sub.i], and N[P.sup.(4).sub.i] based on ranks of adjusted means of the genotypes in each environment, and defined stable genotypes as those whose position in relation to the others remained unaltered in the set of environments assessed.
According to Huehn (1990), the nonparametric procedures have the following advantages over the parametric stability methods: they reduce the bias caused by outliers, no assumptions are needed about the distribution of the observed values, they are easy to use and interpret, and additions or deletions of one or few genotypes do not cause much variation of results.
Many statistical procedures have been proposed to study G x E interactions (Westcott, 1986; Crossa, 1990; Lin and Binns, 1994; Kang and Gauch, 1996). Most of these procedures, however, fail to distinguish between significant crossover and noncrossover (usual) interactions (Baker, 1990). Nonparametric statistical procedures for the test of crossover interactions have been developed in the field of medicine and...
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