A Multivariate Method for Classifying Cultivars and Studying Group × Environment × Trait Interaction

Abstract

each observation with p traits measured in each environment is normally distributed. For r environments, the Classification methods are used in genetic resource conservation vector of each observation has dimensions 1 ϫ rp, where and plant breeding. The two-stage Ward-Modified Location Model (Ward-MLM) clustering strategy defines initial groups by the Ward rp ϭ trait-environment combinations (variables). method and the MLM is then used to improve those groups. The Lawrence and Krzanowski (1996) used the Location three-way clustering strategy considers the same trait measured in Model (LM), originally proposed by Olkin and Tate different environments as different variables (environment-trait com-(1961), for classifying n individuals when p continuous bination), so that the resulting clusters of cultivars have a small traits and q categorical traits are measured in one envigroup ϫ environment interaction (GEI) for all the traits included in ronment. The LM combines the levels of all q categorical the study. An important component of the GEI is the imperfect traits in one multinomial variable, W, with m levels (w ϭ genotypic correlation or crossover interaction (COI). This study used 1,2,…,m). Franco et al. (1998) modified the LM and the three-way Ward-MLM clustering strategy in three different data proposed the Modified Location Model (MLM), by assets with the objectives of (i) evaluating the ability of the Ward-MLM suming that the m levels of the W variable and the pmethodology for clustering cultivars into groups with low COI, (ii) obtaining a graphical representation of the variables in a low dimen-multinormal variables for each subpopulation, are indesional scatter plot produced by the multidimensional scaling method pendent. The authors proposed using the MLM in a (MDS) in which the GEI of continuous and categorical traits and two-stage clustering strategy where initial groups are environments can be visualized, and (iii) studying how the relationship defined by the Ward (or any other hierarchical clusterbetween a pair of traits changes across environments. The three-way ing strategy) method and the MLM is then used with Ward-MLM strategy produced groups of cultivars with low levels of those groups (Ward-MLM). COI. The increment of the correlation coefficient values betweenFranco et al. (1999) extended the Ward-MLM stratgroups with respect to the total correlation coefficients indicated that egy to the case of clustering three-way data of cultivar ϫ the groups formed by the three-way Ward-MLM strategy comprised environment ϫ trait. Thus, the vector of each observasubsets of individuals that had similar trait responses across envition for r environments is 1 ϫ (rp ϩ 1). The three-way ronments. Ward-MLM clustering strategy considers the same trait measured in different environments as different variables (environment-trait combinations). Since the Abbreviations: GM, Gaussian Mixture; LM, Location model; MLM, when all measured traits are continuous. The authors Modified location model; EM, Expectation maximizatio...

Soft-riser bench terrace design for the hilly loess region of Shaanxi Province, China

“…Afforestation can help conserve soil on degraded land by reducing soil erosion (Oscar, 2001), increasing soil organic matter, improving soil structure (Clark and Clark, 2000), assisting in nutrient cycling (Thomas, 2001), and improving landscape (Franco et al, 2003) and climate (Kooten et al, 2002) cultivate livelihoods in agroforestry that reduce pressure on forested lands (Ivanko, 2001). The increased soil cohesion or reinforcement provided by roots varies among plant species and soil types (Campbell and Hawkins, 2003;Thapa, 2003).…”

Genetic divergence on castor bean using the ward-mlm strategy

“…In the second stage, the mean of the vectors of the quantitative variable for each subpopulation, independent of the W values, is estimated by MLM procedure (CABRAL et al, 2010;FRANCO et al, 2003;CROSSA, 2002). Therefore, this strategy allows one to define the optimal number of groups and calculate the average of groups with high accuracy, using all available information on the genotypes, whether quantitative or qualitative variables (CROSSA; FRANCO, 2004).…”

Exploration of relationships between physiological parameters and growth performance of rice (Oryza sativa L.) seedlings under salinity stress using multivariate analysis

“…Cluster analysis was suggested as an effective method for comparing cultivars (Jolliffe et al, 1989). Cluster methods have been used to characterize plant germplasm and group genotypes into homogeneous clusters when trials were conducted under non-saline conditions at different locations (Crossa et al, 1995;Franco et al, 1999Franco et al, , 2003. Traditional Philippine upland rice cultivars have been classified by clusters analysis on growth characters under non-saline conditions (Schlösser et al, 2000).…”