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of variety means using cluster analysis and dendrograms. Exp. Agricult. 25 :259–269. Christie B.R. Comparison of variety means using cluster analysis and dendrograms

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We investigated how cluster analysis and diversity-ordering can be used for the classification of geographically and historically distinct plant and insect communities. The study sites include fens and Brachypodium pinnatum dominated grasslands. The stands of the fen vegetation type could be arranged into similar groups by cluster analysis, principal component analysis and diversity ordering techniques. In the case of the B. pinnatum dominated grasslands of diverse development, however, no groups could be differentiated on the basis of either diversity ordering or ordination. Of the various cluster analyses, the result of global optimisation was similar to those of PCA ordination and diversity ordering techniques.

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Kaufman, L., Rousseeuw, P. J. (2005) Finding Groups in Data. An Introduction to Cluster Analysis . Wiley Series in Probability and Statistics. Wiley, Hoboken, N. J. Rousseeuw P. J

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Molecular-based characterization of open-pollinated varieties (OPVs) in maize is useful to define their unique profiles. A total of 58 SSR markers selected from a panel of 70 were used for genotyping three samples of 30, 50 and 100 plant bulks for each of 32 OPVs. The SSR markers detected a total of 253 alleles in the 32 maize OPVs across the three bulk samples. The number of alleles per marker varied from 2 to 7, with an overall mean of 4.36. The genetic distance among the OPVs varied from 0.17 to 0.93 with an average of 0.70 ± 0.007 for bulk samples of 30 plants, 0.20 to 0.91 with an overall mean of 0.70 ± 0.007 for bulk samples of 50 plants and from 0.30 to 0.95 with an average of 0.75 ± 0.006 for bulk samples of 100 plants. Cluster analysis separated the 32 maize OPVs into two major groups, which were further separated into two sub-groups for each type of bulk sample. The groupings of the OPVs into two major groups and their corresponding sub-groups was consistent with known breeding history (common parentage) and common target traits during development of the OPVs irrespective of the sample size used. However, in the bulk samples of 50 and 100 plants, some sub-groups were composed of OPVs with mixed maturity classes and diverse genetic backgrounds. Of the three independent bulk samples, the smallest sample size of 30 plants was found to be optimal for characterizing heterogeneous and heterozygous maize populations and OPVs owing to its cost-effectiveness and relative ease of sample processing.

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Cereal Research Communications
Authors: M. Rajabi Hashjin, M.H. Fotokian, M. Agahee Sarbrzeh, M. Mohammadi, and D. Talei

Knowledge of morpho-protein patterns of genetic diversity improves the efficiency of germplasm conservation and development. The objective of present study was to evaluate 116 genotypes of Triticum turgidum from seven countries in terms of morphological traits and seed protein banding patterns. The results showed highly significant differences among the genotypes for the traits. The correlation between grain yield and weight per spike was significant and positive, while the correlation between days to heading, length of peduncle and plant height was significant and negative. The factor analysis classified the traits in to four main groups which accounted for 74.4% of the total variability. Sixteen allelic compositions were identified in the genotypes for high molecular weight glutenin subunits. The three alleles were present at the Glu-A1 locus and 8 alleles at Glu-B1. The null allele was observed more frequently than the 1 and 2 alleles. Two alleles, namely 17 + 18 and 20, represented more frequent alleles at Glu-B1 locus. The genetic variability in Glu-A1and Glu-B1 loci were 0.42 and 0.81, respectively. The cluster analysis based on morphological traits and HMW-GS clustered the genotypes in to six and seven groups, respectively. The results indicated the presence of high genetic variability among the genotypes. Our findings suggest that the plants belong to different clusters can be used for hybridization to generate useful recombinants in the segregating generations, the genetics and breeding programs for improvement of durum wheat.

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The use of genetic markers allows the study of polymorphism and genetic distances between maize lines in greater depth than can be achieved on the basis of phenotype and DUS traits. The analysis of polymorphism between 46 maize inbred lines with known genetic background and the classification of these lines in related groups was carried out by means of morphological description, isoenzyme analysis, RAPD analysis, and identification using gene-linked microsatellite (SSR) markers. The genetic distance or degree of relationship between the lines was determined using cluster analysis. Only a very limited extent of allele polymorphism could be detected in isoenzyme analyses; the 46 lines formed only 18 gel electrophoresis groups. Nevertheless, on the basis of RAPD and SSR markers, all the lines could be distinguished from each other. This was reflected by the PIC (polymorphism index content) values, which ranged from 0.04 to 0.55 (mean 0.27) for the various enzyme loci, while far higher values were obtained for RAPD and SSR markers (0.20–0.91, mean 0.61, and 0.54–0.90, mean 0.73, respectively). Due to the large number of lines, two lines, derived from each other or from common parents, were chosen from each related group as the basis for grouping the lines according to genetic background. It was found that, while the individual marker systems only partially reflected the actual relationships between the lines, a joint processing of the genetic markers, supplemented with morphological data, revealed a close correlation between the groups formed on the dendrogram and the genetic background.

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In previous studies a minimum message length fuzzy clustering method was applied to vegetation data and shown to give sensible estimates for the number of clusters as well as consistent estimates of cluster parameters. The minimum message length method provides a principled method of choosing between models and between classes of models. It comprises 2 components; one coding the model and its associated (meta)parameter values, the other coding the data, given the model. The program uses uncorrelated Gaussian distributions as a model for the distribution of attributes within clusters. This assumption may not be acceptable and in this paper a more general model, the t-distribution, has been examined. The t-distribution provides a class of thick-tailed models, while including the Gaussian as a subclass. This should be appropriate in hierarchical clustering where, even if the final clusters had internal Gaussian distributions, the upper levels would not. In addition, it may provide a better model of within-cluster distribution of the attributes even in the final clusters. Although forcing the use of t-distributions was not profitable, allowing a choice between Gaussian and t-distributions for each attribute in each class resulted in improved results. This was despite only one attribute actually selecting the t-distribution over the Gaussian.

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Studies involving morphological description with both dominant (RAPD) and codominant (SSR, isoenzyme) molecular markers were made on 28 maize inbred lines of known genetic background with a final aim of prediction of heterosis. The genetic distance and degree of relationship between the lines was determined using cluster analysis. Only a very limited extent of allele polymorphism could be detected in isoenzyme analyses as the 28 lines formed only 16 gel electrophoretic groups, indicating that certain lines had identical isoenzyme patterns. On the basis of RAPD and gene-specific microsatellite (SSR) markers, however, all the lines could be distinguished from each other. When the lines were grouped according to genetic background it was found that although the individual marker systems only partially reflected the actual relationships between the lines, a joint processing of the data, supplemented with morphological data, revealed a close correlation between the groups formed on the dendrogram and the genetic background.

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Coenological results of six areas of several temperate grassland associations compared are taken in communities of, Asplenio septentrionali-Melicetum ciliatae, Cleistogeni-Festucetum sulcatae, Festucetum vaginatae, Potentillo-Festucetum pseudodalmaticae, Salvio nemorosae-Festucetum rupicolae, and Seslerietum heuflerianae-hungaricae associations. All of these stands of the associations are in protected areas, but these sample areas are close to endangered zones. We tried to refer to their function in ecophysiological respect of these grasslands.

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Breckenridge, J. N. (1989): Replicating cluster-analysis — methods, consistency, and validity. — Multivar. Behavioral. Res. 24 : 147–161. Breckenridge J. N

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