Showing papers on "Dendrogram published in 2010"

Molecular characterization and genetic diversity analysis of Jatropha curcas L. in India using RAPD and AFLP analysis

Abstract: Jatropha curcas L. belongs to family Euphorbiaceae, native to South America and widely distributed in South and Central America, attained significant importance for its seed oil which can be converted to biodiesel, a renewable energy source alternative to conventional petro-diesel. Very few attempts were made to understand the extent of genetic diversity that exists in J. curcas. Therefore, the present investigation was undertaken to asses the genetic diversity among 28 diverse germplasm collected from distinct geographical areas in India. The overall percentage of polymorphism (PP) was found to be 50.70 and 60.95 by RAPD and AFLP, respectively. The mean PP was found to be 9.72 and 20.57 by RAPD and AFLP, respectively. The mean genetic similarity was observed to be 0.89 by RAPD and 0.88 by AFLP. Among the germplasm JCI20 found to be the most diverged one. The dendrogram analysis of RAPD and AFLP data showed good congruence, but better resolution and more polymorphism was observed with AFLP. When the dendrogram of RAPD was compared with AFLP dendrogram, the major clustering pattern was found to be similar; however, changes in minor grouping were observed. In both RAPD and AFLP analysis clustering of germplasm did not show any correlation with the geographical area of collection. Low genetic diversity observed in J. curcas and the clustering pattern indicates that the distribution of species might have happened through anthropogenic activity and warrants the need for widening the genetic base. The present study will provide pavement for further intra-population studies on narrow geographical areas, to understand the population genetic structure, phylogeography, molecular ecological studies. The marker information and the characterized germplasm help in further improvement of the species through marker assisted breeding programs.

On goodness‐of‐fit measure for dendrogram‐based analyses

Abstract: Clustering methods are widely used tools in many aspects of science, such as ecology, medicine, or even market research, that commonly deal with dendrogram-based analyses. In such analyses, for a given initial dissimilarity matrix, the resulting dendrogram may strongly vary according to the selected clustering methods. However, numerous dendrogram-based analyses require adequate measurement for assessing of which of the clustering methods preserves most faithfully the initial dissimilarity matrix. While cophenetic correlation coefficient-based measures have been widely used for this purpose, we emphasize here that it is not always a suitable approach. We thus propose a measure based on a matrix norm, the 2-norm, to adequately check which of the resulting ultrametric distance matrices related to the dendrograms is the closest to the initial dissimilarity matrix. In addition, we also propose an objective way to define a benchmark value (threshold value) in order to assess whether the degree of conformity between the ultrametric distance matrix selected and the initial dissimilarity matrix is satisfactory. Our proposal may notably be incorporated within a recently proposed approach that involves the use of clustering methods in environmental science and beyond. In ecology, various functional diversity indices based on clustering species from their functional dissimilarities may benefit from this overall approach.

Analysis of genetic diversity in banana cultivars (Musa cvs.) from the South of Oman using AFLP markers and classification by phylogenetic, hierarchical clustering and principal component analyses

Abstract: Banana is an important crop grown in Oman and there is a dearth of information on its genetic diversity to assist in crop breeding and improvement programs. This study employed amplified fragment length polymorphism (AFLP) to investigate the genetic variation in local banana cultivars from the southern region of Oman. Using 12 primer combinations, a total of 1094 bands were scored, of which 1012 were polymorphic. Eighty-two unique markers were identified, which revealed the distinct separation of the seven cultivars. The results obtained show that AFLP can be used to differentiate the banana cultivars. Further classification by phylogenetic, hierarchical clustering and principal component analyses showed significant differences between the clusters found with molecular markers and those clusters created by previous studies using morphological analysis. Based on the analytical results, a consensus dendrogram of the banana cultivars is presented.

Hierarchical Agglomerative Clustering with Ordering Constraints

Abstract: Many previous researchers have converted background knowledge as constraints to obtain accurate clustering. These clustering methods are usually called constrained clustering. Previous ordering constraints are instance level non-hierarchical constraints, like must-link and cannot-link constraints, which do not provide hierarchical information. In order to incorporate the hierarchical background knowledge into agglomerative clustering, we extend instance-level constraint to hierarchical constraint in this paper. We name it as ordering constraint. Ordering constraints can be used to capture hierarchical side information and they allow the user to encode hierarchical knowledge such as ontologies into agglomerative algorithms. We experimented with ordering constraints on labeled newsgroup data. Experiments showed that the dendrogram generated by ordering constraints is more similar to the pre-known hierarchy than the dendrogram generated by previous agglomerative clustering algorithms. We believe this work will have a significant impact on the agglomerative clustering field.

RAPD Analysis among Pigeon pea (Cajanus cajan (L.) Mill sp.) Cultivars for their Genetic Diversity

Abstract: The genetic diversity of 17 cultivars of pigeon pea using 17 random amplified polymorphic DNA (RAPD) markers has been reported. A total of 198 bands were scored corresponding to an average of 11.6 bands per primer with 148 bands showing polymorphism (74.7%). Nine out of eighteen primers gave more than 80% polymorphism. Jaccard similarity coefficient ranged from 0.272 to 0.778. A dendrogram constructed based on the UPGMA clustering method revealed two major clusters. Cluster-I comprises of 12 cultivars which was further differentiated into two sub-clusters having six cultivars each. The cluster-II includes remaining five cultivars. The cultivar IPA-3088 was quite unique from the remaining cultivars as evident in the dendrogram.

Efficient clustering approach using incremental and hierarchical clustering methods

Abstract: There are many clustering methods available and each of them may give a different grouping of datasets. It is proven that hybrid clustering algorithms give efficient results over the other algorithms. In this paper, we propose an efficient hybrid clustering algorithm by combining the features of leader's method which is an incremental clustering method and complete linkage algorithm which is a hierarchical clustering procedure. It is most common to find the dissimilarity between two clusters as the distance between their centorids or the distance between two closest (or farthest) data points. However, these measures may not give efficient clustering results in all cases. So, we propose a new similarity measure, known as cohesion to find the intercluster distance. By using this measure of cohesion, a two level clustering algorithm is proposed, which runs in linear time to the size of input data set. We demonstrate the effectiveness of the clustering procedure by using the leader's algorithm and cohesion similarity measure. The proposed method works in two steps: In the first step, the features of incremental and hierarchical clustering methods are combined to partition the input data set into several smaller subclusters. In the second step, subclusters are merged continuously based on cohesion similarity measure. We demonstrate the effectiveness of this framework for the web mining applications.

The genetic characterization of Turkish watermelon (Citrullus lanatus) accessions using RAPD markers

Abstract: Genetic diversity of the Turkish watermelon genetic resources was evaluated using different Citrullus species, wild relatives, foreign landraces, open pollinated (OP) and commercial hybrid cultivars by RAPD markers. The germplasm was consisted of 303 accessions collected from various geographical regions. Twenty-two of 35 RAPD primers generated a total of 241 reproducible bands, 146 (60.6%) of which were polymorphic. Based on the RAPD data the genetic similarity coefficients were calculated and the dendrogram was constructed using UPGMA (Unweighted pair-group method with arithmetic average). Cluster analysis of the 303 accessions employing RAPD data resulted in a multi-branched dendrogram indicating that most of the Turkish accessions belonging to var. lanatus of Citrullus lanatus (Thunb.) Matsum et Nakai were grouped together. Accessions of different Citrullus species and Praecitrullus fistulosus (Stocks) Pangalo formed distant clusters from C. lanatus var. lanatus. Among 303 accessions, a subset of 56 accessions was selected representing different groups and a second dendrogram was constructed. The genetic similarity coefficients (GS) within the Turkish accessions were ranged from 0.76 to 1.00 with 0.94 average indicating that they are closely related. Taken together, our results indicated that low genetic variability exist among the watermelon genetic resources collected from Turkey contrary to their remarkable phenotypic diversity.

Comparative evaluation of maize inbred lines (zea mays l.) according to dus testing using morphological, physiological and molecular markers

Abstract: A major challenge facing those involved in the testing of new plant varieties for Distinctness, Uniformity and Stability (DUS) is the need to compare them against all those of 'common knowledge'. A set of maize inbred lines was used to compare how morphological, physiological characterization and RAPD molecular marker described variety relationships. All the inbred lines were confirmed as morphologically and physiologically distinct. At morphological level the maximum genetic distance (10.8) and least genetic distance (1.6) were found. For physiological characters distance varied from 0.35 to 1.92 and results from dendrogram, which was made on the basis of dissimilarity matrix, were grouped into five major clusters. From RAPD, random primers provide polymorphic amplification products; the distance varying 0.42 to 0.65 and dendrogram showed that these lines formed close clusters due to the less variation in these lines at molecular level. In the present study, the molecular markers also exposed useful genetic diversity and the visual displays appeared to disperse the lines somewhat more evenly over the plot than the morphological and physiological methods.

Particle Swarm Optimization Based Hierarchical Agglomerative Clustering

Abstract: Clustering- an important data mining task, which groups the data on the basis of similarities among the data, can be divided into two broad categories, partitional clustering and hierarchal. We combine these two methods and propose a novel clustering algorithm called Hierarchical Particle Swarm Optimization (HPSO) data clustering. The proposed algorithm exploits the swarm intelligence of cooperating agents in a decentralized environment. The experimental results were compared with benchmark clustering techniques, which include K-means, PSO clustering, Hierarchical Agglomerative clustering (HAC) and Density-Based Spatial Clustering of Applications with Noise (DBSCAN). The results are evidence of the effectiveness of Swarm based clustering and the capability to perform clustering in a hierarchical agglomerative manner.

Morphological and molecular characterization of Saudi wheat genotypes under drought stress

Abstract: The objectives of the present study were to compare the application and utility of random amplified polymorphic DNA (RAPD) and inter-simple sequence repeat (ISSR) marker techniques for analysis of genetic diversity among Saudi wheat genotypes under drought stress, compare genetic diversity estimated using molecular markers with agronomic performance under water stress to establish the degree of association between these techniques and develop drought tolerance-associated DNA markers. Twelve wheat genotypes were used in this study. They were evaluated phenotypically for drought tolerance and were planted under four irrigation treatments over two seasons to expose genotypes to different levels of drought stress during the grain filling period. The UPGMA dendrogram generated from the standardized agronomic data separated the twelve wheat genotypes into three main groups, which diverged at a similarity index of 0.42. The average genetic similarity among the twelve wheat genotypes was 0.50, with value ranging from 0.34 to 0.68. Two types of molecular markers, RAPD and ISSR, were assayed to determine the genetic diversity of 12 wheat genotypes. A high level of polymorphism was found with both RAPD and ISSR markers. In RAPD analyses, a total of 322 fragments were produced by the 30 primers. Of these 322 amplified fragments, 18.63% were not polymorphic; whereas, the remaining bands (81.37%) were polymorphic in one or more in the twelve genotypes. In ISSR analyses, 192 out of 238 bands (80.67%) were polymorphic. The dendrogram based on RAPD markers was not in accord with the dendrogram based on ISSR markers. The combined dendrogram agreed better with the groups of the wheat genotypes based on pedigree analysis than the dendrogram generated by ISSR or RAPD data alone. The correlation coefficient between RAPD and ISSR matrix was highly significant (0.534**, p > 0.001). Additionally, both RAPD and ISSR matrices showed significantly positive correlation (r = 0.94**and r = 0.77**, respectively) with RAPD+ISSR matrix. Specific RAPD and ISSR markers were developed successfully to identify drought tolerance genotype (Ksu103 and Ksu105) from drought sensitive genotype (Yecora Rojo). Thus, the markers identified in this study should be applicable for marker–assisted selection for the drought tolerance in wheat breeding programs.

Genetic relationships of the genera Onobrychis, Hedysarum, and Sartoria using seed storage proteins

Abstract: Fifteen species belonging to 3 genera (Onobrychis, Hedysarum and Sartoria), collected from different geographical regions of Turkey were studied for the polypeptide patterns of their seed storage proteins. The variability of seed storage proteins was analysed by sodium dodecyl sulphate-polyacrylamide gel electrophoresis (SDS-PAGE). As many as 72 bands were scored and a dendrogram was constructed using UPGMA (unweighted pair group method with arithmetic mean). The dendrogram of the electrophoretic protein profiles of seeds showed 2 main clusters. While the first cluster with further subclusters included Onobrychis species, the second cluster included Sartoria and Hedysarum species present in 2 separate subclusters. The results showed that Sartoria and Hedysarum are closer to each other than they are to Onobrychis. It is also suggested that Sartoria hedysaroides should be included in the genus Hedysarum. Additionally, it is concluded that seed storage protein profiles could be useful markers in studies of genetic diversity, genetic relationships, and classification of adapted cultivars.

A New Hierarchical Clustering Algorithm on Fuzzy Data (FHCA)

Abstract: 134 Abstract—This paper presents a novel approach to cluster Fuzzy numbers using hierarchical method to be called (FHCA). In this approach a Dendrogram is drawn over fuzzy numbers until we could cluster fuzzy numbers using hierarchical cluster tree with inconsistency coefficient or other useful measures. All the similar previous methods extended FCM (Fuzzy Clustering Method) to support fuzzy data. On contrary, the present work is based on hierarchical method, i.e., we extended the hierarchical clustering algorithm to cluster fuzzy data for the first time. Finally this approach has been compared with some of the newly presented methods in the literature. The major advantage of the algorithm is its fault tolerance against noisy samples.

Genetic similarity of Jatropha curcas accessions based on AFLP markers

Abstract: The genetic relationships between accessions of Jatropha (Jatropha curcas) were determined based on AFLP marker. A set of 50 plants from 12 accessions of J. curcas was analyzed with molecular data from 164 loci generated from 17 AFLP primer combinations. Molecular variance of data was analyzed by total decomposition between and within accessions. An UPGMA dendrogram was constructed based on genetic distances estimated by Jaccard's similarity coefficient. The well-defined dendrogram showed a cophenetic value of 0.91. Groups of plants were observed in six of the 12 accessions studied with similarity of over 30 %, indicating high genetic variability. The variation among accessions was estimated to be 0.275, also indicating high variability. These results show that the genetic variability of the studied J. curcas accessions is structured according to the origin and that a greater number of populations should be sampled to increase the genetic diversity of the studied genebank.

Evaluation Of Genetic Diversity In Pea (Pisum sativum L) Using RAPD Analysis

Abstract: Four RAPD primers (GM10, GM37, GM52 and GM100) were used to estimate genetic diversity in five Pisum cultivars. A total of 16 bands were scored corresponding to an average of 4 bands per primer with 6 bands showing polymorphism (37.5%). One out of 4 primers gave 75% polymorphism. Jaccard similarity coefficient ranged from 0.7692 to 0.9630. Similarity index reveals the maximum similarity between cultivars KPMR 925(G2) and KPMR 926(G3) , KPMR 926(G3) and KPMR 927(G4) i.e. 0.9630 and 0.963 respectively while distantly related cultivars were KPMR 922(G1) and KPMR926(G2) with Similarity index 0.7692. A dendrogram constructed based on the UPGMA clustering method revealed two major clusters. Cluster – I and Cluster-II comprising of two cultivars each. The cultivar KPMR 922(G1) occupies a distinct place as revealed in the dendrogram.

Genetic diversity of bee ecotypes in Turkey and evidence for geographical differences.

Abstract: Honeybees collected from 56 different areas of Turkey were analysed, using 12 morphometric characters. The multivariate statistical analysis of data and discriminant function analysis established seven different ecotypes spreading according to different coordinates of regions. UPGMA dendrogram based on the Mahalonobis distance showed that the studied colonies were clustered in four main regional groups like A. m. anatoliaca in central Anatolia, A.m. caucasica in the northern Anatolia, A. m. meda in southern and south-eastern Anatolia and A. m. carnica in the European part of Turkey.

Assessing genetic diversity of some potato (Solanum tuberosum L.) genotypes grown in Turkey using the AFLP marker technique

Abstract: In the present study, the level of polymorphism and the genetic relationships among 26 potato genotypes were studied by means of molecular markers using the amplified fragment length polymorphism (AFLP) technique. DNA was extracted from fresh leaves of the seedlings. Selective amplification products revealed a total of 191 polymorphic bands ranging from 8 to 45 for each combination. Scoring results were used to generate a tree in JMP software. The 26 samples formed six clades with varying number of members between one and eleven. Genetic distances among genotypes were calculated according to Jaccard’s formula, in Phylip 3.0 software. According to the results of genetic distance, dendrogram showed that genotypes 6/7-4 and 6/7-2 were the closest genotypes with a genetic distance of 0.13. On the other hand, genotypes Posof-10 and Marabel were the most distinct from each other with a genetic distance value of 0.55. The AFLP marker results showed a great consistency along with their pedigrees indicating the AFLP technique as a useful tool in the calculation of genetic distance of the potato genotypes.

Agglomerative Hierarchical Clustering

Abstract: 1. Abstract In this paper agglomerative hierarchical clustering (AHC) is described. The algorithms and distance functions which are frequently used in AHC are reviewed in terms of computational efficiency, sensitivity to noise and the types of clusters created. Techniques used in evaluating the resulting cluster set are described and dendrograms are explained and their usefulness in determining an optimal final cluster number is explored. The application of AHC to document collection searches is reviewed including a comparison of the performance of the AHC algorithms. In data mining, classification is a form of supervised learning where a model is trained on known class labels in the training dataset. If class labels are not available clustering can be used where the desired outcome is that instances within a cluster are more similar to each other than to instances in other clusters. As the model is not trained on class labels clustering is a form of unsupervised learning. Common applications of clustering include image grouping, genetic information comparison and information retrieval. Clustering types include partitional clustering which divides the dataset into a preselected number of clusters, instance density based clustering approaches and hierarchical clustering which is described in this paper. In divisive hierarchical clustering (DHC) the dataset is initially assigned to a single cluster which is then divided until all clusters contain a single instance. The opposite approach is called agglomerative hierarchical clustering (AHC) where each instance is initially assigned to a separate cluster and the closest clusters are then iteratively joined or agglomerated until all instances are contained in a single cluster (Figure 1). This paper will focus on AHC as it is more frequently used than DHC (Vesanto et al, 2000) and the information contained in this paper is also generally applicable to DHC. One advantage of AHC is that preselection of the final cluster number is not required allowing a domain expert to analyze the resulting cluster hierarchy in order to determine the optimal cluster number. AHC can be applied successfully to both regularly and irregularly shaped clusters if the appropriate algorithm is selected as described in section three. One of the disadvantages of AHC is that the decision to join clusters is localised to the two clusters being joined which can produce poor clustering decisions, and once joined clusters in AHC cannot be separated. AHC has significant computational overhead on large datasets as it requires the creation of a …

Interactive dendrogram controls

Abstract: Embodiments of the invention provide systems and methods for analyzing and presenting, e.g., displaying, a set of data. Analyzing the data can include grouping or clustering data that are similar in some way, e.g., similar ranges of quantities, similar categories, etc. and providing an interactive dendrogram representing the clustered data. More specifically, a method for providing an interactive representation of data of a data set can comprise clustering the data into a hierarchical set of clustered data. A dendrogram can be generated based on the clustered data and representing a hierarchy of the clustered data and displayed on a page of a user interface. A selection of a depth of the dendrogram can be received via the user interface and the page can be updated based on the selection of the depth of the dendrogram.

Analysis of genetic divergence in pea (Pisum sativum L.) using quantitative traits and RAPD markers

Abstract: Genetic diversity among 14 tall and 14 dwarf cultivars/elite lines of pea (Pisum sativum L.) was assessed based on 10 quantitative traits and 72 RAPD primers. Dendrogram based on quantitative traits revealed six clusters. In principal component analysis (PCA), the first three PCs together accounted for 61.48% of the total variation, and the grouping was consistent with that of UPGMA method. RAPD-based dendrogram showed three major clusters; cluster II was further divided into three subclusters. The first three PCs of RAPD data accounted for 29.28% of the total variation, and the grouping pattern was similar to that obtained by UPGMA. The tall genotypes in both the types of clustering indicated a lower level of diversity compared to the dwarf ones.The correlation estimated by Mantel test between the quantitative trait and RAPD matrices was non-significant (r = −0.26) for reason of targetting different genomic regions by RAPD markers the morphological traits. Cophenetic correlations which reflect the goodness of fit for a tree were 0.73 and 0.79 for quantitative traits based and RAPD based dendrogram, respectively.

Enhanced Hierarchical Clustering for Gene Expression data

Abstract: Micro arrays are used to assess the transcriptome of many biological systems that has generated an enormous amount of data. Cluster analysis is a technique used to group and analyze micro array data. Identification of groups of genes that manifest similar expression patterns is a key step in the analysis of gene expression data. Hierarchical clustering is the one of the clustering techniques used for this purpose. In this paper, we design an enhanced hierarchical clustering algorithm which scans the dataset and calculates distance matrix only once unlike other papers, (up to authors' knowledge). Our main contribution is to reduce time, even when a large database is analyzed. Also, the results of hierarchical clustering are represented as a binary tree which gives clarity in grouping and further helps to find clustered objects easily. Our algorithm is able to retrieve number of clusters with the help of cut distance and measures the quality with validation index in order to obtain the best one; does not require initial parameter like number of clusters.

Assessment of genetic diversity among chickpea cultivars of India using RAPD markers

Abstract: Sixty eight chickpea cultivars of India belonging to both Kabuli and Desi types were studied for the diversity using 60 RAPD primers. Among them 50 were found to be polymorphic. On the average 3.55 loci per marker was found for the entire population of 68 cultivars. Based on the banding pattern, the cluster analysis was done using UPGMA and the dendrogram was prepared. The similarity coefficient ranged from 0.71 to 0.90 among the genotypes. The PCA analysis also supported the finding from the dendrogram. It was found that the desi and Kabuli types did not segregate into two distinct groups which indicated that perhaps very few genes were responsible for the differentiation of chickpea in to Desi and Kabuli types during their evolution. In order to broaden the genetic base of the chickpea germplasm of India, efforts should be made to utilize the exotic germplasm and the wild relatives.

The cluster analysis of clones obtained from authochthonous cultivar Kreaca (Vitis vinifera L.)

Abstract: The purpose of this paper was to characterize the clones obtained from Kreaca, autochthonous grapevine cultivar of Banat. Based on examination of 6 important biological and technological properties, phenotypic and genetic divergence of 28 selected clones was established. The divergence was determined using ANOVA and hierarchical cluster analysis. Using variance analysis, for grape weight, yield, total acid content, sugar content and sugar/acid ratio very significant or significant differences were obtained between clones. The UPGA method was used and the Euclidean distance in order to determine the difference between the groups. Two clone groups were obtained on the dendrogram. The objective of clone differentiation was primarily cluster weight, although other properties were taken into account as well. As the most perspective clones for further investigation and production, that can be recommended, were clones 12/5/5, 56/11/7 and 69/11/7.

Morphological Variation and Geographical Distribution of Musa sp. cv. Rastali in Peninsular Malaysia

Abstract: This paper focuses on the morphological variation and geographical distribution of 29 accessions of Musa sp cv Rastali collected from Peninsular Malaysia The Principal Component Analysis (PCA) was carried out to identify the descriptor, ie the most important for characterization and classification of 29 accessions of Rastali Cluster analysis was conducted to explain the relationship among and within groups in the dendrogram, while mapping was carried out using the MapInfo Professional software 100 Seven groups were derived from the dendrogram and from the similarity indices, two accessions shared the value of 0 indicating that they have distinct differences in their reproductive morphology although there are of the same cultivars These differences indicate that the variation exists among the accessions Six accessions share the same value of 1 indicating that they are possible duplicates Two male reproductive morphological characteristics, the male neuter flower along the rachis and male bud shape were responsible to separate three accessions from the main group while bunch compartment and bunch orientation further separate the three accessions The cluster analysis showed that the geographical location, which was either too close or too far, was unrelated to the variation levels among the accessions

Genetic diversity among iranian cantaloupe landraces (cucumis melo l.) using microsatellite markers

Abstract: The genetic diversity among 43 accessions of melon (C.melo L.), 41 from Cantaloupensis group alongside two from Indorus group, was assessed by variation at simple sequence repeats marker bands using 18 pair primers. The extracted genomic DNA was amplified with 12 pair primers and PCR products were separated on a DNA sequencing gels. A total of 98 alleles were identified with an average of 4.90 alleles per primer combination. Genetic distances among the accessions ranged from 0.0 for the most similar to 0.76 for the most-diverged ones. The mean GD (Nei's coefficient) among accessions was 0.219. The average of polymorphic information contents (PIC) for the 12 melon SSR markers was 0.542. CMCT134b, CMTC168, CMBR43 and CMAT141 loci had respectively the highest PICs, which could be used for further analysis. Genetic relationships among accessions were represented by a dendrogram based on similarity coefficient matrix with UPGMA method. Cluster analysis classified the accessions into 11 major groups. Cluster analysis indicated wide range of diversity across the Iranian and foreign accessions. The most distance was detected between Mahali e Darab and Amrikaie (76%). In general, poor relation was found between geographical and genetic diversity, whereas some relations was observed in cluster 2. The tetraploid accessions were mainly placed in the group 1. Principle component analysis had a very good co-ordination with dendrogram of genetic diversity. These results suggest that the SSR markers are valuable tools for identification and diversity analysis in cantaloupensis.

Application of single-linkage clustering method in the analysis of growth rate of gross domestic product (GDP) At 1990 Constant Basic Prices (Million Naira)

Abstract: Single-linkage is one of the methods in cluster analysis, which is used, for determining natural groupings in multi-variate data. Given a data set with one or more characteristics, singlelinkage system classifies the data into clusters so that they are as similar as possible within each cluster and as different as possible between clusters. The objective is to show the closeness or similarity in the growth rate of GDP. Using the MINITAB software the similarity of the growth rate of GDP and the similarity in the years of production were shown. KEYWORDS: Dendrogram, tree-diagram, nearest neighbour, single-linkage clustering, hierarchical clustering

Analysis of Genetic Relationship Ornamental Fritillaria Germplasm Resources by ISSR Markers

Abstract: 22 Ornamental Fritillariagermplasm were used as materials for analyzing their genome polymorphism by ISSR markers.13primers selected from 100primers were used for ISSR amplification.A total of 178bands were generated,of which 160bands were polymorphic bands(the percentage of polymorphic band,PPB=90%).According to the results of ISSR amplification,which were analyzed to Jaccard similarity coefficient by NTSYSpc 2.10esoftware,the genetic similarity coefficient was 0.2338to 0.8788.The clustering dendrogram was constructed by UPGMA method.22Ornamental Fritillaria materials were divided into two major groups while the similarity coefficient was 0.50.The first group included original Sect.Fritillaria,evolvedS ect.Petilliumand Sect.Theresia.The second group included 3ornamental Fritillariain more evolved Sect.Liliorhiza.The species in one sect had closer phylogenetic relationship.