Summary Minimum spanning trees (MST) and single linkage cluster analysis (SLCA) are explained and it is shown that all the information required for the SLCA of a set of points is contained in their MST. Known algorithms for finding the MST are discussed. They are efficient even when there are very many points; this makes a SLCA practicable when other methods of cluster analysis are not. The relevant computing procedures are published in the Algorithm section of the same issue of Applied Statistics. The use of the MST in the interpretation of vector diagrams arising in multivariate analysis is illustrated by an example.

The domestic apple (Malus domestica; also known as Malus pumila Mill.) has become a model fruit crop in which to study commercial traits such as disease and pest resistance, grafting, and flavor and health compound biosynthesis. To speed the discovery of genes involved in these traits, develop markers to map genes, and breed new cultivars, we have produced a substantial expressed sequence tag collection from various tissues of apple, focusing on fruit tissues of the cultivar Royal Gala. Over 150,000 expressed sequence tags have been collected from 43 different cDNA libraries representing 34 different tissues and treatments. Clustering of these sequences results in a set of 42,938 nonredundant sequences comprising 17,460 tentative contigs and 25,478 singletons, together representing what we predict are approximately one-half the expressed genes from apple. Many potential molecular markers are abundant in the apple transcripts. Dinucleotide repeats are found in 4,018 nonredundant sequences, mainly in the 5#-untranslated region of the gene, with a bias toward one repeat type (containing AG, 88%) and against another (repeats containing CG, 0.1%). Trinucleotide repeats are most common in the predicted coding regions and do not show a similar degree of sequence bias in their representation. Bi-allelic single-nucleotide polymorphisms are highly abundant with one found, on average, every 706 bp of transcribed DNA. Predictions of the numbers of representatives from protein families indicate the presence of many genes involved in disease resistance and the biosynthesis of flavor and health-associated compounds. Comparisons of some of these gene families with Arabidopsis (Arabidopsis thaliana) suggest instances where there have been duplications in the lineages leading to apple of biosynthetic and regulatory genes that are expressed in fruit. This resource paves the way for a concerted functional genomics effort in this important temperate fruit crop.

Background: Kiwifruit (Actinidia spp.) are a relatively new, but economically important crop grown in many different parts of the world. Commercial success is driven by the development of new cultivars with novel consumer traits including flavor, appearance, healthful components and convenience. To increase our understanding of the genetic diversity and gene-based control of these key traits in Actinidia, we have produced a collection of 132,577 expressed sequence tags (ESTs).

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Abstract.A [3-galactosidase (EC 3.2.1.23) capable of degrading a number of fruit cell-wall polysaccharides in vitro, was isolated from ripening kiwifruit (Actinidia deliciosa [A. Chev.] C.F. Liang et A.R. Ferguson cv. Hayward). The enzyme has a molecular weight of approximately 60 kDa by gel permeation and consists of several basic isoforms. Several polypeptides were enriched during purification, with 33-, 46-and 67-kDa bands being predominant after sodium dodecyl sulphate-polyacrylamide gel electrophoresis. The optimum activity of the enzyme against p-nitrophenyl-[3-D-galactopyranoside was at pH 3.2, but against a galactan purified from kiwifruit cell walls, it was at pH 4.9. The enzyme was specific for galactosyl residues in the [3-configuration, releasing galactose from a variety of kiwifruit cell-wall polysaccharide fractions including cell wall material, Na2CO3-soluble pectin, high-molecular-weight galactan, xyloglucan, and galactoglucomannan. A galactosylated glucuronomannan found throughout the kiwifruit plant was also a substrate for the enzyme. The results indicate that the enzyme attacks the non-reducing end of galactose side chains, cleaving single galactose residues which may be attached to the 2, 3, 4, or 6 position of the aglycone. Activity of the enzyme in-vitro was too low to account for the total loss of galactose from the cell walls during ripening. If the [3-galactosidase of this study is solely responsible for the removal of galactose from the cell wall during ripening then its in-vivo activity must be much greater than that observed in-vitro.