A new graph-theoretic technique for the analysis of genetic resources data

The problems of analysing genetic resources data are reviewed, with particular reference to the use of graph-theoretic methods and to the concept of “validation”. A taxonomically difficult set of Stylosanthes (Leguminosae) accessions is subjected to classification, a minimum spanning tree, and a two-neighbour network. It is then subjected to a novel multiple-nearest-neighbour approach (program NEBALL) which provides a more detailed and exact summary of the configuration; this is validated by appeal to phytochemical, provenance and performance data. The results suggest that, providing the assumptions implicit in the model are met, the new technique may well be the most powerful yet available for the study of genetic resources data.

[1]  H. T. Clifford,et al.  Interrelationships among the liliatae: A graph theory approach , 1980 .

[2]  P. C. Young,et al.  Probabilistic tests and stopping rules associated with hierarchical classification techniques , 1979 .

[3]  J. H. Ward Hierarchical Grouping to Optimize an Objective Function , 1963 .

[4]  N. E. Borlaug,et al.  The utilization of collections in plant breeding and production. , 1970 .

[5]  W. Williams,et al.  Numerical analysis of variation patterns in the genus Stylosanthes as an aid to plant introduction and assessment , 1971 .

[6]  W. T. WILLIAMS,et al.  Logic of Computer-Based Intrinsic Classifications , 1965, Nature.

[7]  W. T. Williams,et al.  Strategy of evaluation of a collection of tropical herbaceous legumes from Brazil and Venezuela II. Evaluation in the quarantine glasshouse , 1979 .

[8]  W. T. Williams,et al.  Strategy of evaluation of a collection of tropical herbaceous legumes from Brazil and Venezuela I. Ecological evaluation at the point of collection , 1979 .

[9]  Robert S. Hill,et al.  A Stopping Rule for Partitioning Dendrograms , 1980, Botanical Gazette.

[10]  Bruce Tyler,et al.  Studies in Festuca. X. Observations on Germination and Seedling Cold Tolerance in Diploid Festuca pratensis and Tetraploid F. pratensis var. Apennina in Relation to Their Altitudinal Distribution , 1978 .

[11]  W. T. Williams,et al.  Network analysis of genetic resources data: II. The use of isozyme data in elucidating geographical relationships. , 1980 .

[12]  P. MacNaughton-Smith Some statistical and other numerical techniques for classifying individuals , 1966 .

[13]  W. T. Williams TWONET: A New Program for the Computation of a Two-Neighbour Network , 1980, Aust. Comput. J..

[14]  Colin W. Wrigley,et al.  Improved electrophoretic methods for identifying cereal varieties , 1979 .

[15]  R. Prim Shortest connection networks and some generalizations , 1957 .

[16]  H. C. Barrett,et al.  A Numerical Taxonomic Study of Affinity Relationships in Cultivated Citrus and Its Close Relatives , 1976 .

[17]  H. G. Baker,et al.  Taxonomy and the biological species concept in cultivated plants. , 1970 .

[18]  F. A. Bisby,et al.  Effects of varying character definitions on classification of Genisteae (Leguminosae) , 1977 .

[19]  W. T. Williams,et al.  Network analysis of genetic resources data: I. Geographical relationships , 1980 .

[20]  W. T. Williams,et al.  NEBALL and FINGRP: New Programs for Multiple Nearest-Neighbour Analyses , 1981, Aust. Comput. J..

[21]  Robert H Mohlenbrock,et al.  A Revision of the Genus Stylosanthes , 1957 .

[22]  E. J. Burr Cluster Sorting with Mixed Character Types, II - Fusion Strategies , 1970, Aust. Comput. J..

[23]  W. T. Williams,et al.  Strategy of evaluation of a collection of tropical herbaceous legumes from Brazil and Venezuela III. The use of ordination techniques in evaluation , 1979 .

[24]  E. J. Burr Cluster Sorting with Mixed Character Types, I - Standardization of Character Values , 1968, Aust. Comput. J..