Graphs and generalized tracks: quantifying Croizat's panbiogeography

-A quantitative approach to Croizat's panbiogeography is developed using graph theory. Croizat's main analytical tool, the "track" (a line on a map representing the distribution of one or more taxa), is equated with the graph-theoretic concept of the minimal-spanning tree. Tracks can be represented by two different matrices that enable incongruent tracks to be detected and shared elements (biogeographic homologies) to be identified. Tracks can be orientated using both phylogenetic and biogeographic criteria. "Nodes," which are regions where there are large numbers of tracks, are related to the concept of the connectivity of a point. The statistical significance of track concordance can be evaluated using permutation tests of association between matrices. Previous discussions of panbiogeography have often considered panbiogeography to be a phenetic technique similar to cluster analysis using matrices of biotic similarity, or a crude precursor of vicariance biogeography. This is rejected, and the relationship between vicariance biogeography and panbiogeography is discussed. Vicariance biogeography is shown to be a clique method based on the less amenable concept of the minimal Steiner tree. [Biogeography; cladistics; Croizat; generalized tracks; graph theory; panbiogeography; vicariance biogeography.] Tracks of the kind are beginning to win recognition in the literature, and the day cannot be far when they will be taken for granted as the statistical graphs which they factually are. Records of geographic distribution-like points, whatever the kind and nature-can always be connected along a line common to all to establish, to repeat, a graph, that is, one of the primary means of analytical discussion and comparison in science [Croizat, 1964:

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