Recursive Algorithm for Determination of Proximal (Thiessen) Polygons in Any Metric Space

A new and recursive algorithm for determining proximal polygons is based on quadtree concepts. The algorithm can use any distance metric, and produces a quadtree of the image of the proximal polygons. This can be converted to vector form, or be incorporated directly into a quadtree-based geographic information system, in order to solve a number of closest-point problems. The algorithm can also produce the Delaunay triangulation, which is the dual of the proximal polygons. Empirically, the running time of the algorithm is proportional to the number of centers raised to the 1.6 power.     

A lesson from Bass Strait on connectivity conservation

Isolation effects on the distributions of plant species in fragmented forests appear to be weak over tens to hundreds of years and strong over geological eras. The 250 km wide, 6.5 millennia old Bass Strait, and other millennium-scale disjunctions in the range of Eucalyptus regnans forests, were used to determine the effects of intermediate periods of isolation on plant species occurrence and composition. Three of six floristic communities were found on both sides of Bass Strait. The residuals from multiple regression models using climatic variables on the latitude vector were not explained by latitude, indicating negligible isolation effects from Bass Strait. However, there was a lesser compositional effect of disjunctions within land masses than between land masses, suggesting some effect of the larger barrier. No species that commonly occurred with E. regnans and were largely confined to wet forest exhibited absences from any region where the climate and soils were within their range. If areas isolated from each other for millennia can maintain their vascular plant biota, the expenditure of conservation funds on creating corridors to connect large areas separated by anthropogenic landscape modification might require more justification than it is currently afforded.     

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Historical Archaeology -