[1] Magma mixing and crystal fractionation are fundamental processes that lead to the diversity of magma compositions, but rarely are all of the major and trace element data on whole rocks used simultaneously in evaluating proposed models. Polytopic vector analysis (PVA) is an oblique factor analysis procedure designed specifically to evaluate mixing or unmixing (fractional crystallization) in geologic systems using all of the analytes (major and trace elements) simultaneously. It differs from other techniques in that it not only determines the number of end-members and their compositions, but also partitions the relative proportions of the end-members into each sample in the data array. These samples, expressed as proportions of end-members, can be used as input in other multivariate analyses. The purpose of this paper is to use PVA to evaluate some examples of magma mixing and fractional crystallization and use these examples as templates for more complicated systems in order to show both the strengths and the weaknesses of the approach. Five well-constrained examples illustrate how PVA can discriminate between these two processes and provide additional petrogenetic information. Using PVA, mixing between magma types can be easily distinguished from crystal fractionation. With fractional crystallization the endmembers, generated by PVA, are the initial and final liquids and the compositions where new phases join the crystallizing assemblage.
The cotton-top tamarin is a nonhuman primate noted for susceptibility to juvenile onset colitis and subsequent colon cancer. About 80% develop colitis in captive environments outside the tropics. The aim was to determine the prevalence of colitis and colorectal cancer in tamarins living wild in their tropical habitat. Endoscopic biopsy was used to compare severity of colitis, inflammatory/immune cell densities, mucosal dysplasia, and occurrence of cancer in wild tamarins in a tropical habitat with tamarins living captive in a temperate climate. Six colon biopsies from each of 69 captives showed severe colitis in 64.5% of biopsies and moderate colitis in 19.5%. Severe colitis was not found in 88 wild tamarins; 13% had moderate colitis. Densities of polymorphonuclear leukocytes, plasma cells, and mononuclear cells in the lamina propria were related directly to the severity of four grades of colitis (normal, mild, moderate, and severe). Histologic or gross signs of carcinoma were detected in 12 captives and low- or high-grade dysplasia in 15. Neither cancer nor dysplasia was found in any of the wild tamarins. The observations suggest that colitis and cancer in the tamarin model are linked to environmental factors.
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