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New PDF release: A Century in Mathematics in America

By Peter Duren

ISBN-10: 0821801384

ISBN-13: 9780821801383

ISBN-10: 082180152X

ISBN-13: 9780821801529

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We see no in-principle reason why such a space could not be constructed. And encouragingly, a general morphospace has been developed for metazoan hard parts (Thomas and Reif 1993; Thomas, Shearman, and Stewart 2000). But in the meantime, while awaiting a completely general space, we are forced to rely on proxies. One could argue that number of taxa is a good proxy for disparity, but it is known that number of taxa and disparity can and do change somewhat independently, at least within certain clades (Foote 1996).

In the ZFEL view, such processes are treated as either forces or constraints. DNA error correction can be thought of either as a constraint or as the result of a force, selection. In biology, heredity by definition requires reproduction, and therefore implicit in the heredity requirement of the ZFEL is a requirement that organisms reproduce. 5 Constraints and Contrary Tendencies In this section, we consider the various constraints and contrary tendencies—including selection—that act against the ZFEL tendency in evolution, that is, the factors that reduce or limit diversity.

But in fact there is no contradiction. The apparent leveling of diversity is an artifact of the choice of a discrete measure, a measure that has a built-in constraint and that as a result is insensitive to further increases in disparity. Information-theoretic measures of diversity, such as the Shannon index, have this same insensitivity. Alternatively, one could say that the constraint is population size, which limits the degree to which a discrete measure can capture true diversity. In contrast, continuous measures of diversity, such as the statistical variance, range of variation, and so on, are not insensitive in this way.

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A Century in Mathematics in America by Peter Duren


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