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Acta Biotheor. 2013 Jun;61(2):181-201. doi: 10.1007/s10441-012-9168-y. Epub 2013 Jan 8.

Infinite graphs in systematic biology, with an application to the species problem.

Author information

1
Department of Mathematics, The Ohio State University, Columbus, OH, USA. alexander@math.ohio-state.edu

Abstract

We argue that C. Darwin and more recently W. Hennig worked at times under the simplifying assumption of an eternal biosphere. So motivated, we explicitly consider the consequences which follow mathematically from this assumption, and the infinite graphs it leads to. This assumption admits certain clusters of organisms which have some ideal theoretical properties of species, shining some light onto the species problem. We prove a dualization of a law of T. A. Knight and C. Darwin, and sketch a decomposition result involving the internodons of D. Kornet, J. Metz and H. Schellinx. A further goal of this paper is to respond to B. Sturmfels' question, "Can biology lead to new theorems?"

PMID:
23297024
DOI:
10.1007/s10441-012-9168-y
[Indexed for MEDLINE]
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