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Infinite Graphs in Systematic Biology, with an Application to the Species Problem.
MedLine Citation:
PMID:  23297024     Owner:  NLM     Status:  Publisher    
Abstract/OtherAbstract:
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?"
Authors:
Samuel A Alexander
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Publication Detail:
Type:  JOURNAL ARTICLE     Date:  2013-1-8
Journal Detail:
Title:  Acta biotheoretica     Volume:  -     ISSN:  1572-8358     ISO Abbreviation:  Acta Biotheor.     Publication Date:  2013 Jan 
Date Detail:
Created Date:  2013-1-8     Completed Date:  -     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  0421520     Medline TA:  Acta Biotheor     Country:  -    
Other Details:
Languages:  ENG     Pagination:  -     Citation Subset:  -    
Affiliation:
Department of Mathematics, The Ohio State University, Columbus, OH, USA, alexander@math.ohio-state.edu.
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