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arXiv:1201.2869q-bio.PE

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

Samuel Alexander

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?"

arXiv comments
16 pages, 7 figures. Fixing incorrect date in preprint
Journal reference
Acta Biotheoretica 61(2), pp.181--201, 2013
DOI
doi:10.1007/s10441-012-9168-y
Subjects
q-bio.PEPopulations and Evolution math.COCombinatorics

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Linked by 2 identifiable commenters in 3 comments across 3 threads, from Jan 2019 to Oct 2020.

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Discussed in comments3 threads

  1. Humans are more closely related than we commonly think 1 comment

    • The article is about simulation results, but I have a mathematically proven result for an idealized abstract species notion, published in an article in Acta Biotheoretica. Definition: An "infinitary species" is a set X of organisms which is (i) infinite, (ii) ancestrally closed…

      xamuelView on HNParent context

  2. HN-like math research discussion for Ph.D.s 1 comment

    • Nice idea, +1 for LaTeX titles! But the registration system should be way more open, you're discriminating against many math PhD's who are no longer in academia. I would have posted my paper there but I guess "@math.ohio-state.edu" isn't elite enough so I'll post it here and…

      xamuelView on HNParent context

  3. The Erdos Paradox 1 comment

    • I just read you paper, it’s quite fun! This comment was made with the belief that you claimed that all infinite graphs have this property. Anyways, I know it’s an old thread, but if anyone is reading this, I highly recommend reading it. Here is the paper…

      LolWolfView on HNParent context

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