EMERGENCE OF ALLOMETRIC SCALING IN GENEALOGICAL TREES

Paulo R. A. Campos (), Viviane M. de Oliveira () and Leonardo P. Maia ()
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Paulo R. A. Campos: Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas, 13083-970 Campinas SP, Brazil
Viviane M. de Oliveira: Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas, 13083-970 Campinas SP, Brazil
Leonardo P. Maia: Instituto de Física de São Carlos, Universidade de São Paulo, Caixa Postal 369, 13560-970 São Carlos SP, Brazil

Advances in Complex Systems (ACS), 2004, vol. 07, issue 01, 39-46

Abstract: We investigate the emergence of power-law scalings in genealogical trees. Especially, we study the topological properties of genealogical trees both in the neutral evolution and the selective evolution. In all instances, we observe that the topologies of these trees are well described by a power-law scaling$C_k\sim A_k^\eta$, whereAkis the number of nodes which are direct or indirect descendants of nodekandCk=∑jAjwhere the sum is taken over all nodes that contribute toAk. This relation is well known in transportation networks as well as in metabolic networks, and it is referred to as allometric scaling. Furthermore, we observe a slight dependence of the scaling exponent η on the intensity of selection.

Keywords: Allometric scaling; coalescent theory; neutral evolution; selective evolution; power-law scalings (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1142/S0219525904000044

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