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Emergence Of Allometric Scaling In Genealogical Trees

Author

Listed:
  • 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)

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.

Suggested Citation

  • Paulo R. A. Campos & Viviane M. De Oliveira & Leonardo P. Maia, 2004. "Emergence Of Allometric Scaling In Genealogical Trees," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 39-46.
    • Handle: RePEc:wsi:acsxxx:v:07:y:2004:i:01:n:s0219525904000044
    DOI: 10.1142/S0219525904000044
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