Stationary rank-size relation for community of logistically growing groups

Hiromi Seno, Haruo Matsumoto

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


Rank-size relation derived from the size distribution for a number of growing groups is considered with a mathematical model described by a type of von Foerster equation. Size of each group grows in the logistic manner with the common intrinsic growth rate and carrying capacity. New groups are produced from present groups with a reproduction rate, which depends on the size of the mother group. Each group undergoes the extinction probability which depends on the group size. We discuss how the characteristics of some typical rank-size relations of the community of groups depend on the dynamical factors governing the community. It is shown that the typical rank-size relation requires specific form of the size-dependence of extinction rate, and we discuss how the observed typical rank-size relation could really reflect the dynamical factor governing the community.

Original languageEnglish
Pages (from-to)83-108
Number of pages26
JournalJournal of Biological Systems
Issue number1
Publication statusPublished - 1996 Mar


  • Group size
  • Logistic growth
  • Rank-size relation
  • Size distribution
  • Von Foerster equation


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