Branching-diffusion model for the formation of distributional patterns in populations

Yoh Iwasa, E. Teramoto

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

A continuous time branching-diffusion process model is presented to describe the development of spatial distributional patterns of a biological population. In the model each unit moves independently following diffusion processes on a plane, and multiplies or goes extinct at random times. Standard methods for measuring the degree of aggregation used in field ecology are applied to this model population. Kuno's CAindex using quadrat sampling is calculated, and the dependence of the index on time, quadrat size, initial density, and diffusion and branching rules, is discussed. Pielou's α index based on distance measurement is evaluated by the solution of a nonlinear partial differential equation. Both methods show that continuous-time branching-diffusion processes produce a contagious spatial pattern; as in a discrete-time model studied by Iwasa and Teramoto (1977).

Original languageEnglish
Pages (from-to)109-124
Number of pages16
JournalJournal of Mathematical Biology
Volume19
Issue number1
DOIs
Publication statusPublished - Jan 1 1984

Fingerprint

Diffusion Model
Diffusion Process
Branching
branching
Branching process
Continuous Time
Population
Branching Rules
Distance Measurement
Discrete-time Model
Spatial Pattern
Ecology
Population Model
Nonlinear Partial Differential Equations
Process Model
Distance measurement
Aggregation
Multiplication
Partial differential equations
Unit

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics

Cite this

Branching-diffusion model for the formation of distributional patterns in populations. / Iwasa, Yoh; Teramoto, E.

In: Journal of Mathematical Biology, Vol. 19, No. 1, 01.01.1984, p. 109-124.

Research output: Contribution to journalArticle

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