Analytic solution of Hubbell's model of local community dynamics

  • McKane A
  • Alonso D
  • Sole R
  • 1


    Mendeley users who have this article in their library.
  • N/A


    Citations of this article.


Recent theoretical approaches to community structure and dynamics reveal that many large-scale features of community structure (such as species-rank distributions and species-area relations) can be explained by a so-called neutral model. Using this approach, species are taken to be equivalent and trophic relations are not taken into account explicitly. Here we provide a general analytic solution to the local community model of Hubbell's neutral theory of biodiversity by recasting it as an urn model, i.e. a Markovian description of states and their transitions. Both stationary and time-dependent distributions are analysed. The stationary distribution-also called the zero-sum multinomial-is given in closed form. An approximate form for the time-dependence is obtained by using an expansion of the master equation. The temporal evolution of the approximate distribution is shown to be a good representation for the true temporal evolution for a large range of parameter values. (C) 2003 Elsevier Inc. All rights reserved.

Author-supplied keywords

  • Hubbell's neutral theory
  • abundance distribution
  • analytic solution
  • community dynamics
  • sampling theory
  • selectively neutral alleles
  • zero-sum multinomial

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document

There are no full text links


  • A J McKane

  • D Alonso

  • R V Sole

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free