Related Experiment Video
Updated: Aug 30, 2026

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy
Published on: June 15, 2022
Analytic solution of Hubbell's model of local community dynamics
Alan J McKane1, David Alonso, Ricard V Solé
1Department of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK. alan.mckane@man.av.uk
Abstract:
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.
Related Concept Videos
Modeling with Differential Equations
Exponential Equations for Modeling Growth
Population Growth
One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation
On...
Reduced Mass Coordinates: Isolated Two-body Problem
Differential Equations: Problem Solving

