Distinguishing between mean-field, moment dynamics and stochastic descriptions of birth-death-movement processes

Simpson, Matthew, Sharp, Jesse, & Baker, Ruth (2014) Distinguishing between mean-field, moment dynamics and stochastic descriptions of birth-death-movement processes. Physica A Statistical Mechanics and its Applications, 395, pp. 236-246.

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Abstract

Mathematical descriptions of birth–death–movement processes are often calibrated to measurements from cell biology experiments to quantify tissue growth rates. Here we describe and analyze a discrete model of a birth–death-movement process applied to a typical two–dimensional cell biology experiment. We present three different descriptions of the system:

(i) a standard mean–field description which neglects correlation effects and clustering;

(ii) a moment dynamics description which approximately incorporates correlation and clustering effects, and;

(iii) averaged data from repeated discrete simulations which directly incorporates correlation and clustering effects.

Comparing these three descriptions indicates that the mean–field and moment dynamics approaches are valid only for certain parameter regimes, and that both these descriptions fail to make accurate predictions of the system for sufficiently fast birth and death rates where the effects of spatial correlations and clustering are sufficiently strong. Without any method to distinguish between the parameter regimes where these three descriptions are valid, it is possible that either the mean–field or moment dynamics model could be calibrated to experimental data under inappropriate conditions, leading to errors in parameter estimation. In this work we demonstrate that a simple measurement of agent clustering and correlation, based on coordination number data, provides an indirect measure of agent correlation and clustering effects, and can therefore be used to make a distinction between the validity of the different descriptions of the birth–death–movement process.

Impact and interest:

7 citations in Scopus
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6 citations in Web of Science®

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ID Code: 63304
Item Type: Journal Article
Refereed: Yes
Keywords: birth-death process, continuum model, moment dynamics model, patchiness, clustering
DOI: 10.1016/j.physa.2013.10.026
ISSN: 0378-4371
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Biological Mathematics (010202)
Divisions: Current > Institutes > Institute of Health and Biomedical Innovation
Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2013 Elsevier
Copyright Statement: This is the author’s version of a work that was accepted for publication in Physica A Statistical Mechanics and its Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Physica A Statistical Mechanics and its Applications, [VOL 395, (2013)] DOI: 10.1016/j.physa.2013.10.026
Deposited On: 14 Oct 2013 00:28
Last Modified: 01 Feb 2016 17:28

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