### Abstract

A stochastic cellular automata model for the population dynamics of the army ant Eciton burchelli on Barro Colorado Island in Panama is set up. It is simulated on the computer and shown to give good agreement with biological data. It is analysed using two approximations akin to the mean field approximation in statistical mechanics, and good agreement with the simulations is obtained. Finally, the role of distance between successive statary phase bivouacs is discussed with regard to the rate of colony growth. There are two aspects of the biological system studied here that make it of general importance. First, the population is structured, since the size of each colony of army ants is crucial. Second, the spatial behaviour of the population, as in many others, is not diffusionlike, although it is random. This has implications for the kind of model that is chosen.

Original language | English |
---|---|

Pages (from-to) | 471-492 |

Number of pages | 22 |

Journal | Bulletin of Mathematical Biology |

Volume | 58 |

Issue number | 3 |

Publication status | Published - 1996 |

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### ASJC Scopus subject areas

- Agricultural and Biological Sciences(all)

### Cite this

*Bulletin of Mathematical Biology*,

*58*(3), 471-492.

**A mathematical model for the population dynamics of army ants.** / Britton, N. F.; Partridge, L. W.; Franks, N. R.

Research output: Contribution to journal › Article

*Bulletin of Mathematical Biology*, vol. 58, no. 3, pp. 471-492.

}

TY - JOUR

T1 - A mathematical model for the population dynamics of army ants

AU - Britton, N. F.

AU - Partridge, L. W.

AU - Franks, N. R.

PY - 1996

Y1 - 1996

N2 - A stochastic cellular automata model for the population dynamics of the army ant Eciton burchelli on Barro Colorado Island in Panama is set up. It is simulated on the computer and shown to give good agreement with biological data. It is analysed using two approximations akin to the mean field approximation in statistical mechanics, and good agreement with the simulations is obtained. Finally, the role of distance between successive statary phase bivouacs is discussed with regard to the rate of colony growth. There are two aspects of the biological system studied here that make it of general importance. First, the population is structured, since the size of each colony of army ants is crucial. Second, the spatial behaviour of the population, as in many others, is not diffusionlike, although it is random. This has implications for the kind of model that is chosen.

AB - A stochastic cellular automata model for the population dynamics of the army ant Eciton burchelli on Barro Colorado Island in Panama is set up. It is simulated on the computer and shown to give good agreement with biological data. It is analysed using two approximations akin to the mean field approximation in statistical mechanics, and good agreement with the simulations is obtained. Finally, the role of distance between successive statary phase bivouacs is discussed with regard to the rate of colony growth. There are two aspects of the biological system studied here that make it of general importance. First, the population is structured, since the size of each colony of army ants is crucial. Second, the spatial behaviour of the population, as in many others, is not diffusionlike, although it is random. This has implications for the kind of model that is chosen.

UR - http://www.scopus.com/inward/record.url?scp=0001513631&partnerID=8YFLogxK

M3 - Article

VL - 58

SP - 471

EP - 492

JO - Bulletin of Mathematical Biology

JF - Bulletin of Mathematical Biology

SN - 0092-8240

IS - 3

ER -