## Abstract

If constancy is a measure of an ecosystem's (in) variability through time and stability is a measure of the system's ability to damp and recover from environmental perturbations, then constancy depends not only on stability but also on the frequency and amplitude of perturbations-the environmental "noise level". The stability of an ecosystem reflects its texture, extent, and viscosity (fine-scale structure); the noise level experienced by the system ("effective" noise level) reflects the level at any point ("ambient" noise level), the spectrum of stochastic scale (regional distribution of stochasticity), and the system's spatial extent (size, or number of patches included). The coefficient of variation of a limiting stochastic variate is a measure of the effective noise level. If p is the total number of patches in the system (its extent) and n is the number of contiguous patches with noise signals correlated through time (its stochastic scale), then the coefficient of variation is directly proportional to {Mathematical expression} whenever n<p. Thus ecosystems of small stochastic scale n or large size p damp out environmental noise by "spreading the risk" in space, thereby reducing their variability in time.

Original language | English |
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Pages (from-to) | 157-166 |

Number of pages | 10 |

Journal | Bulletin of Mathematical Biology |

Volume | 39 |

Issue number | 2 |

DOIs | |

State | Published - Mar 1977 |

### Bibliographical note

Funding Information:This argument was presented in preliminary form at the first meeting of the Society for Mathematical Biology, May 23-24, 1975, at Bowling Green State University, Bowling Green, Ohio. Support is gratefully acknowledged from NSF Grant GI-20 to It. E. Koenig and W. E. Cooper and from EPA Grant R-803859010 to A. W. A. Brown and E. D. Goodman. I thank J. E. Breck, W. E. Cooper, E. D. Goodman, D. J. Hall, and J. A. Van Sickle for helpful suggestions and discussion, and J, Kropp for typing the manuscript.

### Funding

This argument was presented in preliminary form at the first meeting of the Society for Mathematical Biology, May 23-24, 1975, at Bowling Green State University, Bowling Green, Ohio. Support is gratefully acknowledged from NSF Grant GI-20 to It. E. Koenig and W. E. Cooper and from EPA Grant R-803859010 to A. W. A. Brown and E. D. Goodman. I thank J. E. Breck, W. E. Cooper, E. D. Goodman, D. J. Hall, and J. A. Van Sickle for helpful suggestions and discussion, and J, Kropp for typing the manuscript.

Funders | Funder number |
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National Science Foundation (NSF) | GI-20 |

## ASJC Scopus subject areas

- General Neuroscience
- Immunology
- General Mathematics
- General Biochemistry, Genetics and Molecular Biology
- General Environmental Science
- Pharmacology
- General Agricultural and Biological Sciences
- Computational Theory and Mathematics