### Abstract

Environmental variation is ubiquitous, but its effects on nonlinear population dynamics are poorly understood. Using simple (unstructured) nonlinear models we investigate the effects of correlated noise on the dynamics of two otherwise independent populations (the Moran effect), i.e, we focus on noise rather than dispersion or trophic interaction as the cause of population synchrony. We find that below the bifurcation threshold for periodic behaviour (1) synchrony between populations is strongly dependent on the shape of the noise distribution but largely insensitive to which model is studied, (2) there is, in general, a loss of synchrony as the noise is filtered by the model, (3) for specially structured noise distributions this loss can be effectively eliminated over a restricted range of distribution parameter values even though the model might be nonlinear, (4) for unstructured models there is no evidence of correlation enhancement, a mechanism suggested by Moran, but above the bifurcation threshold enhancement is possible for weak noise through phase-locking, (5) rapid desynchronisation occurs as the chaotic regime is approached. To carry out the investigation the stochastic models are (a) reformulated in terms of their joint asymptotic probability distributions and (b) simulated to analyse temporal patterns.

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

Pages (from-to) | 343-351 |

Number of pages | 8 |

Journal | Oikos |

Volume | 93 |

DOIs | |

Publication status | Published - 2001 |

### Keywords

- SPATIAL SYNCHRONY
- ENVIRONMENTAL CORRELATION
- DYNAMICS
- SCALE
- DISPERSAL
- OUTBREAKS
- PATTERNS
- ECOLOGY
- SYSTEMS
- NOISE

### Cite this

*Oikos*,

*93*, 343-351. https://doi.org/10.1034/j.1600-0706.2001.930217.x

**The impact of stochasticity on the behaviour of nonlinear population models: synchrony and the Moran effect.** / Greenman, J. V.; Benton, Timothy Guy.

Research output: Contribution to journal › Article

*Oikos*, vol. 93, pp. 343-351. https://doi.org/10.1034/j.1600-0706.2001.930217.x

}

TY - JOUR

T1 - The impact of stochasticity on the behaviour of nonlinear population models: synchrony and the Moran effect

AU - Greenman, J. V.

AU - Benton, Timothy Guy

PY - 2001

Y1 - 2001

N2 - Environmental variation is ubiquitous, but its effects on nonlinear population dynamics are poorly understood. Using simple (unstructured) nonlinear models we investigate the effects of correlated noise on the dynamics of two otherwise independent populations (the Moran effect), i.e, we focus on noise rather than dispersion or trophic interaction as the cause of population synchrony. We find that below the bifurcation threshold for periodic behaviour (1) synchrony between populations is strongly dependent on the shape of the noise distribution but largely insensitive to which model is studied, (2) there is, in general, a loss of synchrony as the noise is filtered by the model, (3) for specially structured noise distributions this loss can be effectively eliminated over a restricted range of distribution parameter values even though the model might be nonlinear, (4) for unstructured models there is no evidence of correlation enhancement, a mechanism suggested by Moran, but above the bifurcation threshold enhancement is possible for weak noise through phase-locking, (5) rapid desynchronisation occurs as the chaotic regime is approached. To carry out the investigation the stochastic models are (a) reformulated in terms of their joint asymptotic probability distributions and (b) simulated to analyse temporal patterns.

AB - Environmental variation is ubiquitous, but its effects on nonlinear population dynamics are poorly understood. Using simple (unstructured) nonlinear models we investigate the effects of correlated noise on the dynamics of two otherwise independent populations (the Moran effect), i.e, we focus on noise rather than dispersion or trophic interaction as the cause of population synchrony. We find that below the bifurcation threshold for periodic behaviour (1) synchrony between populations is strongly dependent on the shape of the noise distribution but largely insensitive to which model is studied, (2) there is, in general, a loss of synchrony as the noise is filtered by the model, (3) for specially structured noise distributions this loss can be effectively eliminated over a restricted range of distribution parameter values even though the model might be nonlinear, (4) for unstructured models there is no evidence of correlation enhancement, a mechanism suggested by Moran, but above the bifurcation threshold enhancement is possible for weak noise through phase-locking, (5) rapid desynchronisation occurs as the chaotic regime is approached. To carry out the investigation the stochastic models are (a) reformulated in terms of their joint asymptotic probability distributions and (b) simulated to analyse temporal patterns.

KW - SPATIAL SYNCHRONY

KW - ENVIRONMENTAL CORRELATION

KW - DYNAMICS

KW - SCALE

KW - DISPERSAL

KW - OUTBREAKS

KW - PATTERNS

KW - ECOLOGY

KW - SYSTEMS

KW - NOISE

U2 - 10.1034/j.1600-0706.2001.930217.x

DO - 10.1034/j.1600-0706.2001.930217.x

M3 - Article

VL - 93

SP - 343

EP - 351

JO - Oikos

JF - Oikos

SN - 0030-1299

ER -