### Abstract

The temporal dynamics of many natural populations involve intermittent rarity, that is, the alternation over variable periods of time of phases of extremely low abundance and short outbreaks. In this paper, we show that intermittent rarity can arise in simple community models as a result of competitive interactions within and between species. Intermittently rare species are typified as weak invaders in fluctuating communities. Although the dynamics of intermittent rarity are highly irregular, the distribution of time spent in phases of rarity ('rarity times') involves strong regularity. Specifically, intermittent rarity is governed by a well-defined power law. The scaling exponent (-3/2) is a universal feature of intermittent rarity: it does not depend on species demographic parameters; it is insensitive to environmental stochasticity; and the same exponent is found in very different models of nonstructured populations. The distribution of rarity times implies that the dynamics of rarity have no characteristic time scale. Yet, in practice, the universal scaling law offers a general form of prediction, in which one can calculate the frequency of occurrence of rarity phases of any given duration. Data on marine fish communities support the prediction of a -3/2 power law underlying the dynamics of intermittently rare species. The scale-free dynamics reported here place intermittent rarity in the same class as the critical states of other nonlinear dynamical systems in the physical sciences. At a critical state, general laws govern the systems' dynamics, irrespective to the specific details of the interactions between constituents.

Original language | English (US) |
---|---|

Pages (from-to) | 1505-1521 |

Number of pages | 17 |

Journal | Ecology |

Volume | 80 |

Issue number | 5 |

State | Published - Jul 1999 |

Externally published | Yes |

### Fingerprint

### Keywords

- Chaos
- Community dynamics
- Competition
- Criticality
- Franke-Yakubu model
- Gatto model
- Hochberg-Hawkins model
- Intermittent rarity
- Invasibility
- Power law
- Universal scaling

### ASJC Scopus subject areas

- Ecology

### Cite this

*Ecology*,

*80*(5), 1505-1521.

**Universal power laws govern intermittent rarity in communities of interacting species.** / Ferriere, Regis H J; Cazelles, Bernard.

Research output: Contribution to journal › Article

*Ecology*, vol. 80, no. 5, pp. 1505-1521.

}

TY - JOUR

T1 - Universal power laws govern intermittent rarity in communities of interacting species

AU - Ferriere, Regis H J

AU - Cazelles, Bernard

PY - 1999/7

Y1 - 1999/7

N2 - The temporal dynamics of many natural populations involve intermittent rarity, that is, the alternation over variable periods of time of phases of extremely low abundance and short outbreaks. In this paper, we show that intermittent rarity can arise in simple community models as a result of competitive interactions within and between species. Intermittently rare species are typified as weak invaders in fluctuating communities. Although the dynamics of intermittent rarity are highly irregular, the distribution of time spent in phases of rarity ('rarity times') involves strong regularity. Specifically, intermittent rarity is governed by a well-defined power law. The scaling exponent (-3/2) is a universal feature of intermittent rarity: it does not depend on species demographic parameters; it is insensitive to environmental stochasticity; and the same exponent is found in very different models of nonstructured populations. The distribution of rarity times implies that the dynamics of rarity have no characteristic time scale. Yet, in practice, the universal scaling law offers a general form of prediction, in which one can calculate the frequency of occurrence of rarity phases of any given duration. Data on marine fish communities support the prediction of a -3/2 power law underlying the dynamics of intermittently rare species. The scale-free dynamics reported here place intermittent rarity in the same class as the critical states of other nonlinear dynamical systems in the physical sciences. At a critical state, general laws govern the systems' dynamics, irrespective to the specific details of the interactions between constituents.

AB - The temporal dynamics of many natural populations involve intermittent rarity, that is, the alternation over variable periods of time of phases of extremely low abundance and short outbreaks. In this paper, we show that intermittent rarity can arise in simple community models as a result of competitive interactions within and between species. Intermittently rare species are typified as weak invaders in fluctuating communities. Although the dynamics of intermittent rarity are highly irregular, the distribution of time spent in phases of rarity ('rarity times') involves strong regularity. Specifically, intermittent rarity is governed by a well-defined power law. The scaling exponent (-3/2) is a universal feature of intermittent rarity: it does not depend on species demographic parameters; it is insensitive to environmental stochasticity; and the same exponent is found in very different models of nonstructured populations. The distribution of rarity times implies that the dynamics of rarity have no characteristic time scale. Yet, in practice, the universal scaling law offers a general form of prediction, in which one can calculate the frequency of occurrence of rarity phases of any given duration. Data on marine fish communities support the prediction of a -3/2 power law underlying the dynamics of intermittently rare species. The scale-free dynamics reported here place intermittent rarity in the same class as the critical states of other nonlinear dynamical systems in the physical sciences. At a critical state, general laws govern the systems' dynamics, irrespective to the specific details of the interactions between constituents.

KW - Chaos

KW - Community dynamics

KW - Competition

KW - Criticality

KW - Franke-Yakubu model

KW - Gatto model

KW - Hochberg-Hawkins model

KW - Intermittent rarity

KW - Invasibility

KW - Power law

KW - Universal scaling

UR - http://www.scopus.com/inward/record.url?scp=0032820438&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032820438&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0032820438

VL - 80

SP - 1505

EP - 1521

JO - Ecology

JF - Ecology

SN - 0012-9658

IS - 5

ER -