### Abstract

Animals and many plants are counted in discrete units. The collection of possible values (state space) of population numbers is thus a nonnegative integer lattice. Despite this fact, many mathematical population models assume a continuum of system states. The complex dynamics, such as chaos, often displayed by such continuous-state models have stimulated much ecological research; yet discrete-state models with bounded population size can display only cyclic behavior. Motivated by data from a population experiment, we compared the predictions of discrete-state and continuous-state population models. Neither the discrete- nor continuous-state models completely account for the data. Rather, the observed dynamics are explained by a stochastic blending of the chaotic dynamics predicted by the continuous-state model and the cyclic dynamics predicted by the discrete-state models. We suggest that such lattice effects could be an important component of natural population fluctuations.

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

Pages (from-to) | 602-605 |

Number of pages | 4 |

Journal | Science |

Volume | 294 |

Issue number | 5542 |

DOIs | |

State | Published - Oct 19 2001 |

Externally published | Yes |

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### ASJC Scopus subject areas

- General

### Cite this

*Science*,

*294*(5542), 602-605. https://doi.org/10.1126/science.1063358

**Lattice effects observed in chaotic dynamics of experimental populations.** / Henson, S. M.; Costantino, Robert F; Cushing, Jim M; Desharnais, R. A.; Dennis, B.; King, A. A.

Research output: Contribution to journal › Article

*Science*, vol. 294, no. 5542, pp. 602-605. https://doi.org/10.1126/science.1063358

}

TY - JOUR

T1 - Lattice effects observed in chaotic dynamics of experimental populations

AU - Henson, S. M.

AU - Costantino, Robert F

AU - Cushing, Jim M

AU - Desharnais, R. A.

AU - Dennis, B.

AU - King, A. A.

PY - 2001/10/19

Y1 - 2001/10/19

N2 - Animals and many plants are counted in discrete units. The collection of possible values (state space) of population numbers is thus a nonnegative integer lattice. Despite this fact, many mathematical population models assume a continuum of system states. The complex dynamics, such as chaos, often displayed by such continuous-state models have stimulated much ecological research; yet discrete-state models with bounded population size can display only cyclic behavior. Motivated by data from a population experiment, we compared the predictions of discrete-state and continuous-state population models. Neither the discrete- nor continuous-state models completely account for the data. Rather, the observed dynamics are explained by a stochastic blending of the chaotic dynamics predicted by the continuous-state model and the cyclic dynamics predicted by the discrete-state models. We suggest that such lattice effects could be an important component of natural population fluctuations.

AB - Animals and many plants are counted in discrete units. The collection of possible values (state space) of population numbers is thus a nonnegative integer lattice. Despite this fact, many mathematical population models assume a continuum of system states. The complex dynamics, such as chaos, often displayed by such continuous-state models have stimulated much ecological research; yet discrete-state models with bounded population size can display only cyclic behavior. Motivated by data from a population experiment, we compared the predictions of discrete-state and continuous-state population models. Neither the discrete- nor continuous-state models completely account for the data. Rather, the observed dynamics are explained by a stochastic blending of the chaotic dynamics predicted by the continuous-state model and the cyclic dynamics predicted by the discrete-state models. We suggest that such lattice effects could be an important component of natural population fluctuations.

UR - http://www.scopus.com/inward/record.url?scp=0035914070&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035914070&partnerID=8YFLogxK

U2 - 10.1126/science.1063358

DO - 10.1126/science.1063358

M3 - Article

C2 - 11641500

AN - SCOPUS:0035914070

VL - 294

SP - 602

EP - 605

JO - Science

JF - Science

SN - 0036-8075

IS - 5542

ER -