Power spectra reveal the influence of stochasticity on nonlinear population dynamics

Daniel C. Reuman, Robert A. Desharnais, Robert F Costantino, Omar S. Ahmad, Joel E. Cohen

Research output: Contribution to journalArticle

39 Citations (Scopus)

Abstract

Stochasticity alters the nonlinear dynamics of inherently cycling populations. The power spectrum can describe and explain the impacts of stochasticity. We fitted models to short observed time series of flour beetle populations in the frequency domain, then used a well fitting stochastic mechanistic model to generate detailed predictions of population spectra. Some predicted spectral peaks represent periodic phenomena induced or modified by stochasticity and were experimentally confirmed. For one experimental treatment, linearization theory explained that these peaks represent overcompensatory decay of deviations from deterministic oscillation. In another treatment, stochasticity caused frequent directional phase shifting around a cyclic attractor. This directional phase shifting was not explained by linearization theory and modified the periodicity of the system. If field systems exhibit directional phase shifting, then changing the intensity of demographic or environmental noise while holding constant the structure of the noise can change the main frequency of population fluctuations.

Original languageEnglish (US)
Pages (from-to)18860-18865
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Volume103
Issue number49
DOIs
StatePublished - Dec 5 2006

Fingerprint

Nonlinear Dynamics
Population Dynamics
Population
Noise
Beetles
Flour
Periodicity
Demography

Keywords

  • Flour beetle
  • Fourier transform
  • Strong noise
  • Tribolium
  • Weak noise

ASJC Scopus subject areas

  • Genetics
  • General

Cite this

Power spectra reveal the influence of stochasticity on nonlinear population dynamics. / Reuman, Daniel C.; Desharnais, Robert A.; Costantino, Robert F; Ahmad, Omar S.; Cohen, Joel E.

In: Proceedings of the National Academy of Sciences of the United States of America, Vol. 103, No. 49, 05.12.2006, p. 18860-18865.

Research output: Contribution to journalArticle

Reuman, Daniel C. ; Desharnais, Robert A. ; Costantino, Robert F ; Ahmad, Omar S. ; Cohen, Joel E. / Power spectra reveal the influence of stochasticity on nonlinear population dynamics. In: Proceedings of the National Academy of Sciences of the United States of America. 2006 ; Vol. 103, No. 49. pp. 18860-18865.
@article{a751c6448acc4b6a965518bf7869cbaf,
title = "Power spectra reveal the influence of stochasticity on nonlinear population dynamics",
abstract = "Stochasticity alters the nonlinear dynamics of inherently cycling populations. The power spectrum can describe and explain the impacts of stochasticity. We fitted models to short observed time series of flour beetle populations in the frequency domain, then used a well fitting stochastic mechanistic model to generate detailed predictions of population spectra. Some predicted spectral peaks represent periodic phenomena induced or modified by stochasticity and were experimentally confirmed. For one experimental treatment, linearization theory explained that these peaks represent overcompensatory decay of deviations from deterministic oscillation. In another treatment, stochasticity caused frequent directional phase shifting around a cyclic attractor. This directional phase shifting was not explained by linearization theory and modified the periodicity of the system. If field systems exhibit directional phase shifting, then changing the intensity of demographic or environmental noise while holding constant the structure of the noise can change the main frequency of population fluctuations.",
keywords = "Flour beetle, Fourier transform, Strong noise, Tribolium, Weak noise",
author = "Reuman, {Daniel C.} and Desharnais, {Robert A.} and Costantino, {Robert F} and Ahmad, {Omar S.} and Cohen, {Joel E.}",
year = "2006",
month = "12",
day = "5",
doi = "10.1073/pnas.0608571103",
language = "English (US)",
volume = "103",
pages = "18860--18865",
journal = "Proceedings of the National Academy of Sciences of the United States of America",
issn = "0027-8424",
number = "49",

}

TY - JOUR

T1 - Power spectra reveal the influence of stochasticity on nonlinear population dynamics

AU - Reuman, Daniel C.

AU - Desharnais, Robert A.

AU - Costantino, Robert F

AU - Ahmad, Omar S.

AU - Cohen, Joel E.

PY - 2006/12/5

Y1 - 2006/12/5

N2 - Stochasticity alters the nonlinear dynamics of inherently cycling populations. The power spectrum can describe and explain the impacts of stochasticity. We fitted models to short observed time series of flour beetle populations in the frequency domain, then used a well fitting stochastic mechanistic model to generate detailed predictions of population spectra. Some predicted spectral peaks represent periodic phenomena induced or modified by stochasticity and were experimentally confirmed. For one experimental treatment, linearization theory explained that these peaks represent overcompensatory decay of deviations from deterministic oscillation. In another treatment, stochasticity caused frequent directional phase shifting around a cyclic attractor. This directional phase shifting was not explained by linearization theory and modified the periodicity of the system. If field systems exhibit directional phase shifting, then changing the intensity of demographic or environmental noise while holding constant the structure of the noise can change the main frequency of population fluctuations.

AB - Stochasticity alters the nonlinear dynamics of inherently cycling populations. The power spectrum can describe and explain the impacts of stochasticity. We fitted models to short observed time series of flour beetle populations in the frequency domain, then used a well fitting stochastic mechanistic model to generate detailed predictions of population spectra. Some predicted spectral peaks represent periodic phenomena induced or modified by stochasticity and were experimentally confirmed. For one experimental treatment, linearization theory explained that these peaks represent overcompensatory decay of deviations from deterministic oscillation. In another treatment, stochasticity caused frequent directional phase shifting around a cyclic attractor. This directional phase shifting was not explained by linearization theory and modified the periodicity of the system. If field systems exhibit directional phase shifting, then changing the intensity of demographic or environmental noise while holding constant the structure of the noise can change the main frequency of population fluctuations.

KW - Flour beetle

KW - Fourier transform

KW - Strong noise

KW - Tribolium

KW - Weak noise

UR - http://www.scopus.com/inward/record.url?scp=33845498402&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33845498402&partnerID=8YFLogxK

U2 - 10.1073/pnas.0608571103

DO - 10.1073/pnas.0608571103

M3 - Article

VL - 103

SP - 18860

EP - 18865

JO - Proceedings of the National Academy of Sciences of the United States of America

JF - Proceedings of the National Academy of Sciences of the United States of America

SN - 0027-8424

IS - 49

ER -