Sturdy cycles in the chaotic Tribolium castaneum data series

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Because of the inherent discreteness of individuals, population dynamical models must be discrete variable systems. In case of strong nonlinearity, such systems interacting with noise can generate a great variety of patterns from nearly periodic behavior through complex combination of nearly periodic and chaotic patterns to noisy chaotic time series. The interaction of a population consisting of discrete individuals and demographic noise has been analyzed in laboratory population data Henson et al. (Science 294 (2001) 602; Proc. Roy. Soc. Ser. B 270 (2003) 1549). In this paper we point out that some of the cycles are fragile, i.e. they are sensitive to the discretization algorithm and to small variation of the model parameters, while others remain "sturdy" against the perturbations. We introduce a statistical algorithm to detect disjoint, nearly-periodic patterns in data series. We show that only the sturdy cycles of the discrete variable models appear in the data series significantly. Our analysis identified the quasiperiodic 11-cycle (emerging in the continuous model) to be present significantly only in one of the three experimental data series. Numerical simulations confirm that cycles can be detected only if noise is smaller than a certain critical level and population dynamics display the largest variety of nearly-periodic patterns if they are on the border of "grey" and "noisy" regions, defined in Domokos and Scheuring (J. Theor. Biol. 227 (2004) 535).

Original languageEnglish
Pages (from-to)127-139
Number of pages13
JournalTheoretical Population Biology
Volume67
Issue number2
DOIs
Publication statusPublished - Mar 2005

Fingerprint

Tribolium
Tribolium castaneum
Noise
Population
Population Dynamics
Demography
nonlinearity
time series analysis
population dynamics
demographic statistics
perturbation
time series
simulation

Keywords

  • Chaos
  • Discrete variable models
  • Intermittently periodic patterns
  • Time series analysis

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Ecology, Evolution, Behavior and Systematics

Cite this

Sturdy cycles in the chaotic Tribolium castaneum data series. / Scheuring, I.; Domokos, G.

In: Theoretical Population Biology, Vol. 67, No. 2, 03.2005, p. 127-139.

Research output: Contribution to journalArticle

@article{6073aee4856e438d965700e7c850fb5a,
title = "Sturdy cycles in the chaotic Tribolium castaneum data series",
abstract = "Because of the inherent discreteness of individuals, population dynamical models must be discrete variable systems. In case of strong nonlinearity, such systems interacting with noise can generate a great variety of patterns from nearly periodic behavior through complex combination of nearly periodic and chaotic patterns to noisy chaotic time series. The interaction of a population consisting of discrete individuals and demographic noise has been analyzed in laboratory population data Henson et al. (Science 294 (2001) 602; Proc. Roy. Soc. Ser. B 270 (2003) 1549). In this paper we point out that some of the cycles are fragile, i.e. they are sensitive to the discretization algorithm and to small variation of the model parameters, while others remain {"}sturdy{"} against the perturbations. We introduce a statistical algorithm to detect disjoint, nearly-periodic patterns in data series. We show that only the sturdy cycles of the discrete variable models appear in the data series significantly. Our analysis identified the quasiperiodic 11-cycle (emerging in the continuous model) to be present significantly only in one of the three experimental data series. Numerical simulations confirm that cycles can be detected only if noise is smaller than a certain critical level and population dynamics display the largest variety of nearly-periodic patterns if they are on the border of {"}grey{"} and {"}noisy{"} regions, defined in Domokos and Scheuring (J. Theor. Biol. 227 (2004) 535).",
keywords = "Chaos, Discrete variable models, Intermittently periodic patterns, Time series analysis",
author = "I. Scheuring and G. Domokos",
year = "2005",
month = "3",
doi = "10.1016/j.tpb.2004.11.002",
language = "English",
volume = "67",
pages = "127--139",
journal = "Theoretical Population Biology",
issn = "0040-5809",
publisher = "Academic Press Inc.",
number = "2",

}

TY - JOUR

T1 - Sturdy cycles in the chaotic Tribolium castaneum data series

AU - Scheuring, I.

AU - Domokos, G.

PY - 2005/3

Y1 - 2005/3

N2 - Because of the inherent discreteness of individuals, population dynamical models must be discrete variable systems. In case of strong nonlinearity, such systems interacting with noise can generate a great variety of patterns from nearly periodic behavior through complex combination of nearly periodic and chaotic patterns to noisy chaotic time series. The interaction of a population consisting of discrete individuals and demographic noise has been analyzed in laboratory population data Henson et al. (Science 294 (2001) 602; Proc. Roy. Soc. Ser. B 270 (2003) 1549). In this paper we point out that some of the cycles are fragile, i.e. they are sensitive to the discretization algorithm and to small variation of the model parameters, while others remain "sturdy" against the perturbations. We introduce a statistical algorithm to detect disjoint, nearly-periodic patterns in data series. We show that only the sturdy cycles of the discrete variable models appear in the data series significantly. Our analysis identified the quasiperiodic 11-cycle (emerging in the continuous model) to be present significantly only in one of the three experimental data series. Numerical simulations confirm that cycles can be detected only if noise is smaller than a certain critical level and population dynamics display the largest variety of nearly-periodic patterns if they are on the border of "grey" and "noisy" regions, defined in Domokos and Scheuring (J. Theor. Biol. 227 (2004) 535).

AB - Because of the inherent discreteness of individuals, population dynamical models must be discrete variable systems. In case of strong nonlinearity, such systems interacting with noise can generate a great variety of patterns from nearly periodic behavior through complex combination of nearly periodic and chaotic patterns to noisy chaotic time series. The interaction of a population consisting of discrete individuals and demographic noise has been analyzed in laboratory population data Henson et al. (Science 294 (2001) 602; Proc. Roy. Soc. Ser. B 270 (2003) 1549). In this paper we point out that some of the cycles are fragile, i.e. they are sensitive to the discretization algorithm and to small variation of the model parameters, while others remain "sturdy" against the perturbations. We introduce a statistical algorithm to detect disjoint, nearly-periodic patterns in data series. We show that only the sturdy cycles of the discrete variable models appear in the data series significantly. Our analysis identified the quasiperiodic 11-cycle (emerging in the continuous model) to be present significantly only in one of the three experimental data series. Numerical simulations confirm that cycles can be detected only if noise is smaller than a certain critical level and population dynamics display the largest variety of nearly-periodic patterns if they are on the border of "grey" and "noisy" regions, defined in Domokos and Scheuring (J. Theor. Biol. 227 (2004) 535).

KW - Chaos

KW - Discrete variable models

KW - Intermittently periodic patterns

KW - Time series analysis

UR - http://www.scopus.com/inward/record.url?scp=13744253617&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=13744253617&partnerID=8YFLogxK

U2 - 10.1016/j.tpb.2004.11.002

DO - 10.1016/j.tpb.2004.11.002

M3 - Article

C2 - 15713325

AN - SCOPUS:13744253617

VL - 67

SP - 127

EP - 139

JO - Theoretical Population Biology

JF - Theoretical Population Biology

SN - 0040-5809

IS - 2

ER -