### Abstract

The Lotka-Volterra competition equations with periodic coefficients derived from the MacArthur-Levins theory of a one-dimensional resource niche are studied when the parameters are allowed to oscillate periodically in time. Specifically, niche positions and widths, resource availability and resource consumption rates are allowed small amplitude periodicities around a specified mean value. Two opposite cases are studied both analytically and numerically. First only resource consumption rates are allowed to oscillate while niche dimensions and resource availability are held constant. The resulting oscillations in population densities and the strength of the system stability as they depend upon crucial relative phase and amplitude differences between the species' consumption rates are studied. This leads to a clear notion of "temporal niche" and of the effects that such oscillations can have on competitive coexistence. Secondly, all system parameters are allowed to oscillate, although the oscillatory consumption rates are assumed identical for both species. The effects on the population density oscillations and their averages are studied and the "best" choice of the common, periodic resource consumption rate for these two "identical" species competing for similar (even identical) niches is considered.

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

Pages (from-to) | 381-403 |

Number of pages | 23 |

Journal | Journal of Mathematical Biology |

Volume | 24 |

Issue number | 4 |

DOIs | |

State | Published - Jul 1986 |

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### Keywords

- Lotka-Volterra competition
- MacArthur-Levins theory
- Periodic coefficients
- Temporal niche

### ASJC Scopus subject areas

- Mathematics (miscellaneous)
- Agricultural and Biological Sciences (miscellaneous)

### Cite this

**Periodic Lotka-Volterra competition equations.** / Cushing, Jim M.

Research output: Contribution to journal › Article

*Journal of Mathematical Biology*, vol. 24, no. 4, pp. 381-403. https://doi.org/10.1007/BF01236888

}

TY - JOUR

T1 - Periodic Lotka-Volterra competition equations

AU - Cushing, Jim M

PY - 1986/7

Y1 - 1986/7

N2 - The Lotka-Volterra competition equations with periodic coefficients derived from the MacArthur-Levins theory of a one-dimensional resource niche are studied when the parameters are allowed to oscillate periodically in time. Specifically, niche positions and widths, resource availability and resource consumption rates are allowed small amplitude periodicities around a specified mean value. Two opposite cases are studied both analytically and numerically. First only resource consumption rates are allowed to oscillate while niche dimensions and resource availability are held constant. The resulting oscillations in population densities and the strength of the system stability as they depend upon crucial relative phase and amplitude differences between the species' consumption rates are studied. This leads to a clear notion of "temporal niche" and of the effects that such oscillations can have on competitive coexistence. Secondly, all system parameters are allowed to oscillate, although the oscillatory consumption rates are assumed identical for both species. The effects on the population density oscillations and their averages are studied and the "best" choice of the common, periodic resource consumption rate for these two "identical" species competing for similar (even identical) niches is considered.

AB - The Lotka-Volterra competition equations with periodic coefficients derived from the MacArthur-Levins theory of a one-dimensional resource niche are studied when the parameters are allowed to oscillate periodically in time. Specifically, niche positions and widths, resource availability and resource consumption rates are allowed small amplitude periodicities around a specified mean value. Two opposite cases are studied both analytically and numerically. First only resource consumption rates are allowed to oscillate while niche dimensions and resource availability are held constant. The resulting oscillations in population densities and the strength of the system stability as they depend upon crucial relative phase and amplitude differences between the species' consumption rates are studied. This leads to a clear notion of "temporal niche" and of the effects that such oscillations can have on competitive coexistence. Secondly, all system parameters are allowed to oscillate, although the oscillatory consumption rates are assumed identical for both species. The effects on the population density oscillations and their averages are studied and the "best" choice of the common, periodic resource consumption rate for these two "identical" species competing for similar (even identical) niches is considered.

KW - Lotka-Volterra competition

KW - MacArthur-Levins theory

KW - Periodic coefficients

KW - Temporal niche

UR - http://www.scopus.com/inward/record.url?scp=0022885160&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0022885160&partnerID=8YFLogxK

U2 - 10.1007/BF01236888

DO - 10.1007/BF01236888

M3 - Article

C2 - 3805902

AN - SCOPUS:0022885160

VL - 24

SP - 381

EP - 403

JO - Journal of Mathematical Biology

JF - Journal of Mathematical Biology

SN - 0303-6812

IS - 4

ER -