### Abstract

Original language | English |
---|---|

Pages (from-to) | 289-311 |

Number of pages | 23 |

Journal | Theoretical Population Biology |

Volume | 25 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jun 1984 |

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### Keywords

- subpopulation dynamics
- behaviour fluctuations
- distributed-delay model

### Cite this

*Theoretical Population Biology*,

*25*(3), 289-311. https://doi.org/10.1016/0040-5809(84)90011-X

}

*Theoretical Population Biology*, vol. 25, no. 3, pp. 289-311. https://doi.org/10.1016/0040-5809(84)90011-X

**The dynamics of population models with distributed maturation periods.** / Blythe, S.P.; Nisbet, R.M.; Gurney, William.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The dynamics of population models with distributed maturation periods

AU - Blythe, S.P.

AU - Nisbet, R.M.

AU - Gurney, William

PY - 1984/6

Y1 - 1984/6

N2 - An integro-differential equation for the dynamics of a subpopulation of adults in a closed system where only the adults compete and where there is a distribution of maturation periods is described. We show how the careful choice of a general weighting function based on the gamma distribution with a shift in origin enables us to characterize adequately some observed maturation-period distributions, and also makes local stability and numerical analyses straightforward. Using these results we examine the progression in the behavior of the distributed-delay model as the distribution is narrowed toward the limit of a discrete delay. We conclude that while local stability properties approach those of the limiting equation very rapidly, the persistent fluctuation behavior converges more slowly, with the dominant period and maximum amplitude being least affected by the details of the distribution, and the fine structure of solutions being most sensitive. Finally, we examine the consequences for population modeling, and using several examples of insect populations, conclude that although quite often a full maturation-period distribution should be incorporated in a given model, in many cases a discrete-delay approximation will suffice.

AB - An integro-differential equation for the dynamics of a subpopulation of adults in a closed system where only the adults compete and where there is a distribution of maturation periods is described. We show how the careful choice of a general weighting function based on the gamma distribution with a shift in origin enables us to characterize adequately some observed maturation-period distributions, and also makes local stability and numerical analyses straightforward. Using these results we examine the progression in the behavior of the distributed-delay model as the distribution is narrowed toward the limit of a discrete delay. We conclude that while local stability properties approach those of the limiting equation very rapidly, the persistent fluctuation behavior converges more slowly, with the dominant period and maximum amplitude being least affected by the details of the distribution, and the fine structure of solutions being most sensitive. Finally, we examine the consequences for population modeling, and using several examples of insect populations, conclude that although quite often a full maturation-period distribution should be incorporated in a given model, in many cases a discrete-delay approximation will suffice.

KW - subpopulation dynamics

KW - behaviour fluctuations

KW - distributed-delay model

U2 - 10.1016/0040-5809(84)90011-X

DO - 10.1016/0040-5809(84)90011-X

M3 - Article

VL - 25

SP - 289

EP - 311

JO - Theoretical Population Biology

JF - Theoretical Population Biology

SN - 0040-5809

IS - 3

ER -