### Abstract

An age-structured population is considered in which the birth and death rates of an individual of age a is a function of the density of individuals older and/or younger than a. An existence/uniqueness theorem is proved for the McKendrick equation that governs the dynamics of the age distribution function. This proof shows how a decoupled ordinary differential equation for the total population size can be derived. This result makes a study of the population's asymptotic dynamics (indeed, often its global asymptotic dynamics) mathematically tractable. Several applications to models for intra-specific competition and predation are given.

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

Pages (from-to) | 705-729 |

Number of pages | 25 |

Journal | Journal of Mathematical Biology |

Volume | 32 |

Issue number | 7 |

DOIs | |

State | Published - 1994 |

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### Keywords

- Age-structured population dynamics
- Asymptotic dynamics
- Cannibalism
- Existence/uniqueness
- Global stability
- Hierarchical models
- Intra-specific competition
- McKendrick equations

### ASJC Scopus subject areas

- Agricultural and Biological Sciences (miscellaneous)
- Applied Mathematics
- Modeling and Simulation

### Cite this

**The dynamics of hierarchical age-structured populations.** / Cushing, Jim M.

Research output: Contribution to journal › Article

*Journal of Mathematical Biology*, vol. 32, no. 7, pp. 705-729. https://doi.org/10.1007/BF00163023

}

TY - JOUR

T1 - The dynamics of hierarchical age-structured populations

AU - Cushing, Jim M

PY - 1994

Y1 - 1994

N2 - An age-structured population is considered in which the birth and death rates of an individual of age a is a function of the density of individuals older and/or younger than a. An existence/uniqueness theorem is proved for the McKendrick equation that governs the dynamics of the age distribution function. This proof shows how a decoupled ordinary differential equation for the total population size can be derived. This result makes a study of the population's asymptotic dynamics (indeed, often its global asymptotic dynamics) mathematically tractable. Several applications to models for intra-specific competition and predation are given.

AB - An age-structured population is considered in which the birth and death rates of an individual of age a is a function of the density of individuals older and/or younger than a. An existence/uniqueness theorem is proved for the McKendrick equation that governs the dynamics of the age distribution function. This proof shows how a decoupled ordinary differential equation for the total population size can be derived. This result makes a study of the population's asymptotic dynamics (indeed, often its global asymptotic dynamics) mathematically tractable. Several applications to models for intra-specific competition and predation are given.

KW - Age-structured population dynamics

KW - Asymptotic dynamics

KW - Cannibalism

KW - Existence/uniqueness

KW - Global stability

KW - Hierarchical models

KW - Intra-specific competition

KW - McKendrick equations

UR - http://www.scopus.com/inward/record.url?scp=0004421042&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0004421042&partnerID=8YFLogxK

U2 - 10.1007/BF00163023

DO - 10.1007/BF00163023

M3 - Article

AN - SCOPUS:0004421042

VL - 32

SP - 705

EP - 729

JO - Journal of Mathematical Biology

JF - Journal of Mathematical Biology

SN - 0303-6812

IS - 7

ER -