Age- and density-dependent population dynamics in static and variable environments

William Gurney, R.M. Nisbet

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

We consider a general model of a single-species population with age- and density-dependent per capita birth and death rates. In a static environment we show that if the per capita death rate is independent of age, then the local stability of any stationary state is guaranteed by the requirement that, in the region of the steady state, the density dependence of the birth rate should be negative and that of the death rate positive. In a variable environment we show that, provided the system is locally stable, small environmental fluctuations will give rise to small age structure and population fluctuations which are related to the driving environmental fluctuations by a simple “transfer function.” We illustrate our general theory by examining a model with a per capita death rate which is age and density independent and a per capita birth rate which is zero up to some threshold age a0, adopts a finite density-dependent value up to a maximum age ao + α, and is zero thereafter. We conclude from this model that resonance due specifically to single-species age-structure effects will only be of practical importance in populations whose members have a life cycle consisting of a long immature phase followed by a short burst of intense reproductive effort (α ⪡ ao).
LanguageEnglish
Pages321-344
Number of pages24
JournalTheoretical Population Biology
Volume17
Issue number3
DOIs
Publication statusPublished - Jun 1980

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population dynamics
birth rate
age structure
reproductive effort
density dependence
transfer function
life cycle (organisms)
life cycle
immatures
rate

Keywords

  • death rates
  • local stability
  • birth rate
  • environmental fluctuations

Cite this

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Age- and density-dependent population dynamics in static and variable environments. / Gurney, William; Nisbet, R.M.

In: Theoretical Population Biology, Vol. 17, No. 3, 06.1980, p. 321-344.

Research output: Contribution to journalArticle

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AU - Nisbet, R.M.

PY - 1980/6

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N2 - We consider a general model of a single-species population with age- and density-dependent per capita birth and death rates. In a static environment we show that if the per capita death rate is independent of age, then the local stability of any stationary state is guaranteed by the requirement that, in the region of the steady state, the density dependence of the birth rate should be negative and that of the death rate positive. In a variable environment we show that, provided the system is locally stable, small environmental fluctuations will give rise to small age structure and population fluctuations which are related to the driving environmental fluctuations by a simple “transfer function.” We illustrate our general theory by examining a model with a per capita death rate which is age and density independent and a per capita birth rate which is zero up to some threshold age a0, adopts a finite density-dependent value up to a maximum age ao + α, and is zero thereafter. We conclude from this model that resonance due specifically to single-species age-structure effects will only be of practical importance in populations whose members have a life cycle consisting of a long immature phase followed by a short burst of intense reproductive effort (α ⪡ ao).

AB - We consider a general model of a single-species population with age- and density-dependent per capita birth and death rates. In a static environment we show that if the per capita death rate is independent of age, then the local stability of any stationary state is guaranteed by the requirement that, in the region of the steady state, the density dependence of the birth rate should be negative and that of the death rate positive. In a variable environment we show that, provided the system is locally stable, small environmental fluctuations will give rise to small age structure and population fluctuations which are related to the driving environmental fluctuations by a simple “transfer function.” We illustrate our general theory by examining a model with a per capita death rate which is age and density independent and a per capita birth rate which is zero up to some threshold age a0, adopts a finite density-dependent value up to a maximum age ao + α, and is zero thereafter. We conclude from this model that resonance due specifically to single-species age-structure effects will only be of practical importance in populations whose members have a life cycle consisting of a long immature phase followed by a short burst of intense reproductive effort (α ⪡ ao).

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