The systematic formulation of tractable single-species models incorporating age structure

William Gurney, R.M. Nisbet, J.H. Lawton

Research output: Contribution to journalArticle

173 Citations (Scopus)

Abstract

(1) We develop a mathematically rigorous approach to modelling the effects of age structure, in which the life-history of a species is divided into age classes of arbitrary duration and attention is focused on the sub-populations of the various classes. (2) By assuming that all individuals in a particular age class have the same birth and death rates (which may be time- and density-dependent), we reduce the normal integro-differential equations describing an age-structured population with overlapping generations to a set of coupled ordinary delay-differential equations which are readily integrated numerically. (3) We illustrate the use of the formalism in the construction and analysis of two models of laboratory insect populations: a detailed model of Nicholson's blowflies and a `strategic' model of larval competition intended to refine the design of experiments in progress on the dynamics of the Indian meal-moth Plodia interpunctella (Hubner). (4) The model of Nicholson's blowflies is dynamically identical to a model previously derived heuristically. We have fitted the parameters using a more comprehensive range of data, and have illustrated explicitly the passage of large, quasi-cyclic fluctuations through the age structure. (5) We use the larval competition model to distinguish the effects of `uniform competition' (all larvae competing) and `cohort competition' (larvae of a given age competing). The former can produce quasi-cycles of a type characteristic of delayed regulation, while the latter causes quasi-cycles consisting of `bursts' of population propagating through the age structure. (6) We also use the larval competition model to demonstrate that apparently minor changes in the description of adult survival can induce dramatic alterations in model behaviour. This supports our emphasis on rigour in the formulation of the model, so as to distinguish genuinely interesting dynamics from mathematical artifacts.
LanguageEnglish
Pages479-495
Number of pages17
JournalJournal of Animal Ecology
Volume52
Issue number2
Publication statusPublished - Jun 1983

Fingerprint

age structure
Plodia interpunctella
age class
Calliphoridae
larva
birth rate
larvae
subpopulation
moth
artifact
life history
insect
experimental design
insects
duration
modeling

Keywords

  • cyclic fluctuations
  • insect populations
  • competition model

Cite this

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abstract = "(1) We develop a mathematically rigorous approach to modelling the effects of age structure, in which the life-history of a species is divided into age classes of arbitrary duration and attention is focused on the sub-populations of the various classes. (2) By assuming that all individuals in a particular age class have the same birth and death rates (which may be time- and density-dependent), we reduce the normal integro-differential equations describing an age-structured population with overlapping generations to a set of coupled ordinary delay-differential equations which are readily integrated numerically. (3) We illustrate the use of the formalism in the construction and analysis of two models of laboratory insect populations: a detailed model of Nicholson's blowflies and a `strategic' model of larval competition intended to refine the design of experiments in progress on the dynamics of the Indian meal-moth Plodia interpunctella (Hubner). (4) The model of Nicholson's blowflies is dynamically identical to a model previously derived heuristically. We have fitted the parameters using a more comprehensive range of data, and have illustrated explicitly the passage of large, quasi-cyclic fluctuations through the age structure. (5) We use the larval competition model to distinguish the effects of `uniform competition' (all larvae competing) and `cohort competition' (larvae of a given age competing). The former can produce quasi-cycles of a type characteristic of delayed regulation, while the latter causes quasi-cycles consisting of `bursts' of population propagating through the age structure. (6) We also use the larval competition model to demonstrate that apparently minor changes in the description of adult survival can induce dramatic alterations in model behaviour. This supports our emphasis on rigour in the formulation of the model, so as to distinguish genuinely interesting dynamics from mathematical artifacts.",
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The systematic formulation of tractable single-species models incorporating age structure. / Gurney, William; Nisbet, R.M.; Lawton, J.H.

In: Journal of Animal Ecology, Vol. 52, No. 2, 06.1983, p. 479-495.

Research output: Contribution to journalArticle

TY - JOUR

T1 - The systematic formulation of tractable single-species models incorporating age structure

AU - Gurney, William

AU - Nisbet, R.M.

AU - Lawton, J.H.

PY - 1983/6

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AB - (1) We develop a mathematically rigorous approach to modelling the effects of age structure, in which the life-history of a species is divided into age classes of arbitrary duration and attention is focused on the sub-populations of the various classes. (2) By assuming that all individuals in a particular age class have the same birth and death rates (which may be time- and density-dependent), we reduce the normal integro-differential equations describing an age-structured population with overlapping generations to a set of coupled ordinary delay-differential equations which are readily integrated numerically. (3) We illustrate the use of the formalism in the construction and analysis of two models of laboratory insect populations: a detailed model of Nicholson's blowflies and a `strategic' model of larval competition intended to refine the design of experiments in progress on the dynamics of the Indian meal-moth Plodia interpunctella (Hubner). (4) The model of Nicholson's blowflies is dynamically identical to a model previously derived heuristically. We have fitted the parameters using a more comprehensive range of data, and have illustrated explicitly the passage of large, quasi-cyclic fluctuations through the age structure. (5) We use the larval competition model to distinguish the effects of `uniform competition' (all larvae competing) and `cohort competition' (larvae of a given age competing). The former can produce quasi-cycles of a type characteristic of delayed regulation, while the latter causes quasi-cycles consisting of `bursts' of population propagating through the age structure. (6) We also use the larval competition model to demonstrate that apparently minor changes in the description of adult survival can induce dramatic alterations in model behaviour. This supports our emphasis on rigour in the formulation of the model, so as to distinguish genuinely interesting dynamics from mathematical artifacts.

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KW - competition model

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M3 - Article

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EP - 495

JO - Journal of Animal Ecology

T2 - Journal of Animal Ecology

JF - Journal of Animal Ecology

SN - 0021-8790

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ER -