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

Gurney, William and Nisbet, R.M. and Lawton, J.H. (1983) The systematic formulation of tractable single-species models incorporating age structure. Journal of Animal Ecology, 52 (2). pp. 479-495. ISSN 0021-8790

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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.