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A discrete slug population model determined by egg production.

A discrete slug population model determined by egg production.
A discrete slug population model determined by egg production.
Slugs are significant pests in agriculture (as well as a nuisance to gardeners), and it is therefore important to understand their population dynamics for the construction of efficient and effective control measures. Differential equation models of slug populations require the inclusion of large (variable) temporal delays, and strong seasonal forcing results in a non-autonomous system. This renders such models open to only a limited amount of rigorous analysis. In this paper, we derive a novel batch model based purely upon the quantity of eggs produced at different times of the year. This model is open to considerable reduction; from the resulting two variable discrete-time system it is possible to reconstruct the dynamics of the full population across the year and give conditions for extinction or global stability and persistence. Furthermore, the steady state temporal population distribution displays qualitatively different behavior with only small changes in the survival probability of slugs. The model demonstrates how small variations in the favorability of different years may result in widely different slug population fluctuations between consecutive years, and is in good agreement with field data.
slugs, extinction, global stability, seasonal variation
0218-3390
243-264
Schley, David
0d9ab113-6fb8-4d48-8c32-0241e41e5570
Bees, Martin A.
00f60fb2-afe5-4413-820c-0992262e6a53
Schley, David
0d9ab113-6fb8-4d48-8c32-0241e41e5570
Bees, Martin A.
00f60fb2-afe5-4413-820c-0992262e6a53

Schley, David and Bees, Martin A. (2002) A discrete slug population model determined by egg production. Journal of Biological Systems, 10 (3), 243-264. (doi:10.1142/S0218339002000585).

Record type: Article

Abstract

Slugs are significant pests in agriculture (as well as a nuisance to gardeners), and it is therefore important to understand their population dynamics for the construction of efficient and effective control measures. Differential equation models of slug populations require the inclusion of large (variable) temporal delays, and strong seasonal forcing results in a non-autonomous system. This renders such models open to only a limited amount of rigorous analysis. In this paper, we derive a novel batch model based purely upon the quantity of eggs produced at different times of the year. This model is open to considerable reduction; from the resulting two variable discrete-time system it is possible to reconstruct the dynamics of the full population across the year and give conditions for extinction or global stability and persistence. Furthermore, the steady state temporal population distribution displays qualitatively different behavior with only small changes in the survival probability of slugs. The model demonstrates how small variations in the favorability of different years may result in widely different slug population fluctuations between consecutive years, and is in good agreement with field data.

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More information

Published date: 2002
Keywords: slugs, extinction, global stability, seasonal variation

Identifiers

Local EPrints ID: 29284
URI: http://eprints.soton.ac.uk/id/eprint/29284
ISSN: 0218-3390
PURE UUID: 94a68ca7-c4c7-4b2c-b528-83260d8bf5df

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Date deposited: 12 May 2006
Last modified: 08 Jan 2022 09:57

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Contributors

Author: David Schley
Author: Martin A. Bees

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