Some theoretical and numerical aspects of modelling dispersion in the development of ectotherms
type: Item
instance of: scholarly article
title: Some theoretical and numerical aspects of modelling dispersion in the development of ectotherms
zbMATH Open document ID: 0661.92022
DOI: 10.1016/0898-1221(88)90281-7
author: K. Schuhmacher
author: Horst R. Thieme
publication date: 1988-01-01T00:00:00Z
review text: Many ectotherms develop by passing through several stages (e.g. egg, larva, pupa, imago). For mathematical modelling of that ectothermic development it is assumed that every individual entering the stage with maturity 0 is predestinated to leave it at a certain exit maturity. But between different individuals there are differences in the exit maturities resulting from genetic or spatial heterogeneities. A continuous maturation model is suggested which permits to describe arbitrary distributions of periods of development. The distribution of development duration measured in physiological time is described by the distribution function of exit maturities. The model is formulated by an integral equation relating flow, inflow and outflow of the stage. A Laplace transform technique is applied which permits to identify models for dispersed development as continuous maturation models and to determine the distribution of exit maturities. As an alternative to discrete boxcartrain models discrete approximations of the continuous maturation model are discussed which are robust against fluctuations of maturation and mortality rates.
reviewed by: J.Peil
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 92Cxx
Mathematics Subject Classification ID: 92D50
Mathematics Subject Classification ID: 93C30
zbMATH DE Number: 4081365
zbMATH Keywords: single life stages
zbMATH Keywords: ectothermic animals
zbMATH Keywords: ectotherms
zbMATH Keywords: continuous maturation model
zbMATH Keywords: distributions of periods of development
zbMATH Keywords: physiological time
zbMATH Keywords: exit maturities
zbMATH Keywords: integral equation
zbMATH Keywords: Laplace transform technique
zbMATH Keywords: boxcartrain models
zbMATH Keywords: discrete approximations
zbMATH Keywords: mortality rates
MaRDI profile type: Publication
full work available at URL: 0898-1221(88)90281-7
OpenAlex ID: W2012639753
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 4081365