Some theoretical and numerical aspects of modelling dispersion in the development of ectotherms
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.
scientific article; zbMATH DE number 4081365