Some theoretical and numerical aspects of modelling dispersion in the development of ectotherms

K. Schuhmacher; H. Thieme

doi:10.1016/0898-1221(88)90281-7

Some theoretical and numerical aspects of modelling dispersion in the development of ectotherms

K. Schuhmacher, H. Thieme

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Boxcartrain (i.e. special distributed delay) models simulate the dispersion which is observed in the duration of temperature-driven development of ectothermic animals by adapting the discretization of the developmental process. The procedure suffers from the drawback that only special distribution profiles of developmental duration can be simulated and that profile and discretization are inevitably linked. As an alternative we suggest a continuous maturation model for ectothermic development which can describe arbitrary profiles of developmental duration. We reinterpret and generalize boxcartrain models in this framework and discuss discrete approximations which are robust against fluctuations of maturation and mortality rates.

Original language	English (US)
Pages (from-to)	565-594
Number of pages	30
Journal	Computers and Mathematics with Applications
Volume	15
Issue number	6-8
DOIs	https://doi.org/10.1016/0898-1221(88)90281-7
State	Published - 1988
Externally published	Yes

ASJC Scopus subject areas

Modeling and Simulation
Computational Theory and Mathematics
Computational Mathematics

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10.1016/0898-1221(88)90281-7

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@article{f402c824ac824c5380024ff6d58e9cba,

title = "Some theoretical and numerical aspects of modelling dispersion in the development of ectotherms",

abstract = "Boxcartrain (i.e. special distributed delay) models simulate the dispersion which is observed in the duration of temperature-driven development of ectothermic animals by adapting the discretization of the developmental process. The procedure suffers from the drawback that only special distribution profiles of developmental duration can be simulated and that profile and discretization are inevitably linked. As an alternative we suggest a continuous maturation model for ectothermic development which can describe arbitrary profiles of developmental duration. We reinterpret and generalize boxcartrain models in this framework and discuss discrete approximations which are robust against fluctuations of maturation and mortality rates.",

author = "K. Schuhmacher and H. Thieme",

note = "Funding Information: Acknowledgements--One author (H.T.) was supported by a Heisenberg scholarship of DFG (German research foundation). It is one of the aims of this paper to bridge the gap of language between practical agricultural model builders and mathematicians at least in one direction, namely to help mathematicians to identify and understand some fundamentals of the models which practical people design for pest control. Being mathematicians we needed some help in this respect ourselves and obtained it from J. Baumgacrtner (ETH Zfirich) and J. A. J. Metz (Rijksuniversiteit Leiden). We also thank J. A. J. Metz for various comments on this paper. We particularly thank E. Diclder (BBA Dossenheim) who got us interested in the subject of this article and had numerous discussions with us on the biological side of the problem.",

year = "1988",

doi = "10.1016/0898-1221(88)90281-7",

language = "English (US)",

volume = "15",

pages = "565--594",

journal = "Computers and Mathematics with Applications",

issn = "0898-1221",

publisher = "Elsevier Limited",

number = "6-8",

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TY - JOUR

T1 - Some theoretical and numerical aspects of modelling dispersion in the development of ectotherms

AU - Schuhmacher, K.

AU - Thieme, H.

N1 - Funding Information: Acknowledgements--One author (H.T.) was supported by a Heisenberg scholarship of DFG (German research foundation). It is one of the aims of this paper to bridge the gap of language between practical agricultural model builders and mathematicians at least in one direction, namely to help mathematicians to identify and understand some fundamentals of the models which practical people design for pest control. Being mathematicians we needed some help in this respect ourselves and obtained it from J. Baumgacrtner (ETH Zfirich) and J. A. J. Metz (Rijksuniversiteit Leiden). We also thank J. A. J. Metz for various comments on this paper. We particularly thank E. Diclder (BBA Dossenheim) who got us interested in the subject of this article and had numerous discussions with us on the biological side of the problem.

PY - 1988

Y1 - 1988

N2 - Boxcartrain (i.e. special distributed delay) models simulate the dispersion which is observed in the duration of temperature-driven development of ectothermic animals by adapting the discretization of the developmental process. The procedure suffers from the drawback that only special distribution profiles of developmental duration can be simulated and that profile and discretization are inevitably linked. As an alternative we suggest a continuous maturation model for ectothermic development which can describe arbitrary profiles of developmental duration. We reinterpret and generalize boxcartrain models in this framework and discuss discrete approximations which are robust against fluctuations of maturation and mortality rates.

AB - Boxcartrain (i.e. special distributed delay) models simulate the dispersion which is observed in the duration of temperature-driven development of ectothermic animals by adapting the discretization of the developmental process. The procedure suffers from the drawback that only special distribution profiles of developmental duration can be simulated and that profile and discretization are inevitably linked. As an alternative we suggest a continuous maturation model for ectothermic development which can describe arbitrary profiles of developmental duration. We reinterpret and generalize boxcartrain models in this framework and discuss discrete approximations which are robust against fluctuations of maturation and mortality rates.

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JO - Computers and Mathematics with Applications

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IS - 6-8

ER -

Some theoretical and numerical aspects of modelling dispersion in the development of ectotherms

Abstract

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