Bulletin of Mathematical Biology
, Volume 66, Issue 6, pp 18211850
First online:
Comparison of three models predicting developmental milestones given environmental and individual variation
 Estella GilbertAffiliated withDepartment of Mathematics and Statistics, Utah State University
 , James A. PowellAffiliated withDepartment of Mathematics and Statistics, Utah State University Email author
 , Jesse A. LoganAffiliated withUSDA Forest Service Logan Forestry Sciences Lab, Utah State University
 , Barbara J. BentzAffiliated withUSDA Forest Service Logan Forestry Sciences Lab, Utah State University
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
In all organisms, phenotypic variability is an evolutionary stipulation. Because the development of poikilothermic organisms depends directly on the temperature of their habitat, environmental variability is also an integral factor in models of their phenology. In this paper we present two existing phenology models, the distributed delay model and the Sharpe and DeMichele model, and develop an alternate approach, called the Extended von Foerster model, based on the agestructured McKendrickvon Foerster partial differential model. We compare the models theoretically by examining the biological assumptions made in the basic derivation of each approach. In particular, we focus on each model’s ability to incorporate variability among individuals as well as variability in the environment. When compared against constant temperaturemountain pine beetle (Dendroctonus ponderosae Hopkins) laboratory developmental data, the Extended von Foerster model exhibits the highest correlation between theory and observation.
 Title
 Comparison of three models predicting developmental milestones given environmental and individual variation
 Journal

Bulletin of Mathematical Biology
Volume 66, Issue 6 , pp 18211850
 Cover Date
 200411
 DOI
 10.1016/j.bulm.2004.04.003
 Print ISSN
 00928240
 Online ISSN
 15229602
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Industry Sectors
 Authors

 Estella Gilbert ^{(1)}
 James A. Powell ^{(1)}
 Jesse A. Logan ^{(2)}
 Barbara J. Bentz ^{(2)}
 Author Affiliations

 1. Department of Mathematics and Statistics, Utah State University, 3900 Old Main Hill, Logan, Utah, 843223900, USA
 2. USDA Forest Service Logan Forestry Sciences Lab, Utah State University, Logan, Utah, 843228000, USA