Bulletin of Mathematical Biology
, 66:1821
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
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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
66:1821
 Online Date
 November 2004
 DOI
 10.1016/j.bulm.2004.04.003
 Print ISSN
 00928240
 Online ISSN
 15229602
 Publisher
 SpringerVerlag
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 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