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    Author(s): Estella Gilbert; James A. Powell; Jesse A. Logan; Barbara J. Bentz
    Date: 2004
    Source: Bulletin of Mathematical Biology. 66: 1821-1850.
    Publication Series: Scientific Journal (JRNL)
    Station: Rocky Mountain Research Station
    PDF: View PDF  (655.8 KB)


    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 age-structured McKendrick-von 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.

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    Gilbert, Estella; Powell, James A.; Logan, Jesse A.; Bentz, Barbara J. 2004. Comparison of three models predicting developmental milestones given environmental and individual variation. Bulletin of Mathematical Biology. 66: 1821-1850.


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    phenotypic variability, phenology models, distributed delay model, Sharpe and DeMichele model, Extended von Foerster model

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