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Comparing Fixed- and Variable-Base-Age Site Equations Having Single Versus Multiple Asymptotes

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Site equations compute values of a variable Y as a function of both variable t and a value of the variable Y = Y 0 measured at an arbitrary t = t 0. For example, the plant size (Y) can be defined as a function of both age (t) and a reference size (Y 0) measured at the base age t 0. The base age can be implicit (i.e., implied but hidden), as in fixed-base-age equations [e.g., Y = f(t, S), where S is Y at t = 50], or explicit (i.e., readily exposed and changeable), as in dynamic equations [e.g., Y = f(t, t 0, Y 0)]. Using as the main criterion the ability of an equation to generate concurrent polymorphism and multiple asymptotes, I compare a fixed-base-age height growth site equation with several dynamic equations, derived through the traditional and the Generalized Algebraic Difference Approaches. The comparison leads to conclusions about desirable model properties, the methodologies of derivations, and expected outcomes of the different methodologies. The conclusions suggest that the ability to simulate concurrent polymorphism and multiple asymptotes is an important property of site equations that should be considered during modeling various growth trends. Furthermore, the conclusions suggest that both algebraic difference approaches are more parsimonious and robust than the fixed-base- age approaches. The Generalized Algebraic Difference Approach can increase model usefulness considerably through derivation of more complex equations that can achieve more desirable properties. FOR. SCI. 48(1): 7–23.

Keywords: Model derivation; base-age-invariant equations; biological models; dynamic equations; environmental management; forest; forest management; forest resources; forestry; forestry research; forestry science; model conditioning; natural resource management; natural resources; nonlinear models; site productivity

Document Type: Miscellaneous

Affiliations: Assistant Professor Fiber Supply Assessment, School of Forest Resources, University of Georgia, Athens, Georgia, 30602, Phone: (706)542-8169; Fax: (706)542-8356 biomat@smokey.forestry.uga.edu

Publication date: February 1, 2002

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  • Forest Science is a peer-reviewed journal publishing fundamental and applied research that explores all aspects of natural and social sciences as they apply to the function and management of the forested ecosystems of the world. Topics include silviculture, forest management, biometrics, economics, entomology & pathology, fire & fuels management, forest ecology, genetics & tree improvement, geospatial technologies, harvesting & utilization, landscape ecology, operations research, forest policy, physiology, recreation, social sciences, soils & hydrology, and wildlife management.
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