Generalized algebraic difference approach derivation of dynamic site equations with polymorphism and variable asymptotes from exponential and logarithmic functions

Abstract

The generalized algebraic difference approach (GADA) uses both: two-dimensional functions of explicit time and two-dimensional functions of explicit site to derive a single dynamic equation that is a three-dimensional function of explicit time and implicit site. In 2004 Cieszewski advanced dynamic site equations with polymorphism, and variable asymptotes (Cieszewski, C.J. 2004. GADA derivation of dynamic site equations with polymorphism and variable asymptotes from Richards, Weibull, and other exponential functions. PMRC Tech. Rep. 2004-5, p. 16.) were built with GADA using one general function of time T and two general functions of site X. The function of time is the exponential function Y = MTb, and the functions of site are the quadratic function Z = b1 + b2X + b3X2 and the inverse half-saturation function Z = b1 + b2/(X + b3). We discuss the new dynamic equations based on five exponential substitutions (Richards, Gompertz, Korf, logistic, and log-logistic) and one new logarithmic model substitution in the exponential function of time and 10 special cases of the two functions of site corresponding to their different parameter values. The new dynamic equations presented offer breakthrough flexibility in modeling of the self-referencing dynamics with the exponential and logarithmic functions considered in this article. Copyright © 2008 by the Society of American Foresters.