Generalized algebraic difference approach: Theory based derivation of dynamic site equations with polymorphism and variable asymptotes

Abstract

Biologically realistic site models require the ability to concurrently express variable asymptotes and polymorphism in curve shapes. Moreover, it is only logical and rational to require that these models be invariant to changes in the index or base age. This manuscript explains the Generalized Algebraic Difference Approach that can be used effectively to derive truly base-age invariant difference equations capable of describing concurrent polymorphism and variable asymptotes. This new generic methodology for derivation of even the most complex dynamic equations is mathematically sound. The equations derived with it can be extremely flexible and may generate intricate patterns of concurrent polymorphism and variable asymptotes. This methodology is relevant to all situations in which the dependent variable is a function of an unobservable variable, and the models can be implicitly defined by their initial conditions. It is equally useful for derivation of new equations and for improvement of existing base-age specific equations.