Comparing fixed- and variable-base-age site equations having single versus multiple asymptotes

Abstract

Site equations compute values of a variable Y as a function of both variable t and a value of the variable Y = Yo measured at an arbitrary t= to. For example, the plant size (Y) can be defined as a function of both age (t) and a reference size (Y0) measured at the base age t0. 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, t0, Y0)]. 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.