‘Relationships between relationships’ in forest stands: intercepts and exponents analyses

Abstract

Relationships between diameter at breast height (dbh) versus stand density, and tree height versus dbh (height curve) were explored with the aim to find if there were functional links between correspondent parameters of the relationships, exponents and intercepts of their power functions. A geometric model of a forest stand using a conic approximation suggested that there should be interrelations between correspondent exponents and intercepts of the relationships. It is equivalent to a type of ‘relationship between relationships’ that might exist in a forest stand undergoing self-thinning, and means that parameters of one relationship may be predicted from parameters of another. The predictions of the model were tested with data on forest stand structure from published databases that involved a number of trees species and site quality levels. It was found that the correspondent exponents and intercepts may be directly recalculated from one another for the simplest case when the total stem surface area was independent of stand density. For cases where total stem surface area changes with the drop of density, it is possible to develop a generalization of the model in which the interrelationships between correspondent parameters (exponents and intercepts) may be still established.