On relative maxima of diameter growth, Basal area growth, volume growth, and mean annual increment for individual trees

Abstract

A mathematical demonstration for the fact that maximum individual tree diameter growth occurs at an earlier age than maximum individual tree basal area growth is reviewed. This demonstration assumes that the growth functions are continuous, are twice differentiable with respect to age, and increase monotonically to one maximum, thereafter to decline monotonically. The relationship of the age of maximum individual tree volume growth to the age of basal area growth is also discussed. Mathematical demonstrations are given for the fact that the culmination of mean annual increment occurs earlier for diameter than for basal area, and results on age of maximum growth and mean annual increment are also given for arbitrary power functions in diameter. © 2011 by the Society of American Foresters.