Allometric model of the maximum size–density relationship between stem surface area and stand density

Abstract

An allometric model of the maximum size–density relationship between mean stem surface area and stand density is proposed, and is fitted to data for even-aged pure stands of Japanese cedar (Cryptomeria japonica D. Don) and Japanese cypress (Chamaecyparis obtusa Endl.). To derive the model, the biomass density was defined as the ratio of the mean stem surface area to the side area of an imaginary column, of which radius and height were equal to the radius of the mean area occupied by a tree and mean tree height, respectively. According to the model, the slope of the maximum size–density relationship on logarithmic coordinates can be estimated from the allometric power relationships of mean tree height and biomass density to mean stem surface area. The resulting slope was −1.089 for the cedar and −0.974 for the cypress. The estimated maximum size–density relationship corresponded well with the combinations of mean stem surface area and stand density for the overcrowded stands of cedar and cypress. The steeper slope for cedar was attributed to the allocation of more resources to height growth compared to cypress. The maximum total stem surface area was approximated to be 1.483 ha/ha for cedar and 0.949 ha/ha for cypress stands. The difference in the maximum total stem surface area between the two species was produced by the characteristics related to tree height and stem biomass packing into space already occupied.