A simple and effective forest stand mortality model

Abstract

A whole-stand survival model is presented, that is parsimonious and well-behaved when extrapolated, making it particularly useful in data-poor situations. It is argued, on biological and system-theoretical grounds, that a suitable differential equation for the mortality rate should contain number of trees and top height on the right-hand side, avoiding age, mean diameter, or basal area. Following Eichhorn's hypothesis, site quality can be neglected by modelling rates relative to height growth. The proposed model is $\dr{N}{H} = -a N^b H^c$ , where $N$ is number of trees per unit area, $H$ is top height, and $a$, $b$ and $c$ are parameters to be estimated. The equation can be integrated to predict mortality between any two points in time. Satisfactory performance is demonstrated with a white spruce data set from British Columbia. It is shown that the model generalizes concepts of relative spacing, and mortality models for radiata pine and Douglas-fir used by Beekhuis in New Zealand in the 1960's. Asymptotic behaviour is related to the 3/2, Reineke, and relative spacing self-thinning laws. Limitations of the self-thinning theories and relationships among their various forms are discussed. MCFNS 1(1):1-9.