Analysis of a model currently used for assessing sustainable yield in indigenous forests

Abstract

Problems are identified in the use of a variant of the Usher matrix model to underpin the harvest of beech (Nothofagus spp.) and rimu (Dacrydium cupressinum) on the West Coast of the South Island. The model has been suggested as a means of determining the harvest that is sustainable in the sense of maintaining the present forest structure, and uses as inputs the size structure and estimates of size‐specific radial growth rate. The model contains a bias because the equations for transition coefficients in the projection matrix assume an inappropriate geometric model for stage duration. The effect is to overestimate population growth by about 22% over a 15 year felling cycle. Alternative formulae are given for a more realistic model of fixed stage duration. The mortality rates needed to maintain the initial size structure of the population may be inferred from recursive formulae that are derived here separately for the geometric and fixed models of stage duration. Using a model with fixed stage duration it is found that the method is unworkable, in the sense that no set of mortality rates can be found to keep observed stand structures constant. The estimate of sapling recruitment number used in the harvest calculations does not appear to be well‐founded. Even assuming that the forest is in a steady state and natural mortality is known, the assumption that harvest mortality substitutes for natural mortality rather than adding to it appears to be unwarranted. I suggest that matrix models cannot be used to determine ecologically sustainable forest management without additional information on natural forest dynamics and the response to harvesting.