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

Problems are identified in the use of a variant of the Usher matrix model t o underpin the harvest of beech (Nothofagus spp.) and rimu (Dacrydium cupre ssinum) 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 struc ture 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 effe ct 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 str ucture of the population may be inferred from recursive formulae that are d erived 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 un workable, in the sense that no set of mortality rates can be found to keep observed stand structures constant. The estimate of sapling recruitment num ber used in the harvest calculations does not appear to be well-founded. Ev en assuming that the forest is in a steady state and natural mortality is k nown, the assumption that harvest mortality substitutes for natural mortali ty rather than adding to it appears to be unwarranted. I suggest that matri x models cannot be used to determine ecologically sustainable forest manage ment without additional information on natural forest dynamics and the resp onse to harvesting.