Estimating the stock recovery rate using matrix models

Abstract

The stock recovery rate, that is the ratio of the exploitable wood stock at the end of a felling cycle over the exploitable wood stock at the beginning of this cycle, is a key parameter used in the management plans of the natural forests in central Africa. Estimating this rate requires a model of forest dynamics. Forest managers usually use a formula that is based on a simple model that assumes constant vital rates. A generalization of this formula is based on matrix models of population dynamics. The stock recovery rate at the end of the k th felling cycle can be simply computed using matrix models. The asymptotic stock recovery rate (that is the limit as k tends to infinity) is the asymptotic growth rate (that is the dominant eigenvalue) of a transition matrix that includes harvest. The estimate of the stock recovery rate can be completed by its confidence interval using bootstrap methods. When applied to sapelli ( Entandrophragma cylindricum, Meliaceae), a major timber species in central Africa, it turns out that a few thousands observations are required to estimate the stock recovery rate with an accuracy of at least 10%. The number of observations available on an experimental site in the Central African Republic does not permit to do better than an accuracy of about 45% at level 95%. This does not permit to conclude whether the asymptotic stock recovery rate is greater or less than one. As a conclusion, in management plans in central Africa, stock recovery rates should be given together with an indication of the variability of their estimate (standard error or confidence limits).