Designing permanent sample plots by using a spatially hierarchical matrix population model

Summary.  Designing permanent sample plots is a key issue in forestry where long‐term data are required to assess the sustainability of forest logging. The data that are collected in permanent sample plots are used to set parameters in a population dynamics matrix model which in turn is used to predict stock recovery rates for each species. The sampling plan for permanent plots can be designed to estimate stock recovery rates with a required accuracy at a given confidence level, while minimizing installation costs. This can be formulated as a constrained optimization problem (one constraint for each species). The question then is to quantify sampling variability, i.e. the variability of model predictions that are generated by the distribution of parameter estimators. In this study, we address the question of sampling variability for a size‐classified population matrix model in a hierarchical context where sample size is itself random and driven by a multivariate spatial point process. An approximate expression is given for the accuracy of the stock recovery rate estimator. This expression is the limit of the accuracy as the expectation of sample size tends to ∞. We extend this expression to the multispecies case. To a first approximation, interactions between species do not affect the accuracy of the stock recovery rate for each species. A sampling plan is designed using the data for three species in a tropical rainforest in French Guiana. The optimal sampling plan appears to be determined by the most constrained species.