How many trees are necessary to fit an accurate volume model for the Amazon forest? A site-dependent analysis

The use of forest resources by communities in the Amazon, or of such resources globally, begins with the quantification of the yield potential of the standing forests. Notably, wood volume, biomass, and carbon are the principal variables quantified through forest inventories associated with estimation processes such as allometric models. These processes involve a large number of trees for log scaling, which often would not need to be cut in an exploratory survey. Thus, the aim of this study was to estimate how many trees are necessary to fit an accurate volume model for a community forest management plan in the Amazonian forest. This information can contribute to reducing the number of trees cut down, time, and costs of future field surveys. The research was developed using volume data of six species present in a forest management unit located in the municipality of Novo Repartimento, Pará, Brazil. Initially, the volumes of the 318 trees were estimated using single and double input allometric models. Then, for each tested model, 1000 bootstrap resampling simulations were performed, and were repeated for different sample sizes (5, 6, 7…, to n − 1), species, and for all species. The volumetric models were fit for each simulation to obtain the reliability index (RI%) and the allowable error limit (AEL%) for six error limits (EL%) varying between 10 and 35%. The minimum number of trees was determined when the average tendency of RI% was statistically equal to or below AEL% at a specific EL% level. The t-test was used to compare AEL% with the mean tendency of the RI%. The single input allometric model at the 35% error level provided an accurate model using a sample of 39 trees for each species and 158 trees for all species. A minimum of 29 and 81 sample trees were required for each species and for all species, respectively, to provide a precise double input allometric model at a minimum EL% of 20%. These results show that it is possible to fit accurate models with a minimum number of sample trees for volumetric estimation purposes in the Brazilian Amazonian forests. However, there is a limitation in proposing a sample size for other regions of the Amazon Forest, because the representative number of trees required for a reliable model depends on the site, stand conditions, rarity of the species, time, and expenditure in log scaling procedures.