Tree volume estimation for small silvopastoral systems: do we really need the height variable to obtain sufficiently accurate results?

The objective of this study was to evaluate and compare the performance of single and double-entry volumetric models in estimating tree volume of eucalypt trees in different silvopastoral systems in Coronel Pacheco, Minas Gerais State, Brazil. Diameter at breast height, total height, and diameter outside the bark along the stems of the sample trees were recorded. Four single-entry and five double-entry volume models were fitted to the observed data for six strata consisting of different Eucalyptus genetic material and three silvopastoral systems, and were compared to select the best alternative. Double-entry models, specifically logarithmic Spurr and logarithmic Schumacher & Hall, fitted statistically better then single-entry ones for all but one of the strata, where they were overcome by the Husch’s model. However, although the superiority of the former can have been easily verified by different and complementary statistics, we found that the volume estimates provided by the best double-entry and the best single-entry model of each stratum differed by a quantity that can be considered irrisory, from both practical and monetary points of view. In a per tree basis, the differences, in absolute values, did not surpassed 0.051 m3, or only US$ 0.25, considering a market value of US$ 4.90/m3. And even when simulating a real scenario of batch sales for each stratum, by simple extrapolation of the mean volume and considering their effective tree stand, such differences did not exceed ±0.25 m3/ha, or ±US$ 1.20/ha. These findings suggest that the smallholder farmer does not need to estimate the height of its trees; more than this, he/she can save money by not having to do a complete forest inventory and by using single-entry models such as the Husch model for estimating the wood volume of his/her plant stand. Another highlight or reinforcement of this work is that the use of the Furnival index was crucial for a reliable selection of the best models, once it allows for comparisons at the same scale of variation.