Estimating volume of eucalyptus trees for small-scale silvopastoral systems: do we really need height for accurate estimates?

Double-entry volume equations require measurement of diameter and height variables, making forest inventory more expensive. This can be limiting for small farms. Then the single-entry volume equations, where diameter at breast height (DBH) is the independent variable, are a cost-effective option for these landowners because they optimize data collection due to the use of one readily available variable (the DBH) and require few resources. The objective of this study was to evaluate the effective contribution of the height in the estimation of eucalypt trees volume for small-scale silvopastoral systems. For this, four single-entry and five double-entry volumetric models were fitted to the data for six different silvopastoral systems in Coronel Pacheco, Minas Gerais State, Brazil. The six strata consisted of combinations of three different Eucalyptus genetic material and three silvopastoral systems, and the models were compared aiming the selection of the best of each type in each system. Double-entry models, specifically logarithmic Spurr and logarithmic Schumacher-Hall, fitted better than single-entry ones for all but one of the strata, where they were overcome by the Husch's model. Although the superiority of the formers 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. On a per tree basis, the sum of the differences for each stratum, in absolute value, did not surpass 0.051 m3, or only US$ 0.25, considering a market value of US$ 4.90/m3. And 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. Following the same logic, even when comparing the best double-entry model to the worst single-entry one for each stratum, we still observed only negligible differences. Considering the sampled trees, these differences amounted to a balance per stratum of only - 0.015 to + 0.032 m3 (or between - US$ 0.07 and + US$ 0.16). When extrapolated to the total trees in each stratum, the overall balance did not exceed an absolute value of 0.283 m3 (or US$1.39). These results suggest that the contribution of height may be negligible in estimating the volume of eucalyptus trees for small silvopastoral systems. Consequently, smallholders may not benefit from measuring tree heights. Rather, they may save money by foregoing a comprehensive forest inventory and instead using single-entry models, such as the Husch model, to estimate the wood volume of their forest stands. 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 among models both with and without a log transformation of the volume.