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Background: Individual-tree taper and volume equations are essential for forest management. They provide estimates of volume that are incorporated into plot-level volume equations and also into growth and yield models to estimate volumes per hectare in forest crops. Moreover, taper equations allow forest managers to estimate dimensions of logs that can be cut from stems in their forests when they have measured diameters at breast height and heights of trees in inventories. Compatible taper and volume equations have the property that the same individual tree volume can be estimated either from the tree volume equation or by integrating the taper equation. Durable eucalypt species such as Eucalyptus globoidea Blakely, however, have especially valuable heartwood and so managers require estimates of the volumes and shapes of heartwood zones within trees. Simple overall wood taper and volume equations would therefore be inadequate. Methods: 74 Eucalyptus globoidea trees were destructively sampled in 8 different trial plots throughout New Zealand. Tree ages were 7 to 29 years old, the DBHs were 11 to 67.6 cm and the heights were 7.2 to 35.4 m. All trees were felled and lengths and taper diameters outside bark were measured. To measure taper diameters of heartwood and sapwood, discs were cut at irregular intervals along the stems. Heartwood and sapwood components were identified by applying methyl orange dye and quantified using image analysis. In this study we extended compatibility so that sums of estimated volumes of separate components of stems, bark, sapwood and heartwood, would equal overall tree volume estimates. In addition, taper equations were made for outside bark, inside bark and heartwood that were compatible with their respective volume equations. Parameters of five volume equations for whole stem, whole wood, bark, sapwood, and heartwood were simultaneously estimated. Compatible taper equations for whole stem, stem wood and heartwood were estimated so that they were compatible with the volume equations, thereby creating a fully compatible system. Results: Root mean squared error (RMSE) of volume models were 0.1248298 m3 for heartwood, 0.05496807 m3 for sapwood, 0.1539625 m3 for wood inside bark, 0.1108201 m3 for bark and 0.1439786 m3 for wood including bark. RMSE of taper models was 2.572765 cm for heartwood, 2.348552 cm for wood inside bark and 2.474088 cm for wood including bark. Conclusions: A compatible system of multiple taper and volume equations can be fitted through the simultaneous fitting of parameters with minimal bias and precision levels of  ± 0.055-0.154 m3 for volume equations and ± 2.35 to 2.57 cm for taper equations. Leave-one-out cross-validation of the fitted models yielded very similar levels of precision and bias to those encountered when fitting models with the entire dataset.

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