The meaning of compatibility in systems of taper and volume equations has been extended. It is desirable and possible to develop completely compatible taper and volume equation systems that have algebraic compatibility and numeric consistency among all the component equations. Two such taper and volume systems were developed for slash pine in the southeastern United States. One was derived from a recently developed merchantable volume equation (Zhao and Kane 2017), and the other was derived from the well-known Max and Burkhart segmented polynomial taper equation (1976). Three fitting methods were used to obtain numerically consistent estimates of parameters in these two systems. The performance of the systems associated with fitting methods were evaluated with taper, merchantable volume and total volume predictions, and bias trends over different dbh classes, total height classes, and different relative height intervals. The new system outperformed the Max-Burkhart taper-based system for merchantable and total volume predictions and was competitive in diameter prediction. Optimization of parameters of the system for both taper and cumulative volume simultaneously is preferable to separate optimization for taper or volume only.

There is an increasing interest in estimating biomass for longleaf pine (Pinus palustris Mill.), an important tree species in the southeastern U.S. Most of the individual-tree allometric models available for the species are local, relying on stem diameter outside bark at breast height (DBH) and total tree height (HT), but seldom include stand-level variables such as stand age, basal area or stand density. Using the biomass dataset of 296 longleaf pine trees sampled in the southeastern U.S. by different forestry research institutions, we developed a set of local and general systems of tree biomass equations to predict total tree total above-stump biomass, bole biomass outside bark, live branch biomass and live foliage biomass. The local systems were based on DBH or DBH and HT, and the general systems included in addition to DBH and HT, stand-level variables such as age, basal area and stand density. This paper reports the first set of general allometric equations reported for longleaf pine trees. These systems of biomass equations provide tools to support managers in making management decisions for the species in a variety of ecological, silvicultural and economics applications. The systems can be applied to trees growing over a large geographical area and having a wide range of ages and stand characteristics.