Analysis and evaluation of the simultaneous growth and yield equations presented by Beck and Della-Bianca (1972) for predicting basal area growth and cubic-foot volume growth and yield in yellow-poplar stands after a single thinning indicated that a separate set of coefficients was required for stands thinned twice. A joint loss function involving both volume and basal area was used to estimate the coefficients in the system of equations. The estimates obtained were analytically compatible, invariant for projection length, and numerically equivalent with alternative applications of the equations. Given estimates of basal area and cubic-foot volume from these equations, board-foot volumes can also be calculated.

As an adjunct to the stand level equations, compatible stand tables were derived by solving for the parameters of the Weibull distribution from attributes predicted with the stand-level equations. This procedure for estimating the parameters of the diameter distributions of the stands before thinning gave reasonable estimates of number of trees, basal area, and cubic-foot volume per acre by diameter class. The thinning algorithm removes a proportion of the basal area from each diameter class and produces stand and stock tables after thinning from below that are consistent with those generated before thinning.

Finally, volume ratio equations were fitted to provide estimates of merchantable volume, i.b. or o.b., to either a specified diameter or height limit, where volume between any two diameter or height limits can be obtained through subtraction. Through rearrangement of the ratio equations, implicit taper functions were specified to predict height at a given diameter and diameter at a given height.