Accounting for bias and uncertainty in nonlinear stand density indices

Several commonly used stand density indices, such as Reineke's stand densit y index, Drew and Flewelling's relative density index, and Curtis's relativ e density index, depend in a nonlinear fashion on stand-level means of meas ured variables. Thus, the stand-level index value is not necessarily the me an of the plot-level index values. We show formally that this dependency in troduces a bias that depends on the sample size or number of plots and on t he variance-covariance structure of the measured variables. We then present formulas for estimating the bias and variance or stand ard error of estima ted densities based on a priori knowledge of the variances and covariances or on observed sample data. We also present and compare bootstrap and jackk nife methods of estimating the bias and variance associated with sample est imates. The results suggest that for some indices, the bias and variance ar ising from quick "grab samples" may be large enough to be of practical sign ificance. These results have strong implications for the development and in terpretation of stocking guides derived from single plots or from measureme nt schemes other than those employed in practical applications.