Design-Unbiased Estimation and Alternatives for Sampling Trees on Plantation Rows
Authors: Lynch Thomas B. , Hamlin David , Ducey Mark J. , Borders Bruce E. 
Published: June 2018

Recently, methods for inventories of forest plantations have been proposed based on the use of remote sensing to estimate total row length, followed by the estimation of plantation row attributes, such as number and volume or weight of trees, at randomly selected field locations on the ground within a forest plantation of interest. While we are aware of instances in which such inventories have been performed, to our knowledge, no scientific studies of this approach have previously appeared. Many plantation inventories have been performed by traditional methods, such as Bitterlich (point) sampling and fixed-size plot sampling. Random plot sizes including a fixed number of rows are possible but the resulting estimators are typically not unbiased. Plot sampling and Bitterlich sampling can be problematic in plantations because inventory crews may gravitate towards the establishment of sample points in similar locations relative to row spacing, e.g., midway between rows, compromising the assumption of random point location in the tract area. We propose and test five novel estimators which are based on sampling a fixed number of trees at random sample locations on rows. The methods we propose can be used to estimate tract-level quantities of any tree attribute, including the number of trees, total volume, basal area, and others. Fixed row lengths may be sampled at randomly determined field locations on rows. Alternatively, distance sampling methods can be used to sample a fixed number of trees subsequent to, or nearest to, a randomly located point on a plantation row. Ducey’s recently-developed estimator for point-to-particle sampling on lines can be applied to sampling on rows. A “mean of ratios” (MR) estimator can be based on the average ratio of the sum of the sample trees’ attributes divided by the length of line occupied by the sample trees. A “ratio of means” (RM) estimator can be based on the ratio of the mean of the sample trees’ attributes for all random points divided by the mean sample line length for all random points. For either of these ratio estimators, the line length may be chosen to include the gap between trees into which the random sample point falls (G-MR, mean of ratios including the sample gap and G-RM, ratio of means estimator including the sample gap), or it may be chosen to begin subsequent to that gap (NG-MR, mean of ratios not including the sample gap and NG-RM, ratio of means not including the sample gap). A simulation was used to test each of these techniques on typical plantation row populations. Two row populations were used in the simulation. One had relatively uniform spacing between trees on a row, which resembles the characteristics of young plantations. The second population contained numerous gaps, typical of more mature plantations that have been thinned and may be experiencing mortality. In the simulations, the estimators were used to estimate the number of trees in each population. Trends in other variables, such as volume or basal area, were similar to those for te estimated number of trees in the populations. The simulation results showed that the G-MR method had the smallest root mean square error followed by the NG-RM. Ducey’s method and the fixed-length row plot were both design-unbiased. Both the latter methods had low root mean square errors but these were slightly higher than some of the other methods. In contrast to the other methods tested, the NG-MR and G-RM methods were both substantially biased on a simulated row population containing large gaps which might occur due to mortality or thinning. The estimators which had good performance in simulations—Ducey’s method, G-MR, NG-RM, and fixed-length row sampling—are viable alternatives to traditional methods of sampling plantations, such as Bitterlich sampling and fixed-size plot sampling, if accurate plantation row lengths can be measured.