A retrospective on the accuracy and precision of plotless forest density estimators in ecological studies

Abstract

Sampling point-to-tree distances is a simple plotless technique for estimating forest density that is readily applied in modern stands and retroactively with historical surveys. Although plotless density estimators (PDEs) have been applied in over 1000 ecological publications, the accuracy and precision of the techniques remain poorly understood and depend on the statistical estimator used, the underlying spatial pattern of the forest sampled, and the tree survey methodology. The four most commonly applied PDEs are related formulations: Cottam, Pollard, Morisita, and Shanks, a family of equations that differ in the order of mathematical operations. Since the 1950s, the Cottam IV PDE has found common use as the "point-quarter method." The Pollard PDE prevails in the statistical literature. Both Cottam and Pollard PDEs are theoretically rigorous for trees distributed according to a complete spatial randomness (CSR) spatial point process. The Morisita PDE was developed in a 1957 publication, with four-tree (Morisita IV) and two-tree (Morisita II) variants, and is the basis for higher distance rank g-tree estimators. The Shanks PDE is formally described here for the first time. We review and evaluate the performance of these four PDEs on CSR and a variety of non-CSR forests using spatial patterns simulated from known spatial point processes, 14 mapped modern stands, and historical public land surveys (PLSs). We found that the Cottam and Pollard PDEs lacked accuracy for non-CSR patterns. The Morisita PDEs are appropriate for non-CSR forests, but the Morisita IV has sensitivity to local dispersion. The Morisita II PDE has high accuracy even under non-CSR distributions yielding density estimates within 10% of the true value for a variety of non-CSR patterns, but has considerable variability at small sample sizes. In conjunction with the Morisita II, the potentially biased Cottam and Pollard PDEs can be indicators of the type of non-CSR pattern. No plotless estimator is efficacious for use with small sample sizes such as found in a single stand. Morisita II PDE is recommended as a robust choice for sampling for large and non-CSR data sets such as the PLS witness tree database.

Land‐use and climatic causes of environmental novelty in Wisconsin since 1890

“…, Cogbill et al. ) and United States Forest Service Forest Inventory and Analysis (FIA) data (Forest Inventory Analysis Program , Gray et al. ).…”

“…() and Cogbill et al. (), then multiplying the stem density estimates by average stem basal area, calculated using diameter at breast height (DBH) and allometries from Jenkins et al. ().…”

“…Biomass-weighted estimates of forest composition are based on Public Land Survey System (PLSS) records (Schulte et al 2007, Liu et al 2011, Goring et al 2016, Cogbill et al 2018 and United States Forest Service Forest Inventory and Analysis (FIA) data (Forest Inventory Analysis Program 2007, Gray et al 2012). PLSS records provide an estimate of mid-to late-1800s forests, while FIA observations are from the most recent full plot inventory (2007)(2008)(2009)(2010)(2011) (Goring et al 2016).…”

“…Goring et al (2016) developed 8-km gridded data sets of composition, stem density, and biomass for the PLSS and FIA data, aggregating the PLSS data from their native resolutions of individual trees sampled at corner points at 1 mile spacing (1 mile = 1.61 km) and FIA data from their native resolutions of individual trees within 7.2 m fixed-radius plots. Biomass estimates for the PLSS data were calculated by first calculating point-level stem densities at each survey location, using the two nearest trees and stem-density estimators described by Goring et al (2016) and Cogbill et al (2018), then multiplying the stem density estimates by average stem basal area, calculated using diameter at breast height (DBH) and allometries from Jenkins et al (2004). Biomass estimates for the FIA data were also calculated using DBH and allometries for all individual trees with DBH > 20.32 cm (8 inches), to match the PLSS data (Goring et al 2016).…”

Estimating historical forest density from land‐survey data: a response to Baker and Williams (2018)

“…Moreover, regardless of the number of trees sampled at a point, the application of the Cottam estimator to single trees (Shanks variant), as used by B&W, greatly overestimates the scaling factor compared to larger pools (Cogbill et al 2018). In addition, the 4nn and 2nn sampling have different responses to nonrandom or heterogeneous dispersion (Cogbill et al 2018). Thus, the Voronoi areas of at least one-half the trees are wrongly scaled and the pooling of 4nn and 2nn corners incorporates many VAs that are underestimated.…”