A remarkable study design for unraveling the relationship between tree size and density: An easy-to-install design with a small footprint for any type/size of forest ownership.

By Dan Opalach, PhD, and Jim Arney, PhD, Forest Biometrics Research Institute (FBRI)

Forest Biometrics Research Institute (FBRI) has a unique program whereby their supporting organizations can request a site visit from Dr. Jim Arney and Dr. Dan Opalach.[1]  One such site visit was requested by Mr. Tim Drake, Lone Rock’s Head Inventory Forester.  Tim invited Jim and Dan to inspect four Nelder plots that Tim installed five years ago on Lone Rock timberland in Jackson County, Oregon, close to the town of Butte Falls.  This site visit occurred on June 26, 2019.  Also attending the woods tour on behalf of Lone Rock was Mr. Joe Newton, Lands Manager, and Mr. Mike Backen, Silviculturist.

What is a Nelder Plot?

A Nelder plot is a systematic planting design in which plants or trees are planted at the intersection of circular arcs and linear spokes (Barry 2013, Arney 2019a).  Figure 1 is a Nelder plot layout showing the arrangement of trees in one quadrant of a circular plot.  This chart was developed by Arney (2019b).  Note how tree density decreases as you move from the center of the plot to the outermost arc.  This is the distinguishing characteristic of a Nelder plot.  It allows researchers to collect tree growth data across a wide range of densities in a compact area.  The Nelder plot design is much more efficient and not very expensive relative to traditional fixed-area research plots (Arney 2016, Newton et al. 2018).  For many years Arney (2016) has been recommending the installation and remeasurement of Nelder plots to collect growth and yield information.  The following is an excerpt from Arney (2016) that succinctly summarizes the benefits of the Nelder plot design:


“Only the Nelder designed plot installations have provided robust datasets across both tree size and density. These Nelder plots are robust and efficient because they provide a balanced, orthogonal distribution of observations of tree growth and mortality. This plot design requires a very small acreage per installation. It makes efficient use of a small number of trees per plot. The individual tree is the experimental unit. The Nelder plots not only provided robust datasets for analyses, but resulted in clear relationships by size and density when using only hundreds of trees instead of thousands.”


Figure 1. Nelder plot layout showing the arrangement of trees in one quadrant of a circular plot with 12 arcs and 40 spokes per circle. Note how the density decreases from 1,581 trees per acre down to 83 trees per acre as you move from the innermost arc to the outermost arc. The innermost arc and the outermost arc are buffers. Thus, the usable density data for this Nelder plot design will come from the 10 arcs between the two buffer arcs. This chart was developed by Arney (2019b).

Nelder plots that have been in the ground for a while (10 years or more) can be seen on Google Earth.  One of the best sets of Nelder plots on the planet is located near Alsea, Oregon, at 44°23’15”N 123°33’33”W (Figure 2).  These plots were installed by Dr. Mike Newton and Dr. Elizabeth Cole back in 1980 to study the growth and mortality of Douglas-fir as a function of size and density.  See Newton et al. (2018) for preliminary analyses of these data.

Figure 2.  Screenshot of Google Earth showing the location of Douglas-fir Nelder plots established by Dr. Mike Newton and Dr. Elizabeth Cole in 1980.


Lone Rock’s Nelder Plots

Lone Rock established four Nelder plots in 2014—two were planted with Douglas-fir and two were planted with ponderosa pine.  The Douglas-fir Nelder plots consist of 8 arcs with 40 spokes.  The innermost arc and outermost arc are buffers.  The 6 arcs between the two buffers range in density from 186 trees per acre to 709 trees per acre.  The ponderosa pine Nelder plots consist of 12 arcs with 40 spokes.  The 10 arcs between the two buffers range in density from 109 trees per acre to 1,210 trees per acre.  A fence was constructed around the Douglas-fir Nelder plots to protect the trees from animal damage.  The entire fenced area is 3 acres in size.  A fence was not installed around the ponderosa pine Nelder plots.


Figure 3.  Tim Drake (background center) explains the Nelder plot design used for the ponderosa pine plots.  Mike Backen (to the right of Tim) followed up with a rundown of the various silvicultural treatments he uses to grow trees in this Lone Rock tract.  He is doing a great job.  As you can see, there is not much competing with the pine trees for the site’s resources.  Also shown in the picture are Jim Arney (in the front) and Brett Ragon (way on the left).


Figure 4.  The camera that took this picture was located at the center of a ponderosa pine Nelder plot.  The pine trees planted in the innermost arc are the ones up close.  (The tall trees in the background are in the adjacent stand.)  As you progress from the innermost arc to the outermost arc of the Nelder plot, tree density decreases.  The pine trees in the innermost arc are at a density of 1,581 trees per acre.  They were planted 5.7 feet apart.

Prior to planting seedlings on the plots, the planting spots were carefully flagged so that seedlings were planted at the intersections of designated spokes and arcs.  (Take a quick look at the markers in Figure 1.  Each marker is located at the intersection of a spoke and arc.)  It is critical to plant the seedlings in the desired spoke and arc configuration to ensure each individual tree is subject to the appropriate level of competition from its neighbors.  From a silvicultural perspective, the plots were treated just like adjacent timber stands.  High quality plug seedlings were planted (in the proper spots!) and vegetation management treatments were applied to control unwanted competition from grass and brush species.  After five years, survival in the Douglas-fir Nelder plots and the ponderosa pine Nelder plots averages 81% and 97%, respectively.  These averages are not unexpected given the site conditions for this Lone Rock tract.  Sometimes gophers can be real hard on the Douglas-fir according to Mike Backen, Lone Rock’s Silviculturist.

Lone Rock intends to thin one of the Douglas-fir plots and one of the ponderosa pine plots.  That is why they initially established two plots for each of the species.  The trees on one of the plots can be thinned, while the trees on the other Nelder plot continue to grow at their respective densities.  Information such as this is needed to develop thinning regimes that (1) may increase a landowner’s financial returns, or (2) produce stand structures that are needed to meet non-financial objectives.


Figure 5.  The camera that took this picture was located at the center of a Douglas-fir Nelder plot.  The trees in the foreground are 5 years old.  The trees in front were planted on the innermost arc of the Nelder plot.  (The tall trees in the background are in the adjacent stand.)  As you progress from the innermost arc to the outermost arc of the Nelder plot, tree density decreases.  In this picture, you can “see” the spokes of the Nelder plot because the Douglas-fir trees are lined up quite nicely.  The trees in the innermost arc are at a density of 927 trees per acre.  They were planted 7.4 feet apart.

Lone Rock established the Nelder plots to collect site-specific growth information for the two most important commercial timber species that they manage.  Over the next several decades they will periodically remeasure the trees on the Nelder plots and compare their actual development to FPS projections.  From a modeling perspective, FPS is the only program that can appropriately project the development of trees and stands growing under a broad range of stocking densities and thinning regimes.  FPS in an individual-tree distance-independent model which allows it to make such projections.  These data and analyses will allow Lone Rock to “fine-tune” growth and yield projections and cash flow projections for its timberlands.  At FBRI we are looking forward to adding the Lone Rock data to the existing permanent plot database used to develop the nonparametric models embedded within FPS.  Their data will be an important contribution to the development of optimal timber management regimes for Douglas-fir and ponderosa pine.


For More Information

FBRI will assist any forest management team desiring to install a pair of Nelder plots in any major tree species.  In fact, earlier this year, FBRI assisted Mr. Andrew Puerini with the Grand Ronde’s Natural Resources Department in the establishment of two Nelder plots planted in February with Douglas-fir and western redcedar.

FBRI is a strong advocate for the establishment of Nelder plots to collect much needed growth data for species of commercial importance throughout the United States and Canada.  Of particular interest are Nelder plots planted with secondary species where data are lacking.  A lofty FBRI goal is to get Nelder plots established in each of the principal forest regions in the United States and Canada.  The resulting high-quality growth data will be used to calibrate FPS so it can be relied upon to produce accurate forecasts for forests throughout North America.

For those of you interested in finding out more contact Dr. Jim Arney, FBRI President and Forest Biometrician, at (406) 649-0040 use the contact form below.


Referenced Information

Arney, J. D.  2016.  Mathematics of Trees—Analysis of the FPS Universal Library.  Forest Biometrics Research Institute, Portland, Oregon.  152 pp.

Arney, J. D.  2019a.  What is a Nelder plot and why do we care.  Forest Biometrics Research Institute, E-Forester note dated February 22, 2019.

Arney, J. D. 2019b.  Update for Nelder spreadsheet calculations.  Email sent to Tim Drake and others dated June 28, 2019.

Barry, Ronald P.  2013.  Nelder plots.  10.1002/9780470057339.van009.pub2.  Encyclopedia of Environmetrics.

Newton, M. J., Cole, E. C., and Arney, J. D.  2018.  Nelder Plot Designs for Growth Models—Preliminary Results.  Forest Biometrics Research Institute Annual Meeting, November 14, 2018.  Portland, Oregon.

[1] Dr. Jim Arney and Dr. Dan Opalach are FBRI forest biometricians and provide technical support services to FBRI member organizations.

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