This addendum to Helm (2010) describes an additional condition to be met when converting and comparing frequencies of randomly distributed plants. Density (number of plants of interest per sample plot area) and frequency (fraction of sample plots with presence of a plant of interest, expressed per sample plot area) can be influenced by plot edge (i.e., plot boundary) effects that differ based on plot shape and size. Abundance comparisons should consider stem base diameter (or size of whatever character is used to establish presence) relative to plot area and distance between plot edges. Base of stem contained entirely within a plot is a common criterion for presence. Concerns could arise, for example, with abundance comparisons in studies that used differently shaped or sized plots, where stem bases are large and may be evident as occurring on both sides of a plot edge (i.e., the plot edge bisecting the stem).

As plot edge length relative to plot size (‘‘edge-to-area ratio’’) increases, the expected percentage of stem bases only partially contained within a plot increases. Edge length refers to the perimeter of a plot, the circumference of a circle, for example. Edge-to-area ratio increases with decreasing plot area of a given shape and differs among plot shapes of a given area, with this ratio increasing from circles to squares to rectangles to thinner rectangles. For example, as a rectangular plot becomes thinner while maintaining a given area, edge length increases. This increase continues to a plot dimension where the long-side edges of a plot become so close to each other that all stems recorded would be only partially contained because stem base diameters would exceed plot width. This would result in a misleading frequency and density of zero, if the criterion for presence requires that stem bases be contained entirely within plots. This is not a practical circumstance but illustrates progression to the most extreme case of edge effects. Greig-Smith (1983) advised against using plots that have high edge-to-area ratios, such as elongated rectangles. Circular or square plots, both of which have low edge-to-area ratios, are recommended and commonly used.

If the criterion for presence under random spatial distribution is based on a dimensionless point, such as the center of a stem for example, edge-to-area ratios are not of concern because those points can not be classified as contained partially within a plot. Edge effects are inconsequential when stem base diameter is small relative to plot area and distance between plot edges, which is typically the case in studies on understory plants because of thin stems and the use of circular or square plots.

Because of edge effects on abundance measures, the additional condition to be met is that the stem-base diameter (or size of whatever character is used to establish presence) is small relative to plot area and to the distance between plot edges such that the character used to establish presence may be reasonably recorded as occurring entirely within a plot or entirely outside a plot, as is typical in studies on understory plants.

LITERATURE CITED Greig-Smith, P. 1983. Quantitative plant ecology, 3rd ed. University of California Press, Berkeley, California.

Helm, S.R. 2010. A calculation of expected plant frequency. Castanea 75:226–231.