1. CHAPTER 3 Community Sampling and Measurements From: McCune, B. & J. B. Grace. 2002. Analysis of Ecological Communities. MjM Software Design, Gleneden Beach, Oregon http://www.pcord.comhttp://www.pcord.com Tables, Figures, and Equations

2. Table 3.1. Cutoff points for cover classes. Question marks for cutoff points represent classes that are not exactly defined as percentages. Instead, another criterion is applied, such as number of individuals. Cutoffs in parentheses are additional cutoffs points used by some authors.

3. Figure 3.1 Expected percent frequency of presence in sample units (SU) as a function of density (individuals/SU).

4. Relative density of species j is the proportion of the p species that belong to species j:

5. These relative measures are commonly expressed as percents, by multiplying the proportions by 100, for example:

6. Importance values are averages of two or more of the above parameters, each of which is expressed on a relative basis. For example, a measure often used for trees in eastern North American forests is: IV% = (Relative frequency + relative dominance + relative density) / 3

7. Table 3.2. Example of identical importance values representing different community structures. Species 1Species 2 Relative Density428 Relative Dominance1044 Sum52 IV%26

8. Box 3.1. Example of stand description, based on individual tree data from fixed- area plots. The variance-to-mean ratio, V/M, is a descriptor of aggregation, values larger than one indicating aggregation and values smaller than one indicating a more even distribution than random. The variance and mean refer to the number of trees per plot. IV and other measures are defined in the text. Raw data for three tree species in each of four 0.03 hectare plots. Each number represents the diameter (cm) of an individual tree.

9. Box 3.1, cont. Frequencies, counts, total basal areas, stand densities, and stand basal areas.

10. Box 3.1, cont. Relative abundances, importance values, and variance statistics.

11. Table 3.3. Average accuracy and bias of estimates of lichen species richness and gradient scores in the southeastern United States. Results are given separately for experts and trainees in the multiple-expert study. Extracted from McCune et al. (1997). N = sample size. % Deviation from expert ActivityNSpecies richness Score on climatic gradient Score on air quality gradient % of expertBiasAcc.BiasAcc.Bias Reference plots1661-394.4+2.411.1-10.5 Multiple-expert study, experts 395-53.6+3.64.7-4.7 Multiple-expert study, trainees 354-468.0+8.05.0-5.0 Certifications774-262.7+2.42.1-2.1 Audits350-5010.3+3.76.0+2.7

12. If S obs is the observed number of species, x obs is the observed value of variable x, and x true is the true value of parameter x, then:

13. Table 3.4. Raw data for two-dimensional example of accuracy and bias, plotted in Figure 3.2. Personxy xy 13.05.240.9-0.4 14.05.14-0.61.1 14.02.64-1.1-2.0 20.9-0.75-2.7 20.1-2.95-3.1-1.2 20.4-2.951.3-1.9 30.0 30.60.3 3-2.1-1.6 Figure 3.2. Two-dimensional example of accuracy and bias. Each person (1, 2,..,5) aims at the center (0,0), representing the “true value.” Deviations are measured in two dimensions, x and y.

14. Table 3.5. Inaccuracy and bias for two-dimensional example (Fig. 3.2). Inaccuracy (Ave. distance Average bias Personto 0,0)xy 15.753.674.30 22.320.47-2.17 31.10-0.50-0.43 41.51-0.27-0.43 52.84-1.50-1.37

15. Table 3.6. Tradeoffs between few-and-large and many-and- small sample units. Few-and-largeMany-and-small Bias against cryptic species Higher. There is a hazard that some species, particularly cryptic species, are inadvertently missed by the eye. Lower. Small sample units force the eye to specific spots, reducing inadvertent observer selectivity in detection of species. Degree of visual integration High. The use of visual integration over a large area is an effective tool against the normally high degree of heterogeneity, even in "homogeneous" stands. Low. Minimal use is made of integrative capability of eye, forcing the use of very large sample size to achieve comparable level of representation of the community. Inclusion of rare to uncommon species High. Visual integration described above results in effective "capture" of rare species in the data. Low. Unless sample sizes are very large, most rare to uncommon species are missed.

16. Table 3.6. (cont.) Accuracy of cover data on common species Lower. Cover classes in large sample units result in broadly classed cover estimates with lower accuracy and precision than that compiled from many small sample units. Higher. More accurate and precise cover estimates for common species. Bias of cover estimates for rare species High (overestimated).Low. Sampling timeVaries by complexity and degree of development of vegetation. No consistent difference from many-and-small. Varies by complexity and degree of development of vegetation. No consistent difference from few-and-large. Analysis timeFaster. With a single large plot, data entry at site level leads directly to site-level analysis. Slower. Point data or microplot data require initial data reduction (by hand, calculator, or computer) to site-level abundance estimates.

17. Table 3.6. (cont.) Analysis optionsEstimates of within-site variance are poor or impossible, restricting analyses to individual sites as sample units. Within-site variance estimates are possible as long as sample units are larger than points. RecommendationsThe extreme case (single large plot) is most useful with extensive (landscape level) inventory methods. In many cases it is better to compromise with a larger number of medium- sized sample units. The extreme case (point sampling) is most useful when rare to uncommon species are of little concern and accurate estimates are desired for common species. In most cases a compromise by using a smaller number of larger sample units is better.

18. The following formula rescales aspect to a scale of zero to one, with zero being the coolest slope (northeast) and one being the warmest slope (southwest). where  = aspect in degrees east of true north. A very similar equation but ranging from zero to two, was published by Beers et al. (1966).

19. The plane-corrected distance D' for a distance D on an angle of S above the horizontal is: D' = D/cos S.