CHAPTER 3 Community Sampling and Measurements

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

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.

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.

12. If Sobs is the observed number of species, xobs is the observed value of variable x, and xtrue 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. 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).

15. Table 3.6. Tradeoffs between few-and-large and many-and-small sample units.

16. Table 3.6. (cont.)

17. Table 3.6. (cont.)

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 q = 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.