1. Community Diversity – Measures and Techniques What is the best way to describe community diversity? Is it: 1.Species richness – the total number of species encountered in samples (or in the entire community if sampled areas are combined to determine the asymptotic richness)…or… 2.A measure of species diversity. There are many suggested measures (see Table 9.2, pg.216). The most widely used are: a. Simpson’s Index (or a direct derivative from it), b. Shannon-Weiner Information Theory diversity (or a derivative), c. Brillouin’s index, d. Pielou’s index e. Fisher’s 

2. Simpson’s index is: This index generally emphasizes the more common species in the value of the index. Those species contribute more to the sum of squares of proportions, while rare species contribute little. If there are no really common species, then the index works well. This index also does not require full knowledge of the community to make statistical comparisons. Russell Lande showed that there is an unbiased version of this index (N is the number of individuals sampled):

3. Shannon-Weiner Information Theory diversity is: As long as the same base is used, you don’t really have to determine logs base 2, but that is the theoretical requirement. This index places greater emphasis on rare species. To try to portray the distribution of species abundances, H’ is frequently compared with the maximum possible value, which would be found if all species were equally abundant. If all species were equally abundant:

4. The ratio H’/ln s is called evenness. Since the index is based on logs, the Shannon-Weiner index is sometimes ‘corrected’ by presenting e H’, though this ‘correction is not common in the literature. The problem with information theory is that to make appropriate statistical comparisons you need to know how many total species comprise the community. Then the comparisons you make are between individual samples and the total community. Differences are subjected to typical kinds of statistical analysis. The basic index and evenness measures are described as “biased”. Yet this remains probably the most commonly used index of diversity.

5. Brillouin’s index is: This index also emphasizes the effect of rare species. Note that it uses n i, the number of individuals in the species, and can’t be used with alternative measures like biomass. Brillouin’s index also has an evenness ratio. The formula is too complicated to insert here; look it up if you want to use Brillouin’s index in a research context.

6. Pielou’s index is closely related to Brillouin’s, and similarly provides a better indication of rare species contribution than common species. It is: There is one last index that has fallen out of favor recently. It isn’t even listed in the text, but can be very valuable in low diversity or early successional communities. Fisher’s index is called , and requires iterative calculation using the number of species and the number of individuals. It comes from Fisher’s log series estimate of community structure, sometimes called a ‘broken stick’ model.

7. There are actually two steps to determine . First you need to know the number of species and number of individuals in your samples. From this information you calculate x: Then you use the calculated x to further calculate  : In practice there is no explicit equation solution for x, so a computer program (not really very complicated) is used to get x, and from it calculating  is straightforward.

8. Sampling schemes in community studies The text considers first a European approach in which a large sample plot, called a relevé, is subjectively chosen to represent the community. A species-area curve is constructed by collecting samples representing a series of ‘nested’ quadrats, slowly expanding the total area sampled within the relevé. This approach typically uses species richness as the measure of diversity.

9. In North American ecology, the typical method is to collect data from randomly placed, small quadrats. Some ecologists instead use regularly placed (evenly spaced) quadrats. While sizes vary depending on the community, typically the quadrats range in area from ¼ m 2 to around 1 m 2. In forests, it is obvious that larger sample areas would be required.

10. The data (numbers of individuals or biomass of each species) is then used to calculate (and compare) any of the diversity statistics. What shape should these quadrats be? There are arguments among ecologists about this. One view is to use square quadrats. This approach is frequently used when vegetation is to be mapped, so that distances between individuals and species is being collected. A rigid frame supports a clear plexiglas sheet marked with grid squares. Sheets of thin clear plastic can be laid over the support, and plants mapped onto the sheet. On the other hand, if biomass or numbers of individuals are the data of interest, circular quadrats are more frequently used. Hoops enclosing the appropriate area can be tossed to randomize placement.

11. One of the arguments advanced to support using circular, rather than square quadrats, is that if there are spatial gradients in the distribution of species, the corners of the square (or rectangular) quadrats will ‘pick up’ species more likely to differ from the basic pattern within the sample area than is the case with circular sample areas. A completely different approach is to collect samples along a transect, which is a long line (e.g. an extended tape measure). Species or the numbers of individuals of species can be counted if the occur within some specific distance (10 cm, 20 cm, 1m) on either side of the line. This is called the belt transect approach. A related approach uses the line-intercept method. Now you only count those individuals whose bodies ‘make contact’ with the transect line.

12. In addition to quantitative data in the form of numbers or biomass, there are other approaches used in studies of distributions, rather than abundances. In this case, data can take the form of frequencies of occurrence. What fraction of quadrats in an area contain species A? Is this fraction statistically similar to or different from the fraction in another community. A slightly more quantitative measure (but frequently only approximated) is to use basal cover (or canopy cover for trees). What area of ground is covered by the plant or plants of a species? Using frame quadrats and plastic sheets, drawing the area occupied by a species permits later use of various tools to quantify cover. There are also various systems dividing cover into ‘classes’:

13. The simplest classification is traceable to Braun-Blanquet, but here are the three shown in the text:

14. The methods described thus far are hard (or impossible) to use in studies of forests. There, plotless methods are usually employed. One of the simplest is the point-centred quadrat method: Choose (usually using random number tables) a series of random points distributed over the forest area being studied. From each point use a compass to set basic compass directions (basically axes) pointing N, S, E and W, dividing the area around this point into four quarters. Measure the distance (and record the species) closest to the point within each quarter. Typically these distances are converted into local densities for the species encountered. In herbaceous or grassland communities, harvests to determine biomass are readily completed. What do you do in a forest?

15. There are two parts to generating an estimate of tree biomass: 1.Use triangulation methods to estimate the height of the tree. 2.Measure the DBH – diameter at breast height (a standard height above ground). Sometimes, for trees grown commercially, only the second measure is needed. There are standardized tables to convert DBH to biomass. However, in a natural forest trees may extend vertically to reach the canopy while not having grown to the same DBH. Then you need both measures to estimate biomass.

16. The point-centred quadrat is the first technique presented that also provides data about the spatial structure of the community. Another method is called Morishita’s index of dispersion. To calculate it you are back to point-centred quadrats to study the distribution of a species. The formula for the index is: where you measure the number of individuals within a given radius (using different radii) of the focal (central) individual. n is the number of focal individuals and m i is the number of individuals within the radius of focal individual i.

17. While the Morishita index can take on a range of values, if: I  > 1 the population has a clumped distribution. I  = 1 the population is randomly distributed. and I  < 1 the population is ‘uniformly’ distributed.