GEOG 442

Biogeography

Comparing Different Biodiversity Measures

In this lab, you'll calculate several different measures of biodiversity commonly used in biogeography and ecology and compare the impressions of species diversity they convey. The data have been adapted from a study of land cover and land management practices as they affect the diversity of ants in Costa Rica:

Roth, Dana S.; Perfecto, Ivette; and Rathcke, Beverly. 1994. The effects of management systems on ground-foraging ant diversity in Costa Rica. Ecological Applications 4, 3: 423-436.

You have data for 11 field sites, at which ground-foraging ants were trapped and then identified. Some 109 species were recorded somewhere among these 11 sites, with different mixes on different sites. You are provided data on the relative abundances of each species on each of the 11 sites. For each site, then, the relative abundances add up to 1.00 (plus or minus some rounding errors).

The field sites are grouped by land use. The first three, highlighted in blue, are primary forest, or relatively undisturbed tropical forest. The next two, highlighted in green, are abandoned cacao plantations reverting to forest. The next group of three, highlighted in yellow, are productive cacao plantations still in business. The last two, highlighted in orange, are banana plantations in production. The question here is what effect do these different land uses and land covers have on the diversity of ants foraging on them? From what you know of biogeography, which land use is likelier to support the greatest biodiversity? Which land use is likelier to support the least? (you may want to Google "cacao plantations" and "banana plantations" to get a better sense)? Now, let's go test these hunches.

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Getting Your Data

To get the data on which this lab is based, click here. You will be asked what to do with the file, since it's a Calc spreadsheet, not a web page. Select Save File As and then specify where you'd like to keep it. If you're doing this at home, stash it anyplace you normally keep data. If you're in our labs, please save it to a flash drive or e-mail it to yourself, because the student files on the system are purged each night.

 

Calculating Diversity Indices

Select one field site from each of the four land use types (you might want to consult with your peers to ensure that you don't all pick the exact same four). For each site, one column (black text) provides relative abundance (or p_i) data by species. At the bottom of the column, you'll see I've already summed it to make sure it adds up to unity (1). In the box immediately below that sum, in Row 113, please calculate Species Richness. To do that, type =count(e2:e110) in Cell E113 (if you were working with Site PF:CCL in Column E). That gives you the number of species found at that site (even if only one measly ant from that species was recorded out of thousands of trapped ants). Now that you have that formula done, put your cursor on that cell, hit Control-C to copy it into your Clipboard, and then paste it into the appropriate cell in Row 113 for each of your other 3 sites by hitting Control-V.

In the column to the right of your site data (that would be F, if you were working with Site PF:CCL, for example), you can begin the calculation of Shannon's Diversity Index or H:

To do this, calculate p_i * natural logarithm of p_i (the power you would have to raise e or 2.71828 to get the original relative abundance). Sounds awful? Naaah! Let's say that your abundance for some ant species was listed in cell E5 for the sake of argument. In cell F5, you would type =E108*LN(E108) and hit Enter. Voilà! You'll get some small negative number.

Now, copy that formula (Control-C) and then paste it next to every cell for which you have abundance data (you could copy the cell down the column, but you'll get a messy pile of computer schmutz beside any blank cell, so you'd wind up manually erasing them). This tediousness is why I'm only having you do one example per land use type. Aw, shucks, I did this part for you -- the columns of red numbers -- because it really is tedious but you really do have to avoid attempting to take a logarithm of 0 or blanks.

Now, at the bottom of the column, in the white box in row 114, type in the formula for the Shannon Index above. In spreadsheet-speak, it comes out =-1*(sum(f2:F110)), assuming you were working with Site PF:CCL in Column E and F (and don't forget that negative sign right after the equals sign).

It's hard to interpret this raw H, so most biogeographers like to index it as a proportion of the maximum H that could possibly exist with the number of species at the site. Remember that the Shannon approach to biodiversity tries to get at the evenness of individuals or biomass in a species, rather than just a simple present/absent census (as in species richness). To calculate the maximum H (H_max), just take the natural logarithm of the species richness. In other words, in the box provided in Row 115, type =LN(E113), assuming we're talking about the first site, PF:CCL, in Column E.

Now you have H_max, just divide H by H_max. That's all there is to the Shannon Equitability Index (E_H). To do that, in Row 116 for your site (let's say Site PF:CCL), you'd type =F114/F115. You now can copy the working formula from that cell, say, Cell F116, and paste it into the right box for each of the other three sites. Actually, it's okay just to do the formula in the second row and copy it down. You won't get error messages for having taken the log of 0, just a bunch of 0's and those won't affect the calculations for the Simpson's indices.

Now, you can figure out the Simpson's Index (D).

That involves squaring each ant species' relative abundance (p_i). If you were working with Site PF:CCL, for example, you would start with, say, Cell G5 and type =E5^2. You will get small positive numbers less than 1. Copy that formula and paste it in every cell in Column G where there's a relative abundance listed in Column E. Do the same for the corresponding p_i² entries for your other three field sites.

Below those columns, in Row 117, sum these squares. Type =sum(g2:g110), for example, if you were working with Site PF:CCL. Copy that formula to the appropriate cells in Row 117 under each of your other three sites.

The raw Simpson's Index or D is kind of counter-intuitive. A highly diverse site is closer to 0 and a not very diverse site is closer to 1. So, a lot of biogeographers flip that around by taking the inverse, hence Simpson's Inverse Diversity Index. To do this, go to Row 118 below the raw Simpson's Index and type =1-G117 (assuming you're working on Site PF:CCL again). Copy that to the proper cells in Row 118 under each of your other three sites.

There's yet another Simpson's measure: the Simpson Reciprocal Index. This is simply 1/D. So, you would use Row 119 and type, say, 1/G117.

At this point, you can calculate Simpson's Equitability Index (E_D). Divide Simpson's Reciprocal Index by the Species Richness. If you were doing this for Site PF:CCL, in Cell G120, you'd type =G119/E113.

Comparing Land Uses by Biodiversity Indices

So, now you have biodiversity indices coming out of your ears. What can you do with them all? You might want to create another smaller table or spreadsheet, just the site name and its Species Richness, Shannon's Diversity Index, Shannon's Equitability, Simpson's Inverse Diversity Index, and Simpson's Equitability Index, so you can compare them side by side, site by site. List which site you used as the example for each of the four land uses:

Primary Forest: ______________________________

Abandoned Cacao: ______________________________

Producing Cacao: ______________________________

Banana Plantation: ______________________________

Biodiversity Measure	Primary Forest	Abandoned Cacao	Producing Cacao	Banana Plantation
Species Richness
Shannon's H
Shannon's EH
Simpson's InvD
Simpson's ED

It is really helpful to create five bar charts, one for each of the diversity measures (Y axes), with one bar for each site (named along the X axis).

Eyeballing the tables and/or bar charts, how did your hypotheses hold up? Compare your results with those of your peers who did different sites. Which kind of land use had the highest biodiversity? Is it the one you expected? Which one had the lowest? Is it what you expected? Comparing your results with your peers', how would you group land uses by ant biodiversity? How does plain ol' species richness perform in comparison with these Shannon and Simpson measures that try to incorporate evenness? In which way do the Shannon and Simpson measures overrepresent diversity in the case of the banana plantations?

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first placed on the web: 11/05/08
last revised: 04/15/19
© Dr. Christine M. Rodrigue