Calculating a. Introduction:

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1 Calculating a Biodiversity Index Introduction: The simplest way to measure biodiversity is to count the number of species at a site; this number gives scientists a measurement of species richness. By comparing species richness at two sites, scientists learn something about biodiversity. But a simple survey of species richness does not necessarily give scientists an complete picture of biodiversity in an ecosystem because it does not place any importance on relative abundance or dominance 1. For example, compare two diverse ecosystems: The first ecosystem contains 55 species of trees, yet there are only 1 or 2 individuals of 54 of those species and 200 individuals of a single species. The second ecosystem contains 40 species of trees, and there are 50 individuals of each species. Which ecosystem is more diverse? The first ecosystem does have a species richness larger than the second ecosystem. Yet that first ecosystem is made up of only one dominant species. Even though the second ecosystem contains fewer species, it is made up of a rich balance of those species and would be considered more diverse by most scientists. When measuring biodiversity in an ecosystem, patterns must be taken into account. This does not mean that the number of species is not important, but it is only one part of the biodiversity equation. 1 The term relative abundance is used by ecologists to describe the number of individuals of a species relative to the total number of individuals of all species found in a plot. Dominance is sometimes used to describe the same attributes as relative abundance; however, dominance can also refer to relative canopy cover or relative basal area. BI.1

2 There are many methods to measure biodiversity within an ecosystem 2. A common measure used by scientists is the Shannon- Weiner Biodiversity Index. It is probably easiest to calculate the Shannon-Weiner Biodiversity Index using a graphing calculator or math software, such as Microsoft Excell. FORMULA FOR THE SHANNON-WEINER BIODIVERSITY INDEX H = [ ( )] ( p i ) ln p i H represents the symbol for the amount of diversity in an ecosystem. H will be the greatest if the species are all equally abundant. pi represents the proportion, or relative abundance, of each individual species to the total (measured from 0 to 1). ln pi represents the natural logarithm of pi Student Exercise Have your students use the following example to calculate a biodiversity index for two imaginary (and extremely simplified) forest biodiversity plots. Example: Your students have chosen to compare the tree census data from their biodiversity plot with the tree data from another school. They want to be able to determine which plot has a greater biodiversity by using the Shannon-Weiner Biodiversity Index. The following table illustrates the data both schools have collected: 2 ANY biodiversity index is a simplistic way to describe a complex ecosystem or environment, which is why there are so many biodiversity measurement methods (indices). BI.2

3 School Biodiversity Plot #1 Biodiversity Index Tree Species (sp) sp1 sp2 sp3 sp4 sp5 Total Number of individuals (N) School Biodiversity Plot #2 Tree Species (sp) Number of individuals (N) sp1 sp2 sp3 sp4 sp5 sp6 sp7 Total Upon first glance, plot #2 seems to have a higher amount of diversity because it has the most number of species. However, if you look closely, you ll notice that there are 7 species in plot #2, but only one is abundant (sp6). Let s use the Shannon-Weiner Index and see if our initial observations are accurate. Step 1: Calculate the p i values The p i values, or proportions, for each of the plots must be calculated. Divide the number of individuals of each species by the total number of individuals in the plot. For example, in plot #1, there are 160 total organisms. Out of those 160, we have to find the proportion that are species #1, the proportion that are species #2, the proportion that are species #3 and so on So for species #1 in plot #1: p 1 = 26 / 160 = 0.16 (In other words, species #1 makes up 16% of all species in plot #1.) BI.3

4 Step 2: Calculate the natural log for proportion (ln p i ) Once the p i values have been calculated for all species, the natural log of each of these values is calculated. Again, for species #1 in plot #1: ln p 1 = ln (0.16) = Repeat for each species. Step 3: Multiply the original proportion by the natural log of that proportion (p i )(ln p i ) The natural log of each proportion is multiplied by the original proportion (p i )(ln p i ) for each species. Species #1 in plot #1: (p 1 )(ln p 1 ) = (0.16)(-1.82) = Repeat each of these steps for all species from in both plots and you end up with the following tables for each biodiversity plot: School Biodiversity Plot #1 Tree Species (sp) sp1 sp2 sp3 sp4 sp5 Sum (Σ) Number of individuals (N) Proportion (N/ΣΝ) (p i ) Natural log of p i (ln p i ) (p i )(ln p i ) (-H ) BI.4

5 School Biodiversity Plot #2 Tree Species (sp) sp1 sp2 sp3 sp4 sp5 sp6 sp7 Sum (Σ) Number of individuals (N) Proportion (N/ΣΝ) (p i ) Natural log of p i (ln p i ) (p i )(ln p i ) (-H ) Step 4: Calculating the Shannon-Weiner Biodiversity Index Now you have the values you need to calculate the Shannon-Weiner Biodiversity Index for Plot #1 and Plot #2. H = [ ( )] ( p i ) ln p i For Plot #1: H 1 = - [ ] H 1 = - [-1.56 ] = 1.56 For Plot #2: H 2 = - [ ] H 2 = - [-0.89] = 0.89 Step 5: Conclusions According to the Shannon-Weiner Biodiversity Index, Plot #1 is the most diverse, because it has a higher index (1.56) than Plot #2 (0.89). Despite the fact that Plot #2 has a higher species richness value, the evenly spread abundance of species found in Plot #1 makes it more diverse. The biodiversity index calculation contradicts our initial expectation that Plot #2 was more diverse! BI.5

6 Notes on Calculating a Biodiversity Index Other methods for calculating a biodiversity index exist, like the Simpson Biodiversity Index (see below) may be simpler to use than the Shannon-Weiner Biodiversity Index. These other indices sometimes yield different results because each index places different degrees of importance on factors such as species richness or relative abundance. When comparing diversity measures for a single place at two different times, or two locations which draw on the same pool of species, it is necessary to account for species that are absent in one census but present in the other. These species have p = 0.0, but in order to calculate the natural log set p=0.001 (or use the Simpson index instead). FORMULA FOR CALCULATING THE SIMPSON BIODIVERSITY INDEX H = 1 p i 2 ( ) Note: the proportion (p i ) is the same value used in the Shannon-Weiner Biodiversity BI.6