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### Quantifying Biodiversity

#### by NIMBioS

Biodiversity is a measure of the different kinds of organisms in a region or other defined area. It includes the number of species and their range of adaptations, traits that can be behavioral, physical or physiological. These traits enhance an organism’s fitness, its ability to pass on its genes to another generation through reproduction. In this activity, students will learn about biodiversity and how to use the Simpson’s Diversity Index to explain probability and biodiversity in an area.

Grade Level: 10th – 12th grade
Subject Matter: Life Science, Mathematics

Activity Materials
Field data table (provided)

Vocabulary
Biodiversity: a measure of the different kinds of organisms in a region or other defined area. It includes the number of species and their range of adaptations, traits that can be behavioral, physical or physiological.
Species richness: the number of species in a region or specified area
Species evenness: the degree of equitability in the distribution of individuals among a group of species. Maximum evenness is the same number of individuals among all species.
Hypothesis: an educated guess based on knowledge.
Probability: a way of expressing the likelihood that an event will occur
Simpson’s Diversity Index: a way to express how diverse a sample is based on a probability.

What to Do
1. Examine your data, as follows: An ecologist goes out into the field and collects information from two separate plots of the same size but with one big difference: Plot 1 is in the woods and Plot 2 is in a pasture. The ecologist is interested in the types of insects that are found in the plots and whether there is a difference between the two plots. See field data table below:

2. Based on the field data, answer the following questions:
a. Which plot has more species richness?
b. Which plot has more species evenness?
c. Which plot has more biodiversity?

3. Check your answers, as follows:
a. Plot 1, the woods, has more species richness because in Plot 2, the pasture, there are no butterflies. Plot 1 has five species while Plot 1 only has four species present.
b. Plot 1 also has more species evenness. There is close to the same number of individuals in each group.
c. Therefore, plot 1 is more diverse than Plot 2 because species richness is higher and the species are more evenly distributed.

4. Sometimes it is difficult to compare two or more items when talking to more than one person. One person’s notion of “large” may be another person’s “small,” so in order for scientists to understand each other, items can be measured or counted in a way that is universal to everyone. In order to understand how diverse an area is we can do a math problem that shows us in terms of a probability how diverse the area is. Probability is a way of expressing the likelihood that an event will occur
For example: If I toss a coin how what is the probability of the coin landing on heads? One side of the quarter is heads and the other side of the quarter is tails, so we can say you have a half or ½ or 0.5 or 50% chance of the quarter landing on the heads side. Another way you can say this is you are about 50% sure the quarter will land on the side with the head.

5. Simpson’s Diversity Index is a way to express how diverse a sample is based on a probability. The probability can be explained as follows: If you close your eyes and pick out an individual organism from a sample and then you repeat by closing your eyes and picking out another individual from your sample, what is the probability that the organisms will be different species? If the probability is high, for example 0.8 then you have an 80% chance of picking out different species so you have high diversity in your sample.
Let’s take a look at the math behind this index!

Let’s define the variables:
D= Simpsons Index of Diversity
Σ = summation
S= number of species
ni= number of individuals within the ith species
N= total number of individuals within the sample

Let’s calculate D for plot 1 in the table:
Let’s do the numerator (top part) in parentheses first:
*Use each observation to get count n, then multiply it by (n-1) and add those products together.
=(50(50-1)+36(36-1)+35(35-1)+55(55-1))
=50(49)+36(35)+35(34)+55(54)
=2450+1260+1190+2970
=7870

Now let’s calculate the denominator.
Remember N = total number of individuals counting all species in your plot.

In plot 1:
50+36+35+55=176=N

For the denominator we have to calculate:
N(N-1)= 176(175)=30,800

Next let’s put it all together:
D=1-(7870/30800)
D=1-(0.256)
D=0.744

So what does this mean? If you randomly pick two individuals in plot 1 you have a 74.4% chance of those two individuals being different species. We can say the diversity in the plot is high.

6. Now calculate Simpson’s Diversity Index for Plot 2. Remember to start with the numerator. Then calculate the denominator. Then divide the numerator by denominator. Then subtract your fraction from 1. Based on your calculations, which plot is more diverse?

Extended Activities and Links
More biodiversity modules, worksheets and a data set at:
http://www.nimbios.org/education/GSMNP_STImaterials

___________________

In Biology by Numbers, learn about the ways math can solve biological problems. Produced by the National Institute for Mathematical and Biological Synthesis (NIMBioS).

##### About NIMBioS

The views expressed are those of the author and are not necessarily those of Science Friday.

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