## Digging even deeper

Species richness and %dominance are very simple measures. ** It would be nice if there was a score that somehow summarize the shape of the whole graph.** We could imagine communities that are not at all alike, but have the same richness and dominance -- like the ones on the right.

So what to do? As a starting point, we could figure out the **percentage of each species in the community**. But how can we summarize this into a single index?

If we just add all the percentages, we will always come out to 100% . What we need is a way to combine the percentages that reflects something about both the number of species and the how common each species is.

**Let's do some experimenting with a really simple community** -- just 3 kinds of insects, conveniently named Bugs A, B, and C:

Pristine stream: 50% Bug A, 25% Bug B, 25% Bug C

Polluted stream: 50% Bug A, 49% Bug B, 1% Bug C

Which of these 2 communities has greather %dominance?

How to think about squaring a percentage:

When you square a percentage between 0 and 1, you ALWAYS get a number smaller than what you started with. Why? Think of the decimal as a fraction

**25% = 1/4. **

So squaring the fraction is the same as saying **"one-fourth of one-fourth"** -- clearly smaller than the original one-fourth.

And, even better, as the original fraction gets smaller, the squared fraction gets TINY.** One-tenth of one-tenth** is pretty small, and **one-hundredth of one-hundredth** is really tiny.

So, how can we distinguist between these communities without listing out all the species percentages??? We can't just add them (because we'll always get 1.0) ... but** if we square each percentage FIRST, then add, we'll get some number less than**.

Let's give it a try. For the pristine stream, we have:

.50^{2} + .25^{2} + .25^{2} =

.25 + 0.0625 + 0.0625 =

0.375

We'll call this **Simpson's Dominance**. Now you try the the polluted stream:

### There are 3 species in the polluted stream: 50% Bug A, 49% Bug B, and 1% Bug C. What is the Simpson's dominance index

(To make this problem interactive, turn on javascript!)

- Starting with Bug A ... : 0.50 squared is 0.25
- ...about Bug B... : 0.49 squared is 0.24
- ...about Bug C... : 0.01 squared is 0.0001
- ...adding them up... : 0.25 + 0.24 +0.0001 = ...

#### I think I have the answer: 0.4901

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