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## AP®︎/College Biology

# Simpson's index of diversity

AP.BIO:

ENE‑4 (EU)

, ENE‑4.A (LO)

, ENE‑4.A.1 (EK)

Species number and relative abundance affect the diversity of a community. We can use Simpson's index of diversity to quantify and compare the diversity of different communities.

## Want to join the conversation?

- Just a question about the formula; in my text book I have a formula D = 1 - sum of (n/N)^2.

Why are these formulas different?(3 votes) - I tried the last question "Community #4" that has 1 organism from 5 different species and I got -1. Is it possible to get an answer less than 0?(2 votes)
- Hey Sophie!! Not entirely sure how you got -1, but let's work through it here. So the total number of organisms N in your example would be 5, and n(i) would be one; then by the formula, the diversity index is 1 - (1(0) + 1(0) + 1(0) + 1(0) + 1(0))/(5*4) , which simplifies to 1 - 5/20 = 0.75.

In fact to answer your original question, it's not possible to get an index less than 0(check out the Community 3 in the example in the video) because no matter the population size, having just one species will yield a diversity of 0. Similarly, it's not possible to have an index greater than 1, since if you have an infinitely large population, the value of the second term minimizes at 0 and the index becomes 1.

Hope this helps!!(2 votes)

- Does the equation have to be 1 - (Σn(n-1))/(N(N-1))

or can it just be (Σn(n-1))/(N(N-1))? And by JUST having (Σn(n-1))/(N(N-1)), will it just mean the values are interpreted the other way? (i.e. the smaller the value the higher the biodiversity)(1 vote)

## Video transcript

- [Instructor] So in this table here we have two different communities, community one and community two, and each of them contain
three different species. And we see the populations of
those three different species. And we also see that the total number of individuals in each
community is the same. They both have a total
of 1,000 individuals. Now, my question to you, just intuitively based on the data in this table, which community would you
say is more diverse and why, community one or community two? All right, now let's
think about this together. So as we already talked about, they have the same number of individuals, and you might be thinking
that the number of species could be related to the
diversity, and you'd be right. The number of species does
contribute to the diversity, but we're dealing with a
situation where both communities have the same number of species. They each have three species. But when we look at the data, it's clear that community
two is mostly species A and you have very small groups
of species B and species C, while community one is more evenly spread. So just intuitively it
feels like community one is maybe more diverse, but this was just on my
intuition or our intuition, and the numbers are pretty clear here. It's evenly distributed
amongst the species here, and here it's very heavily
weighted on species A, but it might not always be this clear. So it'd be useful to have
some type of quantitative way to measure the diversity of a population. And lucky for us, there is a
quantitative way to do that called Simpson's, I'll write it down, Simpson's diversity index, and the way you calculate it, it's equal to one minus the sum of, for each species you take
the number of that species divided by the community size squared. So for each of the species,
you do this calculation, square it and then you add it
up for each of those species. So let's figure out
Simpson's diversity index for both communities
one and community two. And I encourage you you
could pause the video and try to work on it on your own before I work through it with you. So let's start with community one. So I'll say diversity
index for community one. I'll just put that in parentheses, is going to be equal to one minus, so we have 325 over, over 1,000 squared. Remember, we're gonna sum
on each of these species plus 305, 305 over 1,000 squared plus 370 over 1,000 squared. And I need to close my parentheses, and I can simplify this a bit. This is going to be equal to one minus, so all of these thousand squares, a thousand squared is a million. So it's gonna be everything
over 1 million, 1 million, and then we're going to have 325 squared, plus 305 squared, plus 370 squared. And that is going to give us 325 squared, plus 305 squared, plus 370
squared is equal to that. That's the numerator here,
and I'm willing to divide that by a million divided by, one, one, two, three, one, two, three. And that is a million. It equals this. And then I'm gonna subtract that from one. So let's put a negative sign here and say, plus one is equal to 0.664. So this is going to be
approximately equal to 0.6664. Now let's do the same
thing for community two. So if I write it over here, the diversity index for community
two is going to be equal to one minus, I put a
big parenthesis here, and we're going to have
925 over 1,000 squared, plus 40 over 1,000 squared, plus 35 over 1,000 squared. And if we simplify in a similar way, that's gonna be equal to one minus all these thousand squares. That's just a million, and
that's a common denominator. And so you're gonna have 925 squared, plus 40 squared, plus 35 squared. And then this is going to be approximately equal to 925 squared, plus 40 squared, plus 35 squared is equal to
this divided by a million. So divided by one, one,
two, three, one, two, three. Yep, six zeros is equal to that. And then you subtract
that from one and you get, which is approximately equal to 0.142. And so we see very clearly when we use Simpson's diversity index that consistent with our
intuition community two has a lower diversity
index than community one. And it's consistent with our intuition that it is less diverse. And I encourage you after this video think about why that
makes mathematical sense.