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Current time:0:00Total duration:7:04

AP Bio: ENE‑4 (EU), ENE‑4.A (LO), ENE‑4.A.1 (EK)

[Instructor] When we look at communities of organisms, an interesting
question to think about is how diverse
are those communities? And here I have two example communities and each of them is made
up of species of circles. Each species is represented
by a different color. And so pause this video. Intuitively, which of these communities would you think to be more diverse? Well, if you look a community number one you see that it has two different colors of circles, or we could view that as two different species, while
community number two has four different species. So intuitively we would say that community number two is more diverse. But how could we actually
quantify these things? Well, to help us do that biologists have developed a tool, which is known as Simpson's Index of Diversity. And so it's gonna be a number between zero and one where one is a,
you could say a very, very diverse community and
zero'd be not diverse at all. And so let me write this down. So the index is going to be,
this is gonna be the index of diversity. And then capital N is
going to be the total population in that community,
so the total number of individuals of all species. So number of all individuals, individuals. And then n sub i is going
to be the number of, we could view that as the ith species. So number of individuals,
viduals, in ith species where i I'm saying, you
know, here there's two species so that'd be the first species and they're the second species. So i would be one and then i would be two. Here there's four, so you would have it the number of individuals
for the first, second, third, or fourth. So how do you put all of
these numbers together to get the index of diversity? Well, we would get this formula. And we're gonna apply it a few times to see why it makes sense. So Simpson's Index of
Diversity is gonna be equal to one minus the sum of
the product of n sub i times n sub i minus one, all of that over capital N times capital N minus one. Now to see why this makes
sense, let's calculate Simpson's Index of Diversity
for each of these communities. So for community number
one, won't you let me scroll a little bit so that
we can do it right over here. Community number one,
I could write Simpson's Index of Diversity's going to be equal to one minus, and actually let me do the denominator right over here. What's the total population size? We have one, two, three, four, five, six, seven, eight, nine, 10, 11, 12. So capital N is 12. So we're gonna have 12 times
12 minus one, so 12 times 11. And then up here we're
going to first think about the population of blues. We could view that as our first species. So one, two, three,
four, five, six, seven. So we're gonna have seven
times seven minus one, so seven times six. Seven times six. And then to that we are going to add the population of our second species. One, two, three, four, five. So it's going to be five times one less than that, which would be four. And so what is this going to get us? We are going to get, this is
going to be equal to one minus. Up here we have 42 plus
20, so it's 62 over. And then down here, 12 times 11 is 132. And so this is going to be equal to, I can get a calculator out for that. 62 divided by 132 is equal to that. Put a negative sign on it
and then add it to one. So plus one is equal to 0.53. So this is approximately 0.53. Now I encourage you,
pause the video and see if you can now apply
Simpson's Index of Diversity to community number two,
if you can solve that on your own before we do it together. All right, now let's do it together. So in this situation, community
number two, I will do it. Let me draw a little line here so that we don't get confused. So in this situation, our Simpson's Index of Diversity's gonna
be equal to one minus. Our denominator's going to be, let's see. We have one, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13. So we have 13 individuals,
so it's gonna be 13 times one less than 13. So 13 times 12. And then our numerator is
going to be, let's see. We could view the yellow
as our first species. So there's four of them. One, two, three, four. So it's going to be four
times one less than that. Then we could think
about our orange species. There's three of them. So it's gonna be plus three
times one less than that. And then we could think
about our light blue species. There's two of them. So it's gonna be plus two
times one less than that. And then we can think
about our teal species. One, two, three, four. So it's gonna be plus four
times one less than that. And so that is going to be equal to, it's going to be equal to one minus, see, well, I have 12
plus six, which is going to be 18, plus two, which
is 20, plus 12, which is 32. One minus 32 over. And then what is 13 times 12? Let's see, that's going
to be equal to 156. 156. And I can get my calculator out again. And I am going to get 32
divided by 156 is equal to that. And then I will need to subtract that from one to get 0.79, roughly. So this is approximately equal to 0.79. So what's neat about this is this gave us numbers that confirmed
what we knew intuitively, that this community right over here by Simpson's Index of
Diversity is more diverse than that community right over there. And if you wanna see
perfect lack of diversity imagine a community that only had, imagine a community that
only had one species in it. I encourage you to figure that out. Think about what Simpson's
Index of Diversity would be. Say that this was community
three right over here. Community number three. Think about what the index of diversity would be for that community, if they just had those three individuals
and they were all one species. And similarly, I encourage you think about community number four. Community number four. Well, maybe it has one
of each species, like, think about what Simpson's
Index of Diversity would be for this community.

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