Community 1 contains 100 individuals distributed among four species: 5A, 5B, 85C, and 5D. Community 2 contains 100 individuals distributed among three species: 30A, 40B, and 30C. Calculate the Shannon diversity (H) for each community. Which community is more diverse?

Video transcript

Hello everyone. And in today's video we have the following problem. What is the shine on diversity index or age for a community with 200 individuals. So our total is going to be 200 distributed among four species. Species A. Is said to have 20 members. Species B. Has said to have 30 members. Species C. Has said to have 70 members. And species D. Has said to have 80 members. So I want you to pay close attention to the number of species or the number of members in each species and the total number of individuals that we have in the community. As these numbers are going to be very important to solve this problem. So recall from previous videos what the china and diversity index formula is. We have that the china and diversity index is equal to the negative sum of pi. And this pie value is nothing more than just the number of individuals in each species Divided by the total number of individuals in the community which is 200. So now that we know this, let's start setting up the equation for the china diversity index so that we will be able to solve the problem. We have that age or the china diversity index equals the negative some of each of these just groups of species. And so we have that species A. Has 20 total members. So pie is going to be 20 Divided by 200 because that is the total that we see in our community. And we're going to multiply this by the natural log of the same value of pi. which is going to be 20 divided by 200 for species A. We're going to close that parentheses. And since we're looking for the addition of each of the groups, we're going to add it by group B. So we're going to perform the same procedure for group B. We have that pie for group B. Since it has 30 members, is going to be 30 divided by 200. And we're going to multiply these by the natural log of 30. Again divided by 200 which is the same value of pi. We're going to close this parenthesis and we're going to add once again in this this case for group C which is going to be members total. As we see here, that group C is going to be 70 divided by 200 times the natural log of this same value of pi, which is going to be Which is going to be 70 divided by 200. We close the parentheses and now we go up to group D which is going to have 80 members. As we see here we have the 80 divided by 200 or the value of pi times the natural log of 80 divided by 200 or the value of pi. Again we close that parentheses and we close our entire equation. Now I want you to pull out your calculators and perform these calculations and the final value that you're going to get for these solution. For the problem is going to be that the Shannon Diversity index is 1.2 for this community, looking at our answer choices. This correlates with choice B, which is 1.2, and that is going to be your final answer. So thank you very much for sticking around until the end of the video. I really hope this video helped you.