# Lab: biodiversity

Shannon's index of diversity (H): 1. pour into your “pond” a random number of colored goldfish. Calculate the total, the number for each color, and the Shannon’s index for this trial:

Example:

n = 37

yellow = 25/37 = 0.675

orange = 6/37 = 0.162

green = 1/37 = 0.027

red = 5/37 = 0.135

H = (.675*-.393) + (.162*-1.82) + (.027*-3.61) + (.135* -2.00)

H = .265 + .294 + .097 + .27

H = 0.926

1. Repeat with both a more diverse and a monoculture ecosystem. What do you notice about the range of H?
2. Statistics folks use Chi-squared analysis of a system like this. How could you use this?
3. Imagine two ponds separated by 10 kilometers. How could you prove that they were once connected?
Original biodiversity, Pond one:

n total =

yellow fish (one fish)

orange fish (two fish)

red fish (red fish)

green fish (blue fish)

x for each color

x/n

ln (x/n)

x/n * ln(x/n)

H total

Low biodiversity: pond two:

n total =

yellow fish (one fish)

orange fish (two fish)

red fish (red fish)

green fish (blue fish)

x for each color

x/n

ln (x/n)

x/n * ln(x/n)

H total

High biodiversity: pond three

n total =

yellow fish (one fish)

orange fish (two fish)

red fish (red fish)

green fish (blue fish)

x for each color

x/n

ln (x/n)

x/n * ln(x/n)

H total