Question

comparing ecosystems: calculate the diversity index of each ecosystem below using the equation for simpson’s diversity index.
ecosystem a:

population	n (# of individuals)
marabou stork
african elephant
nile crocodile

what is n?
calculate the biodiversity index of ecosystem a. show your work.

ecosystem b:

population	n (# of individuals)
marabou stork
african elephant
nile crocodile

what is n?
calculate the biodiversity index of ecosystem b. show your work.

Explanation:

Step1: Count individuals in Ecosystem A

• Acacia trees: 3 (from the image: three trees)
• Marabou stork: 2 (two storks)
• African elephant: 3 (three elephants)
• Nile crocodile: 2 (two crocodiles)
• Total \( N = 3 + 2 + 3 + 2 = 13 \)
• Simpson’s Diversity Index formula: \( D = 1 - \frac{\sum n(n - 1)}{N(N - 1)} \)
• Calculate \( \sum n(n - 1) \):
• Acacia: \( 3(3 - 1) = 6 \)
• Stork: \( 2(2 - 1) = 2 \)
• Elephant: \( 3(3 - 1) = 6 \)
• Crocodile: \( 2(2 - 1) = 2 \)
• Sum: \( 6 + 2 + 6 + 2 = 16 \)
• \( N(N - 1) = 13(13 - 1) = 156 \)
• \( D = 1 - \frac{16}{156} = 1 - \frac{4}{39} = \frac{35}{39} \approx 0.897 \)

Step2: Count individuals in Ecosystem B

• Acacia trees: 1 (one tree)
• Marabou stork: 2 (two storks)
• African elephant: 6 (six elephants)
• Nile crocodile: 1 (one crocodile)
• Total \( N = 1 + 2 + 6 + 1 = 10 \)
• Calculate \( \sum n(n - 1) \):
• Acacia: \( 1(1 - 1) = 0 \)
• Stork: \( 2(2 - 1) = 2 \)
• Elephant: \( 6(6 - 1) = 30 \)
• Crocodile: \( 1(1 - 1) = 0 \)
• Sum: \( 0 + 2 + 30 + 0 = 32 \)
• \( N(N - 1) = 10(10 - 1) = 90 \)
• \( D = 1 - \frac{32}{90} = 1 - \frac{16}{45} = \frac{29}{45} \approx 0.644 \)

Answer:

• Ecosystem A: \( N = 13 \), Diversity Index \( \approx 0.897 \)
• Ecosystem B: \( N = 10 \), Diversity Index \( \approx 0.644 \)