High School

Community 1 has 4 species: 5A, 5B, 85C, and 5D in a population of 100.
Community 2 has 3 species: 30A, 40B, and 30C in a population of 100.

Determine the Shannon diversity (H) for each community.

Answer :

Final answer:

The Shannon diversity (H) for Community 1 is 0.665 and for Community 2 is 1.031.

Explanation:

To calculate the Shannon diversity index (H) for each community, we need to determine the relative abundance of each species in the community.

For Community 1, we can calculate the relative abundance for each species by dividing the population of the species by the total population of the community:

  • Relative abundance of 5A: 5/100 = 0.05
  • Relative abundance of 5B: 5/100 = 0.05
  • Relative abundance of 85C: 85/100 = 0.85
  • Relative abundance of 5D: 5/100 = 0.05

Now, we can calculate the Shannon diversity index (H) using the formula:

H = -Σ(pi * ln(pi))

where pi represents the relative abundance of each species. Plugging in the values for Community 1, we get:

H = -(0.05 * ln(0.05) + 0.05 * ln(0.05) + 0.85 * ln(0.85) + 0.05 * ln(0.05)) = 0.665

To calculate the Shannon diversity index for Community 2, follow the same steps and plug in the relative abundances:

  • Relative abundance of 30A: 30/100 = 0.3
  • Relative abundance of 40B: 40/100 = 0.4
  • Relative abundance of 30C: 30/100 = 0.3

Calculating H for Community 2 using the formula gives us:

H = -(0.3 * ln(0.3) + 0.4 * ln(0.4) + 0.3 * ln(0.3)) = 1.031

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