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Answer :
Final answer:
To calculate the Shannon diversity index (H) for each community, we need to use the formula H = -Σ(pi * ln(pi)). For Community 1 with 5A, 5B, 85C, and 50D, the Shannon diversity index is approximately 0.241. For Community 2 with 30A, 40B, and 30C, the Shannon diversity index is approximately 0.673. Community 2 is more diverse than Community 1.
Explanation:
To calculate the Shannon diversity index (H) for each community, we need to use the formula H = -Σ(pi * ln(pi)), where pi represents the proportion of individuals belonging to each species, and ln denotes the natural logarithm.
For Community 1, we have 100 individuals distributed among four species: 5 individuals of species A, 5 individuals of species B, 85 individuals of species C, and 50 individuals of species D. To calculate the Shannon diversity index:
1. Calculate the proportion of each species: A = 5/100 = 0.05, B = 5/100 = 0.05, C = 85/100 = 0.85, D = 50/100 = 0.5.
2. Calculate the value of pi * ln(pi) for each species: A = -0.05 * ln(0.05), B = -0.05 * ln(0.05), C = -0.85 * ln(0.85), D = -0.5 * ln(0.5).
3. Sum up the values from step 2: -0.05 * ln(0.05) + -0.05 * ln(0.05) + -0.85 * ln(0.85) + -0.5 * ln(0.5) = 0.241.
Therefore, the Shannon diversity index for Community 1 is approximately 0.241 (expressed using two significant figures).
Similarly, for Community 2 with 30 individuals of species A, 40 individuals of species B, and 30 individuals of species C:
1. Calculate the proportion of each species: A = 30/100 = 0.3, B = 40/100 = 0.4, C = 30/100 = 0.3.
2. Calculate the value of pi * ln(pi) for each species: A = -0.3 * ln(0.3), B = -0.4 * ln(0.4), C = -0.3 * ln(0.3).
3. Sum up the values from step 2: -0.3 * ln(0.3) + -0.4 * ln(0.4) + -0.3 * ln(0.3) = 0.673.
Therefore, the Shannon diversity index for Community 2 is approximately 0.673 (expressed using two significant figures).
By comparing the Shannon diversity indices, we can determine which community is more diverse. In this case, Community 2 with a Shannon diversity index of 0.673 is more diverse than Community 1 with a Shannon diversity index of 0.241.
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