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?

검증된 단계별 안내

Understand the Shannon diversity index formula: \( H = -\sum (p_i \cdot \ln(p_i)) \), where \( p_i \) is the proportion of each species in the community.

Calculate the proportion \( p_i \) for each species in Community 1: \( p_A = \frac{5}{100} \), \( p_B = \frac{5}{100} \), \( p_C = \frac{85}{100} \), \( p_D = \frac{5}{100} \).

Calculate the Shannon diversity index \( H \) for Community 1 using the formula: \( H_1 = -(p_A \cdot \ln(p_A) + p_B \cdot \ln(p_B) + p_C \cdot \ln(p_C) + p_D \cdot \ln(p_D)) \).

Calculate the proportion \( p_i \) for each species in Community 2: \( p_A = \frac{30}{100} \), \( p_B = \frac{40}{100} \), \( p_C = \frac{30}{100} \).

Calculate the Shannon diversity index \( H \) for Community 2 using the formula: \( H_2 = -(p_A \cdot \ln(p_A) + p_B \cdot \ln(p_B) + p_C \cdot \ln(p_C)) \). Compare \( H_1 \) and \( H_2 \) to determine which community is more diverse.

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주요 개념

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Shannon Diversity Index

The Shannon Diversity Index (H) is a mathematical formula used to quantify the diversity within a community. It considers both the number of species present (richness) and the evenness of the distribution of individuals among those species. The formula is H = -Σ (p_i * ln(p_i)), where p_i is the proportion of individuals belonging to the ith species. A higher value of H indicates greater diversity.

Species Richness

Species richness refers to the number of different species present in a community. It is a fundamental aspect of biodiversity, providing a simple count of species without considering their relative abundance. In the given question, Community 1 has four species, while Community 2 has three species, which affects the calculation of diversity indices.

Species Evenness

Species evenness measures how equal the populations of different species are within a community. It is an important component of biodiversity, as communities with similar numbers of individuals across species are considered more even. In the question, Community 2 has a more even distribution of individuals among its species compared to Community 1, impacting the Shannon diversity calculation.