To calculate the Simpson's Diversity Index for two different communities and determine which one is more diverse, we can use the following steps:
### Community 1
Total organisms: 10,000
Number of species: 10
1. Calculate the proportion of each species in the community.
- Since the organisms are equally distributed, each species has:
[tex]\[
\text{Number of organisms per species} = \frac{\text{Total organisms}}{\text{Number of species}} = \frac{10000}{10} = 1000
\][/tex]
2. Calculate the proportion of each species:
[tex]\[
p_1 = \frac{1000}{10000} = 0.1
\][/tex]
3. Compute the sum of the squared proportions:
[tex]\[
D_1 = \sum (p_1^2) = 10 \times (0.1^2) = 10 \times 0.01 = 0.1
\][/tex]
Simpson’s Diversity Index for Community 1 is 0.1.
### Community 2
Total organisms: 2,000
Number of species: 20
1. Calculate the proportion of each species in the community.
- Since the organisms are equally distributed, each species has:
[tex]\[
\text{Number of organisms per species} = \frac{\text{Total organisms}}{\text{Number of species}} = \frac{2000}{20} = 100
\][/tex]
2. Calculate the proportion of each species:
[tex]\[
p_2 = \frac{100}{2000} = 0.05
\][/tex]
3. Compute the sum of the squared proportions:
[tex]\[
D_2 = \sum (p_2^2) = 20 \times (0.05^2) = 20 \times 0.0025 = 0.05
\][/tex]
Simpson’s Diversity Index for Community 2 is 0.05.
### Comparison
The Simpson’s Diversity Index values are:
- Community 1: 0.1
- Community 2: 0.05
The lower the value of Simpson's Diversity Index, the higher the diversity of the community.
Hence, Community 2 (with an index of 0.05) is more diverse than Community 1 (with an index of 0.1).
