area 1 has SDI 0.67 area two has SDI 0.19 compare the diversity
area 1 37, 32, 25
Area 2 7, 3, 88
To compare the diversity between the two areas, we can calculate the Simpson's Diversity Index (SDI) for each area.
For Area 1:
Total number of individuals (N1) = 37 + 32 + 25 = 94
Proportion of individuals of each species:
- Species 1: 37/94
- Species 2: 32/94
- Species 3: 25/94
SDI for Area 1 = 1 - [(37/94)^2 + (32/94)^2 + (25/94)^2]
= 1 - [0.1379 + 0.1132 + 0.0890]
= 1 - 0.3401
= 0.6599
For Area 2:
Total number of individuals (N2) = 7 + 3 + 88 = 98
Proportion of individuals of each species:
- Species 1: 7/98
- Species 2: 3/98
- Species 3: 88/98
SDI for Area 2 = 1 - [(7/98)^2 + (3/98)^2 + (88/98)^2]
= 1 - [0.0051 + 0.0009 + 0.7606]
= 1 - 0.7666
= 0.2334
Comparing the SDI values, we can see that Area 1 has a higher diversity (SDI 0.67) compared to Area 2 (SDI 0.19). This suggests that Area 1 has a greater variety and evenness of species present compared to Area 2.
To compare the diversity between area 1 and area 2 based on the given Standardized Diversity Index (SDI) values, we need to calculate the diversity index for each area and compare the results.
The formula to calculate the SDI is as follows:
SDI = Σ[(pi)*(ln(pi))]
Where:
- Σ represents the summation symbol.
- pi refers to the proportion of each species in the area (expressed as a decimal).
- ln(pi) is the natural logarithm of pi.
Let's start by calculating the diversity index for area 1:
For area 1, we have the following proportions:
- Species 1: 37
- Species 2: 32
- Species 3: 25
To obtain the proportion, divide each species count by the total count:
- Proportion of Species 1 = 37 / (37 + 32 + 25)
- Proportion of Species 2 = 32 / (37 + 32 + 25)
- Proportion of Species 3 = 25 / (37 + 32 + 25)
Now, calculate the natural logarithm of each proportion:
- ln(Proportion of Species 1) = ln(37 / (37 + 32 + 25))
- ln(Proportion of Species 2) = ln(32 / (37 + 32 + 25))
- ln(Proportion of Species 3) = ln(25 / (37 + 32 + 25))
Next, multiply each proportion by its respective natural logarithm:
- (Proportion of Species 1) * (ln(Proportion of Species 1))
- (Proportion of Species 2) * (ln(Proportion of Species 2))
- (Proportion of Species 3) * (ln(Proportion of Species 3))
Sum up all these values to find the diversity index for area 1.
Repeat the same steps for area 2, using the given species counts: 7, 3, and 88.
Once you have both diversity index values, you can compare them to determine which area has higher or lower diversity. In this case, area 1 has an SDI of 0.67, while area 2 has an SDI of 0.19. Therefore, area 1 has higher diversity than area 2.
To compare the diversity of areas 1 and 2, we can use the Simpson's Diversity Index (SDI).
Step 1: Calculate the proportional abundance of each species in each area by dividing the individual count by the total count for that area.
In area 1:
- Proportional abundance of species 1: 37 / (37 + 32 + 25) = 0.39
- Proportional abundance of species 2: 32 / (37 + 32 + 25) = 0.34
- Proportional abundance of species 3: 25 / (37 + 32 + 25) = 0.27
In area 2:
- Proportional abundance of species 1: 7 / (7 + 3 + 88) = 0.07
- Proportional abundance of species 2: 3 / (7 + 3 + 88) = 0.02
- Proportional abundance of species 3: 88 / (7 + 3 + 88) = 0.91
Step 2: Calculate the square of each of these proportional abundances.
In area 1:
- Squared proportional abundance of species 1: (0.39)^2 = 0.15
- Squared proportional abundance of species 2: (0.34)^2 = 0.12
- Squared proportional abundance of species 3: (0.27)^2 = 0.07
In area 2:
- Squared proportional abundance of species 1: (0.07)^2 = 0.005
- Squared proportional abundance of species 2: (0.02)^2 = 0.0004
- Squared proportional abundance of species 3: (0.91)^2 = 0.83
Step 3: Calculate the sum of the squared proportional abundances for each area.
In area 1: 0.15 + 0.12 + 0.07 = 0.34
In area 2: 0.005 + 0.0004 + 0.83 = 0.8354
Step 4: Calculate the SDI for each area using the formula: 1 - (sum of squared proportional abundances)
In area 1: 1 - 0.34 = 0.66
In area 2: 1 - 0.8354 = 0.1646
Step 5: Compare the SDI values of the two areas.
Area 1 has an SDI of 0.66, while area 2 has an SDI of 0.1646. This indicates that area 1 has higher diversity compared to area 2 based on the Simpson's Diversity Index values.