Calculate the density of plant species and the species diversity index based on the provided data.

The formula for density is:

$$\text{Density} = \frac{\text{Total number of individuals of a species}}{\text{Total area sampled}}$$

Based on the instructions, you would have counted the "NUMBER OF PLANT" in a marked area of $10\,\text{m}^2$. If the table was filled, you would sum the "NUMBER OF PLANT" from all tosses (quadrats) to get the total number of individuals. The total area sampled would be the area of one quadrat ($10\,\text{m}^2$) multiplied by the number of times the toss was repeated (e.g., 10 times, as per the table rows).

For example, if the total number of plants counted across all 10 tosses was $N$ and each toss covered $10\,\text{m}^2$, the total area sampled would be $10 \times 10\,\text{m}^2 = 100\,\text{m}^2$.

$$\text{Density} = \frac{N}{100\,\text{m}^2}$$

The unit for density would typically be individuals per square meter (e.g., plants/m$^2$).

A.ii) Calculate the species diversity index

To calculate a species diversity index, you need to know not only the total number of individuals but also how many different species are present and the number of individuals for each species. The provided table only asks for "NUMBER OF PLANT", which implies a total count, not a breakdown by species. Assuming you have identified different species, a common index is the Shannon-Wiener Diversity Index ($H$).

The formula for the Shannon-Wiener Diversity Index is:

$$H = - \sum_{i=1}^{S} (p_i \ln p_i)$$

Where:

• $H$ is the Shannon-Wiener Diversity Index.
• $S$ is the total number of species in the community.
• $p_i$ is the proportion of individuals belonging to species $i$ relative to the total number of individuals ($p_i = \frac{n_i}{N}$).
• $n_i$ is the number of individuals of species $i$.
• $N$ is the total number of individuals of all species.
• $\ln$ is the natural logarithm.

To calculate this, you would need to:

1. Identify all distinct plant species found in your sampled area.
2. Count the number of individuals for each identified species ($n_i$).
3. Calculate the total number of individuals ($N = \sum n_i$).
4. For each species, calculate its proportion ($p_i = n_i / N$).
5. Multiply each $p_i$ by its natural logarithm ($\ln p_i$).
6. Sum these values and multiply by -1 to get $H$.

This index provides a measure of both species richness (number of species) and species evenness (how evenly distributed the individuals are among the species).