Population Density

Population density is a measure of the number of individuals of a given species occupying a specific portion of an environment or territory.

|D = \dfrac{n}{A}|

where

|\text{D}| represents the population density (number of individuals per unit area)
|\text{n}| represents the number of individuals in the population (individuals)
|\text{A}| represents the area occupied by the population (units can vary).

If there are |\text{200 bears}| in a forest of |\text{170 km}^2|, what is the density of this population?

Population density is often expressed as a decimal number because it is an average. So even if the density of a hare population is |0{.}5 \text{ hares/km}^2|, in reality, there isn’t half a hare per square kilometre; this is a unit rate. And, based on this rate, we can assume that there would be on average 1 hare per |\text {2 km}^2|.

To find the moose population density in this territory, count the number of individuals observed in each of the five plots and determine the area occupied by these individuals. Here are the 3 steps to follow:

1. Count the number of moose

To find the number of moose in this territory, just count the number of individuals observed in each of the five plots. The number of moose in the picture is represented as follows: |14, 5, 20, 16, 11|.

|\begin{align} N &= 14 + 5 + 20 + 16 + 11 \\
N &= \text{66 moose}
\end{align}|

There are |\text{66 moose}| .

2. Find the occupied area

To find the area occupied, simply multiply the number of plots by the area of ​​a plot. In the picture above, there are 5 plots of |\text {10 km}^2| each.

 |\begin{align} A &= 5 \times \text{10 km}^2 \\
A &= \text{50 km}^2  
\end{align}|  

3. Calculate the population density

To calculate the moose population density in this territory, use the following formula: |\displaystyle D = \frac{n}{A}| and replace the variables with the information that has been calculated.

|\begin{align} D = \dfrac{n}{A} \Rightarrow D&= \dfrac{\text {66 moose}}{\text {50 km}^2} \\ D &= \text {1.32 moose/km}^2 \end{align}|

So there is |\text{1.32 moose/km}^2|.

It would also be possible to estimate the total moose population in this |\text {100 km}^2| territory by multiplying the density by the total area of the territory.

|\begin{align} \text {1.32 moose/km}^2 \times 100 =\text {132 moose/km}^2 \end{align}|

Here we find |\text {132 individuals}| for a territory of |\text {100 km}^2|.