C4.1 Populations and communities

In a chi-squared test, the expected frequency for any cell is calculated as: $E=\frac{\text{Row Total}\times \text{Column Total}}{\text{Overall Total (N)}}$

For the cell where both species are present: Row total (Festuca present) = 30, Column total (Plantago present) = 20, Overall total N = 50.

$E=\frac{30\times 20}{50}=\frac{600}{50}=12$

The expected frequency of quadrats containing both species, if they are distributed independently, is 12.

We need the expected (not observed) frequency for the cell where both species are present, calculated under the null hypothesis of no association.

15 would result from $\frac{30\times 25}{50}$ — but the column total for Plantago present is 20, not 25. This is incorrect.

20 is the column total for Plantago present, not the expected frequency for a single cell. Confusing totals with expected values is a common error.

10 might result from incorrectly dividing $\frac{20\times 30}{60}$ or another arithmetic error. It does not follow from the correct formula applied to these data.

Applying $E=\frac{30\times 20}{50}=12$ confirms that 12 is the correct expected frequency.

Red foxes are motile (mobile) organisms — they move freely through their habitat and cannot be confined to a fixed sampling area.

Quadrat sampling is designed for sessile organisms such as plants, corals, and barnacles. The capture–mark–release–recapture (CMR) method is specifically designed for motile animals, using marked individuals as tracers within the population.

In CMR, individuals are captured, marked, and released. A second sample estimates the proportion of marked individuals, allowing calculation of total population size $N=\frac{M\times n}{m}$.

CMR is the appropriate method because foxes are motile and static quadrats cannot reliably count freely moving animals.

The question tests whether you can match the correct population estimation method to the type of organism being studied.

Quadrat sampling is used for sessile organisms (e.g., plants, barnacles). Foxes move freely, so they would not remain within a quadrat long enough to be counted — this option is incorrect.

The chi-squared test assesses whether two species are distributed independently. It does not calculate total population size, so this option is incorrect.

While transects can be useful for mapping distributions, the claim that random sampling cannot be applied to mammals is false, and transects alone do not estimate total population size effectively for wide-ranging animals.

Capture–mark–release–recapture is the correct choice — it is the standard method for estimating populations of motile organisms like foxes.