(a) Calculate the estimated population density of these beetles per \(100\text{ m}^2\). Show your working.
(b) Explain two precautions the ecologists must take when marking the beetles to ensure the accuracy of the mark-release-recapture method.
(c) Suggest how a high rate of emigration during the five-day period would affect the calculated population size estimate.
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Worked solution
First, calculate the total estimated population size (\(N\)) using the Lincoln Index formula:
\(N = \frac{M \times C}{R}\)
where:
- \(M\) (number marked initially) = \(120\)
- \(C\) (total captured in second sample) = \(150\)
- \(R\) (number recaptured with marks) = \(18\)
\(N = \frac{120 \times 150}{18} = \frac{18,000}{18} = 1000\) beetles.
Next, convert the woodland area into square metres:
\(2.5\text{ hectares} \times 10,000\text{ m}^2\text{ ha}^{-1} = 25,000\text{ m}^2\).
Finally, calculate the density per \(100\text{ m}^2\):
\(\text{Density} = \left(\frac{1000}{25,000}\right) \times 100 = 4\text{ beetles per } 100\text{ m}^2\).
(b)
1. The paint must be non-toxic so it does not increase the mortality rate of marked beetles compared to unmarked ones.
2. The paint must not make the beetles more visible to predators, which would also artificially increase their mortality rate.
3. The paint must be waterproof/durable so it does not rub off before the second capture.
(c)
If marked beetles emigrate (leave the study area), fewer marked beetles will be available for recapture. This will decrease the value of \(R\) (recaptures), which acts as the denominator. A smaller denominator results in an overestimation of the total population size.
Marking scheme
- Correct formula or substitution to find total population: \(\frac{120 \times 150}{18}\) (1 mark)
- Correct total population of 1000 beetles (1 mark)
- Conversion of area to \(25,000\text{ m}^2\) (1 mark)
- Correct final density of 4 (1 mark)
Part (b): 3 Marks (Max 3)
- Non-toxic paint / does not affect survival (1 mark)
- Disguised/does not increase predation risk (1 mark)
- Does not hinder movement or mating behaviour (1 mark)
- Paint is permanent/does not rub off (1 mark)
Part (c): 2.1 Marks
- Explains that emigration leads to fewer marked individuals in the area/less chance of recapture (1 mark)
- Correctly identifies that the calculated population size will be an overestimate (1.1 marks)