Mark–Recapture in a Meadow About to Be Mowed
A conservation group must decide whether a population of flightless beetles in a 2.5-hectare meadow can survive a planned autumn mowing. In June they hand-collect 80 beetles, mark each with a small paint dot, and release them at the point of capture. The next morning they return and collect 240 beetles, of which 60 carry marks. The team also finds that the beetles' larval food plants flower most densely in one corner of the meadow.
A field assistant later admits that the 80 marked beetles were released beside that densest patch of food plant, and that the second sample was collected mostly within 10 m of the release point. From published work on the same species: each female lays about 40 eggs, the sex ratio is 1:1, and roughly 5% of eggs produce adults that survive to breed the following spring. The meadow currently supports about 40 flowering food plants per square metre.
1. Calculate the population estimate from the mark–recapture data, then assess how much confidence you should place in it.
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Lincoln–Petersen estimate: N ≈ (M × C)/R = (80 × 240)/60 = 320 beetles, a density of 320/2.5 = 128 per hectare.
Assumptions the estimate needs: closed population (no births, deaths, immigration, emigration between samples), all animals equally catchable, marks not lost or overlooked, marked animals mix randomly back into the population, and the second sample is large enough for the proportion to be stable.
Where this study breaks the assumptions: the assistant's account describes a non-random release and a non-random sampling effort. Marked beetles were put in prime habitat and the recapture effort was concentrated on that same patch, so the probability that a marked beetle was recaptured was higher than for an unmarked beetle elsewhere in the meadow. In the formula, R is inflated relative to what random mixing would give, so the denominator is too large and 320 is an underestimate of true abundance - possibly a substantial one.
Confidence: low. The number should be treated as a floor, not a working estimate. A defensible revision would spread release points and sampling effort across the whole meadow (or use a grid), and would repeat the exercise, ideally with a second method such as distance sampling or repeated trapping over several days.
2. Using the life-history data, decide whether the population is replacing itself, and then work out the effect of the mowing reducing egg-to-adult survival from 5% to 2%.
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Baseline: with 320 beetles and a 1:1 sex ratio, there are 160 females. Egg production = 160 × 40 = 6,400 eggs. At 5% survival to breeding adulthood, next spring's adults = 6,400 × 0.05 = 320.
Interpretation: recruitment exactly equals the current population, so the population is at replacement - λ ≈ 1.0, no margin. A stable count at replacement rate is fragile: it only looks healthy because adult survival is not even in the calculation; if adults also die between years, the true λ is below 1 and the population is already declining.
With mowing (2% survival): 6,400 × 0.02 = 128 adults the following spring. That is a 60% drop in one generation (λ ≈ 0.4). Even 3% survival would give only 192.
Judgement: the estimate of 320 is itself a likely underestimate of abundance but the ratio argument does not depend on it - the model says the population has essentially zero buffer. A 60% survival hit in a single year is not something a replacement-level population can absorb, so the burden of proof should sit with the mowing plan, not with the conservation group.
3. Recommend a mowing regime with justification, and state what you would monitor to check whether the recommendation worked.
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Vulnerable stage first. The life table implies the bottleneck is egg-to-adult survival (5%), not adult numbers. Larvae feed on the food plants through summer and (as described) persist in the soil over winter. Mowing in autumn removes the standing vegetation that shelters the soil surface, compacts the ground with machinery, and removes the flowering plants that must set seed for next year's larval food - squarely on the vulnerable stage.
Recommendation:
- Move mowing to late winter/early spring, when larvae are least exposed near the surface and plants are dormant, accepting that this is a compromise and not a certainty.
- Mow in rotating strips or blocks, leaving 30–50% of the meadow unmown each year as refuge, rather than a whole-site cut.
- Cut high (10–15 cm) and remove cuttings, to reduce compaction and thatch.
- Keep the dense flowering corner unmown every year, since it drives larval food supply.
Monitoring: fixed transects of flowering-plant density; a properly randomised mark–recapture estimate each June at the same effort; and counts of newly emerged adults in spring, which respond directly to larval survival. Pre-agreed trigger: if spring emergence falls below ~80% of baseline, suspend mowing the following year. The plan should be treated as a hypothesis with a decision rule attached, not a fixed prescription.