Mark-recapture of a threatened river fish after a flood
A conservation team is assessing a population of a threatened freshwater fish in a 2.5 km stretch of river. In March they catch 120 fish, mark them with a fin clip, and release them. Two weeks later they catch 90 fish, of which 18 are marked. A flood between samples may have washed some fish downstream, and anglers report catching several marked fish outside the stretch. The team also finds that marked fish are more likely to be caught in the baited traps because the fin clip makes them slower. They calculate a Lincoln index of 600 and propose a no-fishing zone. A second survey in September, after the flood, catches 80 fish with 8 marked, but only 60 of the original marked fish are known to be alive. The team must decide whether the population is declining and whether the no-fishing zone is justified.
1. Calculate the Lincoln index from the March data. Explain the direction of bias from each violation of the assumptions: downstream movement, angling removal, and higher catchability of marked fish.
Read the worked answer
Lincoln index: N = (M × C) / R = (120 × 90) / 18 = 600.
Bias directions:
- Flood/downstream movement: if marked fish are washed downstream and leave the sampled stretch, the proportion of marked fish in the second sample falls, so R is too small and N is overestimated.
- Angling removal outside the stretch: marked fish are removed from the population, again reducing R and overestimating N.
- Marked fish more catchable: if the fin clip makes them slower and easier to trap, R is too large, so N is underestimated.
The observed 18 could be inflated by the catchability effect, while the flood and angling push the estimate the other way. The net direction is uncertain, so 600 should not be treated as a precise population size. It is an index, not a census.
2. Use the September data to decide whether the population has halved. Show the calculation and explain the uncertainty.
Read the worked answer
Using the number of marked fish known to be alive, N = (60 × 80) / 8 = 600. This is the same as the March estimate. If the population had really fallen to 300 and 60 marked fish were alive, the marked fraction would be 60/300 = 0.20, and the expected number marked in a catch of 80 would be 16, not 8. The September result is therefore more consistent with a population of about 600 than with a halving to 300, provided the assumptions hold.
However, the recapture count of 8 is small, so random error is large and the estimate has wide confidence limits. The flood may have changed fish distribution and catchability, and some marked fish outside the stretch may be alive but not 'known'. If the true number alive is below 60, the estimate falls. The data do not show a clear decline, but they do not prove stability either.
3. Recommend a better monitoring design and decide how the team should use the no-fishing zone proposal.
Read the worked answer
A better design would use several recapture occasions within a short closed period, individually identifiable tags such as PIT tags, equal sampling effort, and sampling both upstream and downstream of the 2.5 km stretch. Record angling captures and use catch per unit effort alongside mark-recapture. Report confidence intervals and test whether estimates from successive surveys overlap. If fish move in and out of the stretch, a larger river section or a metapopulation approach is needed.
For the no-fishing zone, the current evidence is not strong enough to demonstrate a decline, but it may still be justified as a precautionary measure if the species is threatened, the population is small, and angling is an additional mortality source. The zone should be paired with monitoring so that its effect can be evaluated; it should not be presented as proven necessary by a single uncertain estimate.