How Many Invasive Fish? A Mark–Recapture Estimate Under Pressure
A team studying a reservoir near Coimbatore wants to know how many individuals of the introduced cichlid Oreochromis mossambicus are present. In June they catch 200 fish by gill net, clip the upper lobe of the caudal fin, and release them at the same sites. Three weeks later, using the same nets, they catch 250 fish, of which 32 carry the clip. During those three weeks a heavy monsoon shower raised the water level and the reservoir spilled over its weir for four days; anglers reported catching large numbers of cichlids in the river downstream. Over five years, two native cyprinids have fallen from 40% to 12% of the catch. The team's report states the population as 1,562 fish and recommends complete eradication. The Forest Department asks whether to attempt eradication, promote a fishery for the cichlid as cheap protein, or do nothing.
1. Reproduce the estimate, list the assumptions of the Lincoln–Petersen method, and judge which assumptions were violated and in which direction each violation biases the estimate.
Read the worked answer
Estimate. N = (M × C) / R = (200 × 250) / 32 = 1,562.5, i.e. about 1,560 fish, where M = marked in first sample, C = total in second sample, R = marked recaptures.
Assumptions of Lincoln–Petersen:
- The population is closed - no births, deaths, immigration or emigration between samples.
- All individuals are equally catchable in both samples.
- Marks are not lost and do not affect survival or catchability.
- Marked animals mix randomly with unmarked ones.
- The second sample is a random sample of the population.
Violations here:
- Spill over the weir → open population. Fish left the reservoir (emigration) and may have entered from upstream (immigration). The closure assumption fails outright.
- Fin-clipping may raise mortality or make marked fish more conspicuous or slower, lowering R.
- Anglers removed fish selectively, another source of mortality.
- Gill nets are not equally catchable for all sizes, so the sample is biased toward a size class, and catchability may differ between marked and unmarked fish.
Direction of bias. If marked fish die, emigrate or are caught by anglers disproportionately, R falls and N = MC/R rises. The reported 1,562 is therefore likely an overestimate, and in any case it describes a population that no longer existed at the time of recapture. The number should be reported as an index with confidence limits, not as a census.
2. Judge the three options put to the Forest Department, using the ecology of the species and the hydrology of the reservoir.
Read the worked answer
Option 1 - complete eradication: not feasible here. The reservoir has spilled into the river, so the species is no longer contained; eradication would require the whole river system to be treated, and cichlids are mouth-brooding, highly fecund and breed repeatedly, so recruitment compensates for removal. Culling with nets removes a fraction and can even reduce competition among survivors, raising recruitment. Eradication is realistic only in small, closed, drainable water bodies.
Option 2 - promote a fishery: partially useful but risky. Targeted removal can reduce cichlid density and gives a livelihood, but the gear used (fine gill nets) also takes juvenile native cyprinids as bycatch, and a market for the cichlid invites further introductions and restocking. It must be regulated: gear restrictions, no restocking, a closed season during native fish breeding, and monitoring of bycatch.
Option 3 - do nothing: indefensible. The native cyprinids have fallen from 40% to 12% of the catch, a real decline in native biodiversity in a biodiversity-sensitive hill zone.
Best judgement. Accept that eradication is unachievable, and adopt a containment and mitigation plan: prevention of further spread (no live transport, no stocking), physical or electrical barriers at the outlet where practical, sustained removal effort plus bycatch-safe gear rules, habitat and flow restoration for native species, and a monitoring programme with defined trigger points.
3. Redesign the study so that the estimate would be defensible, and justify each change.
Read the worked answer
Redesign, with reasons:
- Sample when the population is closed - conduct marking and recapture within a short window in the dry season, after the spillway has closed, so emigration and immigration cannot occur between samples. This restores the closure assumption.
- Use multiple recapture occasions instead of one, applying the Schnabel or a similar multiple-census estimator. Several small samples average out the chance effects that make a single R of 32 so variable, and they permit internal checks for closure.
- Test marking effects directly - hold fin-clipped and unclipped fish in enclosures for the study period and compare survival; if clipping is harmful, use a less damaging mark (a small fin punch, or a numbered tag) and check tag loss by double-marking a subset.
- Standardise and randomise effort - the same net mesh, soak time and sites, with sampling spread across depth and habitat so that size- and habitat-specific catchability is reduced.
- Use catch-per-unit-effort as a supporting index and record angler catches to quantify removal.
- Report uncertainty - a confidence interval, not a single figure, and state the assumptions that were tested and those that were not.
The estimate should then be presented as an estimate of abundance with its limits, from which a management decision (how much removal is sustainable) can be made - rather than as a precise census supporting an impossible eradication target.