How many mice remain? - briefly
Three mice remain.
How many mice remain? - in detail
The precise count of surviving rodents depends on initial quantity, removal mechanisms, and observation period. Begin with the original number of individuals. Subtract any known losses: predation, disease, experimental removal, or natural death. If losses occur at a constant rate, apply the formula N = N₀ × (1 – r)ᵗ, where N₀ is the starting count, r is the proportion removed per time unit, and t is the number of intervals elapsed.
When loss rates vary, calculate each interval separately:
- Record the number removed in the first interval.
- Update the remaining count.
- Repeat for subsequent intervals, using the specific removal proportion for each period.
If direct counts are impractical, estimate using sampling:
- Select a representative subset of the habitat.
- Count individuals within the sample area.
- Extrapolate to the total area by multiplying the sample count by the ratio of total area to sample area.
- Adjust for detection probability, typically determined through mark‑recapture trials.
Mark‑recapture method:
- Capture a sample, mark each mouse, and release.
- After a set time, capture a second sample.
- Apply the Lincoln–Petersen estimator: N̂ = (M × C) / R, where M is the number marked initially, C is the size of the second capture, and R is the number of marked individuals recaptured.
Statistical confidence intervals accompany these estimates, providing a range within which the true count likely falls. Report the central estimate together with its lower and upper bounds to convey uncertainty.
In summary, determine the surviving number by:
- Accounting for all documented removals.
- Applying appropriate decay formulas for constant loss rates.
- Using interval‑by‑interval subtraction for variable rates.
- Employing sampling or mark‑recapture techniques when direct enumeration is infeasible, and presenting results with confidence intervals.