How many mice remain?

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:

  1. Select a representative subset of the habitat.
  2. Count individuals within the sample area.
  3. Extrapolate to the total area by multiplying the sample count by the ratio of total area to sample area.
  4. 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.