Thought Experiment Pond: Lincoln-Peterson 

Thought Experiment: Bass in Our Pond

Let's say we want to know how many largemouth bass live in our imaginary pond.

First sampling event (marking):

• We catch 50 bass

• We mark each one with a fin clip or tag

• We release all 50 back into the pond

• Wait a week for them to mix back into the population

Second sampling event (recapture):

• We catch 40 bass total

• Of these 40, we find 8 have marks from our first sample

• So: M = 50, C = 40, R = 8

Calculation: N̂ = (M × C) / R N̂ = (50 × 40) / 8 N̂ = 2,000 / 8 N̂ = 250 bass

Interpretation: Our pond has approximately 250 largemouth bass.

Checking the math another way:

• We marked 50 out of ~250 fish = 20% of the population

• In our second sample, 8 out of 40 = 20% were marked

• The proportions match! This gives us confidence in the estimate.

For sunfish in the same pond: If you wanted to estimate sunfish separately, you'd do the exact same process but only mark and count sunfish. You might find something like:

• Mark 100 sunfish (easier to catch in numbers)

• Recapture 75 total, with 15 marked

• N̂ = (100 × 75) / 15 = 500 sunfish

The beauty of this method is its simplicity, though in practice you'd want to do multiple mark-recapture sessions to get confidence intervals around your estimate.