Yes, very nice! Thanks for reminding us of this simple technique and it's justification.
My only problem with the explanation is that it carefully avoids using any formulas with variables. Even the simplest mathematical formula sounds daunting when written out in words, and in my opinion scientists should work to gradually train the general public to understand and accept the use of simple formulas. Call it basic mathematical literacy.
Let me try rewriting the steps:
***
Take the ecologist's way of estimating populations:
Catch a first sample of specimens: count, mark, and then release them: Let N1 be the number of specimens marked this way.
After enough time passes for the sample to have mixed well with the local population, take another sample, mark them differently and note how many are given the new mark and how many of these now have both marks.
Let N2 be the number marked with the second mark, and N12 be the number that have both marks 1 and 2.
The population estimate can be generated from just this data - though follow on samples would usually be taken.
The estimated population (N) is given by N = N1 N2 /N12
Justification: it is reasonable to suppose that the fraction of those found previously marked in the second sample is the same as or close to the ratio of the number in the first count compared to the entire population: N12 / N2 = N1 /N. Multiply/divide both sides by the same things to get a formula for N alone as given above.
***
Of course, to us an equation is worth a thousand words. But it also seems to me that multiplying and dividing is within the grasp of the average person I meet, and the above will probably be more comprehensible to the average person than an equationless version - assuming the variables in the formula are carefully explained.
Just a little weekend musing,
KC
-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of brian whatcott
Sent: Friday, 18 January 2013 11:18 PM
To: phys-l@mail.phys-l.org
Subject: [Phys-L] Estimating animal populations
It happens too rarely: stumbling across a method of clever simplicity.
Take the ecologist's way of estimating populations:
catch a sample and mark the specimens then release them.
After enough time for the sample to have mixed well with the local population, take another sample, mark them differently and note how many were marked in the previous sample.
The population estimate can be generated from just this data - though follow on samples would usually be taken.
The estimated population is given by the first count times second count divided by the number
re-caught of those marked first time.
Justification: it is reasonable to suppose that the number in the second sample includes the number previously marked in a similar ratio to the number in the entire population compared with the number in the first count.....