Lincoln+Index

=Lincoln Index=
 * A Capture, Mark, Release and Recapture method**

The [|Lincoln Index] is used as a method to estimate the population size of animals which are difficult to observe, for example they move around.

The idea behind this method of population measurement is to sample a population in a certain area and to mark the individuals captured (this should obviously be non toxic). These individuals are released and allowed to remix with the population. Then the method is repeated and the proportion of marked and unmarked individuals are recorded.

The assumptions of this method are that:-


 * mixing is complete
 * Marks do not disappear
 * Marks are not harmful, this also means that the marks do not increase the rate of predation
 * It is equally easy to catch every individual
 * There is no immigration, emigration, births or deaths between samples.

If math n_1 math = number of animals marked in the first sample who are marked and returned math n_2 math = Number of animals captured in the second sample math m_2 math = number of animals marked in the second sample math N math = total population

Then the Lincoln Index gives us

math \frac {m_2}{n_2} = \frac {n_1}{N} math

or it can also be written as

math N = \frac {n_1 \times n_2}{m_2} math

An experiment
You will be given a box containing a known population of rice grains in beans.

You will need to capture a population of rice and mark them. Release the grains back into the wild of the box. Mix them up and do the capture again. This will generate data for you to estimate the population of rice. Check this against the known population - you teacher will have this.