When you flip a coin, there are only 2 sides - heads and tails. The theoretical probability for each is:

P(H) = 1/2 = 0.5

P(T) = 1/2 = 0.5

When a spinner has 5 equal sized sectors of red, orange, yellow, green and blue, the theoretical probability for each is:

P(red) = 1/5 = 0.2

P(orange) = 1/5 = 0.2

P(yellow) = 1/5 = 0.2

P(green) = 1/5 = 0.2

P(blue) = 1/5 = 0.2

When you toss a 6-sided dice, there are 6 sides. The theoretical probability (to the nearest hundredth) for each is:

P(1) = 1/6 = 0.17

P(2) = 1/6 = 0.17

P(3) = 1/6 = 0.17

P(4) = 1/6 = 0.17

P(5) = 1/6 = 0.17

P(6) = 1/6 = 0.17

Population Proportion

=

Sample Proportion

proportion of animals originally captured

=

proportion of (marked) animals recaptured

captured organiMs (M)

=

recaptured marked organisms (m)

Bead Capture Tag Recapture

Capture-tag-recapture is a popular method for estimating a population of animals like birds, fish, or large mammals that make long range movements.

For this activity:

• Take a large number of white beads and place them in a jar.
• Draw out a handful and count them. This is the number in the first capture.
• Place in the jar a number of black beads equal to the number of white beads captured. These are the tagged beads.
• Thoroughly mix the beads so that the black beads are evenly dispersed in the jar.
• Draw a second handful of beads and determined the fraction of this sample that has been recaptured.

How can this be used to estimate the total population?

To take an example, say that you remove 27 white beads and you tag them by replacing them by black beads. In the second capture, you remove 42 beads, with 6 of them black.

What does that tell you?

• The number of tagged black beads is 27.
• The number of tagged black beads is about 6/42 = 1/7 of the total number of beads.
• Thus the total number of beads is about 27 X 7 = 189.

This census method works well for animals that thoroughly explore a habitat. The time between the capture and the recapture should long enough so that the the inhabitants of the population have had time to explore the habitat. However, this interval of time should not be so long that the inhabitants have a significant chance of dying or that a sizable new population has been born.

source:  http://gears.tucson.ars.ag.gov/beepop/capture.html

Estimating Tadpole Populations

Population estimates of tadpoles are difficult to obtain. One way to estimate populations of tadpoles is to use capture-recapture techniques. Dyeing tadpoles using Neutral Red Dye has been used in the past by various researchers (Herreid and Kinney 1966, Guttman and Creasey 1973, Travis 1981, Sinsch 1997).

Soaking Hyla arenicolor tadpoles in a 0.005% dye solution (0.05 g dye per 1 liter of water) for 15 minutes noticeably stained tadpoles for up to 30 hours. After collecting and dyeing tadpoles, we released them into the pool in which they had been captured and re-sampled the pool two hours later. On 24 July at Boot Spring, we captured and dyed 61 tadpoles and recaptured 36 tadpoles along with 32 tadpoles that were not dyed.....The population estimate was 115 tadpoles in the sampled pool.

source:  http://www.mp1-pwrc.usgs.gov/amphib/primenet/dye.html

Let's look how this calculation was made:

M/N   = m/n

61/total population = 36/68

61/total population = 0.53

total population = 61/0.95 = 115

The population estimate is 115 tadpoles.

captured organiMs (M)

recaptured marked organisms (m)