# How to Calculate Animal Population Density

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The calculations involved in estimating animal population density are relatively straightforward. However, reasonable estimates require accurate raw data. A random sample must be taken in which each animal has an equal chance of capture, and the sample population must randomly redistribute itself once re-released. While marked animals must stay marked, the second sample must be taken quickly to minimize the effects of births, deaths and migration on the population size. For sedentary populations, the small samples taken -- known as quadrats -- must be reasonably representative of the whole population. Additional quadrat sampling may be required if the data appears too varied.

### Things You'll Need

• Population data
• defined sample area
• calculator

## Calculation of Mobile Animal Populations

• Use the Lincoln-Peterson Index to calculate density. This simple, capture-recapture method has been used effectively since the 1930s.

• Assign variables. N (number) is the number that you are looking for, the total number of animals. Use m (marked) to represent the number of animals taken in the first capture and marked. Use r (remarked) to represent the number of recaptured animals. Utilize n to represent the number of animals captured the second time.

• Apply the Lincoln-Peterson index which states that the percentage of marked individuals to the total population should equal the percentage of remarked individuals to the recaptured population. This statement is represented by the formula m/N = r/n.

• Rearrange the equation to solve for the total population number. The formula becomes N = mn/r.

• Consider using a standard deviation equation to check for accuracy. This will yield an error margin that enables you to state the population with scientifically accepted confidence. Use this formula -- S = the square root of ((m+1)(n+1)(m-r)(n-r)/(r+1)(r+1)(r+2)) -- to calculate standard deviation.

• Interpret the standard deviation calculation. Remember that the larger the deviation, the less accurate the estimate of actual population size is. For example, with an estimated population size of 500, a confidence interval range of +/- 25 (475-525) is more precise than one of +/- 100 (400-600).

## Calculation of Sedentary Animal Populations

• Use a quadrat technique to generalize population density estimates from several small areas into a larger one. A quadrat is a small area in which the actual animal population is counted.

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• Check the data to ensure that the number, size and arrangement of quadrats are reasonably likely to be representative of the population as a whole. For example, if you sample four quadrats and one has two animals, one has 800 animals and two others have 57 animals, you might need to question the sampling methodology.

• Average the number of individuals found in each quadrat. Using the example cited above results in an average of 229 individuals per quadrat -- (2 + 800 + 57 + 57)/4 = 229.

• Multiply the average number obtained by the ratio of the larger area to the quadrat size (they should all be the same). For example, if your sample area is 200 m2 and each quadrat is 2 m2, the ratio calculation is 200 m2/ 2 m2 = 100.

• Estimate population density by multiplying the average number of animals per quadrat by the area ratio obtained. For example, the population density in this sample is calculated by multiplying 229 by 100 in order to come up with 22,900 individuals.

## References

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