About Frequencies

Frequencies

It is very common to express population data as frequencies. Frequencies are like percentages except that they are expressed on a scale of 0 to 1.0. A frequency is the proportion of individuals, alleles, or whatever in an entire population. Thus frequencies are calculated as:

eq. 1: freq(X) = number of X / total number (i.e., population size)

A fancy way to define a frequency is to say that it is the number of some subpopulation normalized to the population size.

A few of things to remember about frequencies:

The sum of the frequencies must add to 1.0.
- For example, let's say that we are dealing with four behavioral strategies, A, B, C, and D in some population. Then:
- freq(A) + freq(B) + freq(C) + freq(D)= 1.00
You can calculate any frequency using eq. #1 above. A quicker method is to find all of the frequencies except one by using eq. 1, and find the remaining one by subtraction.
- Thus, imagine that you used eq. 1 and found freq(A) = 0.10, freq(B) = 0.60, freq(D) = 0.25 -- then:
- freq(C) = 1.00 - freq(A) - freq(B) - freq(D) = 1.00 - 0.10 - 0.60 - 0.25 = 0.05
A common naming convention is use the lower case first letter of the name of the strategy or phenotype to represent the frequency
- Thus freq(Hawk) becomes h.

Note: This convention is usually not used with genes since dominant genes are usually represented in upper case and recessives in lower case.

Try to avoid using ever percentages -- you must convert them back to frequencies before you can use them in most types of calculations. Get used to using frequencies and they'll become second

? Calculate the frequencies of the following phenotypes:
A = 18 individuals,
B = 6 individuals,
C = 29 individuals and
D = 2 individuals
ANS

Problem answers: First find the total population size. It is the sum of all members, thus in this case the sum of A, B, C and D phenotypes:

pop size = # A + # B + # C + # D = 18 + 6 + 29 + 2 = 55

Then use eq. 1 to find the frequency of all but one of these (or all of them if you wish):

a = 18 / 55 = 0.33

b = 6 / 55 = 0.11

c = 29 / 55 = 0.53

d = 1.00 - a - b - c = 0.33 - 0.11 - 0.53 = 0.03

note -- direct calculation of d = 2 / 55 = 0.04 --- the differences are due to rounding errors!