## Genetic distance

One way in which we can measure the genetic similarly of two populations is by estimating the genetic distance between them. There are many different ways in which this can be done, one of the most common being Nei's (1972) standard genetic distance, D. To calculate this, we first need to know Nei's measure of genetic identity (I), which reflects the genetic similarity of populations. For a given locus, this is calculated as:

where pix is the frequency of allele i in population x, piy is the frequency of allele i in population y and m is the number of alleles at the locus (see Box 4.1).

Values of I range from zero to one. Once calculated, they can be used to obtain Nei's D as follows:

Values of D range from zero to infinity. If two populations have similar allele frequencies, i.e. if pix « piy, genetic similarity (I) between the two will approach one and genetic distance (D) will approach zero. At the other extreme, if two populations have no alleles in common, I will be zero and D will be infinity.

 Pgm allele Illinois population Indiana population F 0.146 0.491 M 0.818 0.106 S 0.036 0.403

Box 4.1 Calculating Nei's genetic distance

The data in Table 4.1 represent the allele frequencies of a single allozyme locus (phosphoglucomutase, or Pgm) in two populations of the freshwater zooplankton Daphnia pulex in Illinois and Indiana, USA. We will denote Illinois as population x and Indiana as population y. Since m m 2 m 2 0 5

I = S (pixpiy)/[( Spix2) ( Spiy2)] ' , we first need to calculate the sum i=1 i=1 i=1 of the products of the allele frequencies as follows:

S (pixpiy) = (0:146)(0:491) + (0'818)(0'106) + (0'036)(0'403) i= 1

We then need to calculate the sums of the squared allele frequencies, which for the Illinois population is:

and for the Indiana population is:

Therefore:

I = 0:173/[(0:692)(0:415)]0'5 = 0'173^v/[(0:692)(0:415)] = 0:173/0:536 = 0:323

and because D = — lnI, in this case the genetic distance between the two populations is: