General properties of genetic drift

What I've shown you so far applies only to a haploid population with two individuals. Even I will admit that it isn't a very interesting situation. Suppose, however, we now consider a populaton with $N$ diploid individuals. We can treat it as if it were a population of $2N$ haploid individuals using a direct analogy to the process I described earlier, and then things start to get a little more interesting.

• Each individual in the population produces a large number of gametes.

• Each gamete is an identical copy of its parent, i.e., $A_1$ begets $A_1$ and $A_2$ begets $A_2$.

• The next generation is constructed by picking $2N$ gametes at random from the large number originally produced.

We can then write a general expression for how allele frequencies will change between generations. Specifically, the distribution describing the probability that there will be $j$ copies of $A_1$ in the next generation given that there are $i$ copies in this generation is

$$P(\hbox{$j$\ $A_1$\ in offspring $\vert$\ $i$\ $A_1$\ in pa... ...eft(\frac{i}{2N}\right)\left(1 - \frac{i}{2N}\right) \quad ,$$

i.e., a binomial distribution. I'll be astonished if any of what I'm about to say is apparent to any of you, but this equation implies three really important things. We've encountered two already:

• Allele frequencies will tend to change from one generation to the next purely as a result of sampling error. As a consequence, genetic drift will eventually lead to loss of all alleles in the population except one.

• The probability that any allele will eventually become fixed in the population is equal to its current frequency.

• The population has no memory.⁸ The probability that the offspring generation will have a particular allele frequency depends only on the allele frequency in the parental generation. It does not depend on how the parental generation came to have that allele frequency. This is exactly analogous to coin-tossing. The probability that you get a heads on the next toss of a fair coing is 1/2. It doesn't matter whether you've never tossed it before or if you've just tossed 25 heads in a row.⁹