Throughout evolution, natural selection is one source of genetic change in populations. However it is possible for a mutation to become common in a population entirely by accident through a phenomenon known as genetic drift. 

It works most strongly in small populations or dramatically fluctuating populations.  When non-lethal mutations occurs it is possible not just because of adaptation but by chance it will have more offspring than it's neighbors. 

Sudden environmental changes also may wipe out many individuals not carrying that mutation and so if either of these situations arise, only after a few generations the mutation can appear in most members of the population.  In large, stable populations this is much less likely to happen by accident.

I have created a procedure in Maple to show a simple simulation of how genetic drift through evolution can occur by chance.

Starting with a population of equal numbers of A and B genotypes.   We implement a couple of rules : each type produces two identical offspring and after each generation half the population dies at random.  Although not a steadfast recipe, this simulation demonstrates the gentic drift phenomenon where one genotype becomes extinct entirely by chance. 

Download genetic_drift_pro.mw