ten, so the probability of unequal number of A and B alleles is 10/16. Thus, although the original colony began with an equal number of A and B alleles, quite possibly, the number of alleles in the remaining population of four members will not be equal. The situation of equal numbers is actually less likely than unequal numbers. In the latter case, genetic drift has occurred because the population's allele frequencies have changed due to random sampling. In this example, the population contracted to just four random survivors, a phenomenon known as a population bottleneck. The probabilities for the number of copies of allele A (or B) that survive (given in the last column of the above table) can be calculated directly from the binomial distribution, where the "success" probability (probability of a given allele being present) is 1/2 (i.e., the probability that there are k copies of A (or B) alleles in the combination) is given by: where n=4 is the number of surviving bacteria. Mathematical models Mathematical models of genetic drift can be designed using either branching processes or a diffusion equation describing changes in allele frequency in an idealised population. Wright–Fisher model Consider a gene with two alleles, A or B. In diploidy, populations consisting of N individuals have 2N copies of each gene. An individual can have two copies of the same allele or two different alleles. The frequency of one allele is assigned p and the other q. The Wright–Fisher model (named after Sewall Wright and Ronald Fisher) assumes that generations do not overlap (for example, annual plants have exactly one generation per year) and that each copy of the gene found in the new generation is drawn independently at random from all copies of the gene in the old generation. The formula to calculate the probability of obtaining k copies of an allele that had frequency p in the last generation is then where the symbol "!" signifies the factorial function. This expression can also be formulated using the binomial coefficient, Moran model The Moran model assumes overlapping generations. At each time step, one individual is chosen to reproduce and one individual is chosen to die. So in each timestep, the number of copies of a given allele can go up by one, go down by one, or can stay the same. This means that the transition matrix is tridiagonal, which means that mathematical