 What will happen in the long run? Under the assumptions of the Wright-Fisher model, the sequence of allele frequencies in successive generations \(\{p(0), p(1), p(2), \ldots \}\)constitutes what is known as a Markov chain, that is, a sequence of random variables (stochastic process) where the probability distribution of any variable depends only on the value of the immediately preceding variable. That is, the probability that the allele has a frequency of (say) 0.8 in generation \(t+1\), denoted \(\textit{Prob}(p(t+1) = 0.8)\), depends on the value of \(p(t),\) the allele’s frequency in generation \(t\), but not on its frequency in earlier generations. Importantly, this Markov chain has a special feature, namely that the the two extremal values of \(p(t)\), i.e., 0 and 1, are absorbing boundaries, meaning that if the system reaches one of these boundaries it stays there. That is, if the allele goes extinct in generation \(t\), so has a frequency of zero, then in all subsequent generations its frequency will also be zero (since we are ignoring mutation). Similarly, if the allele goes to fixation in generation \(t\), it will remain fixed in subsequent generations. Formally, we can express these facts as: \(\textit{Prob}(p(t+1) = 0 \mid p(t) = 0) = 1\) and \(\textit{Prob}(p(t+1) = 1 \mid p(t) = 1) = 1\). Since there is no upper bound on the number of generations, eventually random drift must lead the allele to go extinct or to become fixed in the population (and similarly for other alleles). This is because of the absorbing boundary assumption, which implies that every stochastic trajectory must eventually end up at \(p(t) = 0\) or \(p(t) = 1\), for some value of \(t.\)