The introduction of new mutations into a population will be modeled by a stochastic process. We use a random variable named to stand for the mutation rate, which is the expected number of new mutations per individual.
The actual number of mutations per individual will be a random number drawn from a Poisson distribution with a mean of . A Poisson distribution is an integer-valued random number that is often used in modeling random events with integral values. For example, if you know that traffic is fairly constant throughout the day on the street in front of your house, and that an average of 5.3 cars per minute go past your house, the actual number you will see in any one-minute period will be a random number drawn from a Poisson distribution with mean of 5.3. It is a Poisson (integer) variable because you are likely to see 5 cars or 6 cars, but never 5.3 cars.