Eq. 6 is an example of a Poisson Distribution equation. Poisson distributions are mathematical descriptions of large numbers of random events. Starting from a few simple equations that describe random events, these equations generate predictions for the large scale patterns that would result. These resulting distributions have a number of different shapes that are determined by the type of process that is being modeled.
One example of a natural phenomenon that can be modeled using a Poisson distribution is radioactive decay. We know is that there is a certain chance that an unstable nucleus of a certain type will emit energy each moment in time. Thus, decays appear to be random events that have a certain chance of happening each unit of time. Using a type of Poisson distribution known as an exponential decay, which is in form identical to eq. 6 (the basis for our description of the behavior of the stable mixed strategy 'var'), we can either:
Closer to home, the distribution of quitting costs used by a 'var' strategist will also have a negative exponential decay. And that is because just like the radioactive nuclei, there is a certain probability of continuing (quitting) for each increment of cost.
Poisson distributions are extremely important in science in general and in biology in particular. Other versions of the distribution, for example, form the basis for determining whether or not patterns we observe in nature are random as compared to grouped.