I have been looking at a distribution for determining the number of fish in the sea. This is because I am actually interested in calculating the number of bugs in a block of codes, and thought (probably erroneously) that this would be a good start. The size of the fish population was modelled by a Japanese scientist called Niwa in a way that matches the observed shoal sizes quite well.
However, I am not so sure the model has any physical similarities to the number of bugs in a block of code, because although
he modeled this situation with a stochastic differential equation
performed merging-splitting simulations to estimate variance.
I am not so sure this is relevant for bugs. Nevertheless, it is a start.
The fish distribution is called the Niwa distribution (https://sinews.siam.org/Details-Page/modeling-food-systems)
I made a picture of the Niwa distribution with Grapher and compared it to the Poisson (blue), Gaussian (green) and Exponential Function (red).
The Niwa distribution
has exponential-like tails that are much ‘fatter’ than Gaussian ones. Thus, observations of large schools are likely to be much more frequent than Gaussian statistics suggest. This indicates that the use of familiar Gaussian models may easily overestimate the total population.