First-order moment closure approximations for middle-sized systems with non-linear rates

In this paper we consider the problem of approximating the behaviour of middle-sized population models involving non-linear rates. By using a number of case studies, each with a very di_erent non-linear behaviour, we show that binomial and Poisson moment closure approximations have the potential to accurately represent the expected behaviour of these models. We then compare the two approximation methods to the mean field and moment closure approximations in terms of applicability and accuracy, in addition to investigating the empirical distributions, to derive conclusions regarding their strengths and drawbacks.