Two moment closure techniques for an interacting species model

We explore a stochastic analogue for a generalized deterministic interacting species model for two species. By applying two moment closure techniques, we approximate the expected values, variances, and covariance for the two populations and compare the results. First, we assume a multivariate normal distribution with standard additive variances and covariance. Next, we assume a multivariate lognormal distribution with multiplicative variances and covariance. There is good agreement between the two moment closure techniques. For the stable equilibria, the expected values of the populations converge to values that are similar to, but not equal to, the values of the deterministic equilibria. The variances and covariance also converge over time.