Next we consider the dynamics of and D. The odes for these quantities can be regarded as equations for single population dynamics with a variance correction. As an illustration, consider example ( , ) from the example section. The dynamics for this example is given by
in which is also varying in response to changes in and D according to (Eq. 32). The equation for mean population size is now composed of a logistic equation, migration into the population and a variance correction. This set of equations cannot be used to simulate the exact dynamics of the metapopulation, but can set some boundaries in which the mean size of the population might move. Note that the condition for the stability of the trivial equilibrium of the full system (Eq. (28)) is equal to the condition for stability of the set of ode's when is neglected. In fact for the trivial equilibrium. Putting also provides an upper bound to mean population size.