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.
