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Single population

Next we consider the dynamics of tex2html_wrap_inline2210 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 ( tex2html_wrap_inline2088 , tex2html_wrap_inline2346 ) from the example section. The dynamics for this example is given by


in which tex2html_wrap_inline2348 is also varying in response to changes in tex2html_wrap_inline2210 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 tex2html_wrap_inline2348 is neglected. In fact tex2html_wrap_inline2356 for the trivial equilibrium. Putting tex2html_wrap_inline2356 also provides an upper bound to mean population size.

John Val
Wed Feb 26 07:30:07 EST 1997