An Evolutionary Complex System
(Peter Allen's Population Dynamics Model)
Description
of the Model
This model is to examine
the mutual co-evolution of different populations where the landscape
of 'pay-offs' is adaptive, that is really generated by the interactions
of a population with the other populations in the system. In
the space of "possibilities" closely similar behaviours are
considered to be most in competion with each other, since they
require similar resources, and must find a similar niche in
the system. However, we assume that in this particular dimension
there is some "distance" in character space, some level of dissimilarity,
at which two behaviours do not compete.
This version of
the model consists of a two dimensional character space, in
which competion for underlying resources exists, but so also
do other possible interactions. For example, for any two particular
populations i, and j, practising their characteristic behaviours,
there may be an effect of one on the other. This could be
positive, in that side-effects of the activity of j might
in fact provide conditions or effects that help i. Of course,
the effect might equally well be antagonistic, or of course
neutral. Similarly, i may have a positive, negative or neutral
effect on j.
There is also a
competition for underlying resources, that is a crowding
effect: as a spot on the landscape gets crowded the reproduction
rate at that spot decreases. Finally, there is another important
factor which is the fidelity of reproduction, that is accidental
'leakage' of the population through which populations from
i create small numbers of off-spring in the adjacent cells.
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