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4- Two Interacting Species
As a convenient fiction for segueing into the two-species model (Model 2), suppose that
we have just learned a grisly secret: A did not die of natural causes!
In fact, the
death rate
Now suppose that, whenever a B kills an A, it occupies the cell that A had occupied.
In addition, suppose that a B occupying a particular cell can replicate into neighboring
cells that contain A. Denote the average total rate at which it attempts to do this as
the predator birth rate
Model 2 shares some features with the mammalian immune system. Some time after infiltration of the body by an antigen A, the immune system manages to create T-cells and B-cells (represented by B) capable of locating and killing A, and successful destruction of an A stimulates further replication of B. Of course, this is a drastic oversimplification of the rich interplay of biological processes comprising the immune system, many of which are still little-understood or unknown. One can imagine an analog of this process in the computer world, in which A represents computer viruses and B represents a hypothetical anti-virus virus. A third alternative is for A to represent rabbits introduced to Australia by English settlers in 1859; B represents the myxomatosis virus deliberately introduced into the Australian rabbit population in 1950 for the purpose of ridding the continent of what had become a troublesome pest [17]. Regardless of its possible applications to various natural or artificial ecosystems, it Model 2 will prove to be a convenient device for comparing several topologies to one another.
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is entirely attributable to a predator B lurking in the shadows,
conducting brutal random killings of unsuspecting As.
. Similarly, there is a predator death rate
at
which a cell occupied by B becomes empty. The characteristics of A remain the same as
in the previous section; it can only replicate into empty cells. As before, all births and
deaths associated with various cells are uncorrelated and asynchronous.