Stability in 2 islands
Spatial
parameter pvalues indicated by row and column headers: alphas are in black (alpha1 on top, alpha 2 below) - betas are in blue (beta1 to left, beta 2 to right)
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Subplots were run with the combination of the 4 spatial
parameters at corresponding row and column headers- host migration on the
y-axis varying between .01 and .39 and parasite migration varying on the
y-axis between .01 and .39. Observations:
The collection of plots is mirrored about y=-x, this is equivalent to
declaring the parasite the host and vice-versa. This works since equations
are symmetric.
The
"cis" configuration seems very stable while the "trans"
configuration seems very unstable. i.e. An island that is under strong
selection for both parsite and host exchanging migrants with an island that
is under weaker selection for both, is much more stable than a system with
one island under strong selection on parasite and weak on host and reversed
for the other island.
A very
interesting result: Stability in a system is equally dependent on host and
parasite migration rates (i.e. each plot is symmetric) despite the fact that
selction may be overall higher on one species than the other (e.g. .01 .16 .04 .04). It will be
interesting to see if this holds for islands >2.
The
system is still unstable at very low migration rates below 1%.
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.01 .01 |
.01 .04 |
.01 .16 |
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.04 .01 |
.04 .04 |
.04 .16 |
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.16 .01 |
.16 .04 |
.16 .16 |
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.01 .01 |
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.01 .04 |
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.01 .16 |
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.04 .01 |
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.04 .04 |
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.04 .16 |
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.16 .01 |
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.16 .04 |
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.16 .16 |
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