Equations used
within this model
Verbal descriptions
of the analytic results, figures from corresponding simulations included.
Parameter
intensity and bifurcation diagrams A small collection of bifurcation plots
(cis-configuration) showing the effects selection coefficients iterating 1 or
both migration rates.
Preliminary
Bifurcation Diagrams This was the first attempt at a bifurcation diagram of
the model. It is a simple 2-island system holding parasite migration at 10%.
Shows a zoom in of the point where the polymorphic equilibria is believed to
become unstable, a simple bifurcation pattern is not believed to exist.
Parameter intensity as a linear function on period Some plots showing (qualitatively) that halving all alphas and betas appear to halve the periodicity of the system. Need to look at linearized model and see how accurate it is at predicting the period.
2 Island Stability Gallery A collection of stability plots for a 2-island system with 81 plots (each containing ~1500 points) showing stability or lack of stability at the stable polymorphic equilibrium. Some spiffy preliminary observations within.
Another 2 island stability gallery Some more 2-island stability plots but with magnitude of the largest eigenvalue instead of just stable or unstable.
A 4-island stability gallery Some 4-island stability plots. Interesting to note that that the plots are still symmetric with respect to parasite and host migration rates. Also note that the range of the stable polymorphic equilibrium can be discontinuous.
Initial starting frequencies do not appear to affect long-term
behavior
Initial frequencies. Emerging limit cycle or equilibrium is independent of initial allele frequencies, suggesting only 1 behavior in the system is stable.
Observations on Local Adaptation
If the island system exhibits cycling- A
species on an island with a strong selection coefficient will be locally
adapted. This appears
to be from the species "leading" the oscillations
and switching before other islands. These islands still often experience
periods of local maladaptation.
If the island is at equilibrium- A species has
a very simple expression for local adaptation. A species on an island with a
weak
selection coefficient will be locally adapted. Further the
local adaptation across all islands will sum to zero for each species.
Local adaptation of the entire island system
across time even when cycles are present is extremely low (below 0.1% in almost
all
cases). Some island systems produce moments of an adapted
system but this is usually followed
quickly by a period of maladaptation.
Gallery
This is a gallery for a collection of phase plots with a combined frequency
over time plot.
Gallery moved here.
Alternate LA
This was an investigation to see if weighting local adaptation by the product
of the allele frequencies produced a significant change in local adaptaion
levels within the system. It reduced local adaptation by around 6-fold on
average, never increasing local adaptation values. The weighted local
adaptation values are marked with an extra "*".
LA observations
this has the analyticly derived local adaptation values for a system at
equilibrium, as well as observations of selection coefficients as predictors of
local adaptation for equilibrium and nonequilibrium systems.
Sources and sinks
The 2 Island source-sink
gallery has some simulations and preliminary results concerning affects of
sources and sinks on local adaptation and stability of the polymorphic
equilibrium. Single island
sink has some analytic results for the stability of equilibria when
reciving fixed allele frequencies from a source.