What could be interesting would be to derive the adaptive dynamics of the underlying problem!

For now we do not find anything very interesting because it seems we are taking dispersion parameters that are just too high (actual parameters [1e-3 1e-1]). Indeed, the geotrait variance across simulations is barely changing.

We thus suggest to take values from 10-6 to 10-3.

Same with 10e-6 . But this is because we used the wrong initial conditions! As with geotrait experiment, we should have a uniform distribution over the geographic space. Hence we decide to launch again simulations.

We also took a=0 which is equivalent to say that there is no ecological gradient.

Results of Gillepsie simulation

Cool plot, using StatsPlots

We can see that spatial distribution follows nicely the carrying capacity curve.