Group-level events, like fission and extinction, catalyze the evolution of cooperation in group-structured populations by creating new paths from uncooperative population states to more cooperative states. Group-level events allow cooperation to thrive under unfavorable conditions such as low intra-group assortment and moderate rates of migration, and can greatly speed up the evolution of cooperation when conditions are more favorable. The time-dependent effects of fission and extinction events are studied and illustrated here using a PDE model of a group-structured population based loosely on populations of hunter-gatherer tribes. By solving the PDE numerically we can compare models with and without group- level events, and explicitly calculate quantities associated with dynamics, like how long it takes a small population of cooperators to become a majority, as well as equilibrium population densities.
I worked on this topic primarily in summer 2014, with occasional contributions into early 2016 under the direction of Burt Simon. My primary contributions involved handling all software and experimental simulations, but I aided in the narrative framing and editing of the paper as well. There is ample room for extending the work, but ultimately I did not venture into this field for my doctoral research.
I now recognize that we were attempting to answer an inverse problem in this paper and managed to get a glimpse of the solution by solving many forward problems, holding certain parameters fixed.
The motivation behind the linguistic choice of “catalyst” refers to the broadening of favorable conditions when group-level effects are factored into a population model.
Were I to redo this, I would define our Quantity of Interest as “Time to x% Cooperation,” and invert a density that represents a reasonable time period for the evolution of cooperation.
Undoubtedly, this would yield a set-valued solution that holistically describes the various conditions under which cooperation could have taken hold in societies under our proposed model.
It would be very interesting to see the relative likelihoods on parameters relating to group-level and population-level events, but ultimately it would make the same point as was shown in the paper: there are more conditions under which a “mutation of cooperation” could become established as the prevalent trait in a population.