Modelling Evolution in Structured Populations Involving Multiplayer Interactions

Abstract

We consider models of evolution in structured populations involving multiplayer games. Whilst also discussing other models, we focus on the modelling framework developed by Broom and Rychtář (J Theor Biol 302:70-80, 2012) onwards. This includes key progress so far, the main gaps and limitations, the relationship and synergies with other models and a discussion of the direction of future work. In this regard as well as discussing existing work, there is some new research on the applicability and robustness of current models with respect to using them to model real populations. This is an important potential advance, as previously all of the work has been entirely theoretical. In particular, the most complex models will have many parameters, and we concentrate on considering simpler versions with a small number of parameters which still possess the key features which would make them applicable. We find that these models are generally robust, in particular issues that can arise related to small payoff changes at critical values and removal of pivotal vertices would have similar effects on other modelling system including evolutionary graph theory. These often occur where it can be argued that there is a lack of robustness in the real system that the model faithfully picks up, and so is not a problematic feature.

Mercenary punishment in structured populations

“…Our prime motivation by revisiting their model was to explore whether the assumption that the population is structured offers new, previously not observed behavior. Notably, this last question becomes a standard one in the last decade because several previous models underlined that the change from a randomly mixed population to a more realistic one where players have limited interactions with their neighbors can alter the system behavior qualitatively [58,59,60].…”

Tactical cooperation of defectors in a multi-stage public goods game

“…We consider the generalized problem both in wellmixed and in structured populations. While the former is mathematically feasible in several cases, but the latter option in general is significantly closer to realistic situations [45,46,47,48,49,50,51] Therefore it is always instructive to compare the system behaviors for both conditions [52,53,54]. For a proper comparison with previous results of traditional P GG we here apply a square lattice topology to describe a spatially structured population where every player has four nearest neighbors, hence they form a G = 5 member group [44].…”

Network topology and movement cost, not updating mechanism, determine the evolution of cooperation in mobile structured populations

“…In the context of this framework, several types of movement models have been studied, a review of which is provided in [ 43 ] together with an analysis of their robustness and applicability. Models with completely independent movement are defined as those under which individuals move independently of both their past positions and of each other’s simultaneous movements [ 41 , 44 ].…”