IsoMaTrix: a framework to visualize the isoclines of matrix games and quantify uncertainty in structured populations

Abstract

SummaryEvolutionary game theory describes frequency-dependent selection for fixed, heritable strategies in a population of competing individuals using a payoff matrix, typically described using well-mixed assumptions (replicator dynamics). IsoMaTrix is an open-source package which computes the isoclines (lines of zero growth) of matrix games, and facilitates direct comparison of well-mixed dynamics to structured populations in two or three dimensions. IsoMaTrix is coupled with a Hybrid Automata Library module to simulate structured matrix games on-lattice. IsoMaTrix can also compute fixed points, phase flow, trajectories, velocities (and subvelocities), delineated "region plots" of positive/negative strategy velocity, and uncertainty quantification for stochastic effects in structured matrix games. We describe a result obtained via IsoMaTrixs spatial games functionality, which shows that the timing of competitive release in a cancer model (under continuous treatment) critically depends on the initial spatial configuration of the tumor. Availability and implementationThe code is available at: https://github.com/mathonco/isomatrix.