Never Mind The No-Ops: Faster and Less Volatile Simulation Modelling of Co-Evolutionary Species Interactions via Spatial Cyclic Games

Issues in co-evolutionary population dynamics have long been studied via computationally intensive simulations of minimally simpleagent-based models, known as Evolutionary Spatial Cyclic Games (ESCGs), involving multiple interacting biological species in whicheach agent has its own unique spatial location in a cell on a regular lattice, and can move from cell to cell over time. Many papershave been published exploring the dynamics of ESCGs where competitive inter-species predator/prey relationships are modelled viathe cyclic game Rock-Paper-Scissors (RPS) for three species, or Rock-Paper-Scissors-Lizard-Spock (RPSLS) for five. At the core ofthese simulations is the Elementary Step (ES), in which one or two agents are chosen at random to either compete to the death, orto reproduce, or to move location. ESCG studies typically involve executing trillions of ESs and hence the computational efficiencyof the core ES algorithm is a key concern. In this paper I demonstrate that the de facto standard “Original ES” (OES) algorithm iscomputationally inefficient both in time and in space due to the implicit execution of many “no-op” commands (i.e., commands that donothing) and because at steady state large numbers of cells can be empty, and yet empty cells serve no purpose. I present a new RevisedES (RES) algorithm which eliminates these inefficiencies, and I show empirically that ESCGs with RES exhibit qualitatively the samecharacteristics as those with OES, and are also markedly more stable. The more stable dynamics of RES-based simulations means thatthey can be run with smaller lattices than when using OES, leading to reductions in total simulation times of 85% or more. Pythonsource code developed for the experiments reported here is freely available on GitHub.