Simulating the Generalised Spatial Lokta-Volterra Equations with Multiple Species on GPUs with Automatic Code Generation

Ken A. Hawick, Daniel P. Playne, and Chris J. Scogings

Keywords

LotkaVolterra, cycles, food chains, spatial complexity

Abstract

The Lotka-Volterra equations are a common starting point for ecological models of food chains and can be extended to model interacting cross-predatory species in a spatial arrangement. We model longer food chains and more complex predatory-prey relationships on 2 and 3 dimensional spatial systems. We use a semi-automatic code generator to produce code that uses graphical processing units (GPUs) to accelerate the computational performance of the time-integrated model. We compare several (complex) different time integration schemes and discuss the precision implications for model stability as well as parallel performance results. We report on the effects of cycles in the food chain as well as emergent complexity in the spatial patterns of the system and present new findings on phase relationships amongst even/odd numbers of species in the simulated spatial food chain.

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