Speeding up the simulation of population spread models

1. Simulating spatially explicit population models to predict population spread allows environmental managers to make better-informed decisions. Accurate simulation requires high spatial resolution, which, using existing techniques, can require prohibitively large amounts of computational resources (RAM, CPU, etc). 2. We developed and implemented a novel algorithm for the simulation of integro-difference equations (IDEs) modelling population spread, including stage structure, which uses adaptive mesh refinement. 3. We measured the accuracy of the adaptive algorithm by comparing the results of simulations using the adaptive and a standard non-adaptive algorithm. The relative error of the population's spatial extent was low (<0·05) for a range of parameter values. Comparing efficiency, we found that our algorithm used up to 10 times less CPU time and RAM than the non-adaptive algorithm. 4. Our approach provides large improvements in efficiency without significant loss of accuracy, so it enables faster simulation of IDEs and simulation at scales and at resolutions that have not been previously feasible. As an example, we simulate the spread of a hypothetical species over the UK at a resolution of 25 m. We provide our implementation of the algorithm as a user-friendly executable application.