On the performance of four methods for the numerical solution of ecologically realistic size-structured population models

1. Size-structured population models (SSPMs) are widely used in ecology to account for intraspecific variation in body size. Three characteristic features of size-structured populations are the dependence of life histories on the entire size distribution, intrinsic population renewal through the birth of new individuals, and the potential accumulation of individuals with similar body sizes due to determinate or stunted growth. Because of these three features, numerical methods that work well for structurally similar transport equations may fail for SSPMs and other transport-dominated models with high ecological realism, and thus their computational performance needs to be critically evaluated. 2. Here, we compare the performance of four numerical solution schemes, the fixed-mesh upwind (FMU) method, the moving-mesh upwind (MMU) method, the characteristic method (CM), and the Escalator Boxcar Train (EBT) method, in numerically solving three reference problems that are representative of ecological systems in the animal and plant kingdoms. The MMU method is here applied for the first time to SSPMs, whereas the three other methods have been employed by other authors. 3. Our results show that the EBT method performs best, except for one of the three reference problems, in which size-asymmetric competition affects individual growth rates. For that reference problem, the FMU method performs best, closely followed by the MMU method. Surprisingly, the CM method does not perform well for any of the three reference problems. 4. We conclude that life-history features should be carefully considered when choosing the numerical method for analyzing ecologically realistic size-structured population models.