Spatially explicit individual-based modeling using a fixed super-individual density

Abstract

Individual-based models (IBMs) of planktonic microorganisms (e.g., bacterioplankton, phytoplankton) have to simulate large numbers of individuals. Because of computational limitations these models rely on simulating a number of super-individuals that are representative of a larger number of individuals. Using a fixed representative number (the number of individuals one super-individual represents) results in a lower computational resolution (number of super-individuals) at times and in areas of low individual densities, which is undesirable when (a) large temporal and/or spatial gradients exist and (b) variability in state variables or behavior at low densities is important. Various methods exist that fix the number of super-individuals in the global model domain by allowing the representative number to vary in time. Those methods solve the problem introduced by large temporal gradients, but do not address spatial gradients. This paper presents an accounting method that maintains an approximately constant super-individual density in time and space. Each spatial model segment has a local super-individual population that is resampled when the number shrinks or grows outside user-specified bounds, or when the variance of the representative numbers exceeds a user-specified threshold. This local method is compared to a global method and evaluated quantitatively against the analytical solution to an instantaneous input (slug release) into a river, and qualitatively in a biogeochemical phytoplankton model applied to a point source nutrient discharge into a river. Computations are performed using the iAlgae individual-based phytoplankton modeling framework. The applications demonstrate that the local method results in a spatially uniform or density-independent relative error, and it is computationally more efficient at controlling relative error at low densities. However, for the same total number of super-individuals, it is computationally more demanding and therefore less efficient at controlling absolute error. The local method is superior to the global method for the biogeochemical model application, because a significant spatial gradient (front) exists and the dynamics at the low densities affects the model behavior downstream.