A size-structured matrix model to simulate dynamics of marine community size spectrum

Several types of size-based models have been developed to model the size spectra of marine communities, in which abundance scales strongly with body size, using continuous differential equations. In this study, we develop a size-structured matrix model, which can be seen as a discretization of the Mckendrick-von Foerster equation, to simulate the dynamics of marine communities. The developed model uses a series of simple body size power functions to describe the basic processes of predator–prey interactions, reproduction, metabolism, and non-predation mortality based on the principle of mass balance. Linear size spectra with slopes of approximately –1 are successfully reproduced by this model. Several examples of numerical simulations are provided to demonstrate the model’s behavior. Size spectra with cut-offs and/or waves are also found for certain parameter values. The matrix model is flexible and can be freely manipulated by users to answer different questions and is executed over a shorter numerical calculation running time than continuous models.