Patterns in soil organic carbon dynamics: integrating microbial activity, chemotaxis and data-driven approaches

Models of soil organic carbon (SOC) frequently overlook the effects of spatial dimensions and microbiological activities. In this paper, we focus on two reaction-diffusion chemotaxis models for SOC dynamics, both supporting chemotaxis-driven instability and exhibiting a variety of spatial patterns as stripes, spots and hexagons when the microbial chemotactic sensitivity is above a critical threshold. We use symplectic techniques to numerically approximate chemotaxis-driven spatial patterns and explore the effectiveness of the piecewice dynamic mode decomposition (pDMD) to reconstruct them. Our findings show that pDMD is effective at precisely recreating chemotaxis-driven spatial patterns, therefore broadening the range of application of the method to classes of solutions different than Turing patterns. By validating its efficacy across a wider range of models, this research lays the groundwork for applying pDMD to experimental spatiotemporal data, advancing predictions crucial for soil microbial ecology and agricultural sustainability.