  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.
