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

TL;DR

This paper investigates soil organic carbon dynamics through reaction-diffusion chemotaxis models, demonstrating how microbial activity influences spatial pattern formation and validating data-driven methods for pattern reconstruction.

Contribution

It introduces the use of symplectic techniques and pDMD to analyze and reconstruct chemotaxis-driven spatial patterns in SOC models, expanding their applicability.

Findings

pDMD effectively reconstructs chemotaxis-driven patterns

Models exhibit stripe, spot, and hexagon patterns above a sensitivity threshold

Validation across models supports broader application in ecological data analysis

Abstract

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.