Thermodynamic heterogeneity patterns reveal higher-order soil organization in indigenous agroecosystems of the U.S. Southwest

Trevan Flynn 

Soil spatial heterogeneity and diversity support the stability and productivity of food systems, yet their multidimensional structure remains difficult to quantify at spatial scales relevant to agricultural resilience. A process-based framework grounded in fundamental physical principles is therefore needed to describe these spatial processes across landscapes. The aim of this study was to develop a mechanistic three-dimensional thermodynamic pedodiversity index constrained by physical continuity. The framework was applied to ancestral and contemporary indigenous agroecosystems of the U.S. Southwest. Eight gridded soil properties were transformed into thermodynamic exergy states using a three-dimensional biweight multi-pass convolution applied across spatial directions, with the surface layer subject to atmospheric forcing. Local inverse Moran’s I was then calculated to quantify the pedodiversity patterns. Linking thermodynamic principles to the landscape scale revealed that long-term crop production aligns with structured pedodiversity patterns rather than with pedodiversity magnitude alone. Persistent Hopi dryland agriculture corresponded with moderately to highly organized pedodiversity patterns, whereas more specialized Navajo pastoral systems occurred in landscapes characterized by lower pedodiversity organization. These results suggest that pedodiversity represents only one component of soil resilience and multifunctionality. Higher-order spatial processes, interpreted alongside indigenous ecological knowledge, are necessary to understand how soils support sustained agroecosystems. Integrating process-based applied mathematics with Indigenous knowledge systems may therefore provide a pathway toward identifying higher-order functions capable of inferring soil resilience and multifunctionality.