Integrating systematic review and Bayesian weighting to derive a minimum dataset for soil health assessment in arid and semi-arid regions

Soil health assessment in arid and semi-arid regions necessitates strong frameworks capable of combining a wide range of physical, chemical, and biological indicators. This study systematically analyzed 141 manuscripts to establish a Minimum Dataset of soil health indicators and to refine their relative importance through a Bayesian weighting approach. The selection methodology yielded a core collection of six physical, four chemical, and two biological indicators. Since each of the 141 studies considered reports its own subset of soil health indicators, not a common and homogeneous set shared by the entire literature, but a specific selection from time to time defined by individual authors, synthesizing data from heterogeneous sources generates a structural problem of missing data when attempting to estimate a unique and comparable weight vector across studies. To solve this problem without resorting to ad hoc imputation of the missing numerical values, a Bayesian Expectation-Maximization algorithm was developed, which iteratively redistributes the missing probability mass of the indicators not reported in each study, in proportion to the weights currently estimated for the entire corpus, until convergence to a final, probabilistically consistent weight vector. This approach allowed us to distinguish the weights obtained for the global dataset (arid and semi-arid regions) and for the Mediterranean basin. Globally, the most influential indicators were soil organic carbon, electrical conductivity, cation exchange capacity, bulk density, and pH, indicating a balanced contribution of physical and chemical parameters. In contrast, the Mediterranean dataset demonstrated a different pattern, with soil microbial respiration and soil organic carbon emerging as prominent markers, followed by clay content, silt, and cation exchange capacity playing minor roles. This Bayesian-weighted MDS offers a transferable, quantitatively grounded alternative to existing soil health assessment frameworks for arid and semi-arid regions.