An animal welfare index based on productivity-entropy/extropy measurements

Animal welfare assessment in livestock systems is often constrained by data scarcity and subjective indicators. Here, we introduce the Productivity-Entropy Welfare Index (PEWI), a novel framework that redefines welfare as an emergent property of the production system itself. By combining two simple, routinely available measures (productive homogeneity (quantified via Shannon-Lad extropy) and relative productivity), PEWI captures how evenly and how well a system performs. Applied to five consecutive production cycles in a dairy herd, PEWI remained remarkably stable in homogeneity yet showed that welfare variations were driven almost entirely by changes in relative productivity. Strikingly, while a conventional qualitative welfare index (CWI) saturated in high-welfare scenarios, PEWI maintained high resolution and detected subtle but critical reorganizations that homogeneity measures alone missed. In two additional validation cases, namely a sheep flock with confirmed poor welfare and a bovine herd with excellent welfare, PEWI correctly discriminated extreme conditions (values approaching 0 and 1, respectively) despite both systems exhibiting nearly identical homogeneity. These findings demonstrate that animal welfare can be meaningfully tracked using only production records, without specialized clinical data. PEWI offers a parsimonious, scalable, and sensitive tool for data-limited smallholder systems, situating welfare assessment within the broader context of non-equilibrium complex systems and the entropy–extropy symmetry.