Continuous Livestock Archetypes for Characterizing Structural Heterogeneity in Dual-Purpose Cattle Farms in the Ecuadorian Amazon

Farm typologies assume discrete groups, although structural heterogeneity in Amazonian cattle systems may follow continuous gradients. We evaluated whether 164 dual-purpose cattle farms in the Sumaco Biosphere Reserve, Ecuador, were better represented by mutually exclusive types or continuous archetypal configurations and whether these configurations were economically differentiated. Factor analysis of mixed data, permutation-based dimensional retention, clusterability assessment, archetypal analysis, bootstrap resampling, economic validation, and repeated cross-validation were integrated. Two structural dimensions explained 40.1% of inertia: livestock intensification and infrastructure, and farm scale and land use; agreement with multiple factor analysis was high (Procrustes R2 = 0.990). The Gap statistic supported k = 1, providing no evidence for defensible discrete farm groups. Archetypal analysis identified three continuous configurations: lower-input, livestock intensification, and large-scale land-use. Many farms occupied intermediate positions, showing varying affinities to the three configurations rather than exclusive membership in one. Greater affinity to livestock intensification was associated with the highest annual net benefit and pasture opportunity cost, whereas large-scale land-use showed intermediate economic performance. Predictive accuracy remained modest despite lower errors for archetype-based models. Continuous livestock archetypes provide a screening framework for differentiated management, but farm decisions require current economic, productive, and parcel information.