Entropy as an objective, not as a measure: scale and scope of land-use diversity in regional planning. Evidence from the thirty municipalities of Córdoba, Colombia

This is the authors' abstract. We don't add key points for this paper.

Land-use diversity is moving from description towards prescription. As a measure it is well studied, and its dependence on the size of the unit of observation is established. As an objective inside a planning model it is almost unused: a systematic review of 114 agricultural and forestry sector and allocation models finds diversification addressed in eight, optimised as a criterion in one, and Shannon entropy used as an optimisation target in none, because in that literature entropy calibrates rather than targets. The gap is closing, and multi-objective sector models have begun to carry land-use diversity as a co-equal objective. This paper asks what the known properties of the measure imply once it becomes the target. Two decisions the modeller makes and rarely reports settle what is being optimised. The first is scale. Regional entropy splits exactly into the area-weighted mean entropy within the units that make up the region and the difference in composition between them, and the second term is never negative. For the thirty municipalities of Córdoba, Colombia, between 2019 and 2025, the between-municipality term accounts for 22.1 to 26.2 per cent of regional crop entropy, and the region appears 45 to 57 per cent more diverse than its area-weighted average municipality. A model told to maximise the regional figure can therefore meet its objective by specialising whole municipalities, which is the reverse of what a resilience rationale intends. The second decision is scope, the membership of the land-use set, and it can invert how the indicator responds to policy. Adding pasture, which covers at least 86 per cent of agricultural land, drops the regional figure from 5.5 to below 1.9 effective uses. Adding coca, which grew from 1.7 to 4.0 per cent of sown area between 2019 and 2023, raises measured diversity where coca is a minority crop and lowers it where coca dominates, so an entropy-based monitoring indicator would penalise a substitution programme that worked. We recommend reporting the partition whenever diversity enters as an objective, optimising the term that matches the policy intent, and stating which land uses the count includes. Funding: Bicentennial Doctoral Excellence Scholarship programme (Becas de Excelencia Doctoral del Bicentenario), with resources from the Science, Technology and Innovation Fund of the General Royalties System of Colombia (Sistema General de Regalías), administered by Universidad del Norte. Working paper. The record and its identifier are public; the files are under restricted access while a version of the paper is prepared for journal submission. Access to the files can be requested through this record.