Use of Lorenz curves and Gini coefficients to assess yield inequality within paddocks

Abstract

The opportunity for site-specific management of crops depends on both the magnitude and spatial structure of yield variation. This study explored the applicability of Lorenz curves and Gini coefficients ( G) to characterise the magnitude of the variation in grain yield. Maize crops were grown in farmers fields in a semi-arid region of central Argentina. Major sources of yield variation between and within paddocks included season, soil type and topography, rate of nitrogen fertiliser (nil to 132 kg N ha −1), and the interactions among these factors. Nitrogen treatments were applied in a complete block strip trial (strip size∼700 m×9.8 m) with three replicates. Data were collected with an AgLeader™ yield monitor, and GIS software was used to create 9.8 m×9.8 m grids over the observations. Average yield in 0.7–2.8 ha field sections ranged from 1.6 to 7.0 t ha −1. Gini coefficient ranged from 0.027 to 0.191 whereas its theoretical limits are 0 for a perfectly uniform population, and 1 for a theoretical population of infinite size where all units but one yield 0. Conditions conducive to high yield, e.g. adequate availability of nitrogen and water, reduced crop yield inequality, as quantified with G. The agronomic relevance of G was summarised in an inverse relationship with yield. Lorenz curves seemed particularly apt to present crop heterogeneity in terms of inequality, and to highlight the relative contribution of low- and high-yielding sections of the field to total paddock yield. Lorenz curves and Gini coefficients provide a potentially useful extension tool, a complement to yield maps and other statistical indices of yield variation, and further contact points between site-specific management, economics and ecology.