Vol.:(0123456789) 1 3 Journal of Crop Science and Biotechnology https://doi.org/10.1007/s12892-021-00128-y ORIGINAL RESEARCH Assessing NPK use efciency of commercial inoculants in cassava (Manihot esculenta Cratz): an application of data envelopment analysis Oscar Burbano‑Figueroa 1  · Jazmin Vanessa Pérez‑Pazos 1  · Milena Moreno‑Moran 1 Accepted: 3 November 2021 © The Author(s), under exclusive licence to Korean Society of Crop Science (KSCS) 2021 Abstract Plant growth promoting microorganisms (PGPMs) are inhabitants of the rhizosphere that are able to provide better growth and biomass accumulation. Current agronomic practices have depleted these communities, which has created the opportu- nity for the development of commercial inoculants. These products use strains that are able to interact with a wide range of plant species and survive in diverse environments. The use of these generalist strains is required for providing a widespread solution that aggregates enough demand to reach market scale. Growth promotion by generalist strains may be suboptimal in comparison to the efect provoked by native and host-specifc populations, but these specialist strains are not a market- available solution. In this work, we assess the nitrogen, phosphorus and potassium (NPK) use efciency provided by com- mercial inoculants to cassava plants using Data Envelopment Analysis (DEA) to demonstrate the advantages of conceiving nutrient-limited yield as a production function. We also estimate the prospective production frontier that commercial inocu- lants can provide to cassava plants. Our results suggest that commercial inoculants have potential for improving cassava yields via improved NPK use efciency. The methods presented here ofer an ecological/economic production framework for the assessment of PGPMs and PGPMs-based commercial inoculants that can be extended to other laboratory, greenhouse or feld situations. The simple, intuitive and graphical approximation that DEA ofers will facilitate the understanding of the concept of technical efciency and the role of commercial inoculants on closing yield gaps. Keywords Cassava · Commercial inoculants · Data envelopment analysis · DEA · Technical efciency · NPK · Yield gaps · Nutrient-limited yield Introduction In an environment with perfect provision of water and nutrients (yield-limiting factors) and no losses related to pests, diseases and weeds (yield-reducing factors), plants can reach the maximum theoretical yield, i.e., the potential yield. The constraints imposed by yield-limiting factors on crop productivity are represented by production functions (Silva et al. 2017). A production function describes the efect of additional inputs over the production output (Kay et al. 2019). The simplest model of this kind is a single variable control system with one input and one output. For the case of yield-limiting factors, these simple models are production functions describing resource (water or nutrients) limited yields. In farm production situations, for a given fxed level of inputs (resources), it is possible to obtain a wide range of output (yield) levels. This situation-specifc relation between inputs and outputs is called technical efciency. Diferences in technical efciency explains why under the same produc- tion situations, two farms with the same level of resources obtain diferent levels of yield. The representation of yield- limiting factors as a production function ofers a structured perspective that separates the efect of resource levels and efciency in the use of these resources (Silva et al. 2017) (Supp Data 1). The challenges of designing better fertilization practices can be framed as production functions representing nutri- ent-limited yield. In this approach, the concept of technical efciency commonly applied to farms is extended to tech- nological products that can increase efciency of operation units. This production function perspective also highlights * Oscar Burbano-Figueroa burbano.fgueroa1@gmail.com; oburbano@agrosavia.co 1 The Plant Interactions Laboratory, Corporación Colombiana de Investigación Agropecuaria (AGROSAVIA), Turipaná Research Center, Vía Montería-Cereté Km 13, 230558 Cereté, Córdoba, Colombia