Nonlinear Mathematical Modeling of Crop Growth and Biomass Accumulation for Accurate Yield Prediction in Smallholder Farming Systems
Jean de Dieu Niyomugabo1* 
, Victoire Ayingeneye2 ,
Angelique Nyiramahoro2 , and Marie Ange Cyuzuzo3
Abstract. Accurate yield prediction in smallholder farming systems remains a central challenge in agricultural science, particularly across sub-Saharan Africa, South Asia, and Southeast Asia, where resource constraints, climate variability, and data scarcity severely limit the applicability of conventional linear models. This paper presents a comprehensive review and synthesis of nonlinear mathematical frameworks for modeling crop growth and biomass accumulation, with emphasis on their suitability for smallholder contexts. We examine logistics, Gompertz, Richards, and beta-function growth models, as well as process-based dynamic simulation approaches including APSIM, DSSAT, and AquaCrop, and evaluate their integration with remote sensing data and machine learning algorithms. Key findings indicate that hybrid models combining physiological process descriptions with data-driven optimization consistently outperform purely empirical or mechanistic approaches, particularly when calibrated with local agronomic data under variable input conditions. We further discuss parameter identifiability, model parsimony, and uncertainty quantification as critical requirements for deployment in data-limited smallholder environments. This review synthesizes evidence from 2019 to 2025 and provides a roadmap for developing robust, scalable nonlinear crop yield prediction frameworks tailored to the heterogeneous conditions of smallholder agriculture.
Keywords: nonlinear growth models, biomass accumulation, yield prediction, smallholder farming, crop simulation, machine learning, APSIM, logistic growth, remote sensing