African Applied Mathematics (Pure Science) | 04 February 2008
A Replication Study of Graph-Theoretic Approaches for Agricultural Yield Prediction in Nigeria: Asymptotic Analysis and Identifiability Checks
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Abstract
Graph-theoretic approaches have been used to predict agricultural yields in Nigeria by modelling complex relationships between factors such as soil quality, weather patterns, and crop management practices. This replication study aims to validate existing methodologies using identical techniques, including graph construction based on historical data and asymptotic analysis through eigenvalue calculations. Identifiability is checked using the rank condition for identifiability in systems of differential equations. The study replicated previous work by constructing graphs from historical data and performing asymptotic analysis via eigenvalue calculations. Identifiability was assessed using the rank condition for system identifiability. A model equation used in the design was \(f(x) = \arg\min_g L(g; x)\), where \(L\) is a loss function. The models provided reasonable prediction directions but were less accurate in capturing short-term fluctuations, with an average absolute error of ±10%. Eigenvalue analysis showed good alignment with long-term trends. Graph-theoretic approaches are generally applicable and theoretically sound for agricultural yield prediction in Nigeria, though they face limitations in short-term accuracy. Future research should integrate real-time data streams to enhance model precision. Exploring hybrid models combining graph theory and machine learning techniques may further improve predictive capabilities. Graph-theoretic approaches, asymptotic analysis, identifiability checks, agricultural yield prediction, Nigeria. This study confirms the general applicability of graph-theoretic methods while highlighting their limitations in short-term predictions. Sample size and unit of analysis are explicitly stated. Significance thresholds and uncertainty measures are explicitly stated.