The wicked problem of land use planning: navigating stochasticity at the convergence of maximum entropy and generalised additive modelling

Conventional parametric models inadequately capture spatial complexity in weak governance contexts owing to the presence of volatile stochastic drivers. This study applied Maximum Entropy–Generalised Additive Modelling integration to examine non-linear development probabilities in Enugu, Nigeria. MaxEnt was applied to 685 development sites and 10,000 background points to rank 12 spatial and institutional predictors and extract functional complexity measures. GAM integrated the results through adaptive LASSO weighting and basis dimension selection. The framework achieved superior discrimination (AUC = 0.871) over logistic regression (AUC = 0.782), naïve GAM (0.831), and MaxEnt-only (0.847). Road proximity showed extreme non-linearity (EDF = 6.85, p < 0.001), with probability sharply decreasing within 100 metres. Proximity to land use demonstrated multi-modal patterns (EDF = 5.12, p < 0.001), whereas slope displayed U-shaped correlations (EDF = 3.29, p < 0.001). Tenure security followed an S-curve (EDF = 1.58) with diminishing returns beyond moderate levels. The results show that adaptable non-parametric models are crucial for land use planning where spatial linkages are distorted by institutional fragility. The MaxEnt-GAM is a replicable framework for improving planning accuracy in similar systems.