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February 28, 2026Open Access

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

Key Points

The research aims to enhance land use planning by integrating maximum entropy and generalised additive modelling to capture spatial complexities in weak governance settings.
Applied Maximum Entropy to 685 development sites and 10,000 background points.
Ranked 12 spatial and institutional predictors for development probabilities.
Integrated GAM with adaptive LASSO weighting and basis dimension selection.
Utilized AUC to evaluate discrimination of models compared to logistic regression and naïve GAM.
MaxEnt-GAM achieved AUC of 0.871, outperforming other models like logistic regression (0.782).
Road proximity showed significant non-linearity with sharp decreases in probability within 100 meters.
Proximity to land use exhibited multi-modal patterns while slope demonstrated U-shaped correlations.
Tenure security showed an S-curve with diminishing returns at moderate levels.

Abstract

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.

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