Journal Article

Applying the maximum entropy principle to neural networks enhances multi‐species distribution models

Bonnet, Pierre, Joly, Alexis, Ryckewaert, Maxime, Marcos, Diego, Servajean, Maximilien, Botella, Christophe

2026

Overview

The increasing volume of presence‐only (PO) data generated by citizen science initiatives has greatly expanded biodiversity databases, but the statistical use of these data in species distribution models (SDMs) remains limited by strong sampling biases and the absence of reliable absence information. Existing approaches based on Poisson point processes, such as Maxent, provide powerful tools, yet rely on predefined features that restrict their flexibility and scalability. We introduce DeepMaxent, a new SDM framework that leverages neural networks to learn a shared, data‐driven feature extractor across multiple species while remaining grounded in the maximum entropy principle of Maxent, enabling efficient learning even on very large datasets with thousands of species. DeepMaxent uses a normalized Poisson likelihood, which models the probability of choosing each site given a species, to estimate species‐specific suitability surfaces directly from PO observations. In other words, the model predicts suitable locations for each species rather than predicting which species occurs at a given site. We evaluate DeepMaxent on two contrasting datasets: the National Centre for Ecological Analysis and Synthesis (NCEAS) benchmark, containing six small case studies designed to evaluate the impact of spatial sampling biases, and the much larger GeoPlant, dataset covering the whole of Europe. Using PO data for calibration and independent presence–absence data for validation, DeepMaxent consistently outperforms Maxent and leading deep learning‐based SDMs. Compared with Maxent, it achieves an area under the ROC curve of 0.768 versus 0.760 on NCEAS, 0.860 versus 0.823 on GeoPlant and enables the use of high‐dimensional data modalities, such as satellite images, for which Maxent is unsuitable. DeepMaxent combines the normalized Poisson formulation of Maxent with the learnable features, shared among species, of deep learning approaches. This results in better performance than either Maxent or previous deep learning methods, and lower compute requirements than single‐species SDMs, while the formulation makes the method compatible with the integration of survey data to further improve sampling bias correction.

• Publisher: John Wiley & Sons, Inc,Wiley
• Subject: Bias / Biodiversity / Biodiversity and Ecology / Computer Science / Data Analysis, Statistics and Probability / Datasets / Deep learning / DeepMaxent / Ecology, environment / Entropy / Environmental Sciences / Feature extraction / Geographical distribution / Humanities and Social Sciences / Life Sciences / Machine Learning / Maximum entropy / maximum entropy principle / Methods and statistics / Modeling and Simulation / Neural networks / Physics / presence‐only data / Sampling / sampling bias / Satellite imagery / Species / species distribution model / Statistical analysis / Statistics / Target‐Group Background