Maxent

MaxEnt, short for maximum entropy modeling, is a statistical method used to estimate species geographic distributions from presence-only data. Based on the principle of maximum entropy, it aims to find the least biased distribution that agrees with known environmental constraints derived from observed presences.

The model fits a probabilistic distribution p(x) over the study area, formulated as p(x) ∝ exp(∑i λi fi(x)), where fi are feature functions of environmental variables (such as temperature, precipitation, elevation) and λi are parameters learned from data. The training process chooses λi so that the expected value of each feature under p matches the empirical average across presence locations. Regularization controls model complexity to prevent overfitting.

Inputs include georeferenced presence records and a background sample that represents available environmental conditions; background points help distinguish suitable from merely common environments. The primary output is a raster map of relative suitability or predicted probability of presence, along with response curves and measures of variable importance.

MaxEnt is widely used in ecology, conservation planning, and biogeography, particularly when true absence data are unavailable. Strengths include effectiveness with small sample sizes and presence-only data. Limitations include sensitivity to sampling bias and background selection, potential overfitting if not regularized, and extrapolation beyond the range of training data.

Origin and software: The method was introduced by Phillips, Dudík, and Schapire in 2004 as Maximum Entropy Modeling of Species Geographic Distributions, with the MaxEnt software package developed by Steven Phillips and colleagues. Since then it has been updated and integrated into GIS workflows and ecological modeling literature.