A statistical explanation of MaxEnt for ecologists
Open accessAbstract
MaxEnt is a program for modelling species distributions from presence-only species records. This paper is written for ecologists and describes the MaxEnt model from a statistical perspective, making explicit links between the structure of the model, decisions required in producing a modelled distribution, and knowledge about the species and the data that might affect those decisions. To begin we discuss the characteristics of presence-only data, highlighting implications for modelling distributions. We particularly focus on the problems of sample bias and lack of information on species prevalence. The keystone of the paper is a new statistical explanation of MaxEnt which shows that the model minimizes the relative entropy between two probability densities (one estimated from the presence data and one, from the landscape) defined in covariate space. For many users, this viewpoint is likely to be a more accessible way to understand the model than previous ones that rely on machine learning concepts. We then step through a detailed explanation of MaxEnt describing key components (e.g. covariates and features, and definition of the landscape extent), the mechanics of model fitting (e.g. feature selection, constraints and regularization) and outputs. Using case studies for a Banksia species native to south-west Australia and a riverine fish, we fit models and interpret them, exploring why certain choices affect the result and what this means. The fish example illustrates use of the model with vector data for linear river segments rather than raster (gridded) data. Appropriate treatments for survey bias, unprojected data, locally restricted species, and predicting to environments outside the range of the training data are demonstrated, and new capabilities discussed. Online appendices include additional details of the model and the mathematical links between previous explanations and this one, example code and data, and further information on the case studies.
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“, specifically the cylindrical equalarea projection – “+proj=cea +lat_ts=0 +lon_0 = 0 +x_0 = 0 +y_0 = 0 +datum=WGS84 +no_defs”), because conventional non-equal area projections have grids which vary in their area the further away from the equator, and MaxEnt randomly samples cells from the available geographic space,…”
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- Authors
- Elith, J., Phillips, S. J., Hastie, T., Dudík, M., Chee, Y. E., & Yates, C. J.
- Affiliations
- The University of Melbourne (AU)
- AT&T (United States) (US)
- Stanford University (US)
- Government of Western Australia (AU)
- Corresponding author
- Elith, Jane
- Venue
- Diversity and Distributions
- Publisher
- Wiley
- Published
- 2010-11-25
- Volume
- 17
- Issue
- 1
- Pages
- 43-57
- ISSN
- 0967-9952 (ISSN-L)
- 1366-9516
- OpenAlex
- W1568201516
- Cited by
- 6,699
- References
- 60
- Citations by year
- 2026: 468 · 2025: 627 · 2024: 554 · 2023: 583 · 2022: 610 · 2021: 548 · 2020: 516 · 2019: 435 · 2018: 430 · 2017: 381 · 2016: 359 · 2015: 301 · 2014: 350 · 2013: 268 · 2012: 198
- FWCI
- 101.84
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Diversity and Distributions (publishedVersion)
- Funders
- Australian Research Council
- Topics
- Physical Sciences › Environmental Science › Ecological Modeling › Species Distribution and Climate Change
- Physical Sciences › Environmental Science › Nature and Landscape Conservation › Ecology and Vegetation Dynamics Studies
- Physical Sciences › Environmental Science › Ecology › Wildlife Ecology and Conservation
- Keywords
- MaxEnt, species distribution modeling, presence-only data, Kullback-Leibler divergence, sampling bias, species prevalence, feature selection, regularization, survey bias, Banksia, riverine fish, vector data
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