The MaxEnt software package is one of the most popular tools for species distribution and environmental niche modeling, with over 1000 published applications since 2006. Its popularity is likely for two reasons: 1) MaxEnt typically outperforms other methods based on predictive accuracy and 2) the software is particularly easy to use. MaxEnt users must make a number of decisions about how they should select their input data and choose from a wide variety of settings in the software package to build models from these data. The underlying basis for making these decisions is unclear in many studies, and default settings are apparently chosen, even though alternative settings are often more appropriate. In this paper, we provide a detailed explanation of how MaxEnt works and a prospectus on modeling options to enable users to make informed decisions when preparing data, choosing settings and interpreting output. We explain how the choice of background samples reflects prior assumptions, how nonlinear functions of environmental variables (features) are created and selected, how to account for environmentally biased sampling, the interpretation of the various types of model output and the challenges for model evaluation. We demonstrate MaxEnt’s calculations using both simplified simulated data and occurrence data from South Africa on species of the flowering plant family Proteaceae. Throughout, we show how MaxEnt’s outputs vary in response to different settings to highlight the need for making biologically motivated modeling decisions.

https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1600-0587.2013.07872.x

A practical guide to MaxEnt for modeling species' distributions: what it does, and why inputs and settings matter

Discover New Methods for Dealing with High-Dimensional Data A sparse statistical model has only a small number of nonzero parameters or weights; therefore, it is much easier to estimate and interpret than a dense model. Statistical Learning with Sparsity: The Lasso and Generalizations presents methods that exploit sparsity to help recover the underlying signal in a set of data. Top experts in this rapidly evolving field, the authors describe the lasso for linear regression and a simple coordinate descent algorithm for its computation. They discuss the application of 1 penalties to generalized linear models and support vector machines, cover generalized penalties such as the elastic net and group lasso, and review numerical methods for optimization. They also present statistical inference methods for fitted (lasso) models, including the bootstrap, Bayesian methods, and recently developed approaches. In addition, the book examines matrix decomposition, sparse multivariate analysis, graphical models, and compressed sensing. It concludes with a survey of theoretical results for the lasso. In this age of big data, the number of features measured on a person or object can be large and might be larger than the number of observations. This book shows how the sparsity assumption allows us to tackle these problems and extract useful and reproducible patterns from big datasets. Data analysts, computer scientists, and theorists will appreciate this thorough and up-to-date treatment of sparse statistical modeling.

Statistical Learning with Sparsity: The Lasso and Generalizations

This software note announces a new open-source release of the Maxent software for modeling species distributions from occurrence records and environmental data, and describes a new R package for fitting such models. The new release (ver. 3.4.0) will be hosted online by the American Museum of Natural History, along with future versions. It contains small functional changes, most notably use of a complementary log-log (cloglog) transform to produce an estimate of occurrence probability. The cloglog transform derives from the recently-published interpretation of Maxent as an inhomogeneous Poisson process (IPP), giving it a stronger theoretical justification than the logistic transform which it replaces by default. In addition, the new R package, maxnet, fits Maxent models using the glmnet package for regularized generalized linear models. We discuss the implications of the IPP formulation in terms of model inputs and outputs, treating occurrence records as points rather than grid cells and interpreting the exponential Maxent model (raw output) as as an estimate of relative abundance. With these two open-source developments, we invite others to freely use and contribute to the software.

https://onlinelibrary.wiley.com/doi/pdf/10.1111/ecog.03049

Opening the black box: an open-source release of Maxent

Summary
Recent studies have demonstrated a need for increased rigour in building and evaluating ecological niche models (ENMs) based on presence-only occurrence data. Two major goals are to balance goodness-of-fit with model complexity (e.g. by ‘tuning’ model settings) and to evaluate models with spatially independent data. These issues are especially critical for data sets suffering from sampling bias, and for studies that require transferring models across space or time (e.g. responses to climate change or spread of invasive species). Efficient implementation of procedures to accomplish these goals, however, requires automation.
We developed ENMeval, an R package that: (i) creates data sets for k-fold cross-validation using one of several methods for partitioning occurrence data (including options for spatially independent partitions), (ii) builds a series of candidate models using Maxent with a variety of user-defined settings and (iii) provides multiple evaluation metrics to aid in selecting optimal model settings. The six methods for partitioning data are n−1 jackknife, random k-folds ( = bins), user-specified folds and three methods of masked geographically structured folds. ENMeval quantifies six evaluation metrics: the area under the curve of the receiver-operating characteristic plot for test localities (AUCTEST), the difference between training and testing AUC (AUCDIFF), two different threshold-based omission rates for test localities and the Akaike information criterion corrected for small sample sizes (AICc).
We demonstrate ENMeval by tuning model settings for eight tree species of the genus Coccoloba in Puerto Rico based on AICc. Evaluation metrics varied substantially across model settings, and models selected with AICc differed from default ones.
In summary, ENMeval facilitates the production of better ENMs and should promote future methodological research on many outstanding issues.

https://besjournals.onlinelibrary.wiley.com/doi/pdf/10.1111/2041-210X.12261

ENMeval: An R package for conducting spatially independent evaluations and estimating optimal model complexity for Maxent ecological niche models

Ecological data often show temporal, spatial, hierarchical (random effects), or phylogenetic structure. Modern statistical approaches are increasingly accounting for such dependencies. However, when performing cross-validation, these structures are regularly ignored, resulting in serious underestimation of predictive error. One cause for the poor performance of uncorrected (random) cross-validation, noted often by modellers, are dependence structures in the data that persist as dependence structures in model residuals, violating the assumption of independence. Even more concerning, because often overlooked, is that structured data also provides ample opportunity for overfitting with non-causal predictors. This problem can persist even if remedies such as autoregressive models, generalized least squares, or mixed models are used. Block cross-validation, where data are split strategically rather than randomly, can address these issues. However, the blocking strategy must be carefully considered. Blocking in space, time, random effects or phylogenetic distance, while accounting for dependencies in the data, may also unwittingly induce extrapolations by restricting the ranges or combinations of predictor variables available for model training, thus overestimating interpolation errors. On the other hand, deliberate blocking in predictor space may also improve error estimates when extrapolation is the modelling goal. Here, we review the ecological literature on non-random and blocked cross-validation approaches. We also provide a series of simulations and case studies, in which we show that, for all instances tested, block cross-validation is nearly universally more appropriate than random cross-validation if the goal is predicting to new data or predictor space, or for selecting causal predictors. We recommend that block cross-validation be used wherever dependence structures exist in a dataset, even if no correlation structure is visible in the fitted model residuals, or if the fitted models account for such correlations.

https://onlinelibrary.wiley.com/doi/pdf/10.1111/ecog.02881

Cross-validation strategies for data with temporal, spatial, hierarchical, or phylogenetic structure

Presence-only records may provide data on the distributions of rare species, but commonly suffer from large, unknown biases due to their typically haphazard collection schemes. Presence-absence or count data collected in systematic, planned surveys are more reliable but typically less abundant.We proposed a probabilistic model to allow for joint analysis of presence-only and survey data to exploit their complementary strengths. Our method pools presence-only and presence-absence data for many species and maximizes a joint likelihood, simultaneously estimating and adjusting for the sampling bias affecting the presence-only data. By assuming that the sampling bias is the same for all species, we can borrow strength across species to efficiently estimate the bias and improve our inference from presence-only data.We evaluate our model's performance on data for 36 eucalypt species in south-eastern Australia. We find that presence-only records exhibit a strong sampling bias towards the coast and towards Sydney, the largest city. Our data-pooling technique substantially improves the out-of-sample predictive performance of our model when the amount of available presence-absence data for a given species is scarceIf we have only presence-only data and no presence-absence data for a given species, but both types of data for several other species that suffer from the same spatial sampling bias, then our method can obtain an unbiased estimate of the first species' geographic range.

/pdf/bias-correction-in-species-distribution-models-pooling-d0cjwrog5l.pdf

Bias correction in species distribution models: pooling survey and collection data for multiple species.

Summary
Presence-only data are widely used for species distribution modelling, and point process regression models are a flexible tool that has considerable potential for this problem, when data arise as point events.
In this paper, we review point process models, some of their advantages and some common methods of fitting them to presence-only data.
Advantages include (and are not limited to) clarification of what the response variable is that is modelled; a framework for choosing the number and location of quadrature points (commonly referred to as pseudo-absences or ‘background points’) objectively; clarity of model assumptions and tools for checking them; models to handle spatial dependence between points when it is present; and ways forward regarding difficult issues such as accounting for sampling bias.
Point process models are related to some common approaches to presence-only species distribution modelling, which means that a variety of different software tools can be used to fit these models, including maxent or generalised linear modelling software.

https://besjournals.onlinelibrary.wiley.com/doi/pdf/10.1111/2041-210X.12352

Point process models for presence-only analysis

To perform inference after model selection, we propose controlling the selective type I error; i.e., the error rate of a test given that it was performed. By doing so, we recover long-run frequency properties among selected hypotheses analogous to those that apply in the classical (non-adaptive) context. Our proposal is closely related to data splitting and has a similar intuitive justification, but is more powerful. Exploiting the classical theory of Lehmann

Optimal Inference After Model Selection

Summary 1. Presence-only records may provide data on the distributions of rare species, but commonly suffer from large, unknown biases due to their typically haphazard collection schemes. Presence–absence or count data collected in systematic, planned surveys are more reliable but typically less abundant. 2. We proposed a probabilistic model to allow for joint analysis of presence-only and survey data to exploit their complementary strengths. Our method pools presence-only and presence–absence data for many species and maximizes a joint likelihood, simultaneously estimating and adjusting for the sampling bias affecting the presence-only data. By assuming that the sampling bias is the same for all species, we can borrow strength across species to efficiently estimate the bias and improve our inference from presence-only data. 3. We evaluate our model’s performance on data for 36 eucalypt species in south-eastern Australia. We find that presence-only records exhibit a strong sampling bias towards the coast and towards Sydney, the largest city. Our data-pooling technique substantially improves the out-of-sample predictive performance of our model when the amount of available presence–absence data for a given species is scarce 4. If we have only presence-only data and no presence–absence data for a given species, but both types of data for several other species that suf fer from the same spatial sampling bias, then our method can obtain an unbiased estimate of the first species’ geographic range.

SPECIAL FEATURE PAPER: NEW OPPORTUNITIES AT THE INTERFACE BETWEEN ECOLOGY AND STATISTICS Bias correction in species distribution models: pooling survey and collection data for multiple species

Presence-only data abounds in ecology, often accompanied by a background sample. Although many interesting aspects of the species’ distribution can be learned from such data, one cannot learn the overall species occurrence probability, or prevalence, without making unjustified simplifying assumptions. In this forum article we question the approach of Royle et al. (2012) that claims to be able to do this.

/pdf/inference-from-presence-only-data-the-ongoing-controversy-2pgtuaaouc.pdf

William Fithian

Papers

Bias correction in species distribution models: pooling survey and collection data for multiple species.

Point process models for presence-only analysis

Optimal Inference After Model Selection

SPECIAL FEATURE PAPER: NEW OPPORTUNITIES AT THE INTERFACE BETWEEN ECOLOGY AND STATISTICS Bias correction in species distribution models: pooling survey and collection data for multiple species

Inference from presence-only data; the ongoing controversy