Opportunities for improved distribution modelling practice via a strict maximum likelihood interpretation of MaxEnt

Maximum entropy (MaxEnt) modelling, as implemented in the Maxent software, has rapidly become one of the most popular methods for distribution modelling. Originally, MaxEnt was described as a machine‐learning method. More recently, it has been explained from principles of Bayesian estimation. MaxEnt offers numerous options (variants of the method) and settings (tuning of parameters) to the users. A widespread practice of accepting the Maxent software's default options and settings has been established, most likely because of ecologists’ lack of familiarity with machine‐learning and Bayesian statistical concepts and the ease by which the default models are obtained in Maxent. However, these defaults have been shown, in many cases, to be suboptimal and exploration of alternatives has repeatedly been called for. In this paper, we derive MaxEnt from strict maximum likelihood principles, and point out parallels between MaxEnt and standard modelling tools like generalised linear models (GLM). Furthermore, we describe several new options opened by this new derivation of MaxEnt, which may improve MaxEnt practice. The most important of these is the option for selecting variables by subset selection methods instead of the ?₁‐regularisation method, which currently is the Maxent software default. Other new options include: incorporation of new transformations of explanatory variables and user control of the transformation process; improved variable contribution measures and options for variation partitioning; and improved output prediction formats. The new options are exemplified for a data set for the plant species Scorzonera humilis in SE Norway, which was analysed by the standard MaxEnt procedure in a previously published paper. We recommend that thorough comparisons between the proposed alternative options and default procedures and variants thereof be carried out.     

Assessing the application of a geographic presence-only model for land suitability mapping

Recent advances in ecological modeling have focused on novel methods for characterizing the environment that use presence-only data and machine-learning algorithms to predict the likelihood of species occurrence. These novel methods may have great potential for land suitability applications in the developing world where detailed land cover information is often unavailable or incomplete. This paper assesses the adaptation and application of the presence-only geographic species distribution model, MaxEnt, for agricultural crop suitability mapping in a rural Thailand where lowland paddy rice and upland field crops predominant. To assess this modeling approach, three independent crop presence datasets were used including a social-demographic survey of farm households, a remote sensing classification of land use/land cover, and ground control points, used for geodetic and thematic reference that vary in their geographic distribution and sample size. Disparate environmental data were integrated to characterize environmental settings across Nang Rong District, a region of approximately 1300 sq. km in size. Results indicate that the MaxEnt model is capable of modeling crop suitability for upland and lowland crops, including rice varieties, although model results varied between datasets due to the high sensitivity of the model to the distribution of observed crop locations in geographic and environmental space. Accuracy assessments indicate that model outcomes were influenced by the sample size and the distribution of sample points in geographic and environmental space. The need for further research into accuracy assessments of presence-only models lacking true absence data is discussed. We conclude that the MaxEnt model can provide good estimates of crop suitability, but many areas need to be carefully scrutinized including geographic distribution of input data and assessment methods to ensure realistic modeling results.     

A statistical explanation of MaxEnt for ecologists

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.     

Ecological Niche Models using MaxEnt in Google Earth Engine: Evaluation,guidelines and recommendations

Google Earth Engine (GEE) has revolutionized geospatial analyses by fast-processing formerly demanding analyses from multiple research areas. Recently, maximum entropy (MaxEnt), the most commonly used method in ecological niche models (ENMs), was integrated into GEE. This integration can significantly enhance modeling efficiency and encourage multidisciplinary approaches of ENMs, but an evaluation assessment of MaxEnt in GEE is lacking. Herein, we present the first MaxEnt models in GEE, as well as its first statistical and spatial evaluation. We also identify the limitations of the approach, providing guidelines and recommendations for its easier applicability in GEE.We tested MaxEnt in GEE using 11 case studies. For each case, we used species of different taxa (insects, amphibians, reptiles, birds and mammals) distributed across global and regional extents. Each species occupied habitats with distinct environmental characteristics (nine terrestrial and two marine species) and within divergent ecoregions across five continents. The models were performed in GEE and Maxent software, and both approaches were contrasted for their model discrimination performance (assessed by eight evaluation metrics) and spatial consistency (correlation analyses and two measures of niche overlap/equivalency).MaxEnt in GEE allows setting several parameters, but important analyses and outputs are unavailable, such as automatic selection of background data, model replicates, and analyses of variable importance (concretely, jackknife analyses and response curves). GEE provided MaxEnt models with high discrimination performance (area under the curve mean between all species models of 0.90) and with spatial equivalency in relation to Maxent software outputs (Hellinger's I mean between all species models >0.90).Our work demonstrates the first application and assessment of MaxEnt in GEE at global and regional scales. We conclude that the GEE modeling method provides ENMs with high performance and reliable spatial predictions, comparable to the widely used Maxent software. We also acknowledge important limitations that should be integrated into GEE in the future, particularly those related to the assessment of variable importance. We expect that our guidelines, recommendations and potential solutions to surpass the identified limitations could help researchers easily apply MaxEnt in GEE across different research fields.     

MaxEnt模型参数设置对其所模拟物种地理分布和生态位的影响——以茶翅蝽为例

【目的】生态位模型被广泛应用于入侵生物学和保护生物学研究,现有建模工具中,MaxEnt是最流行和运用最广泛的生态位模型。然而最近研究表明,基于MaxEnt模型的默认参数构建模型时,模型倾向于过度拟合,并非一定为最佳模型,尤其是在处理一些分布点较少的物种。【方法】以茶翅蝽为例,通过设置不同的特征参数、调控倍频以及背景拟不存在点数分别构建茶翅蝽的本土模型,然后将其转入入侵地来验证和比较模型,通过检测模型预测的物种对环境因子的响应曲线、潜在分布在生态空间中的生态位映射以及潜在分布的空间差异性,探讨3种参数设置对MaxEnt模型模拟物种分布和生态位的影响。【结果】在茶翅蝽的案例分析中,特征参数的设置对MaxEnt模型所模拟的潜在分布和生态位的影响最大,调控倍频的影响次之,背景拟不存在点数的影响最小。与其他特征相比,基于特征H和T的模型其响应曲线较为曲折;随着调控倍频的增加,响应曲线变得圆滑。【结论】在构建MaxEnt模型时,需要从生态空间中考虑物种的生态需求,分析模型参数对预测物种分布和生态位可能造成的影响。     

What Users Want and May Need

An increasing number of software tools support designers and other decision makers in making design, production, and purchasing decisions. Some of these tools provide quantitative information on environmental impacts such as climate change, human toxicity, or resource use during the life cycle of these products. Very little is known, however, about how these tools are actually used, what kind of modeling and presentation approaches users really want, or whether the information provided is likely to be used the way the developers intended. A survey of users of one such software tool revealed that although users want more transparency, about half also want an easy-to-use tool and would accept built-in assumptions; that most users prefer modeling of environmental impacts beyond the stressor level, and the largest group of respondents wants results simultaneously on the stressor, impact potential, and damage level; and that although many users look for aggregated information on impacts and costs, a majority do not trust that such an aggregation is valid or believe that there are tradeoffs among impacts. Further, our results show that the temporal and spatial scales of single impact categories explain only about 6% of the variation in the weights between impact categories set by respondents if the weights are set first. If the weights are set after respondents specify temporal and spatial scales, however, these scales explain about 24% of the variation. These results not only help method and tool developers to reconsider some previous assumptions, but also suggest a number of research questions that may need to be addressed in a more focused investigation.     

Bayesian meta-analysis of demographic parameters in three small, temperate passerines

Accurate estimates of population parameters are vital for estimating extinction risk. Such parameters, however, are typically not available for threatened populations. We used a recently developed software tool based on Markov Chain Monte Carlo methods for carrying out Bayesian inference (the BUGS package) to estimate four demographic parameters; the intrinsic growth rate, the strength of density dependence, and the demographic and environmental variance, in three species of small temperate passerines from two sets of time series data taken from a dipper and a song sparrow population, and from previously obtained frequentist estimates of the same parameters in the great tit. By simultaneously modeling variation in these demographic parameters across species and using the resulting distributions as priors in the estimation for individual species, we improve the estimates for each individual species. This framework also allows us to make probabilistic statements about plausible parameter values for small passerines temperate birds in general which is often critically needed in management of species for which little or no data are available. We also discuss how our work relates to recently developed theory on dynamic stochastic population models, and finally note some important differences between frequentist and Bayesian methods.     

ecospat: an R package to support spatial analyses and modeling of species niches and distributions

The aim of the ecospat package is to make available novel tools and methods to support spatial analyses and modeling of species niches and distributions in a coherent workflow. The package is written in the R language (R Development Core Team) and contains several features, unique in their implementation, that are complementary to other existing R packages. Pre‐modeling analyses include species niche quantifications and comparisons between distinct ranges or time periods, measures of phylogenetic diversity, and other data exploration functionalities (e.g. extrapolation detection, ExDet). Core modeling brings together the new approach of ensemble of small models (ESM) and various implementations of the spatially‐explicit modeling of species assemblages (SESAM) framework. Post‐modeling analyses include evaluation of species predictions based on presence‐only data (Boyce index) and of community predictions, phylogenetic diversity and environmentally‐constrained species co‐occurrences analyses. The ecospat package also provides some functions to supplement the ‘biomod2’ package (e.g. data preparation, permutation tests and cross‐validation of model predictive power). With this novel package, we intend to stimulate the use of comprehensive approaches in spatial modelling of species and community distributions.     

The MIGCLIM R package – seamless integration of dispersal constraints into projections of species distribution models

The MIGCLIM R package is a function library for the open source R software that enables the implementation of species‐specific dispersal constraints into projections of species distribution models under environmental change and/or landscape fragmentation scenarios. The model is based on a cellular automaton and the basic modeling unit is a cell that is inhabited or not. Model parameters include dispersal distance and kernel, long distance dispersal, barriers to dispersal, propagule production potential and habitat invasibility. The MIGCLIM R package has been designed to be highly flexible in the parameter values it accepts, and to offer good compatibility with existing species distribution modeling software. Possible applications include the projection of future species distributions under environmental change conditions and modeling the spread of invasive species.     

Predicting the Fate of Biodiversity Using Species�� Distribution Models: Enhancing Model Comparability and Repeatability

Species distribution modeling (SDM) is an increasingly important tool to predict the geographic distribution of species. Even though many problems associated with this method have been highlighted and solutions have been proposed, little has been done to increase comparability among studies. We reviewed recent publications applying SDMs and found that seventy nine percent failed to report methods that ensure comparability among studies, such as disclosing the maximum probability range produced by the models and reporting on the number of species occurrences used. We modeled six species of Falco from northern Europe and demonstrate that model results are altered by (1) spatial bias in species’ occurrence data, (2) differences in the geographic extent of the environmental data, and (3) the effects of transformation of model output to presence/absence data when applying thresholds. Depending on the modeling decisions, forecasts of the future geographic distribution of Falco ranged from range contraction in 80% of the species to no net loss in any species, with the best model predicting no net loss of habitat in Northern Europe. The fact that predictions of range changes in response to climate change in published studies may be influenced by decisions in the modeling process seriously hampers the possibility of making sound management recommendations. Thus, each of the decisions made in generating SDMs should be reported and evaluated to ensure conclusions and policies are based on the biology and ecology of the species being modeled.     

LCI data and data quality

Life cycle inventory (LCI) is becoming an established environmental management tool that quantifies all resource usage and waste generation associated with providing specific goods or services to society. LCIs are increasingly used by industry as well as policy makers to provide a holistic ‘macro’ overview of the environmental profile of a good or service. This information, effectively combined with relevant information obtained from other environmental management tools, is very useful in guiding strategic environmental decision making. LCIs are very data intensive. There is a risk that they imply a level of accuracy that does not exist. This is especially true today, because the availability of accurate LCI data is limited. Also, it is not easy for LCI users, decision-makers and other interested parties to differentiate between ‘good quality’ and ‘poor quality’ LCI data. Several data quality requirements for ‘good’ LCI data can be defined only in relation to the specific study in which they are used. In this paper we show how and why the use of a common LCI database for some of the more commonly used LCI data, together with increased documentation and harmonisation of the data quality features of all LCI data, is key to the further development of LCI as a useful and pragmatic environmental management tool. Initiatives already underway to make this happen are also described.     

Habitat suitability models to make conservation decisions based on areas of high species richness and endemism

Biodiversity positively relates with the provisioning of ecosystem services and preserving areas with elevated diversity of highly-functional species could help to ensure human well-being. Most studies addressed to make these decisions use maps relying on species occurrences, where sites containing several species are proposed as priority conservation areas. These maps, however, may underestimate species richness because of the incompleteness of occurrence data. To improve this methodology, we propose using habitat suitability models to estimate the potential distribution of species from occurrence data, and later shaping richness maps by overlapping these predicted distribution ranges. We tested this proposal with Mexican oaks because they provide several ecosystem services and habitat suitability models of species were calibrated with MaxEnt. We used linear regressions to compare the outputs of these predictive maps with those of maps based on species occurrences only and, for both mapping methods, we assessed how much surface of sites with elevated richness and endemism of oaks is currently included within nature reserves. Both mapping methods indicated that oak species are concentrated in mountain regions of Mexico, but predictive maps based on habitat suitability models indicated higher oak richness and endemism that maps based on species occurrences only. Our results also indicated that nature reserves cover a small fraction of areas harboring elevated richness and endemism of oaks. These results suggest that estimating richness across extensive geographic regions using habitat suitability models quickly provides accurate information to make conservation decisions for highly-functional species groups.     

MaxEnt生态学模型在野生植物近自然林引种区划中的应用——以红姜花为例

近自然林的营建是园林景观的一个重要发展方向。由于待引种的野生植物种类繁多且缺少引种栽培实践,如何在仅有野生分布数据的条件下进行植物的引种区划具有重要意义。Max Ent(Maximum entropy method)的原理是基于物种分布与气候相适应,以物种野生分布数据为基础,寻找物种的潜在分布区,与近自然林条件下野生植物引种区划的需要一致。该文以红姜花为例采用理论和实践检验相结合的方法,对MaxEnt模型的有效性进行评价。在收集红姜花的野生地理分布数据基础上,选择温度、降雨、海拔为环境因子,以75%的数据进行建模,25%的分布数据作为检验作ROC(Receiver operating characteristic)曲线对模型的有效性进行评价。结果表明:ROC曲线下面积AUC值为0.991,评价结果优秀,表明预测模型可靠性高;进一步以全部分布数据在Max Ent中制作区划图,将引种栽培数据的分布位置与区划预测图进行比对,划分适生性等级;在适生性被划分为0~1的11级时,区划图中大于0.01的区域内红姜花即可成功引种。结果证明对于缺少引种栽培实践、拟采用近自然林模式栽培的野生植物,可采用Max Ent生态学模型制作引种区划图。     

Past,current, and future trends of red spiny lobster based on PCA with MaxEnt model in Galapagos Islands,Ecuador

In order to enhance in terms of accuracy and predict the modeling of the potential distribution of species, the integration of using principal components of environmental variables as input of maximum entropy (MaxEnt) has been proposed in this study. Principal components selected previously from the principal component analysis results performed in ArcGIS in the environmental variables was used as an input data of MaxEnt instead of raw data to model the potential distribution of red spiny lobster from the year 1997 to 2015 and for three different future scenarios 2020, 2050, and 2070. One set of six original environmental variables pertaining to the years 1997–2015 and one set of four variables for future scenarios were transformed independently into a single multiband raster in ArcGIS in order to select the variables whose eigenvalues explains more than 5% of the total variance with the purpose to use in the modeling prediction in MaxEnt. The years 1997 and 1998 were chosen to compare the accuracy of the model, showing better results using principal components instead of raw data in terms of area under the curve and partial receiver operating characteristic as well as better predictions of suitable areas. Using principal components as input of MaxEnt enhances the prediction of good habitat suitability for red spiny lobster; however, future scenarios suggest an adequate management by researches to elaborate appropriate guidelines for the conservation of the habitat for this valuable specie with face to the climate change.     

Finessing atlas data for species distribution models

Aim The spatial resolution of species atlases and therefore resulting model predictions are often too coarse for local applications. Collecting distribution data at a finer resolution for large numbers of species requires a comprehensive sampling effort, making it impractical and expensive. This study outlines the incorporation of existing knowledge into a conventional approach to predict the distribution of Bonelli’s eagle (Aquila fasciata) at a resolution 100 times finer than available atlas data. Location Malaga province, Andalusia, southern Spain. Methods A Bayesian expert system was proposed to utilize the knowledge from distribution models to yield the probability of a species being recorded at a finer resolution (1 × 1 km) than the original atlas data (10 × 10 km). The recorded probability was then used as a weight vector to generate a sampling scheme from the species atlas to enhance the accuracy of the modelling procedure. The maximum entropy for species distribution modelling (MaxEnt) was used as the species distribution model. A comparison was made between the results of the MaxEnt using the enhanced and, the random sampling scheme, based on four groups of environmental variables: topographic, climatic, biological and anthropogenic. Results The models with the sampling scheme enhanced by an expert system had a higher discriminative capacity than the baseline models. The downscaled (i.e. finer scale) species distribution maps using a hybrid MaxEnt/expert system approach were more specific to the nest locations and were more contrasted than those of the baseline model. Main conclusions The proposed method is a feasible substitute for comprehensive field work. The approach developed in this study is applicable for predicting the distribution of Bonelli’s eagle at a local scale from a national‐level occurrence data set; however, the usefulness of this approach may be limited to well‐known species.     

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

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.     

Collective decision‐making and fission–fusion dynamics: a conceptual framework

Sociality exists in an extraordinary range of ecological settings. For individuals to accrue the benefits associated with social interactions, they are required to maintain a degree of spatial and temporal coordination in their activities, and make collective decisions. Such coordination and decision‐making has been the focus of much recent research. However, efforts largely have been directed toward understanding patterns of collective behaviour in relatively stable and cohesive groups. Less well understood is how fission–fusion dynamics mediate the process and outcome of collective decisions making. Here, we aim to apply established concepts and knowledge to highlight the implications of fission–fusion dynamics for collective decisions, presenting a conceptual framework based on the outcome of a small‐group discussion INCORE meeting (funded by the European Community's Sixth Framework Programme). First, we discuss how the degree of uncertainty in the environment shapes social flexibility and therefore the types of decisions individuals make in different social settings. Second, we propose that the quality of social relationships and the energetic needs of each individual influence fission decisions. Third, we explore how these factors affect the probability of individuals to fuse. Fourth, we discuss how group size and fission–fusion dynamics may affect communication processes between individuals at a local or global scale to reach a consensus or to fission. Finally, we offer a number of suggestions for future research, capturing emerging ideas and concepts on the interaction between collective decisions and fission–fusion dynamics.     

Calculating autoecological data (optima and tolerance range) for multiple species with the ‘optimos.prime’ R package

The calculation of autoecological data, such as optima and tolerance ranges to environmental variables, can be useful to establish the distribution and abundance of the species. These calculations, although mathematically not complex, can be prone to error when using a large database. We show how to calculate the optimum value and tolerance ranges of multiple species to multiple environmental factors in a single run, by weighted average using a specific R package (‘optimos.prime’). Using sample data from a phytoplankton database, we exemplify the use of the R package and its functions. A stand‐alone version for Windows is also provided, and source code and documents are freely available on GitHub to encourage collaborative work.     

The World Wide Web as a graphical user interface to program macros for molecular graphics,molecular modeling,and structure-based drug design

In this article we describe how the World Wide Web (WWW or Web) has been employed to provide access to computational chemistry software and protein structure data via program macros. We show how the combination of Web technology and macros can automate both the running of chemistry software and the execution of complex operations on protein structures. The current version of the system supports the molecular visualization packages GRASP,¹ RASMOL,² MOLVIEWER-OGL³ and INSIGHT95,⁴ and the ligand design tool GRID⁵ and includes more than 175 in-house protein-ligand complexes. The approach enables in-experienced users to confidently make full use of sophisticated modeling techniques by offering only sensible options, hiding parameter settings, and controlling program invocation and macro excution. Our interface provides both the expert and non-expert alike with powerful tools for protein structure visualization, molecular modeling, and rational drug design.     

A standardised approach to calculating floodplain tree condition to support environmental watering decisions

Ground-based visual assessment of crown condition is a cornerstone of tree condition assessment globally, and numerous condition assessment approaches have evolved to address the needs and perspectives of different users. In Australia’s iconic Murray–Darling Basin (MDB), stands of floodplain eucalypts are increasingly vulnerable to a range of interacting stressors related to climate change and over-extraction of water for consumptive and agricultural use. A standardised approach developed in 2008 for assessing floodplain trees within the MDB provides extensive guidance to ensure field data is collected consistently. However, there is minimal instruction on how to interpret data, and consequently a range of evaluation approaches have evolved. The lack of a standardised reporting framework generated by these different approaches makes it difficult for floodplain managers and environmental water holders to make repeatable, robust decisions for prioritising water allocations across competing locations. To provide improved lines of evidence to support decision making, this paper describes a ‘best-practise’ approach to calculating a tree condition score from field data. Within, we document existing approaches in the southern Murray–Darling Basin, and recommend a method that meets the needs of floodplain managers as a pragmatic reporting, communication and decision support tool that does not require statistical analysis. Case studies and a revised conceptual model of tree decline and recovery are provided to demonstrate the validity of the recommended approach.