Invasive species distribution modeling (iSDM): Are absence data and dispersal constraints needed to predict actual distributions?

Species distribution models (SDMs) based on statistical relationships between occurrence data and underlying environmental conditions are increasingly used to predict spatial patterns of biological invasions and prioritize locations for early detection and control of invasion outbreaks. However, invasive species distribution models (iSDMs) face special challenges because (i) they typically violate SDM's assumption that the organism is in equilibrium with its environment, and (ii) species absence data are often unavailable or believed to be too difficult to interpret. This often leads researchers to generate pseudo-absences for model training or utilize presence-only methods, and to confuse the distinction between predictions of potential vs. actual distribution. We examined the hypothesis that true-absence data, when accompanied by dispersal constraints, improve prediction accuracy and ecological understanding of iSDMs that aim to predict the actual distribution of biological invasions. We evaluated the impact of presence-only, true-absence and pseudo-absence data on model accuracy using an extensive dataset on the distribution of the invasive forest pathogen Phytophthora ramorum in California. Two traditional presence/absence models (generalized linear model and classification trees) and two alternative presence-only models (ecological niche factor analysis and maximum entropy) were developed based on 890 field plots of pathogen occurrence and several climatic, topographic, host vegetation and dispersal variables. The effects of all three possible types of occurrence data on model performance were evaluated with receiver operating characteristic (ROC) and omission/commission error rates. Results show that prediction of actual distribution was less accurate when we ignored true-absences and dispersal constraints. Presence-only models and models without dispersal information tended to over-predict the actual range of invasions. Models based on pseudo-absence data exhibited similar accuracies as presence-only models but produced spatially less feasible predictions. We suggest that true-absence data are a critical ingredient not only for accurate calibration but also for ecologically meaningful assessment of iSDMs that focus on predictions of actual distributions.     

Assessing the effects of pseudo-absences on predictive distribution model performance

Modelling species distributions with presence data from atlases, museum collections and databases is challenging. In this paper, we compare seven procedures to generate pseudo-absence data, which in turn are used to generate GLM-logistic regressed models when reliable absence data are not available. We use pseudo-absences selected randomly or by means of presence-only methods (ENFA and MDE) to model the distribution of a threatened endemic Iberian moth species (Graellsia isabelae). The results show that the pseudo-absence selection method greatly influences the percentage of explained variability, the scores of the accuracy measures and, most importantly, the degree of constraint in the distribution estimated. As we extract pseudo-absences from environmental regions further from the optimum established by presence data, the models generated obtain better accuracy scores, and over-prediction increases. When variables other than environmental ones influence the distribution of the species (i.e., non-equilibrium state) and precise information on absences is non-existent, the random selection of pseudo-absences or their selection from environmental localities similar to those of species presence data generates the most constrained predictive distribution maps, because pseudo-absences can be located within environmentally suitable areas. This study shows that if we do not have reliable absence data, the method of pseudo-absence selection strongly conditions the obtained model, generating different model predictions in the gradient between potential and realized distributions.     

Selecting pseudo-absence data for presence-only distribution modeling: How far should you stray from what you know?

An important decision in presence-only species distribution modeling is how to select background (or pseudo-absence) localities for model parameterization. The selection of such localities may influence model parameterization and thus, can influence the appropriateness and accuracy of the model prediction when extrapolating the species distribution across time and space. We used 12 species from the Australian Wet Tropics (AWT) to evaluate the relationship between the geographic extent from which pseudo-absences are taken and model performance, and shape and importance of predictor variables using the MAXENT modeling method. Model performance is lower when pseudo-absence points are taken from either a restricted or broad region with respect to species occurrence data than from an intermediate region. Furthermore, variable importance (i.e., contribution to the model) changed such that, models became increasingly simplified, dominated by just two variables, as the area from which pseudo-absence points were drawn increased. Our results suggest that it is important to consider the spatial extent from which pseudo-absence data are taken. We suggest species distribution modeling exercises should begin with exploratory analyses evaluating what extent might provide both the most accurate results and biologically meaningful fit between species occurrence and predictor variables. This is especially important when modeling across space or time—a growing application for species distributional modeling.     

Evaluating the ability of habitat suitability models to predict species presences

Models predicting species spatial distribution are increasingly applied to wildlife management issues, emphasising the need for reliable methods to evaluate the accuracy of their predictions. As many available datasets (e.g. museums, herbariums, atlas) do not provide reliable information about species absences, several presence-only based analyses have been developed. However, methods to evaluate the accuracy of their predictions are few and have never been validated. The aim of this paper is to compare existing and new presence-only evaluators to usual presence/absence measures.     

An evaluation of three statistical methods used to model resource selection

The performance of statistical methods for modeling resource selection by animals is difficult to evaluate with field data because true selection patterns are unknown. Simulated data based on a known probability distribution, though, can be used to evaluate statistical methods. Models should estimate true selection patterns if they are to be useful in analyzing and interpreting field data. We used simulation techniques to evaluate the effectiveness of three statistical methods used in modeling resource selection. We generated 25 use locations per animal and included 10, 20, 40, or 80 animals in samples of use locations. To simulate species of different mobility, we generated use locations at four levels according to a known probability distribution across DeSoto National Wildlife Refuge (DNWR) in eastern Nebraska and western Iowa, USA. We either generated 5 random locations per use location or 10,000 random locations (total) within 4 predetermined areas around use locations to determine how the definition of availability and the number of random locations affected results. We analyzed simulated data using discrete choice, logistic-regression, and a maximum entropy method (Maxent). We used a simple linear regression of estimated and known probability distributions and area under receiver operating characteristic curves (AUC) to evaluate the performance of each method. Each statistical method was affected differently by number of animals and random locations used in analyses, level at which selection of resources occurred, and area considered available. Discrete-choice modeling resulted in precise and accurate estimates of the true probability distribution when the area in which use locations were generated was ≥ the area defined to be available. Logistic-regression models were unbiased and precise when the area in which use locations were generated and the area defined to be available were the same size; the fit of these models improved with increased numbers of random locations. Maxent resulted in unbiased and precise estimates of the known probability distribution when the area in which use locations were generated was small (home-range level) and the area defined to be available was large (study area). Based on AUC analyses, all models estimated the selection distribution better than random chance. Results from AUC analyses, however, often contradicted results of the linear regression method used to evaluate model performance. Discrete-choice modeling was best able to estimate the known selection distribution in our study area regardless of sample size or number of random locations used in the analyses, but we recommend further studies using simulated data over different landscapes and different resource metrics to confirm our results. Our study offers an approach and guidance for others interested in assessing the utility of techniques for modeling resource selection in their study area.     

Predicting the distributions of marine organisms at the global scale

We present and evaluate AquaMaps, a presence-only species distribution modelling system that allows the incorporation of expert knowledge about habitat usage and was designed for maximum output of standardized species range maps at the global scale. In the marine environment there is a significant challenge to the production of range maps due to large biases in the amount and location of occurrence data for most species. AquaMaps is compared with traditional presence-only species distribution modelling methods to determine the quality of outputs under equivalently automated conditions. The effect of the inclusion of expert knowledge to AquaMaps is also investigated. Model outputs were tested internally, through data partitioning, and externally against independent survey data to determine the ability of models to predict presence versus absence. Models were also tested externally by assessing correlation with independent survey estimates of relative species abundance. AquaMaps outputs compare well to the existing methods tested, and inclusion of expert knowledge results in a general improvement in model outputs. The transparency, speed and adaptability of the AquaMaps system, as well as the existing online framework which allows expert review to compensate for sampling biases and thus improve model predictions are proposed as additional benefits for public and research use alike.     

Impact of the quality of climate models for modelling species occurrences in countries with poor climatic documentation: a case study from Bolivia

The quality of climate models has largely been overlooked as a possible source of uncertainty that may affect the outcomes of species distribution models, especially in the tropics, where comparatively few climatic stations are available. We compared the geographical discrepancies and potential conservation implications of using two different climate models (Saga and Worldclim) in combination with the species modelling approach Maxent in Bolivia. We estimated ranges of selected bird and fern species biogeographically restricted to either humid montane forest of the northern Bolivian Andes or seasonal dry tropical forests (in the Andes and southern lowlands). Saga and Worldclim predicted roughly similar climate patterns of temperature that were significantly correlated. Precipitation layers of both climate models were also roughly similar, but showed important differences. Species ranges estimated with Worldclim and Saga likewise produced different results. Ranges of species endemic to humid montane forests estimated with Saga had higher AUC (Area under the curve) values than those estimated with Worldclim, which for example predicted the occurrence of humid montane forest bird species near Lake Titicaca, an area that is clearly unsuitable for these species. Likewise, Worldclim overpredicted the occurrence of fern and bird species in the lowlands of the Chapare region and well south of the Andean Elbow, where more seasonal biomes occur. By contrast, Saga predictions were coherent with the known distribution of humid montane forests in the northern Bolivian Andes. Estimated ranges of species endemic to seasonal dry tropical forests predicted with Saga and Worldclim were not statistically different in most cases. However, detailed comparisons revealed that Saga was able to distinguish fragments of seasonal dry tropical forests in rain-shadow valleys of the northern Bolivian Andes, whereas Worldclim was not. These differences highlight the neglected influence of climate layers on modelling results and the importance of using the most accurate climate data available when modelling species distributions.     

Rethinking receiver operating characteristic analysis applications in ecological niche modeling

The area under the curve (AUC) of the receiver operating characteristic (ROC) has become a dominant tool in evaluating the accuracy of models predicting distributions of species. ROC has the advantage of being threshold-independent, and as such does not require decisions regarding thresholds of what constitutes a prediction of presence versus a prediction of absence. However, we show that, comparing two ROCs, using the AUC systematically undervalues models that do not provide predictions across the entire spectrum of proportional areas in the study area. Current ROC approaches in ecological niche modeling applications are also inappropriate because the two error components are weighted equally. We recommend a modification of ROC that remedies these problems, using partial-area ROC approaches to provide a firmer foundation for evaluation of predictions from ecological niche models. A worked example demonstrates that models that are evaluated favorably by traditional ROC AUCs are not necessarily the best when niche modeling considerations are incorporated into the design of the test.     

The evaluation strip: A new and robust method for plotting predicted responses from species distribution models

Increasing use is being made in conservation management of statistical models that couple extensive collections of species and environmental data to make predictions of the geographic distributions of species. While the relationships fitted between a species and its environment are relatively transparent for many of these modeling techniques, others are more ‘black box’ in character, only producing geographic predictions and providing minimal or untraditional summaries of the fitted relationships on which these predictions are based. This in turn prevents robust evaluation of the ecological sensibility of such models, a necessary process if model predictions are to be treated with confidence. Here we propose a new but simple method for visualizing modeled responses that can be implemented with any modeling method, and demonstrate its application using five common methods applied to the prediction of an Australian tree species. This is achieved by insetting an “evaluation strip” into the spatial data layers, which, after predictions have been made, can be clipped out and used for creating plots of the modelled responses. We present findings of the application strip for algorithms GLMs, GAMs, CLIM, DOMAIN and MARS. Evaluation strips can be constructed to investigate either uni-variate responses, or the simultaneous variation in predicted values in relation to two variables. The latter option is particularly useful for evaluating responses in models that allow the fitting of complex interaction terms.     

Modeling and Predicting Species Occurrence Using Broad-Scale Environmental Variables: an Example with Butterflies of the Great Basin

Abstract: If occurrence of individual species can be modeled as a function of easily quantified environmental variables (e.g., derived from a geographic information system [GIS]) and the predictions of these models are demonstrably successful, then the scientific foundation for management planning will be strengthened. We used Bayesian logistic regression to develop predictive models for resident butterflies in the central Great Basin of western North America. Species inventory data and values for 14 environmental variables from 49 locations (segments of canyons) in the Toquima Range ( Nevada, U.S.A.) were used to build the models. Squares of the environmental variables were also used to accommodate possibly nonmonotonic responses. We obtained statistically significant models for 36 of 56 (64%) resident species of butterflies. The models explained 8–72% of the deviance in occurrence of those species. Each of the independent variables was significant in at least one model, and squared versions of five variables contributed to models. Elevation was included in more than half of the models. Models included one to four variables; only one variable was significant in about half the models. We conducted preliminary tests of two of our models by using an existing set of data on the occurrence of butterflies in the neighboring Toiyabe Range. We compared conventional logistic classification with posterior probability distributions derived from Bayesian modeling. For the latter, we restricted our predictions to locations with a high ( 70%) probability of predicted presence or absence. We will perform further tests after conducting inventories at new locations in the Toquima Range and nearby Shoshone Mountains, for which we have computed environmental variables by using remotely acquired topographic data, digital-terrain and microclimatic models, and GIS computation.     

Modelling species distributions with penalised logistic regressions: A comparison with maximum entropy models

An important aspect of species distribution modelling is the choice of the modelling method because a suboptimal method may have poor predictive performance. Previous comparisons have found that novel methods, such as Maxent models, outperform well-established modelling methods, such as the standard logistic regression. These comparisons used training samples with small numbers of occurrences per estimated model parameter, and this limited sample size may have caused poorer predictive performance due to overfitting. Our hypothesis is that Maxent models would outperform a standard logistic regression because Maxent models avoid overfitting by using regularisation techniques and a standard logistic regression does not. Regularisation can be applied to logistic regression models using penalised maximum likelihood estimation. This estimation procedure shrinks the regression coefficients towards zero, causing biased predictions if applied to the training sample but improving the accuracy of new predictions. We used Maxent and logistic regression (standard and penalised) to analyse presence/pseudo-absence data for 13 tree species and evaluated the predictive performance (discrimination) using presence-absence data. The penalised logistic regression outperformed standard logistic regression and equalled the performance of Maxent. The penalised logistic regression may be considered one of the best methods to develop species distribution models trained with presence/pseudo-absence data, as it is comparable to Maxent. Our results encourage further use of the penalised logistic regression for species distribution modelling, especially in those cases in which a complex model must be fitted to a sample with a limited size.     

Use of Community‐Composition Data to Predict the Fecundity and Abundance of Species

Abstract: Species distribution models are critical tools for the prediction of invasive species spread and conservation of biodiversity. The majority of species distribution models have been built with environmental data. Community ecology theory suggests that species co‐occurrence data could also be used to predict current and potential distributions of species. Species assemblages are the products of biotic and environmental constraints on the distribution of individual species and as a result may contain valuable information for niche modeling. We compared the predictive ability of distribution models of annual grassland plants derived from either environmental or community‐composition data. Composition‐based models were built with the presence or absence of species at a site as predictors of site quality, whereas environment‐based models were built with soil chemistry, moisture content, above‐ground biomass, and solar radiation as predictors. The reproductive output of experimentally seeded individuals of 4 species and the abundance of 100 species were used to evaluate the resulting models. Community‐composition data were the best predictors of both the site‐specific reproductive output of sown individuals and the site‐specific abundance of existing populations. Successful community‐based models were robust to omission of data on the occurrence of rare species, which suggests that even very basic survey data on the occurrence of common species may be adequate for generating such models. Our results highlight the need for increased public availability of ecological survey data to facilitate community‐based modeling at scales relevant to conservation.     

Use of Coarse‐Resolution Models of Species’ Distributions to Guide Local Conservation Inferences

Abstract: Distribution models are used increasingly for species conservation assessments over extensive areas, but the spatial resolution of the modeled data and, consequently, of the predictions generated directly from these models are usually too coarse for local conservation applications. Comprehensive distribution data at finer spatial resolution, however, require a level of sampling that is impractical for most species and regions. Models can be downscaled to predict distribution at finer resolutions, but this increases uncertainty because the predictive ability of models is not necessarily consistent beyond their original scale. We analyzed the performance of downscaled, previously published models of environmental favorability (a generalized linear modeling technique) for a restricted endemic insectivore, the Iberian desman (Galemys pyrenaicus), and a more widespread carnivore, the Eurasian otter (Lutra lutra), in the Iberian Peninsula. The models, built from presence–absence data at 10 × 10 km resolution, were extrapolated to a resolution 100 times finer (1 × 1 km). We compared downscaled predictions of environmental quality for the two species with published data on local observations and on important conservation sites proposed by experts. Predictions were significantly related to observed presence or absence of species and to expert selection of sampling sites and important conservation sites. Our results suggest the potential usefulness of downscaled projections of environmental quality as a proxy for expensive and time‐consuming field studies when the field studies are not feasible. This method may be valid for other similar species if coarse‐resolution distribution data are available to define high‐quality areas at a scale that is practical for the application of concrete conservation measures.     

Does the self-similar species distribution model lead to unrealistic predictions?

J. Harte et al. demonstrated that the power law form of the species-area relationship may be derived from a bisected, self-similar landscape and a community-level probability rule. Harte's self-similarity model has been widely applied in modeling species distributions. However, R. D. Maddux showed that this self-similarity model generates biologically unrealistic predictions. We resolve the Harte-Maddux debate by demonstrating that the problems identified by Maddux result from an assumption that the probability of occurrence of a species at one scale is independent of its probability of occurrence at the next. We refer to this as a "non-heritage assumption." By altering this assumption to one in which each species in the community has an occupancy status that is partially inherited across scales (a scale-heritage assumption), the predictions of the self-similarity model are neither mathematically inconsistent nor biologically unrealistic. Harte's self-similarity model remains an important framework for modeling species distributions. Our results illustrate the importance of considering patterns of species co-occurrence, and the way in which species occupancy patterns change with scale, when modeling species distributions.     

Plant Diversity Hotspots in the Atlantic Coastal Forests of Brazil

Abstract:  Plant-diversity hotspots on a global scale are well established, but smaller local hotspots within these must be identified for effective conservation of plants at the global and local scales. We used the distributions of endemic and endemic-threatened species of Myrtaceae to indicate areas of plant diversity and conservation importance within the Atlantic coastal forests ( Mata Atlântica ) of Brazil. We applied 3 simple, inexpensive geographic information system (GIS) techniques to a herbarium specimen database: predictive species-distribution modeling (Maxent); complementarity analysis (DIVA-GIS); and mapping of herbarium specimen collection locations. We also considered collecting intensity, which is an inherent limitation of use of natural history records for biodiversity studies. Two separate areas of endemism were evident: the Serra do Mar mountain range from Paraná to Rio de Janeiro and the coastal forests of northern Espírito Santo and southern Bahia. We identified 12 areas of approximately 35 km² each as priority areas for conservation. These areas had the highest species richness and were highly threatened by urban and agricultural expansion. Observed species occurrences, species occurrences predicted from the model, and results of our complementarity analysis were congruent in identifying those areas with the most endemic species. These areas were then prioritized for conservation importance by comparing ecological data for each.     

A Successful Predictive Model of Species Richness Based on Indicator Species

Abstract:  Because complete species inventories are expensive and time-consuming, scientists and land managers seek techniques to alleviate logistic constraints on measuring species richness, especially over large spatial scales. We developed a method to identify indicators of species richness that is applicable to any taxonomic group or ecosystem. In an initial case study, we found that a model based on the occurrence of five indicator species explained 88% of the deviance of species richness of 56 butterflies in a mountain range in western North America. We validated model predictions and spatial transferability of the model using independent, newly collected data from another, nearby mountain range. Predicted and observed values of butterfly species richness were highly correlated with 93% of the observed values falling within the 95% credible intervals of the predictions. We used a Bayesian approach to update the initial model with both the model-building and model-validation data sets. In the updated model, the effectiveness of three of the five indicator species was similar, whereas the effectiveness of two species was reduced. The latter species had more erratic distributions in the validation data set than in the original model-building data set. This objective method for identifying indicators of species richness could substantially enhance our ability to conduct large-scale ecological assessments of any group of animals or plants in any geographic region and to make effective conservation decisions.     

Species-specific tuning increases robustness to sampling bias in models of species distributions: An implementation with Maxent

Various methods exist to model a species’ niche and geographic distribution using environmental data for the study region and occurrence localities documenting the species’ presence (typically from museums and herbaria). In presence-only modelling, geographic sampling bias and small sample sizes represent challenges for many species. Overfitting to the bias and/or noise characteristic of such datasets can seriously compromise model generality and transferability, which are critical to many current applications - including studies of invasive species, the effects of climatic change, and niche evolution. Even when transferability is not necessary, applications to many areas, including conservation biology, macroecology, and zoonotic diseases, require models that are not overfit. We evaluated these issues using a maximum entropy approach (Maxent) for the shrew Cryptotis meridensis, which is endemic to the Cordillera de Mérida in Venezuela. To simulate strong sampling bias, we divided localities into two datasets: those from a portion of the species’ range that has seen high sampling effort (for model calibration) and those from other areas of the species’ range, where less sampling has occurred (for model evaluation). Before modelling, we assessed the climatic values of localities in the two datasets to determine whether any environmental bias accompanies the geographic bias. Then, to identify optimal levels of model complexity (and minimize overfitting), we made models and tuned model settings, comparing performance with that achieved using default settings. We randomly selected localities for model calibration (sets of 5, 10, 15, and 20 localities) and varied the level of model complexity considered (linear versus both linear and quadratic features) and two aspects of the strength of protection against overfitting (regularization). Environmental bias indeed corresponded to the geographic bias between datasets, with differences in median and observed range (minima and/or maxima) for some variables. Model performance varied greatly according to the level of regularization. Intermediate regularization consistently led to the best models, with decreased performance at low and generally at high regularization. Optimal levels of regularization differed between sample-size-dependent and sample-size-independent approaches, but both reached similar levels of maximal performance. In several cases, the optimal regularization value was different from (usually higher than) the default one. Models calibrated with both linear and quadratic features outperformed those made with just linear features. Results were remarkably consistent across the examined sample sizes. Models made with few and biased localities achieved high predictive ability when appropriate regularization was employed and optimal model complexity was identified. Species-specific tuning of model settings can have great benefits over the use of default settings.     

Assumption‐versus data‐based approaches to summarizing species’ ranges

For conservation decision making, species’ geographic distributions are mapped using various approaches. Some such efforts have downscaled versions of coarse‐resolution extent‐of‐occurrence maps to fine resolutions for conservation planning. We examined the quality of the extent‐of‐occurrence maps as range summaries and the utility of refining those maps into fine‐resolution distributional hypotheses. Extent‐of‐occurrence maps tend to be overly simple, omit many known and well‐documented populations, and likely frequently include many areas not holding populations. Refinement steps involve typological assumptions about habitat preferences and elevational ranges of species, which can introduce substantial error in estimates of species’ true areas of distribution. However, no model‐evaluation steps are taken to assess the predictive ability of these models, so model inaccuracies are not noticed. Whereas range summaries derived by these methods may be useful in coarse‐grained, global‐extent studies, their continued use in on‐the‐ground conservation applications at fine spatial resolutions is not advisable in light of reliance on assumptions, lack of real spatial resolution, and lack of testing. In contrast, data‐driven techniques that integrate primary data on biodiversity occurrence with remotely sensed data that summarize environmental dimensions (i.e., ecological niche modeling or species distribution modeling) offer data‐driven solutions based on a minimum of assumptions that can be evaluated and validated quantitatively to offer a well‐founded, widely accepted method for summarizing species’ distributional patterns for conservation applications.     

Movement distances enhance validity of predictive models

Including the distance species are able to move in predictive models improves conservation practice. Bird inventory projects carried out from 1993 to 2004 in Taiwan provide an opportunity to investigate the relationships among species distribution, movement distance, and the environment. We compared projected distributions of 17 Taiwanese endemic bird species using what we called the Standard Method (i.e. movement distance is zero) and what we called the Buffer Method (i.e. movement distance is longer than zero) in three presence-only models (GARP, MAXENT and LIVES). The Standard Method used species original occurrence records directly while the Buffer Method expanded the occurrence of species to areas 1 km² around each recorded location. We first tested the efficacy of the Buffer Method using ten common species of the 17, and then applied the method to two rare species of the 17. For both the common and rare species, the distributions predicted by the two methods showed slight but important differences. The Buffer Method for all species had a higher average predictive probability, while the Standard Method had a higher maximum predictive probability. Most of the values for the area under the curve (AUC) were over 0.8 with the exceptions of Taiwan Barbet (Megalaima nuchalis) and Taiwan Hwamei (Garrulax taewanus), which have recently separated from Indochinese Barbet (Megalaima annamensis) and Chinese Hwamei (Garrulax canorus), and since 2008 and 2006 have been regarded as species endemic to the study area. Kappa values showed good performance for all species using both methods. The Buffer Method, however, resulted in significantly higher sensitivity and accuracy values for all models of species (p < 0.05). We conclude that when modeling species distribution including the area where the species was censused along with areas within the minimum movement areas better defines the surrounding areas that might supplement core habitat requirements. Therefore, using the Buffer Method, species surrounding distribution can be obtained which provides a better understanding of the species distributions. Given that distribution size is a key to the conservation of species, we suggest the Buffer Method can be used in conservation planning.