A. Townsend Peterson

Evaluating predictive models of species' distributions: criteria for selecting optimal models

Abstract The Genetic Algorithm for Rule-Set Prediction (GARP) is one of several current approaches to modeling species’ distributions using occurrence records and environmental data. Because of stochastic elements in the algorithm and underdetermination of the system (multiple solutions with the same value for the optimization criterion), no unique solution is produced. Furthermore, current implementations of GARP utilize only presence data—rather than both presence and absence, the more general case. Hence, variability among GARP models, which is typical of genetic algorithms, and complications in interpreting results based on asymmetrical (presence-only) input data make model selection critical. Generally, some locality records are randomly selected to build a distributional model, with others set aside to evaluate it. Here, we use intrinsic and extrinsic measures of model performance to determine whether optimal models can be identified based on objective intrinsic criteria, without resorting to an independent test data set. We modeled potential distributions of two rodents ( Heteromys anomalus and Microryzomys minutus ) and one passerine bird ( Carpodacus mexicanus ), creating 20 models for each species. For each model, we calculated intrinsic and extrinsic measures of omission and commission error, as well as composite indices of overall error. Although intrinsic and extrinsic composite measures of overall model performance were sometimes loosely related to each other, none was consistently associated with expert-judged model quality. In contrast, intrinsic and extrinsic measures were highly correlated for both omission and commission in the two widespread species ( H. anomalus and C. mexicanus ). Furthermore, a clear inverse relationship existed between omission and commission there, and the best models were consistently found at low levels of omission and moderate-to-high commission values. In contrast, all models for M. minutus showed low values of both omission and commission. Because models are based only on presence data (and not all areas are adequately sampled), the commission index reflects not only true commission error but also a component that results from undersampled areas that the species actually inhabits. We here propose an operational procedure for determining an optimal region of the omission/commission relationship and thus selecting high-quality GARP models. Our implementation of this technique for H. anomalus gave a much more reasonable estimation of the species’ potential distribution than did the original suite of models. These findings are relevant to evaluation of other distributional-modeling techniques based on presence-only data and should also be considered with other machine-learning applications modified for use with asymmetrical input data.

PREDICTING THE GEOGRAPHY OF SPECIES' INVASIONS VIA ECOLOGICAL NICHE MODELING

Species’ invasions have long been regarded as enormously complex processes, so complex as to defy predictivity. Phases of this process, however, are emerging as highly predictable: the potential geographic course of an invasion can be anticipated with high precision based on the ecological niche characteristics of a species in its native geographic distributional area. This predictivity depends on the premise that ecological niches constitute long‐term stable constraints on the potential geographic distributions of species, for which a sizeable body of evidence is accumulating. Hence, although the entire invasion process is indeed complex, the geographic course that invasions are able to take can be anticipated with considerable confidence.

Effects of sample size on accuracy of species distribution models

Abstract Given increasing access to large amounts of biodiversity information, a powerful capability is that of modeling ecological niches and predicting geographic distributions. Because, sampling species’ distributions is costly, we explored sample size needs for accurate modeling for three predictive modeling methods via re-sampling of data for well-sampled species, and developed curves of model improvement with increasing sample size. In general, under a coarse surrogate model, and machine-learning methods, average success rate at predicting occurrence of a species at a location, or accuracy, was 90% of maximum within ten sample points, and was near maximal at 50 data points. However, a fine surrogate model and logistic regression model had significantly lower rates of increase in accuracy with increasing sample size, reaching similar maximum accuracy at 100 data points. The choice of environmental variables also produced unpredictable effects on accuracy over the range of sample sizes on the logistic regression method, while the machine-learning method had robust performance throughout. Examining correlates of model performance across species, extent of geographic distribution was the only significant ecological factor.

Predicting Species Invasions Using Ecological Niche Modeling: New Approaches from Bioinformatics Attack a Pressing Problem

O 3 February 1999, President Clinton signed an executive order dealing with invasive species in the United States. The order was designed to lay the foundation for a program “to prevent the introduction of invasive species and provide for their control and to minimize the economic, ecological, and human health impacts that invasive species cause” (Clinton 1999). This program includes far-reaching plans to prevent, plan, monitor, and study species’ invasions. Such high-level attention emphasizes the enormity of the problem facing the United States, and in fact the entire world: With ever-growing international commerce, reduced barriers to trade, and increasing human influence, species are moving around, and natural systems are suffering drastic changes. The dimensions of the problem are indeed impressive. Alien plants, animals, and microbes have poured into the United States from all directions. Natural systems have been disrupted, species extinguished, transportation and agriculture compromised, and resources damaged (Carlton 1997–1998, Ogutu-Ohwayo 1997–1998, Richardson 1997–1998, Shiva 1997–1998). In fact, most modern agriculture is based on nonnative organisms; problems arise because questions of when and why some escape and become nuisances remain unanswered. More generally, no proactive approach to combating such species is available—invasive species are dealt with one at a time, as they become problematic. Scientific approaches to a synthetic, and ultimately proactive, understanding of species invasions have developed along several lines, but most have been frustrated by the complex and unpredictable nature of such invasions—which species will invade and which invaders will become serious problems? For example, considerable effort has gone into identifying characteristics of species likely to invade, or of invaders likely to become pests (e.g., Lawton and Brown 1986, Smallwood and Salmon 1992, Carlton 1996). Another line of inquiry and effort has focused on modeling spatial patterns of range expansion after initial invasion (e.g., Mollison 1986, Williamson and Brown 1986, Reeves and Usher 1989, Hastings 1996, Shigesada and Kawasaki 1997, Holway 1998). All in all, though, a general, synthetic, predictive, proactive approach to species invasions is lacking (Mack 1996) but is desperately needed (Hobbs and Mooney 1998).

Predicting distributions of known and unknown reptile species in Madagascar

Despite the importance of tropical biodiversity, informative species distributional data are seldom available for biogeographical study or setting conservation priorities. Modelling ecological niche distributions of species offers a potential soluion; however, the utility of old locality data from museums, and of more recent remotely sensed satellite data, remains poorly explored, especially for rapidly changing tropical landscapes. Using 29 modern data sets of environmental land coverage and 621 chameleon occurrence localities from Madagascar (historical and recent), here we demonstrate a significant ability of our niche models in predicting species distribution. At 11 recently inventoried sites, highest predictive success (85.1%) was obtained for models based only on modern occurrence data (74.7% and 82.8% predictive success, respectively, for pre-1978 and all data combined). Notably, these models also identified three intersecting areas of over-prediction that recently yielded seven chameleon species new to science. We conclude that ecological niche modelling using recent locality records and readily available environmental coverage data provides informative biogeographical data for poorly known tropical landscapes, and offers innovative potential for the discovery of unknown distributional areas and unknown species.

Locating Pleistocene refugia: Comparing phylogeographic and ecological niche model predictions

Ecological niche models (ENMs) provide a means of characterizing the spatial distribution of suitable conditions for species, and have recently been applied to the challenge of locating potential distributional areas at the Last Glacial Maximum (LGM) when unfavorable climate conditions led to range contractions and fragmentation. Here, we compare and contrast ENM-based reconstructions of LGM refugial locations with those resulting from the more traditional molecular genetic and phylogeographic predictions. We examined 20 North American terrestrial vertebrate species from different regions and with different range sizes for which refugia have been identified based on phylogeographic analyses, using ENM tools to make parallel predictions. We then assessed the correspondence between the two approaches based on spatial overlap and areal extent of the predicted refugia. In 14 of the 20 species, the predictions from ENM and predictions based on phylogeographic studies were significantly spatially correlated, suggesting that the two approaches to development of refugial maps are converging on a similar result. Our results confirm that ENM scenario exploration can provide a useful complement to molecular studies, offering a less subjective, spatially explicit hypothesis of past geographic patterns of distribution.

Sensitivity of distributional prediction algorithms to geographic data completeness

Abstract The sensitivity of one algorithm for prediction of geographic distributions of species from point data to depth of geographic information was tested for three species of North American birds. Test species were chosen to represent three distinct distributional patterns—western North America (Pygmy Nuthatch Sitta pygmaea), eastern North America (Barred Owl Strix varia), and the Great Plains in the central part of the continent (Lark Bunting Calamospiza melanocorys). Distributional predictions were made using the expert-system algorithm Genetic Algorithm for Role-set Prediction (GARP). Depth of geographic information was manipulated by rarifying the number of coverages on which predictions were based, from the full complement of eight down to one, using a combination of jackknifing and bootstrapping. In all three species, five of the eight coverages were necessary to arrive at the asymptotic maximum predictive efficiency and to avoid broad variance in resulting predictive efficiencies. Annual mean temperature was a critical variable, in some cases more important than inclusion of additional coverages, to producing accurate distributional predictions.

Calibrating divergence times on species trees versus gene trees: implications for speciation history of Aphelocoma jays

Estimates of the timing of divergence are central to testing the underlying causes of speciation. Relaxed molecular clocks and fossil calibration have improved these estimates; however, these advances are implemented in the context of gene trees, which can overestimate divergence times. Here we couple recent innovations for dating speciation events with the analytical power of species trees, where multilocus data are considered in a coalescent context. Divergence times are estimated in the bird genus Aphelocoma to test whether speciation in these jays coincided with mountain uplift or glacial cycles. Gene trees and species trees show general agreement that diversification began in the Miocene amid mountain uplift. However, dates from the multilocus species tree are more recent, occurring predominately in the Pleistocene, consistent with theory that divergence times can be significantly overestimated with gene‐tree based approaches that do not correct for genetic divergence that predates speciation. In addition to coalescent stochasticity, Haldanes rule could account for some differences in timing estimates between mitochondrial DNA and nuclear genes. By incorporating a fossil calibration applied to the species tree, in addition to the process of gene lineage coalescence, the present approach provides a more biologically realistic framework for dating speciation events, and hence for testing the links between diversification and specific biogeographic and geologic events.

Ecologic and geographic distribution of filovirus disease.

We used ecologic niche modeling of outbreaks and sporadic cases of filovirus-associated hemorrhagic fever (HF) to provide a large-scale perspective on the geographic and ecologic distributions of Ebola and Marburg viruses. We predicted that filovirus would occur across the Afrotropics: Ebola HF in the humid rain forests of central and western Africa, and Marburg HF in the drier and more open areas of central and eastern Africa. Most of the predicted geographic extent of Ebola HF has been observed; Marburg HF has the potential to occur farther south and east. Ecologic conditions appropriate for Ebola HF are also present in Southeast Asia and the Philippines, where Ebola Reston is hypothesized to be distributed. This first large-scale ecologic analysis provides a framework for a more informed search for taxa that could constitute the natural reservoir for this virus family.

Effects of global climate change on geographic distributions of Mexican Cracidae

Although climate change and its implications are a frequent subject of detailed study, the effects of these changes on species’ geographic distributions remain little explored. We present a first cross-species analysis of the effects of global climate change on the distributions of one bird family, the Cracidae, in Mexico, based on projecting models of ecological niches from present conditions to modeled future conditions taken from general circulation models of climate change. Based on two different scenarios of climate change and on three assumptions regarding species’ dispersal abilities, effects on species’ distributions range from drastic reduction to modest increases. These results illustrate the complex nature of species’ geographic responses to environmental change, and emphasize the need for detailed analysis of individual species’ ecological requirements.