A comparative evaluation of presence-only methods for modelling species distribution

In spite of increasing application of presence-only models in ecology and conservation and the growing number of such models, little is known about the relative performance of different modelling methods, and some of the leading models (e.g. GARP and ENFA) have never been compared with one another. Here we compare the performance of six presence-only models that have been selected to represent an increasing level of model complexity [BIOCLIM, HABITAT, Mahalanobis distance (MD), DOMAIN, ENFA, and GARP] using data on the distribution of 42 species of land snails, nesting birds, and insectivorous bats in Israel. The models were calibrated using data from museum collections and observation databases, and their predictions were evaluated using Cohen's Kappa based on field data collected in a standardized sampling design covering most parts of Israel. Predictive accuracy varied between modelling methods with GARP and MD showing the highest accuracy, BIOCLIM and ENFA showing the lowest accuracy, and HABITAT and DOMAIN showing intermediate accuracy levels. Yet, differences between the various models were relatively small except for GARP and MD that were significantly more accurate than BIOCLIM and ENFA. In spite of large differences among species in prevalence and niche width, neither prevalence nor niche width interacted with the modelling method in determining predictive accuracy. However, species with relatively narrow niches were modelled more accurately than species with wider niches. Differences among species in predictive accuracy were highly consistent over all modelling methods, indicating the need for a better understanding of the ecological and geographical factors that influence the performance of species distribution models.     

利用最大熵模型和规则集遗传算法模型预测孑遗植物裸果木的潜在地理分布及格局

利用野外调查的16个居群分布点和7个环境因子图层, 选择最大熵模型(MAXENT)和规则集遗传算法模型(GARP), 在地理和环境空间上模拟了第三纪孑遗植物裸果木(Gymnocarpos przewalskii)在中国西北地区的潜在分布。结果表明: (1)裸果木的潜在适生区全部集中在西北荒漠区, 其中最佳适生区主要集中在3个区域, 一是河西走廊中部和玉门以西、宁夏北部及内蒙古乌拉特后旗; 二是塔里木盆地西北缘; 三是柴达木盆地西北缘两片极小的高度适生区。裸果木的生态位被确定在一个较广的干旱环境空间: 适生区极端最高气温基本上在29.2-36.8 ℃之间, 极端最低气温在-18.3至-13.4 ℃之间; 年平均降水量40-200 mm; 潜在蒸发率在3-15之间。(2) MAXENT和GARP模型都较好地预测了裸果木的潜在分布, 但GARP产生了相对较大、较连续的潜在分布区, 部分过预测了破碎化生境; 而MAXENT预测到的潜在分布区, 在不同区域具有不同的环境适生性指数, 而且成功地排除了不合理的破碎化分布, 从而更直观地展示了裸果木的潜在分布格局和生态位要求。     

Predicting species distributions from small numbers of occurrence records: a test case using cryptic geckos in Madagascar

Aim Techniques that predict species potential distributions by combining observed occurrence records with environmental variables show much potential for application across a range of biogeographical analyses. Some of the most promising applications relate to species for which occurrence records are scarce, due to cryptic habits, locally restricted distributions or low sampling effort. However, the minimum sample sizes required to yield useful predictions remain difficult to determine. Here we developed and tested a novel jackknife validation approach to assess the ability to predict species occurrence when fewer than 25 occurrence records are available. Location Madagascar. Methods Models were developed and evaluated for 13 species of secretive leaf‐tailed geckos (Uroplatus spp.) that are endemic to Madagascar, for which available sample sizes range from 4 to 23 occurrence localities (at 1 km² grid resolution). Predictions were based on 20 environmental data layers and were generated using two modelling approaches: a method based on the principle of maximum entropy (Maxent) and a genetic algorithm (GARP). Results We found high success rates and statistical significance in jackknife tests with sample sizes as low as five when the Maxent model was applied. Results for GARP at very low sample sizes (less than c. 10) were less good. When sample sizes were experimentally reduced for those species with the most records, variability among predictions using different combinations of localities demonstrated that models were greatly influenced by exactly which observations were included. Main conclusions We emphasize that models developed using this approach with small sample sizes should be interpreted as identifying regions that have similar environmental conditions to where the species is known to occur, and not as predicting actual limits to the range of a species. The jackknife validation approach proposed here enables assessment of the predictive ability of models built using very small sample sizes, although use of this test with larger sample sizes may lead to overoptimistic estimates of predictive power. Our analyses demonstrate that geographical predictions developed from small numbers of occurrence records may be of great value, for example in targeting field surveys to accelerate the discovery of unknown populations and species.     

Impact of climate change on vector transmission of Trypanosoma cruzi (Chagas, 1909) in North America

Climate change can influence the geographical range of the ecological niche of pathogens by altering biotic interactions with vectors and reservoirs. The distributions of 20 epidemiologically important triatomine species in North America were modelled, comparing the genetic algorithm for rule‐set prediction (GARP) and maximum entropy (MaxEnt), with or without topographical variables. Potential shifts in transmission niche for Trypanosoma cruzi (Trypanosomatida: Trypanosomatidae) (Chagas, 1909) were analysed for 2050 and 2070 in Representative Concentration Pathway (RCP) 4.5 and RCP 8.5. There were no significant quantitative range differences between the GARP and MaxEnt models, but GARP models best represented known distributions for most species [partial‐receiver operating characteristic (ROC) > 1]; elevation was an important variable contributing to the ecological niche model (ENM). There was little difference between niche breadth projections for RCP 4.5 and RCP 8.5; the majority of species shifted significantly in both periods. Those species with the greatest current distribution range are expected to have the greatest shifts. Positional changes in the centroid, although reduced for most species, were associated with latitude. A significant increase or decrease in mean niche elevation is expected principally for Neotropical 1 species. The impact of climate change will be specific to each species, its biogeographical region and its latitude. North American triatomines with the greatest current distribution ranges (Nearctic 2 and Nearctic/Neotropical) will have the greatest future distribution shifts. Significant shifts (increases or decreases) in mean elevation over time are projected principally for the Neotropical species with the broadest current distributions. Changes in the vector exposure threat to the human population were significant for both future periods, with a 1.48% increase for urban populations and a 1.76% increase for rural populations in 2050.     

An evaluation of a GARP model as an approach to predicting the spatial distribution of non-vagile invertebrate species

One of the primary goals of any systematic, taxonomic or biodiversity study is the characterization of species distributions. While museum collection data are important for ascertaining distributional ranges, they are often biased or incomplete. The Genetic Algorithm for Rule-set Prediction (GARP) is an ecological niche modelling method based on a genetic algorithm that has been argued to provide an accurate assessment of the spatial distribution of organisms that have dispersal capabilities. The primary objective of this study is to evaluate the accuracy of a GARP model to predict the spatial distribution of a non-invasive, non-vagile invertebrate whose full distributional range was unknown. A GARP predictive model based on seven environmental parameters and 42 locations known from historical museum records for species of the trapdoor spider genus Promyrmekiaphila was produced and subsequently used as a guide for ground truthing the model. The GARP model was neither a significant nor an accurate predictor of spider localities and was outperformed by more simplistic BIOCLIM and GLM models. The isolated nature of Promyrmekiaphila populations mandates that environmental layers and their respective resolutions are carefully chosen for model production. Our results strongly indicate that, for modelling the spatial distribution of low vagility organisms, one should employ a modelling method whose results are more conducive to interpretation than models produced by a 'black box' algorithm such as GARP.     

Ecological niches as stable distributional constraints on mammal species, with implications for Pleistocene extinctions and climate change projections for biodiversity

Aim Theoretical work suggests that species’ ecological niches should remain relatively constant over long‐term ecological time periods, but empirical tests are few. We present longitudinal studies of 23 extant mammal species, modelling ecological niches and predicting geographical distributions reciprocally between the Last Glacial Maximum and present to test this evolutionary conservatism. Location This study covered distributional shifts in mammal species across the lower 48 states of the United States. Methods We used a machine‐learning tool for modelling species’ ecological niches, based on known occurrences and electronic maps summarizing ecological dimensions, to assess the ability of ecological niches as modelled in one time period to predict the geographical distribution of the species in another period, and vice versa. Results High intertemporal predictivity between niche models and species’ occurrences indicate that niche conservatism is widespread among the taxa studied, particularly when statistical power is considered as a reason for failure of reciprocal predictions. Niche projections to the present for 8 mammal taxa that became extinct at the end of the Pleistocene generally increased in area, and thus do not support the hypothesis of niche collapse as a major driving force in their extinction. Main conclusions Ecological niches represent long‐term stable constraints on the distributional potential of species; indeed, this study suggests that mammal species have tracked consistent climate profiles throughout the drastic climate change events that marked the end of the Pleistocene glaciations. Many current modelling efforts focusing on anticipating climate change effects on species’ potential geographical distributions will be bolstered by this result — in essence, the first longitudinal demonstration of niche conservatism.     

Does GARP really fail miserably? A response to Stockman et al. (2006)

Stockman et al. (2006 ) found that ecological niche models built using DesktopGARP ‘failed miserably’ to predict trapdoor spider (genus Promyrmekiaphila) distributions in California. This apparent failure of GARP (Genetic Algorithm for Rule‐Set Production) was actually a failure of the authors’ methods, that is, attempting to build ecological niche models using single data points. In this paper, we present a re‐analysis of their original data using standard methods with the data appropriately partitioned into training/testing subsets. This re‐evaluation generated accurate distributional predictions that we contrast with theirs. We address the consequences of model‐building using single data points and the need for a foundational understanding of the principles of ecological niche modelling.     

Ecological niches and potential geographical distributions of Mediterranean fruit fly (Ceratitis capitata) and Natal fruit fly (Ceratitis rosa)

Aim To predict and compare potential geographical distributions of the Mediterranean fruit fly (Ceratitis capitata) and Natal fruit fly (Ceratitis rosa). Location Africa, southern Europe, and worldwide. Methods Two correlative ecological niche modelling techniques, genetic algorithm for rule‐set prediction (GARP) and a technique based on principal components analysis (PCA), were used to predict distributions of the two fly species using distribution records and a set of environmental predictor variables. Results The two species appear to have broadly similar potential ranges in Africa and southern Europe, with much of sub‐Saharan Africa and Madagascar predicted as highly suitable. The drier regions of Africa (central and western regions of southern Africa and Sahelian zone) were identified as being less suitable for C. rosa than for C. capitata. Overall, the proportion of the region predicted to be highly suitable is larger for C. capitata than for C. rosa under both techniques, suggesting that C. capitata may be tolerant of a wider range of climatic conditions than C. rosa. Worldwide, tropical and subtropical regions are highlighted as highly suitable for both species. Differences in overlap of predictions from the two models for these species were observed. An evaluation using independent records from the adventive range for C. capitata and comparison with other predictions suggest that GARP models offer more accurate predictions than PCA models. Main conclusions This study suggests that these species have broadly similar potential distributions worldwide (based on climate), although the potential distribution appears to be broader for C. capitata than for C. rosa. Ceratitis capitata has become invasive throughout the world, whereas C. rosa has not, despite both species having broadly similar potential distributions. Further research into the biology of these species and their ability to overcome barriers is necessary to explain this difference, and to better understand invasion risk.     

海南岛霸王岭热带天然林景观中主要木本植物关键种的潜在分布

在较大的空间尺度上生态位模型是预测物种潜在分布的有效途径之一。为了探讨在热带天然林景观中木本植物(限于乔木和灌木)主要关键种的潜在分布,在对海南岛霸王岭的热带天然林进行按公里网格样方调查的基础上,采用演替地位和最大潜在高度两个功能性指标对物种进行了功能群划分,并在功能群框架下运用优势度指数法进行了关键种的确定;采用基于地理信息系统(Geographic information system, GIS)的基于规则集合预测的遗传算法(Algorithm for rule-set prediction, GARP)生态位模型对主要关键种的地理分布进行了预测,并应用受试者工作特征分析进行了模型精度验证;应用多元线性回归分析对影响各关键种潜在分布的关键因子进行了确定。结果表明:除了顶极次林层乔木功能群和顶极主林层乔木功能群外,在先锋种功能群、顶极灌木种功能群和顶极超冠层乔木功能群中采用优势度指数法划分出的关键种较为理想;一般来讲,在进行预测的8个关键种中,除了先锋主林层乔木种海南杨桐(Adinandra hainanensis),其它3个先锋种毛稔(Melastoma sanquiueum)、银柴(Aporosa chinensis)和枫香(Liquidambar formosana) 在研究区北部、西部以及西南部均具有较高的发生概率,而顶极种除了顶极超冠层乔木种南亚松(Pinus merkusii)外,九节(Psychotria rubra)、高脚罗伞(Ardisia quinquegona)和海南椎(Castanopsis hainanensis)具有相似的潜在分布格局,在研究区中部、东南部和南部地区具有较高的发生概率;相关分析表明极端最低温、年均温、极端最高温、年均降水量、海拔和坡向6大因子是影响研究区关键种潜在分布的关键因子;精度检验表明,GARP模型对8个关键种的潜在分布预测效果均较好,而其中又以银柴和海南椎的预测精度最高。     

Novel methods improve prediction of species' distributions from occurrence data

Prediction of species' distributions is central to diverse applications in ecology, evolution and conservation science. There is increasing electronic access to vast sets of occurrence records in museums and herbaria, yet little effective guidance on how best to use this information in the context of numerous approaches for modelling distributions. To meet this need, we compared 16 modelling methods over 226 species from 6 regions of the world, creating the most comprehensive set of model comparisons to date. We used presence-only data to fit models, and independent presence-absence data to evaluate the predictions. Along with well-established modelling methods such as generalised additive models and GARP and BIOCLIM, we explored methods that either have been developed recently or have rarely been applied to modelling species' distributions. These include machine-learning methods and community models, both of which have features that may make them particularly well suited to noisy or sparse information, as is typical of species' occurrence data. Presence-only data were effective for modelling species' distributions for many species and regions. The novel methods consistently outperformed more established methods. The results of our analysis are promising for the use of data from museums and herbaria, especially as methods suited to the noise inherent in such data improve.     

Transferability and model evaluation in ecological niche modeling: a comparison of GARP and Maxent

We compared predictive success in two common algorithms for modeling species' ecological niches, GARP and Maxent, in a situation that challenged the algorithms to be general – that is, to be able to predict the species' distributions in broad unsampled regions, here termed transferability. The results were strikingly different between the two algorithms – Maxent models reconstructed the overall distributions of the species at low thresholds, but higher predictive levels of Maxent predictions reflected overfitting to the input data; GARP models, on the other hand, succeeded in anticipating most of the species' distributional potential, at the cost of increased (apparent, at least) commission error. Receiver operating characteristic (ROC) tests were weak in discerning models able to predict into broad unsampled areas from those that were not. Such transferability is clearly a novel challenge for modeling algorithms, and requires different qualities than does predicting within densely sampled landscapes – in this case, Maxent was transferable only at very low thresholds, and biases and gaps in input data may frequently affect results based on higher Maxent thresholds, requiring careful interpretation of model results.     

Modelling ecological niches from low numbers of occurrences: assessment of the conservation status of poorly known viverrids (Mammalia, Carnivora) across two continents

The conservation of poorly known species is difficult because of incomplete knowledge on their biology and distribution. We studied the contribution of two ecological niche modelling tools, the Genetic Algorithm for Rule-set Prediction (GARP) and maximum entropy (Maxent), in assessing potential ranges and distributional connectivity among 12 of the least known African and Asian viverrids. The level of agreement between GARP and Maxent predictions was low when < 15 occurrences were available, probably indicating a minimum number below that necessary to obtain models with good predictive power. Unexpectedly, our results suggested that Maxent extrapolated more than GARP in the context of small sample sizes. Predictions were overlapped with current land use and location of protected areas to estimate the conservation status of each species. Our analyses yielded range predictions generally contradicting with extents of occurrence established by the IUCN. We evidenced a high level of disturbance within predicted distributions in West and East Africa, Sumatra, and South-East Asia, and identified within West African degraded lowlands four relatively preserved areas that might be of prime importance for the conservation of rainforest taxa. Knowing whether these species of viverrids may survive in degraded or alternative habitats is of crucial importance for further conservation planning. The level of coverage of species suitable ranges by existing and proposed IUCN reserves was low, and we recommend that the total surface of protected areas be substantially increased on both continents.     

Spatially autocorrelated sampling falsely inflates measures of accuracy for presence‐only niche models

Aim Environmental niche models that utilize presence‐only data have been increasingly employed to model species distributions and test ecological and evolutionary predictions. The ideal method for evaluating the accuracy of a niche model is to train a model with one dataset and then test model predictions against an independent dataset. However, a truly independent dataset is often not available, and instead random subsets of the total data are used for ‘training’ and ‘testing’ purposes. The goal of this study was to determine how spatially autocorrelated sampling affects measures of niche model accuracy when using subsets of a larger dataset for accuracy evaluation. Location The distribution of Centaurea maculosa (spotted knapweed; Asteraceae) was modelled in six states in the western United States: California, Oregon, Washington, Idaho, Wyoming and Montana. Methods Two types of niche modelling algorithms – the genetic algorithm for rule‐set prediction (GARP) and maximum entropy modelling (as implemented with Maxent) – were used to model the potential distribution of C. maculosa across the region. The effect of spatially autocorrelated sampling was examined by applying a spatial filter to the presence‐only data (to reduce autocorrelation) and then comparing predictions made using the spatial filter with those using a random subset of the data, equal in sample size to the filtered data. Results The accuracy of predictions from both algorithms was sensitive to the spatial autocorrelation of sampling effort in the occurrence data. Spatial filtering led to lower values of the area under the receiver operating characteristic curve plot but higher similarity statistic (I) values when compared with predictions from models built with random subsets of the total data, meaning that spatial autocorrelation of sampling effort between training and test data led to inflated measures of accuracy. Main conclusions The findings indicate that care should be taken when interpreting the results from presence‐only niche models when training and test data have been randomly partitioned but occurrence data were non‐randomly sampled (in a spatially autocorrelated manner). The higher accuracies obtained without the spatial filter are a result of spatial autocorrelation of sampling effort between training and test data inflating measures of prediction accuracy. If independently surveyed data for testing predictions are unavailable, then it may be necessary to explicitly account for the spatial autocorrelation of sampling effort between randomly partitioned training and test subsets when evaluating niche model predictions.     

Predicting species distributions from herbarium collections: does climate bias in collection sampling influence model outcomes?

Aim Species distribution models and geographical information system (GIS) technologies are becoming increasingly important tools in conservation planning and decision‐making. Often the rich data bases of museums and herbaria serve as the primary data for predicting species distributions. Yet key assumptions about the primary data often are untested, and violation of such assumptions may have consequences for model predictions. For example, users of primary data assume that sampling has been random with respect to geography and environmental gradients. Here we evaluate the assumption that plant voucher specimens adequately sample the climatic gradient and test whether violation of this assumption influences model predictions. Location Bolivia and Ecuador. Methods Using 323,711 georeferenced herbarium collections and nine climatic variables, we predicted the distribution of 76 plant species using maximum entropy models (MAXENT) with training points that sampled the climate environments randomly and training points that reflected the climate bias in the herbarium collections. To estimate the distribution of species, MAXENT finds the distribution of maximum entropy (i.e. closest to uniform) subject to the constraint that the expected value for each environmental variable under the estimated distribution matches its empirical average. The experimental design included species that differed in geographical range and elevation; all species were modelled with 20 and 100 training points. We examined the influence of the number of training points and climate bias in training points, elevation and range size on model performance using analysis of variance models. Results We found that significant parts of the climatic gradient were poorly represented in herbarium collections for both countries. For the most part, existing climatic bias in collections did not greatly affect distribution predictions when compared with an unbiased data set. Although the effects of climate bias on prediction accuracy were found to be greater where geographical ranges were characterized by high spatial variation in the degree of climate bias (i.e. ranges where the bias of the various climates sampled by collections deviated considerably from the mean bias), the greatest influence on model performance was the number of presence points used to train the model. Main conclusions These results demonstrate that predictions of species distributions can be quite good despite existing climatic biases in primary data found in natural history collections, if a sufficiently large number of training points is available. Because of consistent overprediction of models, these results also confirm the importance of validating models with independent data or expert opinion. Failure to include independent model validation, especially in cases where training points are limited, may potentially lead to grave errors in conservation decision‐making and planning.     

Akaike information criterion should not be a “test” of geographical prediction accuracy in ecological niche modelling

Model complexity in ecological niche modelling has been recently considered as an important issue that might affect model performance. New methodological developments have implemented the Akaike information criterion (AIC) to capture model complexity in the Maxent algorithm model. AIC is calculated based on the number of parameters and likelihoods of continuous raw outputs. ENMeval R package allows users to perform a species-specific tuning of Maxent settings running models with different combinations of regularization multiplier and feature classes and finally, all these models are compared using AIC corrected for small sample size. This approach is focused to find the “best” model parametrization and it is thought to maximize the model complexity and therefore, its predictability. We found that most niche modelling studies examined by us (68%) tend to consider AIC as a criterion of predictive accuracy in geographical distribution. In other words, AIC is used as a criterion to choose those models with the highest capacity to discriminate between presences and absences. However, the link between AIC and geographical predictive accuracy has not been tested so far. Here, we evaluated this relationship using a set of simulated (virtual) species. We created a set of nine virtual species with different ecological and geographical traits (e.g., niche position, niche breadth, range size) and generated different sets of true presences and absences data across geography. We built a set of models using Maxent algorithm with different regularization values and features schemes and calculated AIC values for each model. For each model, we obtained binary predictions using different threshold criteria and validated using independent presence and absences data. We correlated AIC values against standard validation metrics (e.g., Kappa, TSS) and the number of pixels correctly predicted as presences and absences. We did not find a correlation between AIC values and predictive accuracy from validation metrics. In general, those models with the lowest AIC values tend to generate geographical predictions with high commission and omission errors. The results were consistent across all species simulated. Finally, we suggest that AIC should not be used if users are interested in prediction more than explanation in ecological niche modelling.     

Uncertainty in assessing the impacts of global change with coupled dynamic species distribution and population models

Concern over rapid global changes and the potential for interactions among multiple threats are prompting scientists to combine multiple modelling approaches to understand impacts on biodiversity. A relatively recent development is the combination of species distribution models, land‐use change predictions, and dynamic population models to predict the relative and combined impacts of climate change, land‐use change, and altered disturbance regimes on species' extinction risk. Each modelling component introduces its own source of uncertainty through different parameters and assumptions, which, when combined, can result in compounded uncertainty that can have major implications for management. Although some uncertainty analyses have been conducted separately on various model components – such as climate predictions, species distribution models, land‐use change predictions, and population models – a unified sensitivity analysis comparing various sources of uncertainty in combined modelling approaches is needed to identify the most influential and problematic assumptions. We estimated the sensitivities of long‐run population predictions to different ecological assumptions and parameter settings for a rare and endangered annual plant species (Acanthomintha ilicifolia, or San Diego thornmint). Uncertainty about habitat suitability predictions, due to the choice of species distribution model, contributed most to variation in predictions about long‐run populations.     

An evaluation of methods for modelling species distributions

Aim Various statistical techniques have been used to model species probabilities of occurrence in response to environmental conditions. This paper provides a comprehensive assessment of methods and investigates whether errors in model predictions are associated to specific kinds of geographical and environmental distributions of species. Location Portugal, Western Europe. Methods Probabilities of occurrence for 44 species of amphibians and reptiles in Portugal were modelled using seven modelling techniques: Gower metric, Ecological Niche Factor Analysis, classification trees, neural networks, generalized linear models, generalized additive models and spatial interpolators. Generalized linear and additive models were constructed with and without a term accounting for spatial autocorrelation. Model performance was measured using two methods: sensitivity and Kappa index. Species were grouped according to their spatial (area of occupancy and extent of occurrence) and environmental (marginality and tolerance) distributions. Two‐way comparison tests were performed to detect significant interactions between models and species groups. Results Interaction between model and species groups was significant for both sensitivity and Kappa index. This indicates that model performance varied for species with different geographical and environmental distributions. Artificial neural networks performed generally better, immediately followed by generalized additive models including a covariate term for spatial autocorrelation. Non‐parametric methods were preferred to parametric approaches, especially when modelling distributions of species with a greater area of occupancy, a larger extent of occurrence, lower marginality and higher tolerance. Main conclusions This is a first attempt to relate performance of modelling techniques with species spatial and environmental distributions. Results indicate a strong relationship between model performance and the kinds of species distributions being modelled. Some methods performed generally better, but no method was superior in all circumstances. A suggestion is made that choice of the appropriate method should be contingent on the goals and kinds of distributions being modelled.     

Non-stationarity and local approaches to modelling the distributions of wildlife

Despite a growing interest in species distribution modelling, relatively little attention has been paid to spatial autocorrelation and non-stationarity. Both spatial autocorrelation (the tendency for adjacent locations to be more similar than distant ones) and non-stationarity (the variation in modelled relationships over space) are likely to be common properties of ecological systems. This paper focuses on non-stationarity and uses two local techniques, geographically weighted regression (GWR) and varying coefficient modelling (VCM), to assess its impact on model predictions. We extend two published studies, one on the presence–absence of calandra larks in Spain and the other on bird species richness in Britain, to compare GWR and VCM with the more usual global generalized linear modelling (GLM) and generalized additive modelling (GAM). For the calandra lark data, GWR and VCM produced better-fitting models than GLM or GAM. VCM in particular gave significantly reduced spatial autocorrelation in the model residuals. GWR showed that individual predictors became stationary at different spatial scales, indicating that distributions are influenced by ecological processes operating over multiple scales. VCM was able to predict occurrence accurately on independent data from the same geographical area as the training data but not beyond, whereas the GAM produced good results on all areas. Individual predictions from the local methods often differed substantially from the global models. For the species richness data, VCM and GWR produced far better predictions than ordinary regression. Our analyses suggest that modellers interpolating data to produce maps for practical actions (e.g. conservation) should consider local methods, whereas they should not be used for extrapolation to new areas. We argue that local methods are complementary to global methods, revealing details of habitat associations and data properties which global methods average out and miss.     

Using ecological niche modelling to evaluate niche stability in deep time

Aim To investigate relative niche stability in species responses to various types of environmental pressure (biotic and abiotic) on geological time‐scales using the fossil record. Location The case study focuses on Late Ordovician articulate brachiopods of the Cincinnati Arch in eastern North America. Methods Species niches were modelled for a suite of fossil brachiopod species based on five environmental variables inferred from sedimentary parameters using GARP and Maxent . Niche stability was assessed by comparison of (1) the degree of overlap of species distribution models developed for a time‐slice and those generated by projecting niche models of the previous time‐slice onto environmental layers of a second time‐slice using GARP and Maxent , (2) Schoener’s D statistic, and (3) the similarity of the contribution of each environmental parameter within Maxent niche models between adjacent time‐slices. Results Late Ordovician brachiopod species conserved their niches with high fidelity during intervals of gradual environmental change but responded to inter‐basinal species invasions through niche evolution. Both native and invasive species exhibited similar levels of niche evolution in the invasion and post‐invasion intervals. Niche evolution was related mostly to decreased variance within the former ecological niche parameters rather than to shifts to new ecospace. Main conclusions Although the species examined exhibited morphological stasis during the study interval, high levels of niche conservatism were observed only during intervals of gradual environmental change. Rapid environmental change, notably inter‐basinal species invasions, resulted in high levels of niche evolution among the focal taxa. Both native and invasive species responded with similar levels of niche evolution during the invasion interval and subsequent environmental reorganization. The assumption of complete niche conservatism frequently employed in ecological niche modelling (ENM) analyses to forecast or hindcast species geographical distributions is more likely to be accurate for climate change studies than for invasive species analyses over geological time‐scales.     

珍稀濒危植物野生莲的适生分布区预测

基于野生莲（Nelumbo nucifera Gaertn.）136个分布点的数据和14个环境因子参数,运用规则集遗传算法（GARP）和最大熵（MaxEnt）两个生态位模型对他们在我国的适生分布区进行预测。结果显示：根据GARP和MaxEnt模型计算得到的ROC曲线下面积的AUC均值分别为0.861和0.964,其中MaxEnt模型的AUC值更大,预测结果更精准。MaxEnt模型预测结果表明,莲的最适分布区主要集中在四川、湖北、湖南等地的大部分地区,江西北部,以及黑龙江、辽宁、浙江、广东等地的小部分地区。刀切法（Jackknife）检测结果表明,影响莲适生分布区的主要环境因子包括：水汽压、海拔、年平均气温、多年平均降水量、最热季节平均温度、最冷季节平均温度、最干月降水量、最冷月最低温和最热月最高温等。适生区环境因子的统计分析结果显示,野生莲最适宜生长在海拔1~2216 m、年降水量丰富（1202.50 mm）、年均温约为16.19℃、最热月温度范围在24.60℃~35.10℃、最冷月均温不低于-0.53℃的地区。研究结果可为有效保护中国野生莲资源提供有利依据。