Spatial autocorrelation in predictors reduces the impact of positional uncertainty in occurrence data on species distribution modelling

Aim To investigate the impact of positional uncertainty in species occurrences on the predictions of seven commonly used species distribution models (SDMs), and explore its interaction with spatial autocorrelation in predictors. Methods A series of artificial datasets covering 155 scenarios including different combinations of five positional uncertainty scenarios and 31 spatial autocorrelation scenarios were simulated. The level of positional uncertainty was defined by the standard deviation of a normally distributed zero‐mean random variable. Each dataset included two environmental gradients (predictor variables) and one set of species occurrence sample points (response variable). Seven commonly used models were selected to develop SDMs: generalized linear models, generalized additive models, boosted regression trees, multivariate adaptive regression spline, random forests, genetic algorithm for rule‐set production and maximum entropy. A probabilistic approach was employed to model and simulate five levels of error in the species locations. To analyse the propagation of positional uncertainty, Monte Carlo simulation was applied to each scenario for each SDM. The models were evaluated for performance using simulated independent test data with Cohen’s Kappa and the area under the receiver operating characteristic curve. Results Positional uncertainty in species location led to a reduction in prediction accuracy for all SDMs, although the magnitude of the reduction varied between SDMs. In all cases the magnitude of this impact varied according to the degree of spatial autocorrelation in predictors and the levels of positional uncertainty. It was shown that when the range of spatial autocorrelation in the predictors was less than or equal to three times the standard deviation of the positional error, the models were less affected by error and, consequently, had smaller decreases in prediction accuracy. When the range of spatial autocorrelation in predictors was larger than three times the standard deviation of positional error, the prediction accuracy was low for all scenarios. Main conclusions The potential impact of positional uncertainty in species occurrences on the predictions of SDMs can be understood by comparing it with the spatial autocorrelation range in predictor variables.     

Estimating and controlling for spatial structure in the study of ecological communities

Aim Variation partitioning based on canonical analysis is the most commonly used analysis to investigate community patterns according to environmental and spatial predictors. Ecologists use this method in order to understand the pure contribution of the environment independent of space, and vice versa, as well as to control for inflated type I error in assessing the environmental component under spatial autocorrelation. Our goal is to use numerical simulations to compare how different spatial predictors and model selection procedures perform in assessing the importance of the spatial component and in controlling for type I error while testing environmental predictors. Innovation We determine for the first time how the ability of commonly used (polynomial regressors) and novel methods based on eigenvector maps compare in the realm of spatial variation partitioning. We introduce a novel forward selection procedure to select spatial regressors for community analysis. Finally, we point out a number of issues that have not been previously considered about the joint explained variation between environment and space, which should be taken into account when reporting and testing the unique contributions of environment and space in patterning ecological communities. Main conclusions In tests of species‐environment relationships, spatial autocorrelation is known to inflate the level of type I error and make the tests of significance invalid. First, one must determine if the spatial component is significant using all spatial predictors (Moran's eigenvector maps). If it is, consider a model selection for the set of spatial predictors (an individual‐species forward selection procedure is to be preferred) and use the environmental and selected spatial predictors in a partial regression or partial canonical analysis scheme. This is an effective way of controlling for type I error in such tests. Polynomial regressors do not provide tests with a correct level of type I error.     

Incorporating uncertainty in predictive species distribution modelling

Motivated by the need to solve ecological problems (climate change, habitat fragmentation and biological invasions), there has been increasing interest in species distribution models (SDMs). Predictions from these models inform conservation policy, invasive species management and disease-control measures. However, predictions are subject to uncertainty, the degree and source of which is often unrecognized. Here, we review the SDM literature in the context of uncertainty, focusing on three main classes of SDM: niche-based models, demographic models and process-based models. We identify sources of uncertainty for each class and discuss how uncertainty can be minimized or included in the modelling process to give realistic measures of confidence around predictions. Because this has typically not been performed, we conclude that uncertainty in SDMs has often been underestimated and a false precision assigned to predictions of geographical distribution. We identify areas where development of new statistical tools will improve predictions from distribution models, notably the development of hierarchical models that link different types of distribution model and their attendant uncertainties across spatial scales. Finally, we discuss the need to develop more defensible methods for assessing predictive performance, quantifying model goodness-of-fit and for assessing the significance of model covariates.     

Evaluation of habitat suitability index models by global sensitivity and uncertainty analyses: a case study for submerged aquatic vegetation

Habitat suitability index (HSI) models are commonly used to predict habitat quality and species distributions and are used to develop biological surveys, assess reserve and management priorities, and anticipate possible change under different management or climate change scenarios. Important management decisions may be based on model results, often without a clear understanding of the level of uncertainty associated with model outputs. We present an integrated methodology to assess the propagation of uncertainty from both inputs and structure of the HSI models on model outputs (uncertainty analysis: UA) and relative importance of uncertain model inputs and their interactions on the model output uncertainty (global sensitivity analysis: GSA). We illustrate the GSA/UA framework using simulated hydrology input data from a hydrodynamic model representing sea level changes and HSI models for two species of submerged aquatic vegetation (SAV) in southwest Everglades National Park: Vallisneria americana (tape grass) and Halodule wrightii (shoal grass). We found considerable spatial variation in uncertainty for both species, but distributions of HSI scores still allowed discrimination of sites with good versus poor conditions. Ranking of input parameter sensitivities also varied spatially for both species, with high habitat quality sites showing higher sensitivity to different parameters than low‐quality sites. HSI models may be especially useful when species distribution data are unavailable, providing means of exploiting widely available environmental datasets to model past, current, and future habitat conditions. The GSA/UA approach provides a general method for better understanding HSI model dynamics, the spatial and temporal variation in uncertainties, and the parameters that contribute most to model uncertainty. Including an uncertainty and sensitivity analysis in modeling efforts as part of the decision‐making framework will result in better‐informed, more robust decisions.     

Treatments of Uncertainty and Variability in Ecological Risk Assessment of Single-Species Populations

The selection of the most appropriate model for an ecological risk assessment depends on the application, the data and resources available, the knowledge base of the assessor, the relevant endpoints, and the extent to which the model deals with uncertainty. Since ecological systems are highly variable and our knowledge of model input parameters is uncertain, it is important that models include treatments of uncertainty and variability, and that results are reported in this light. In this paper we discuss treatments of variation and uncertainty in a variety of population models. In ecological risk assessments, the risk relates to the probability of an adverse event in the context of environmental variation. Uncertainty relates to ignorance about parameter values, e.g., measurement error and systematic error. An assessment of the full distribution of risks, under variability and parameter uncertainty, will give the most comprehensive and flexible endpoint. In this paper we present the rationale behind probabilistic risk assessment, identify the sources of uncertainty relevant for risk assessment and provide an overview of a range of population models. While all of the models reviewed have some utility in ecology, some have more comprehensive treatments of uncertainty than others. We identify the models that allow probabilistic assessments and sensitivity analyses, and we offer recommendations for further developments that aim towards more comprehensive and reliable ecological risk assessments for populations.     

A spatially-explicit model of alien plant richness in Tenerife (Canary Islands)

Biological invasions are one of the major threats to biodiversity, especially in oceanic islands. In the Canary Islands, the relationships between plant Alien Species Richness (ASR) and their environmental and anthropogenic determinants were thoroughly investigated using ecological models. However, previous predictive models rarely accounted for spatial autocorrelation (SAC) and uncertainty of predictions, thus missing crucial information related to model accuracy and predictions reliability. In this study, we propose a Generalized Linear Spatial Model (GLSM) for ASR under a Bayesian framework on Tenerife Island. Our aim is to test whether the inclusion of SAC into the modelling framework could improve model performance resulting in more reliable predictions. Results demonstrated as accounting for SAC dramatically reduced the model's AIC (ΔAIC = 4423) and error magnitudes, showing also better performances in terms of goodness of fit. Calculation of uncertainty related to predicted values pointed out those areas where either the number of observations (e.g. under-sampled areas) or the reliability of the environmental predictors was lower (e.g. low spatial resolution in highly heterogeneous environments). Although our results confirmed what was already observed in other ecological studies, such as the important role of roads in ASR spread, methodological considerations on the applied modelling approach point out the importance of considering spatial autocorrelation and researcher's prior knowledge to increase the predictive power of statistical models as well as the correctness in terms of coefficients estimates. The proposed approach may serve as an essential management tools highlighting those portions of territory that will be more prone to biological invasions and where monitoring efforts should be addressed.     

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.     

Multi‐model comparison highlights consistency in predicted effect of warming on a semi‐arid shrub

A number of modeling approaches have been developed to predict the impacts of climate change on species distributions, performance, and abundance. The stronger the agreement from models that represent different processes and are based on distinct and independent sources of information, the greater the confidence we can have in their predictions. Evaluating the level of confidence is particularly important when predictions are used to guide conservation or restoration decisions. We used a multi‐model approach to predict climate change impacts on big sagebrush (Artemisia tridentata), the dominant plant species on roughly 43 million hectares in the western United States and a key resource for many endemic wildlife species. To evaluate the climate sensitivity of A. tridentata, we developed four predictive models, two based on empirically derived spatial and temporal relationships, and two that applied mechanistic approaches to simulate sagebrush recruitment and growth. This approach enabled us to produce an aggregate index of climate change vulnerability and uncertainty based on the level of agreement between models. Despite large differences in model structure, predictions of sagebrush response to climate change were largely consistent. Performance, as measured by change in cover, growth, or recruitment, was predicted to decrease at the warmest sites, but increase throughout the cooler portions of sagebrush's range. A sensitivity analysis indicated that sagebrush performance responds more strongly to changes in temperature than precipitation. Most of the uncertainty in model predictions reflected variation among the ecological models, raising questions about the reliability of forecasts based on a single modeling approach. Our results highlight the value of a multi‐model approach in forecasting climate change impacts and uncertainties and should help land managers to maximize the value of conservation investments.     

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.     

Model-based uncertainty in species range prediction

Aim Many attempts to predict the potential range of species rely on environmental niche (or ‘bioclimate envelope’) modelling, yet the effects of using different niche‐based methodologies require further investigation. Here we investigate the impact that the choice of model can have on predictions, identify key reasons why model output may differ and discuss the implications that model uncertainty has for policy‐guiding applications. Location The Western Cape of South Africa. Methods We applied nine of the most widely used modelling techniques to model potential distributions under current and predicted future climate for four species (including two subspecies) of Proteaceae. Each model was built using an identical set of five input variables and distribution data for 3996 sampled sites. We compare model predictions by testing agreement between observed and simulated distributions for the present day (using the area under the receiver operating characteristic curve (AUC) and kappa statistics) and by assessing consistency in predictions of range size changes under future climate (using cluster analysis). Results Our analyses show significant differences between predictions from different models, with predicted changes in range size by 2030 differing in both magnitude and direction (e.g. from 92% loss to 322% gain). We explain differences with reference to two characteristics of the modelling techniques: data input requirements (presence/absence vs. presence‐only approaches) and assumptions made by each algorithm when extrapolating beyond the range of data used to build the model. The effects of these factors should be carefully considered when using this modelling approach to predict species ranges. Main conclusions We highlight an important source of uncertainty in assessments of the impacts of climate change on biodiversity and emphasize that model predictions should be interpreted in policy‐guiding applications along with a full appreciation of uncertainty.     

Evaluation of a Mysis bioenergetics model

Direct approaches for estimating the feeding rate of the opossumshrimp Mysis relicta can be hampered by variable gut residencetime (evacuation rate models) and non-linear functional responses(clearance rate models). Bioenergetics modeling provides analternative method, but the reliability of this approach needsto be evaluated using independent measures of growth and foodconsumption. In this study, we measured growth and food consumptionfor M. relicta and compared experimental results with thosepredicted from a Mysis bioenergetics model. For Mysis rearedat 10°C, model predictions were not significantly differentfrom observed values. Moreover, decomposition of mean squareerror indicated that 70% of the variation between model predictionsand observed values was attributable to random error. On average,model predictions were within 12% of observed values. A sensitivityanalysis revealed that Mysis respiration and prey energy densitywere the most sensitive parameters affecting model output. Byaccounting for uncertainty (95% CLs) in Mysis respiration, weobserved a significant improvement in the accuracy of modeloutput (within 5% of observed values), illustrating the importanceof sensitive input parameters for model performance. These findingshelp corroborate the Mysis bioenergetics model and demonstratethe usefulness of this approach for estimating Mysis feedingrate.     

Spatial autocorrelation and the selection of simultaneous autoregressive models

Aim Spatial autocorrelation is a frequent phenomenon in ecological data and can affect estimates of model coefficients and inference from statistical models. Here, we test the performance of three different simultaneous autoregressive (SAR) model types (spatial error = SAR_err, lagged = SAR_lag and mixed = SAR_mix) and common ordinary least squares (OLS) regression when accounting for spatial autocorrelation in species distribution data using four artificial data sets with known (but different) spatial autocorrelation structures. Methods We evaluate the performance of SAR models by examining spatial patterns in model residuals (with correlograms and residual maps), by comparing model parameter estimates with true values, and by assessing their type I error control with calibration curves. We calculate a total of 3240 SAR models and illustrate how the best models [in terms of minimum residual spatial autocorrelation (minRSA), maximum model fit (R²), or Akaike information criterion (AIC)] can be identified using model selection procedures. Results Our study shows that the performance of SAR models depends on model specification (i.e. model type, neighbourhood distance, coding styles of spatial weights matrices) and on the kind of spatial autocorrelation present. SAR model parameter estimates might not be more precise than those from OLS regressions in all cases. SAR_err models were the most reliable SAR models and performed well in all cases (independent of the kind of spatial autocorrelation induced and whether models were selected by minRSA, R² or AIC), whereas OLS, SAR_lag and SAR_mix models showed weak type I error control and/or unpredictable biases in parameter estimates. Main conclusions SAR_err models are recommended for use when dealing with spatially autocorrelated species distribution data. SAR_lag and SAR_mix might not always give better estimates of model coefficients than OLS, and can thus generate bias. Other spatial modelling techniques should be assessed comprehensively to test their predictive performance and accuracy for biogeographical and macroecological research.     

Characterizing,Propagating, and Analyzing Uncertainty in Life‐Cycle Assessment: A Survey of Quantitative Approaches

Life‐cycle assessment (LCA) practitioners build models to quantify resource consumption, environmental releases, and potential environmental and human health impacts of product systems. Most often, practitioners define a model structure, assign a single value to each parameter, and build deterministic models to approximate environmental outcomes. This approach fails to capture the variability and uncertainty inherent in LCA. To make good decisions, decision makers need to understand the uncertainty in and divergence between LCA outcomes for different product systems. Several approaches for conducting LCA under uncertainty have been proposed and implemented. For example, Monte Carlo simulation and fuzzy set theory have been applied in a limited number of LCA studies. These approaches are well understood and are generally accepted in quantitative decision analysis. But they do not guarantee reliable outcomes. A survey of approaches used to incorporate quantitative uncertainty analysis into LCA is presented. The suitability of each approach for providing reliable outcomes and enabling better decisions is discussed. Approaches that may lead to overconfident or unreliable results are discussed and guidance for improving uncertainty analysis in LCA is provided.     

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.     

A spatially explicit method for evaluating accuracy of species distribution models

Aim Models predicting the spatial distribution of animals are increasingly used in wildlife management and conservation planning. There is growing recognition that common methods of evaluating species distribution model (SDM) accuracy, as a global overall value of predictive ability, could be enhanced by spatially evaluating the model thereby identifying local areas of relative predictive strength and weakness. Current methods of spatial SDM model assessment focus on applying local measures of spatial autocorrelation to SDM residuals, which require quantitative model outputs. However, SDM outputs are often probabilistic (relative probability of species occurrence) or categorical (species present or absent). The goal of this paper was to develop a new method, using a conditional randomization technique, which can be applied to directly spatially evaluate probabilistic and categorical SDMs. Location Eastern slopes, Rocky Mountains, Alberta, Canada. Methods We used predictions from seasonal grizzly bear (Ursus arctos) resource selection functions (RSF) models to demonstrate our spatial evaluation technique. Local test statistics computed from bear telemetry locations were used to identify areas where bears were located more frequently than predicted. We evaluated the spatial pattern of model inaccuracies using a measure of spatial autocorrelation, local Moran’s I. Results We found the model to have non‐stationary patterns in accuracy, with clusters of inaccuracies located in central habitat areas. Model inaccuracies varied seasonally, with the summer model performing the best and the least error in areas with high RSF values. The landscape characteristics associated with model inaccuracies were examined, and possible factors contributing to RSF error were identified. Main conclusions The presented method complements existing spatial approaches to model error assessment as it can be used with probabilistic and categorical model output, which is typical for SDMs. We recommend that SDM accuracy assessments be done spatially and resulting accuracy maps included in model metadata.     

Sensitivity analysis of the tree distribution model Phenofit to climatic input characteristics: implications for climate impact assessment

Species distributions are already affected by climate change. Forecasting their long‐term evolution requires models with thoroughly assessed validation. Our aim here is to demonstrate that the sensitivity of such models to climate input characteristics may complicate their validation and introduce uncertainties in their predictions. In this study, we conducted a sensitivity analysis of a process‐based tree distribution model Phenofit to climate input characteristics. This analysis was conducted for two North American trees which differ greatly in their distribution and eight different types of climate input for the historic period which differ in their spatial (local or gridded data) and temporal (daily vs. monthly) resolution as well as their type (locally recorded, extrapolated or simulated by General Circulation Models). We show that the climate data resolution (spatial and temporal) and their type, highly affect the model predictions. The sensitivity analysis also revealed, the importance, for global climate change impact assessment, of (i) the daily variability of temperatures in modeling the biological processes shaping species distribution, (ii) climate data at high latitudes and elevations and (iii) climate data with high spatial resolution.     

Integrating models with data in ecology and palaeoecology: advances towards a model-data fusion approach

It is increasingly being recognized that global ecological research requires novel methods and strategies in which to combine process-based ecological models and data in cohesive, systematic ways. Model-data fusion (MDF) is an emerging area of research in ecology and palaeoecology. It provides a new quantitative approach that offers a high level of empirical constraint over model predictions based on observations using inverse modelling and data assimilation (DA) techniques. Increasing demands to integrate model and data methods in the past decade has led to MDF utilization in palaeoecology, ecology and earth system sciences. This paper reviews key features and principles of MDF and highlights different approaches with regards to DA. After providing a critical evaluation of the numerous benefits of MDF and its current applications in palaeoecology (i.e., palaeoclimatic reconstruction, palaeovegetation and palaeocarbon storage) and ecology (i.e. parameter and uncertainty estimation, model error identification, remote sensing and ecological forecasting), the paper discusses method limitations, current challenges and future research direction. In the ongoing data-rich era of today's world, MDF could become an important diagnostic and prognostic tool in which to improve our understanding of ecological processes while testing ecological theory and hypotheses and forecasting changes in ecosystem structure, function and services.     

Mathematical modelling — a management tool for aquatic ecosystems?

Mathematical modelling may serve as a rational and powerful tool in the management of complex ecosystems. However, ecosystem models are drastic simplifications of the real world. As a rule they are based on a rather incomplete and scattered knowledge of the system in question. Furthermore, ecological systems and in particular marine systems are characterised by a high degree of complexity, spatial and functional heterogeneity, nonlinearity, complex behavioural features such as adptation and self-organisation, and a considerable stochastic element. Nevertheless, if management is to be based on predictions from mathematical models — and it has to be based on some kind of model in at least a broad sense — we need an estimate of prediction accuracy in terms of the management variables and constraints. One possible approach to model uncertainty is a probabilistic interpretation of model predictions, generated by use of Monte-Carlo techniques. Fuzzy data sets and ranges are used. The resulting model response allows the derivation of measures for model credibility. Probability distributions can be computed for certain system states under (un)certain input conditions, representing the effects of insufficient data and structural uncertainty on model-based predictions. Such analysis indicates that prediction uncertainty increases, not only with the uncertainty in the data, but also with increasing distance from the empirical conditions, and with time. Present ecoystem models can be a tool for qualitative discrimination between different management alternatives, rather than a credible means for detailed quantitative predictions of system response to a wide range of input conditions.