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Aim: To propose a species distribution modelling framework and its companion \"iSDM\" R package for predicting the potential and realized distributions of invasive species within the invaded range. Location: Northern France. Methods: The non-equilibrium distribution of invasive species with the environment within the invaded range affects the environmental representativeness of species presenceabsence data collected from the field and introduces uncertainty in observed absences as these may either reflect unsuitable sites or be incidental. To address these issues, we here propose an environmental systematic sampling design to collect presence-absence data from the field and a probability index to sort and subsequently separate environmental absences (EAs: reflecting environmentally unsuitable sites) from dispersal-limited absences (DLAs: reflecting sites out of dispersal reach). We first conducted a comprehensive test based on a virtual species to evaluate the performance of our framework. Then, we applied it on different life stages of a non-native tree species (Prunus serotina Ehrh.) invasive in Europe. Results: Regarding the potential distribution, we found higher model performances for both the virtual species (true skill statistics (TSS) > 0.75) and P. serotina (TSS > 0.68) after carefully selecting absences with a low probability to be DLAs compared with classical models that incorporate both EAs and DLAs (e.g. TSS = 0.11 for P. serotina with 80% of DLAs). On the contrary, both EAs and DLAs as well as dispersal-related covariates were needed to capture the realized distribution of both the virtual species and P. serotina. Main Conclusions: Our framework helps overcoming the conceptual and methodological limitations of the disequilibrium in species' distribution models inherent to invasive species and enables managers to robustly estimate both the realized and potential distributions of invasive species. Although more relevant for modelling the distribution of non-native species, this framework can also be applied to native species.

Aim: Concerns over how global change will influence species distributions, in conjunction with increased emphasis on understanding niche dynamics in evolutionary and community contexts, highlight the growing need for robust methods to quantify niche differences between or within taxa. We propose a statistical framework to describe and compare environmental niches from occurrence and spatial environmental data. Location: Europe, North America and South America. Methods: The framework applies kernel smoothers to densities of species occurrence in gridded environmental space to calculate metrics of niche overlap and test hypotheses regarding niche conservatism. We use this framework and simulated species with pre-defined distributions and amounts of niche overlap to evaluate several ordination and species distribution modelling techniques for quantifying niche overlap. We illustrate the approach with data on two well-studied invasive species. Results: We show that niche overlap can be accurately detected with the framework when variables driving the distributions are known. The method is robust to known and previously undocumented biases related to the dependence of species occurrences on the frequency of environmental conditions that occur across geographical space. The use of a kernel smoother makes the process of moving from geographical space to multivariate environmental space independent of both sampling effort and arbitrary choice of resolution in environmental space. However, the use of ordination and species distribution model techniques for selecting, combining and weighting variables on which niche overlap is calculated provide contrasting results. Main conclusions: The framework meets the increasing need for robust methods to quantify niche differences. It is appropriate for studying niche differences between species, subspecies or intra-specific lineages that differ in their geographical distributions. Alternatively, it can be used to measure the degree to which the environmental niche of a species or intra-specific lineage has changed over time.

ContextThere have been many studies using species distribution models (SDMs) to predict shifts in species distributions due to environmental changes, but few consider effects of data quantity, data quality, or species response shape. Modeling studies using field-sampled data may be impaired to an unknown degree by lack of knowledge on species’ true relationships with environmental changes.ObjectivesUsing simulations with known relationships we assess model predictions, and investigate which models are more sensitive to sample size, detection limit, or species response shape issues when different SDMs are used for predicting species distribution shifts under environmental changes.MethodsWe simulated 16 species response relationships to ecological gradients differing in response shape (skewness and kurtosis) using a generalized β-function. Populations were randomly sampled at different sample sizes and detection limits. Linear discriminant analysis (LDA), multiple logistic regression (MLR), generalized additive models (GAM), boosted regression trees (BRT), random forests (RF), artificial neural networks (ANN), and maximum entropy models (MaxEnt) were developed on sampled datasets and compared for predicting species occurrence. We used these SDMs to predict distribution patterns for virtual species with different response shapes across a real landscape of varying heterogeneity in environmental conditions, and compared them with the probability of occurrence generated by the β-function.ResultsGAM and BRT were sensitive to both sample size and detection limit changes; RF was more affected by detection limit; ANN and MaxEnt were more affected by sample size; LDA and MLR were sensitive to species response shape changes.ConclusionsOverall, if little is known about species response to environmental changes, ANN is recommended especially for large sample size. If a focal species is likely to occur only in a narrow range of environmental conditions, GAM and BRT are preferred for large good-quality datasets, and GAM tends to perform slightly better under varied data conditions; RF is recommended for limited amounts of good-quality data. If a focal species is likely to be present in a wide range of environmental conditions, MaxEnt is preferred but caution should be taken for small sample size. If the goal is to identify potential distributions of invasive or endangered species but data quantity and quality are very limited, LDA and MLR are recommended as they generally provide reasonable model sensitivity.

Aim: The assumption of equilibrium between organisms and their environment is a standard working postulate in species distribution models (SDMs). However, this assumption is typically violated in models of biological invasions where range expansions are highly constrained by dispersal and colonization processes. Here, we examined how stage of invasion affects the extent to which occurrence data represent the ecological niche of organisms and, in turn, influences spatial prediction of species' potential distributions. Location: Six ecoregions in western Oregon, USA. Methods: We compiled occurrence data from 697 field plots collected over a 9-year period (2001-09) of monitoring the spread of invasive forest pathogen Phytophthora ramorum. Using these data, we applied ecological-niche factor analysis to calibrate models of potential distribution across different years of colonization. We accounted for natural variation and uncertainties in model evaluation by further investigating three hypothetical scenarios of varying equilibrium in a simulated virtual species, for which the 'true' potential distribution was known. Results: We confirm our hypothesis that SDMs calibrated in early stages of invasion are less accurate than models calibrated under scenarios closer to equilibrium. SDMs that are developed in early stages of invasion tend to underpredict the potential range compared to models that are built in later stages of invasion. Main conclusions: A full environmental niche of invasive species cannot be effectively captured with data from a realized distribution that is restricted by processes preventing full occupancy of suitable habitats. If SDMs are to be used effectively in conservation and management, stage of invasion needs to be considered to avoid underestimation of habitats at risk of invasion.

Sets of presence records used to model species’ distributions typically consist of observations collected opportunistically rather than systematically. As a result, sampling probability is geographically uneven, which may confound the model's characterization of the species’ distribution. Modelers frequently address sampling bias by manipulating training data: either subsampling presence data or creating a similar spatial bias in non‐presence background data. We tested a new method, which we call ‘background thickening’, in the latter category. Background thickening entails concentrating background locations around presence locations in proportion to presence location density. We compared background thickening to two established sampling bias correction methods – target group background selection and presence thinning – using simulated data and data from a case study. In the case study, background thickening and presence thinning performed similarly well, both producing better model discrimination than target group background selection, and better model calibration than models without correction. In the simulation, background thickening performed better than presence thinning when the number of simulated presence locations was low, and vice versa. We discuss drawbacks to target group background selection, why background thickening and presence thinning are conservative but robust sampling bias correction methods, and why background thickening is better than presence thinning for small sample sizes. Particularly, background thickening is advantageous for treating sampling bias when data are scarce because it avoids discarding presence records.

Global change driven by human activities is causing profound shifts in species distributions. Understanding the mechanisms that influence these dynamics is crucial for biodiversity management. Several mechanistic, spatially explicit models have been proposed to address this issue, but they do not cover the full range of potential functionalities. We present a new open‐source R package called rangr, which integrates population dynamics and dispersal into a mechanistic virtual species simulator. The package can be used to study the effects of environmental change on population growth and range shifts. It extends the capabilities of previously available simulators by allowing simple and straightforward definition of population dynamics (including positive density dependence), extensive possibilities for defining dispersal kernels and the ability to generate virtual ecologist data. We showcased rangr functionality by simulating the invasion of the collared dove (Streptopelia decaocto). First, we demonstrated how to set up a simulation with different dispersal kernels by investigating the role of long‐distance dispersal events on colonisation outcome. Second, we showed the use of rangr to assess the potential of an Allee effect to impede biological invasion. Finally, we used the virtual ecologist framework to determine the timeframe required to detect the spread of an invasive species. The rangr package, which comes with extensive documentation and vignettes, is easy to set up, flexible, fast, fully configurable and capable of emulating the observation process. These features make rangr particularly well suited to generating data that replicate existing wildlife monitoring programmes.

A key assumption in species distribution modeling (SDM) with presence‐background (PB) methods is that sampling of occurrence localities is unbiased and that any sampling bias is proportional to the background distribution of environmental covariates. This assumption is rarely met when SDM practitioners rely on federated museum records from natural history collections for geo‐located occurrences due to inherent sampling bias found in these collections. We use a simulation approach to explore the effectiveness of three methods developed to account for sampling bias in SDM with PB frameworks. Two of the methods rely on careful filtering of observation data—geographic thinning (G‐Filter) and environmental thinning (E‐Filter)—while a third, FactorBiasOut, creates selection weights for background data to bias locations toward areas where the observation dataset was sampled. While these methods have been assessed previously, evaluation has emphasized spatial predictions of habitat potential. Here, we dig deeper into the effectiveness of these methods by exploring how sampling bias not only affects predictions of habitat potential, but also our understanding of niche characteristics such as which explanatory variables and response curves best represent species–environment relationships. We simulate 100 virtual species ranging from generalist to specialist in their habitat preferences and introduce geographic and environmental bias at three intensity levels to measure the effectiveness of each correction method to (1) predict true probability of occurrence across a study area, (2) recover true species–environment relationships, and (3) identify true explanatory variables. We find that the FactorBiasOut most often showed the greatest improvement in recreating known distributions but did no better at correctly identifying environmental covariates or recreating species–environment relationships than G‐Filter or E‐Filter methods. Narrow niche species are most problematic for biased calibration datasets, such that correction methods can, in some cases, make predictions worse.

Aim Presence-only datasets represent an important source of information on species' distributions. Collections of presence-only data, however, are often spatially biased, particularly along roads and near urban populations. These biases can lead to inaccurate inferences and predicted distributions. We demonstrate a new approach of accounting for effort bias in presence-only data by explicitly incorporating sample biases in species distribution modelling. Location Alberta, Canada. Methods First, we used logistic regression to model sampling effort of recorded rare vascular plants, bryophytes and butterflies in Alberta. Second, we simulated presence/absence data for nine 'virtual' species based on three relative occurrence thresholds – common, rare and very rare – for each taxonomic group. We sampled these virtual species using our bias model to represent typical sampling effort characteristic of presence-only datasets. We then modelled the distributions of these virtual species using logistic regression and attempted to recover their original simulated distributions using a sample weighting term (prior weight) estimated as the inverse of probability of sampling. Bias-adjusted model estimates were compared to those obtained from random samples and biased samples without adjustment. We also compared prior-weight adjustment to bias-file and target-group background approaches in Maxent. Results Sample weighting recovered regression coefficients and mapped predictions estimated from unbiased presence-only data and improved model predictive accuracy as evaluated by regression and correlation coefficients, sensitivity and specificity. Similar model improvements were achieved using the Maxent bias-file method, but results were inconsistent for the target-group background approach. Main conclusions These results suggest that sample weighting can be used to account for spatially biased presence-only datasets in species distribution modelling. The framework presented is potentially widely applicable due to availability of online biodiversity databases and the flexibility of the approach.

Sampling bias is an inherent problem in widely available biodiversity data, undermining the robustness of correlative species distribution models (SDMs). To some extent, subsampling occurrence data can account for uneven sampling efforts; yet, conventional approaches subsample in geographical space, while subsampling in environmental space remains underexplored. Here, we compared the effectiveness of subsampling methods that correct sampling bias either in geographical space (spatial gridding, spatial distance thinning) or directly in environmental space (environmental gridding), including two novel approaches introduced here: environmental clustering and environmental distance thinning. We hypothesised that environmental subsampling methods would be more effective in improving SDM performance across its three primary uses: explaining, predicting, and projecting. Using a virtual ecologist framework, we assessed SDM performance against four evaluation tests: replicating true species–environment response curves, predicting within the sampling region via internal cross‐validation and evaluation against independent data, and projecting outside the sampling region. Our findings demonstrate that environmental subsampling methods, especially environmental clustering and environmental distance thinning, outperformed other methods in yielding robust SDMs in almost all evaluation tests. Interestingly, cross‐validation favoured SDMs with no sampling bias correction, highlighting the inability of cross‐validation to identify unbiased models. Our findings emphasise a critical conceptual disconnect: SDMs appearing to perform well in predicting species' distributions may not reliably estimate species–environment relationships, nor transfer predictions onto novel environments. Environmental subsampling methods are reliable approaches for all uses, but are particularly suited for explaining species' niches and transferring predictions across space and/or time, such as when anticipating species' responses to climate change or assessing the risk of biological invasions. Conversely, geographic subsampling methods may suffice for predicting species' distributions within their current environmental context, as required in conservation planning. Our study firmly establishes the critical importance of correcting environmental sampling bias, while also providing reliable solutions for supporting biodiversity conservation in an ever‐changing world.

The use of virtual species to test species distribution models is important for understanding how aspects of the model development process influence model performance. Typically, virtual species are simulated by defining their niche as a function of environmental variables and simulating occurrence probabilistically via Bernoulli trials. This approach ignores endogenous processes known to drive species distribution such as dispersal and population dynamics. To understand whether these processes are important for simulating virtual species we compared the probabilistic simulation approach to those incorporating endogenous processes. This comparison was done by evaluating changes in the relationship between species occurrence and habitat suitability over a number of landscapes with varying spatial structure. We found that the combined effects of population dynamics and dispersal meant the probability of occurrence of a single cell was not only dependent on habitat suitability, but also the number of occupied cells nearby. This resulted in a dependence on the size of clusters of high suitability cells (analogous to patch size) to maintain populations, increased residual spatial autocorrelation and non‐stationarity of the species response between landscapes. These data characteristics are attributes of real species distribution data and are not present in probabilistic simulations. Researchers using virtual species should consider the importance of these characteristics to their study objectives to decide whether the inclusion of endogenous processes is necessary.