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Species distribution and ecological niche models (hereafter SDMs) are popular tools with broad applications in ecology, biodiversity conservation, and environmental science. Many SDM applications require projecting models in environmental conditions non‐analog to those used for model training (extrapolation), giving predictions that may be statistically unsupported and biologically meaningless. We introduce a novel method, Shape, a model‐agnostic approach that calculates the extrapolation degree for a given projection data point by its multivariate distance to the nearest training data point. Such distances are relativized by a factor that reflects the dispersion of the training data in environmental space. Distinct from other approaches, Shape incorporates an adjustable threshold to control the binary discrimination between acceptable and unacceptable extrapolation degrees. We compared Shape's performance to five extrapolation metrics based on their ability to detect analog environmental conditions in environmental space and improve SDMs suitability predictions. To do so, we used 760 virtual species to define different modeling conditions determined by species niche tolerance, distribution equilibrium condition, sample size, and algorithm. All algorithms had trouble predicting species niches. However, we found a substantial improvement in model predictions when model projections were truncated independently of extrapolation metrics. Shape's performance was dependent on extrapolation threshold used to truncate models. Because of this versatility, our approach showed similar or better performance than the previous approaches and could better deal with all modeling conditions and algorithms. Our extrapolation metric is simple to interpret, captures the complex shapes of the data in environmental space, and can use any extrapolation threshold to define whether model predictions are retained based on the extrapolation degrees. These properties make this approach more broadly applicable than existing methods for creating and applying SDMs. We hope this method and accompanying tools support modelers to explore, detect, and reduce extrapolation errors to achieve more reliable models. Keywords: environmental novelty, extrapolation, Mahalanobis distance, model prediction, non‐analog environmental data, transferability [ABSTRACT FROM AUTHOR]

There have been numerous claims in the ecological literature that spatial autocorrelation in the residuals of ordinary least squares (OLS) regression models results in shifts in the partial coefficients, which bias the interpretation of factors influencing geographical patterns. We evaluate the validity of these claims using gridded species richness data for the birds of North America, South America, Europe, Africa, the ex-USSR, and Australia. We used richness in 110x110 km cells and environmental predictor variables to generate OLS and simultaneous autoregressive (SAR) multiple regression models for each region. Spatial correlograms of the residuals from each OLS model were then used to identify the minimum distance between cells necessary to avoid short-distance residual spatial autocorrelation in each data set. This distance was used to subsample cells to generate spatially independent data. The partial OLS coefficients estimated with the full dataset were then compared to the distributions of coefficients created with the subsamples. We found that OLS coefficients generated from data containing residual spatial autocorrelation were statistically indistinguishable from coefficients generated from the same data sets in which short-distance spatial autocorrelation was not present in all 22 coefficients tested. Consistent with the statistical literature on this subject, we conclude that coefficients estimated from OLS regression are not seriously affected by the presence of spatial autocorrelation in gridded geographical data. Further, shifts in coefficients that occurred when using SAR tended to be correlated with levels of uncertainty in the OLS coefficients. Thus, shifts in the relative importance of the predictors between OLS and SAR models are expected when small-scale patterns for these predictors create weaker and more unstable broad-scale coefficients. Our results indicate both that OLS regression is unbiased and that differences between spatial and nonspatial regression models should be interpreted with an explicit awareness of spatial scale.

Summary: Spix's Macaw Cyanopsitta spixii is one of the most endangered Neotropical Psittacidae species. Extinct in the wild in the year 2000, in June 2022 the first cohort of C. spixii was reintroduced to its original habitat. For a successful reintroduction of the species, it is necessary to examine the viability of the population against natural and external threats and the environmental requirements for success. Thus, this paper presents a "Population Viability Analysis" (PVA) for Spix's Macaw. It used the Vortex and RangeShiftR software, biological and environmental data from a bibliographic survey, and information provided by the field team responsible for the reintroduction of the species, and who work directly with the species in captivity. We found that the minimum viable population (MVP) for reintroduction of the species is 20 individuals. However, considering the impact of disease, drought, hunting, and illegal trafficking, this population can only persist if the release of individuals from captivity occurs annually over the next 20 years combined with the reforestation of natural habitat to support population growth. [ABSTRACT FROM AUTHOR]