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• We compare the performance of predictive models for wildcat hybrid occurrence based on (1) global pooled data across individuals, (2) geographically weighted aggregation of individual models, (3) ecologically weighted aggregation of individual models, and (4) combinations of global, geographical and ecological weighting. • We developed predictive models both using GLM and random forest machine learning to compare the performance of these differing algorithms and how they compare in stationary and nonstationary analyses. • We validated the predicted models in four different ways. • Our results show that validation using hold-out data from the individuals used to train the model provides highly biased assessment of true model performance in other locations, with random forest in particular appearing to perform exceptionally (and inaccurately) well when validated by data from the same individuals used to train the models. • Each of these three independent validation data sets gave a different result in terms of the best overall model. • The best overall model produced for potential wildcat occurrence and habitat suitability was obtained by an ensemble average of the global generalized linear model (GLM) and random forest models with the ecologically weighted GLM and random forest models. Species distribution modeling has emerged as a foundational method to predict occurrence and suitability of species in relation to environmental variables to advance ecological understanding and guide conservation planning. Recent research, however, has shown that species-environmental relationships and habitat model predictions are often nonstationary in space, time and ecological context. This calls into question modeling approaches that assume a global, stationary ecological realized niche and use predictive modeling to describe it. This paper explores this issue by comparing the performance of predictive models for wildcat hybrid occurrence based on (1) global pooled data across individuals, (2) geographically weighted aggregation of individual models, (3) ecologically weighted aggregation of individual models, and (4) combinations of global, geographical and ecological weighting. Our study system included GPS telemetry data from 14 individual wildcat hybrids across Scotland. We developed predictive models both using Generalized Linear Models (GLM) and Random Forest machine learning to compare the performance of these differing algorithms and how they compare in stationary and nonstationary analyses. We validated the predicted models in four different ways. First, we used independent hold-out data from the 14 collared wildcat hybrids. Second, we used data from 8 additional GPS collared wildcat hybrids from a previous study that were not included in the training sample. Third, we used sightings data sent in by the public and researchers and validated by expert opinion. Fourth, we used data collected by camera trap surveys between 2012 – 2021 from various sources to produce a combined camera trap dataset showing where wildcats and wildcat hybrids had been detected. Our results show that validation using hold-out data from the individuals used to train the model provides highly biased assessment of true model performance in other locations, with Random Forest in particular appearing to perform exceptionally (and inaccurately) well when validated by data from the same individuals used to train the models. Very different results were obtained when the models were validated using independent data from the three other sources. Each of these three independent validation data sets gave a different result in terms of the best overall model. The average of independent validation across these three validation datasets suggested that the best overall model produced for potential wildcat occurrence and habitat suitability was obtained by an ensemble average of the global Generalized Linear Model (GLM) and Random Forest models with the ecologically weighted GLM and Random Forest models. This suggests that the debate over whether which of GLM vs machine learning approaches is superior or whether global vs aggregated nonstationary modeling is superior may be a false choice. The results presented here show that the best prediction applies a combination of all of these approaches in an ensemble modeling framework. [ABSTRACT FROM AUTHOR]

• There has been little research focused on how habitat selection may depend on individual variation among organisms, geographical location and ecological context of that location and little is known about the extent and drivers of heterogeneity of scale dependence among individuals of a species inhabiting different ecological contexts. • Two of the most important factors for interpreting habitat relationships models include: (1) the relative importance of variables in the model and (2) the spatial scale at which each variable has the largest influence. • Based on the existing evidence we hypothesized that landcover variables will generally be the most important predictors, followed by topography, then soil type (which influence both vegetation and prey), normalized difference vegetation index (NDVI) as an indicator of total vegetation density and perhaps a proxy for prey density, vegetation cover and rabbit abundance. • We also expected a priori that there would be consistent patterns of scale dependence across individual wildcat hybrid models related to different variable groups. We expected topographical features to be selected at broad scales, as they influence broad-scale climatic and ecological conditions. • We also expected that land cover classes and vegetation cover density to be selected at relatively broad scales given past research showing land cover generally influences habitat selection at relatively broad scales. We expected NDVI and soil type to be selected at finer scales, as their variation influences the distribution of resources and limiting conditions within landscapes. • Finally, we expected that rabbit abundance and linear features would affect wildcat hybrid occurrence at the finest scales, given these are resources and conditions that vary over short distances and strongly influence wildcat and wildcat hybrid behavior and habitat use. • Our results were consistent with the hypothesis that there may be consistency regarding which variables or variable groups are most important as predictors of wildcat hybrid occurrence in scotland. • Based on previous research we expected that there would be consistent patterns of scale dependence across individual wildcat hybrid models related to different variable groups. • Our results identify a clear and consistent trend of increasing frequency of inclusion of variables at increasingly broad scales. This is a linear trend in frequency of variables retained increasing as the scale increased. This suggests a consistent and monotonic pattern of more frequent retention of variables at increasingly broad scales. Understanding the scale dependence of species-habitat relationships is an important area of research in species distribution modeling. There has been little research focused on how habitat selection may depend on individual variation among organisms, geographical location and ecological context of that location. Furthermore, little is known about the extent and drivers of heterogeneity of scale dependence among individuals of a species inhabiting different ecological contexts, and few studies have compared scale dependence and variable importance in a spatially replicated framework. Two of the most important factors for interpreting habitat relationships models include: (1) the relative importance of variables in the model and (2) the spatial scale at which each variable has the largest influence. Based on the existing evidence we hypothesize a priori that landcover variables will generally be the most important predictors, followed by topography, then soil type (which influence both vegetation and prey), Normalized Difference Vegetation Index (NDVI) as an indicator of total vegetation density and perhaps a proxy for prey density, vegetation cover and rabbit abundance. We also expected a priori that there would be consistent patterns of scale dependence across individual wildcat hybrid models related to different variable groups. We expected topographical features to be selected at broad scales, as they influence broad-scale climatic and ecological conditions. We also expected that land cover classes and vegetation cover density to be selected at relatively broad scales given past research showing land cover generally influences habitat selection at relatively broad scales. We expected NDVI and soil type to be selected at finer scales, as their variation influences the distribution of resources and limiting conditions within landscapes. Finally, we expected that rabbit abundance and linear features would affect wildcat hybrid occurrence at the finest scales, given these are resources and conditions that vary over short distances and strongly influence wildcat and wildcat hybrid behavior and habitat use. Our results were consistent with the hypothesis that there may be consistency regarding which variables or variable groups are most important as predictors of wildcat hybrid occurrence in Scotland. Based on previous research we expected that there would be consistent patterns of scale dependence across individual wildcat hybrid models related to different variable groups. Finally, our results identify a clear and consistent trend of increasing frequency of inclusion of variables at increasingly broad scales. This is a linear trend in frequency of variables retained increasing as the scale increased. This suggests a consistent and monotonic pattern of more frequent retention of variables at increasingly broad scales. [ABSTRACT FROM AUTHOR]

• Nonstationarity and inter-individual differences in realized habitat niches and species-environment relationships may invalidate assumptions of species distribution modeling. • We assessed how differences in habitat associations were related to (1) geographic distance, (2) multivariate ecological distance, (3) difference in degree of hybridization and (4) difference in sex (male vs female). • We found that the individual models were exceptionally effective in predicting the habitat use and occurrence of the particular individuals on whose data they were trained, but were generally highly divergent and not transferable among individuals. • Ecological distance was supported as being inversely related to ability of a model from one individual to predict occurrence of another individual. • Nonstationary limiting factors in the home ranges of individual wildcat hybrids determine the habitat they select, their expressed species-environment relationship and the description of their realized habitat niches. Little is known about the factors that drive nonstationarity and inter-individual differences in realized habitat niches and species-environment relationships. We explored this topic by developing individual habitat selection models for 14 wildcat hybrids distributed across Scotland, and assessed how differences in their predicted probabilities of occurrence were related to factors including (1) geographic distance, (2) multivariate ecological distance, (3) difference in degree of hybridization and (4) difference in sex (male vs female). We found that the individual models were exceptionally effective in predicting the habitat use and occurrence of the particular individuals on whose data they were trained, but were generally highly divergent and not transferable among individuals. We conducted a reciprocal validation approach where we calculated the AUC for each individual model, predicting the occurrence patterns of the 13 other individuals. We then fit regression and nonparametric splines to evaluate the impacts of geographical distance, ecological distance, hybridization distance and difference in the sex of individuals in the ability of individual wildcat hybrid habitat models to predict the occurrences of other individuals. We found that, of the four factors assessed, ecological distance was supported as being inversely related to ability of a model from one individual to predict occurrence of another individual. The other three factors were not strongly related to differences in reciprocal model predictive ability. This suggests that ecological differences where individual wildcat hybrids reside drive differences in their habitat selection, but that geographical distance, degree of genetic hybridization and difference in the sex of individuals are not consistently associated with differences in model prediction or reciprocal validation performance. These results highlight the effect of ecological limiting factors, and the importance of nonstationary limiting factors in determining the habitat they select, their expressed species-environment relationship and the description of their realized habitat niches. [ABSTRACT FROM AUTHOR]

• We explore spatially varying limiting factors in species-environment relationships using high resolution telemetry data from 14 individual wildcat hybrids distributed across geographical and environmental gradients in Scotland. • We proposed five hypotheses for how nonstationary limiting factors related to the strength of predictor variable effect size. • Our results show that assumptions of global, stationary habitat associations are likely not met in many habitat models. • We found that there were strong relationships between nonstationarity and spatially varying limiting factors. • Future habitat modeling research should explicitly consider scale and context dependence in a nonstationary modeling paradigm. Species distribution modeling is widely used to quantify and predict species-environment relationships. Most past applications and methods in species distribution modeling assume context independent and stationary relationships between patterns of species occurrence and environmental variables. There has been relatively little research investigating context dependence and nonstationarity in species distribution modeling. In this paper we explore spatially varying limiting factors in species-environment relationships using high resolution telemetry data from 14 individual wildcat hybrids distributed across geographical and environmental gradients in Scotland. (1) We proposed that nonstationary limiting factors would be indicated by significant association between statistical measures of variability of predictors and the predictive importance of those variables. (2) We further proposed that most of the limiting factor relationships observed would be related to spatial variation and a lesser amount to mean value of environmental variables within individual study sites. (3) Additionally, we anticipated that when there was a relationship between variation of an environmental factor and its importance as a predictor this relationship would be positive, such that higher variation would be associated with higher importance of the variable as a predictor (following the theory of limiting factors). (4) Conversely, we proposed that when there was a relationship between the mean value of an environmental variable and its importance as a predictor this relationship would be roughly evenly split between positive and negative relationships, given that environmental variables could become limiting either when they are highly abundant or high value, or when they are rare or low value in a particular landscape, depending on the nature of the species-environment relationship for that ecological variable. (5) Finally, we hypothesized that the frequency of supported limiting factor relationships would differ among variable groups, with variables that were directly related to key environmental resources more likely to be limiting than those that would have more indirect impacts on wildcat hybrid habitat selection or foraging. Our results show that assumptions of global, stationary habitat associations are likely not met in many habitat models, requiring explicit consideration of scale and context dependence in a nonstationary modeling paradigm. We found that both the mean value and the standard deviation are strong predictors of whether that variable will be limiting and differentially important as a predictor of occurrence. We confirmed that limiting factors become more limiting when it has higher variability across the sampled data, or when it is rare or not abundant. The frequency of supported limiting factor relationships differed among variable groups, with variables that were directly related to environmental resources likely to be essential for wildcat hybrid ecology more likely to be limiting than those that would have more indirect impacts on wildcat hybrid habitat selection or foraging. [ABSTRACT FROM AUTHOR]