Exploring nonstationary limiting factors in species habitat relationships

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.