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.

中文翻译：

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探索物种栖息地关系中的非平稳限制因素

物种分布模型广泛用于量化和预测物种与环境的关系。物种分布建模中过去的大多数应用和方法都假设物种发生模式与环境变量之间的上下文无关且固定的关系。调查物种分布模型中的上下文依赖性和非平稳性的研究相对较少。在本文中，我们利用分布在苏格兰地理和环境梯度上的 14 个野猫杂交个体的高分辨率遥测数据，探讨了物种与环境关系中空间变化的限制因素。(1) 我们提出，非平稳限制因素将通过预测变量变异性的统计测量与这些变量的预测重要性之间的显着关联来表示。(2)我们进一步提出，观察到的大多数限制因素关系将与空间变化有关，少量与个别研究地点内环境变量的平均值有关。(3) 此外，我们预计，当环境因素的变化与其作为预测变量的重要性之间存在关系时，这种关系将是正的，因此较高的变化将与该变量作为预测变量的较高重要性相关联（遵循限制因素理论）。(4) 相反，我们提出，当环境变量的平均值与其作为预测因子的重要性之间存在关系时，这种关系将大致均匀地分布在正关系和负关系之间，因为环境变量在以下情况下可能会受到限制：在特定景观中，它们是高度丰富或高价值的，或者是稀有或低价值的，这取决于该生态变量的物种与环境关系的性质。(5) 最后，我们假设支持的限制因素关系的频率在变量组之间会有所不同，与关键环境资源直接相关的变量比那些对野猫杂交栖息地选择或产生更多间接影响的变量更可能具有限制性。觅食。我们的结果表明，许多栖息地模型可能不满足全球固定栖息地关联的假设，需要在非平稳建模范式中明确考虑规模和背景依赖性。我们发现平均值和标准差都是强有力的预测因子，可以预测该变量是否具有限制性，并且作为发生的预测因子具有不同的重要性。我们证实，当采样数据具有较高的变异性，或者当它很少或不丰富时，限制因素变得更加限制。支持的限制因素关系的频率在变量组之间有所不同，