Logistic regression is a commonly used building block in ecological modeling, but its additive structure among environmental predictors often assumes compensatory relationships between predictors, which can lead to problematic results. In reality, the distribution of species is often determined by the least-favored factor, according to von Liebig's Law of the Minimum, which is not addressed in modeling. To address this issue, we introduced the min-linear logistic regression model, which has a built-in minimum structure of competing factors. In our empirical analysis of the distribution of Asiatic black bears ($\textit{Ursus thibetanus}$), we found that the min-linear model performs well compared to other methods and has several advantages. By using the model, we were able to identify ecologically meaningful limiting factors on bear distribution across the survey area. The model's inherent simplicity and interpretability make it a promising tool for extending into other widely used ecological models.

翻译：逻辑回归是生态建模中常用的构建模块，但其环境预测变量间的加性结构通常假设预测因子之间存在补偿关系，这可能导致有问题的结果。实际上，根据冯·李比希最小因子定律，物种的分布往往由最不利因子决定，而这一原则在建模中未被考量。为解决此问题，我们引入了具有竞争因子最小结构的内嵌式最小线性逻辑回归模型。在对亚洲黑熊（$\textit{Ursus thibetanus}$）分布的实证分析中，我们发现该模型相较于其他方法表现优异且具有多项优势。通过该模型，我们成功识别了调查区域内影响黑熊分布的具有生态意义的限制因子。该模型固有的简洁性与可解释性，使其成为拓展至其他广泛应用的生态模型中的有前景工具。