Data_Sheet_1_Geometric Complexity and the Information-Theoretic Comparison of Functional-Response Models.pdf

The assessment of relative model performance using information criteria like AIC and BIC has become routine among functional-response studies, reflecting trends in the broader ecological literature. Such information criteria allow comparison across diverse models because they penalize each model's fit by its parametric complexity—in terms of their number of free parameters—which allows simpler models to outperform similarly fitting models of higher parametric complexity. However, criteria like AIC and BIC do not consider an additional form of model complexity, referred to as geometric complexity, which relates specifically to the mathematical form of the model. Models of equivalent parametric complexity can differ in their geometric complexity and thereby in their ability to flexibly fit data. Here we use the Fisher Information Approximation to compare, explain, and contextualize how geometric complexity varies across a large compilation of single-prey functional-response models—including prey-, ratio-, and predator-dependent formulations—reflecting varying apparent degrees and forms of non-linearity. Because a model's geometric complexity varies with the data's underlying experimental design, we also sought to determine which designs are best at leveling the playing field among functional-response models. Our analyses illustrate (1) the large differences in geometric complexity that exist among functional-response models, (2) there is no experimental design that can minimize these differences across all models, and (3) even the qualitative nature by which some models are more or less flexible than others is reversed by changes in experimental design. Failure to appreciate model flexibility in the empirical evaluation of functional-response models may therefore lead to biased inferences for predator–prey ecology, particularly at low experimental sample sizes where its impact is strongest. We conclude by discussing the statistical and epistemological challenges that model flexibility poses for the study of functional responses as it relates to the attainment of biological truth and predictive ability.

在功能响应研究中，使用诸如AIC和BIC等信息标准来评估相对模型性能已成为常规做法，这反映了生态学文献中的趋势。此类信息标准允许对各种模型进行比较，因为它们通过模型参数复杂度（即自由参数的数量）对每个模型的拟合度进行惩罚，从而使得简单模型能够超越拟合度相似但参数复杂度更高的模型。然而，AIC和BIC等标准并未考虑模型复杂性的另一种形式，即几何复杂性，它具体关联于模型的数学形式。具有等效参数复杂性的模型可能在几何复杂性上存在差异，并因此在其灵活拟合数据的能力上有所不同。在本研究中，我们利用费舍尔信息近似法对包括猎物、比例和捕食者依赖的功能响应模型在内的单猎物功能响应模型的大量汇编进行比较、解释和情境化，反映了非线性程度和形式的多样性。由于模型的几何复杂性随数据的潜在实验设计而变化，我们还寻求确定哪些设计最适合在功能响应模型之间平衡竞争。我们的分析表明：（1）功能响应模型之间存在巨大的几何复杂性差异；（2）不存在一种实验设计能够最小化所有模型之间的这些差异；（3）某些模型相对于其他模型在灵活性方面的定性特征甚至可以通过实验设计的变化而被逆转。因此，在实证评估功能响应模型时未能充分认识模型灵活性可能导致对捕食者-猎物生态学产生偏误的推论，尤其是在实验样本量较小的情况下，其影响最为显著。最后，我们讨论了模型灵活性对功能响应研究带来的统计和认识论挑战，这些挑战与实现生物学真理和预测能力相关。