Geometric Complexity and the Information-Theoretic Comparison of Functional-Response Models

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