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

Abstract

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.

Ratio-Dependence in Predator-Prey Systems as an Edge and Basic Minimal Model of Predator Interference

“…Monod was working with low concentrations of bacteria, while Contois experimented with high concentrations (Arditi and Ginzburg, 2012). Nevertheless, compared to AGC, HVH, and BDA trophic functions, universal GRD functions do not demonstrate far superior performance and flexibility in fitting the observed data (Tyutyunov et al, 2010;Prokopenko et al, 2017;Novak and Stouffer, 2021b). Accordingly, simpler models provide just as good approximations to reality.…”

Food web functional responses

“…These were theoretical works, and there has been little subsequent experimental exploration of functional responses in two or more prey systems involving diet choice based on handling/processing time. As a result, major reviews of empirical works have concentrated on studies of functional responses in single resource systems: this includes Jeschke et al (2002Jeschke et al ( , 2004, DeLong (2021), and Novak and Stouffer (2021b). The last of these (DeLong, 2021) has a chapter (Chapter 5) on "multispecies functional responses" and one (Chapter 7) on "optimal foraging".…”

“…Ginzburg and Damuth (2022) have recently argued for an expanded ratio dependence in which the denominator (predator abundance) can be raised to a positive power other than 1. Various reviews have shown significant differences between the results of empirical measurements of predator effects and the original ratio-dependent models (Skalski and Gilliam, 2001;Novak and Stouffer, 2021b). An early critique of ratio dependence pointed out that there were many causes of predator-dependence, virtually none of which led to ratio dependence (Abrams, 1994).…”

“…No predator species is characterized by an exactly ratio dependent response; this was one of many points of agreement in Abrams and Ginzburg (2000). There are some experimental studies where generalized ratio dependence with a predator exponent of 1 fits the data better than other exponents (Novak and Stouffer, 2021b), but there are likely many models that are more consistent with the underlying mechanisms of predator dependence that would provide a better fit in these cases. The goal of ecological theory is to understand natural systems; how they change with environmental shifts and how they evolve over time.…”

“…Current usage of the term "functional response" frequently assumes that the response is a characteristic of a given pair of predator and prey species. This assumption underlies the many attempts to determine the "best" expression for describing such a response (Jeschke et al, 2002(Jeschke et al, , 2004DeLong, 2021;Novak and Stouffer, 2021b). However, several recent experiments have shown that functional response shapes in the simplest case of an isolated predator individual consuming different abundances of a single prey type can be greatly altered by the spatial and physical properties of the experimental environment (Uiterwaal and DeLong, 2018;Juliano et al, 2022).…”