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 information criteria allow comparison across diverse models because they penalize each model...

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Autores principales:	Mark Novak, Daniel B. Stouffer
Formato:	article
Lenguaje:	EN
Publicado:	Frontiers Media S.A. 2021
Materias:	consumer-resource interactions model comparison structural complexity model flexibility nonlinearity experimental design Evolution QH359-425 Ecology QH540-549.5
Acceso en línea:	https://doaj.org/article/d22fd9889c384a079fbaa3eea3b1457b
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id	oai:doaj.org-article:d22fd9889c384a079fbaa3eea3b1457b
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spelling	oai:doaj.org-article:d22fd9889c384a079fbaa3eea3b1457b2021-11-11T09:14:03ZGeometric Complexity and the Information-Theoretic Comparison of Functional-Response Models2296-701X10.3389/fevo.2021.740362https://doaj.org/article/d22fd9889c384a079fbaa3eea3b1457b2021-11-01T00:00:00Zhttps://www.frontiersin.org/articles/10.3389/fevo.2021.740362/fullhttps://doaj.org/toc/2296-701XThe 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.Mark NovakDaniel B. StoufferFrontiers Media S.A.articleconsumer-resource interactionsmodel comparisonstructural complexitymodel flexibilitynonlinearityexperimental designEvolutionQH359-425EcologyQH540-549.5ENFrontiers in Ecology and Evolution, Vol 9 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	consumer-resource interactions model comparison structural complexity model flexibility nonlinearity experimental design Evolution QH359-425 Ecology QH540-549.5
spellingShingle	consumer-resource interactions model comparison structural complexity model flexibility nonlinearity experimental design Evolution QH359-425 Ecology QH540-549.5 Mark Novak Daniel B. Stouffer Geometric Complexity and the Information-Theoretic Comparison of Functional-Response Models
description	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.
format	article
author	Mark Novak Daniel B. Stouffer
author_facet	Mark Novak Daniel B. Stouffer
author_sort	Mark Novak
title	Geometric Complexity and the Information-Theoretic Comparison of Functional-Response Models
title_short	Geometric Complexity and the Information-Theoretic Comparison of Functional-Response Models
title_full	Geometric Complexity and the Information-Theoretic Comparison of Functional-Response Models
title_fullStr	Geometric Complexity and the Information-Theoretic Comparison of Functional-Response Models
title_full_unstemmed	Geometric Complexity and the Information-Theoretic Comparison of Functional-Response Models
title_sort	geometric complexity and the information-theoretic comparison of functional-response models
publisher	Frontiers Media S.A.
publishDate	2021
url	https://doaj.org/article/d22fd9889c384a079fbaa3eea3b1457b
work_keys_str_mv	AT marknovak geometriccomplexityandtheinformationtheoreticcomparisonoffunctionalresponsemodels AT danielbstouffer geometriccomplexityandtheinformationtheoreticcomparisonoffunctionalresponsemodels
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Geometric Complexity and the Information-Theoretic Comparison of Functional-Response Models

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