# Functional responses and predator–prey models: a critique of ratio dependence

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## Abstract

Arditi and Ginzburg (2012) propose ordinary differential equations (ODEs) with ratio-dependent functional responses as the new null model for predation, based on their earlier work on ratio-dependent food chains and a number of functional response measurements. Here, I discuss some of their claims, arguing for a flexible and problem-driven approach to predator–prey modeling. Models to understand population cycles and models to predict the effect of basal enrichment on food chains need not be the same. While ratio-dependent functional responses in ODE models might sometimes be useful as limit cases for food chains, they are not intrinsically more useful than prey-dependent models to understand the effect of a given predator on prey population dynamics—and sometimes less useful, given the small temporal scales considered in many models. “Instantism” is showed to be an invalid criticism when ODEs are interpreted as describing average trajectories of stochastic birth–death processes. Moreover, other modeling frameworks with strong ties to time series statistics, such as stochastic difference equations, should be promoted to improve the feedback loop between field and theoretical research. The main problems of current trophic ecology do not lie in a wrong null model, as ecologists have already several at their disposal. The loose connection of ODE models with empirical data and spatial/temporal scaling up of empirical measurements constitute more serious challenges to our understanding of trophic interactions and their consequences on ecosystem functioning.

## Keywords

Consumer dependence Autoregressive models Kill rate Predation rate Trophic communities Exploitation ecosystems## Notes

### Acknowledgments

For exchanges on the concepts discussed here, I thank D. J. Murrell, J.A. Henden, J. Matthiopoulos, L. New, S. Redpath, G. Gauthier, and N.G. Yoccoz. D.J. Murrell provided detailed comments on a previous version. Two referees and the editor made constructive suggestions that improved the manuscript. Thanks to the participants of the ResearchGate Stochastic Processes list for help with model formulation in Fig. 2.

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