# Community robustness and limiting similarity in periodic environments

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## Abstract

Temporal environmental variation has long been considered as one of the potential factors that could promote species coexistence. A question of particular interest is how the ecology of fluctuating environments relates to that of equilibrium systems. Equilibrium theory says that the more similar two species are in their modes of regulation, the less robust their coexistence will be; that is, the volume of external parameters for which all populations persist shrinks with increasing similarity. In this study, we will attempt to generalize these results to temporally varying situations and establish the precise mathematical relationship between the two. Our treatment considers unstructured populations in continuous time with periodic attractors of fixed period length, where the periodic behavior is due to external forcing. Within these conditions, our treatment is general. We provide a coherent theoretical framework for defining measures of species similarity and niche. Our main conclusion is that all factors that function to regulate population growth may be considered as separate regulating factors for each moment of time. In particular, a single resource becomes a resource continuum, along which species may segregate in the same manner as along classical resource continua. Therefore, we provide a mathematical underpinning for considering fluctuation-mediated coexistence as temporal niche segregation.

## Keywords

Regulation Niche Coexistence Fluctuations Structural stability Robustness## Notes

### Acknowledgements

We thank Peter Abrams, Zoltán Botta-Dukát, Hans Metz, Mercedes Pascual, Liz Pásztor, András Szilágyi, John Vandermeer, and the late Pál Juhász-Nagy for discussions. We would also like to thank two anonymous reviewers for their helpful suggestions. A very special thanks must go to Aaron King, who provided invaluable help with some of the technical details, and without whose patient, constructive criticisms and insights, this project would have been impossible. This research was funded by OTKA grant K81628.

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