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Existence and construction of large stable food webs

Jan O. Haerter, Namiko Mitarai, Kim Sneppen
doi: https://doi.org/10.1101/097907
Jan O. Haerter
1Center for Models of Life, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100 Copenhagen, Denmark
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  • For correspondence: haerter@nbi.dk
Namiko Mitarai
1Center for Models of Life, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100 Copenhagen, Denmark
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Kim Sneppen
1Center for Models of Life, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100 Copenhagen, Denmark
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Abstract

Ecological diversity is ubiquitous despite the restrictions imposed by competitive exclusion and apparent competition. To explain the observed richness of species in a given habitat, food web theory has explored nonlinear functional responses, self-interaction or spatial structure and dispersal — model ingredients that have proven to promote stability and diversity. We here instead return to classical Lotka-Volterra equations, where species-species interaction is characterized by a simple product and spatial restrictions are ignored. We quantify how this idealization imposes constraints on coexistence and diversity for many species. To this end, we introduce the concept of free and controlled species and use this to demonstrate how stable food webs can be constructed by sequential addition of species. When we augment the resulting network by additional weak interactions we are able to show that it is possible to construct large food webs of arbitrary connectivity. Our model thus serves as a formal starting point for the study of sustainable interaction patterns between species.

Footnotes

  • Statement of authorship: All authors developed the theory, performed the data analysis and wrote the manuscript and appendix.

  • Conflict of interest: The authors have no conflicting interests to declare.

Copyright 
The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. All rights reserved. No reuse allowed without permission.
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Posted January 03, 2017.
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Existence and construction of large stable food webs
Jan O. Haerter, Namiko Mitarai, Kim Sneppen
bioRxiv 097907; doi: https://doi.org/10.1101/097907
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Existence and construction of large stable food webs
Jan O. Haerter, Namiko Mitarai, Kim Sneppen
bioRxiv 097907; doi: https://doi.org/10.1101/097907

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