Food Web Assembly Rules for Generalized Lotka-Volterra Equations

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Food Web Assembly Rules for Generalized Lotka-Volterra Equations. / Härter, Jan Olaf Mirko; Mitarai, Namiko; Sneppen, Kim.

In: PLoS Computational Biology, Vol. 12, No. 2, e1004727, 02.2016.

Research output: Contribution to journalJournal articleResearchpeer-review

Harvard

Härter, JOM, Mitarai, N & Sneppen, K 2016, 'Food Web Assembly Rules for Generalized Lotka-Volterra Equations', PLoS Computational Biology, vol. 12, no. 2, e1004727. https://doi.org/10.1371/journal.pcbi.1004727

APA

Härter, J. O. M., Mitarai, N., & Sneppen, K. (2016). Food Web Assembly Rules for Generalized Lotka-Volterra Equations. PLoS Computational Biology, 12(2), [e1004727]. https://doi.org/10.1371/journal.pcbi.1004727

Vancouver

Härter JOM, Mitarai N, Sneppen K. Food Web Assembly Rules for Generalized Lotka-Volterra Equations. PLoS Computational Biology. 2016 Feb;12(2). e1004727. https://doi.org/10.1371/journal.pcbi.1004727

Author

Härter, Jan Olaf Mirko ; Mitarai, Namiko ; Sneppen, Kim. / Food Web Assembly Rules for Generalized Lotka-Volterra Equations. In: PLoS Computational Biology. 2016 ; Vol. 12, No. 2.

Bibtex

@article{d0d136193e344bffa7d37cd9a2049cb3,
title = "Food Web Assembly Rules for Generalized Lotka-Volterra Equations",
abstract = "In food webs, many interacting species coexist despite the restrictions imposed by the competitive exclusion principle and apparent competition. For the generalized Lotka-Volterra equations, sustainable coexistence necessitates nonzero determinant of the interaction matrix. Here we show that this requirement is equivalent to demanding that each species be part of a non-overlapping pairing, which substantially constrains the food web structure. We demonstrate that a stable food web can always be obtained if a non-overlapping pairing exists. If it does not, the matrix rank can be used to quantify the lack of niches, corresponding to unpaired species. For the species richness at each trophic level, we derive the food web assembly rules, which specify sustainable combinations. In neighboring levels, these rules allow the higher level to avert competitive exclusion at the lower, thereby incorporating apparent competition. In agreement with data, the assembly rules predict high species numbers at intermediate levels and thinning at the top and bottom. Using comprehensive food web data, we demonstrate how omnivores or parasites with hosts at multiple trophic levels can loosen the constraints and help obtain coexistence in food webs. Hence, omnivory may be the glue that keeps communities intact even under extinction or ecological release of species.",
author = "H{\"a}rter, {Jan Olaf Mirko} and Namiko Mitarai and Kim Sneppen",
year = "2016",
month = "2",
doi = "10.1371/journal.pcbi.1004727",
language = "English",
volume = "12",
journal = "P L o S Computational Biology (Online)",
issn = "1553-7358",
publisher = "Public Library of Science",
number = "2",

}

RIS

TY - JOUR

T1 - Food Web Assembly Rules for Generalized Lotka-Volterra Equations

AU - Härter, Jan Olaf Mirko

AU - Mitarai, Namiko

AU - Sneppen, Kim

PY - 2016/2

Y1 - 2016/2

N2 - In food webs, many interacting species coexist despite the restrictions imposed by the competitive exclusion principle and apparent competition. For the generalized Lotka-Volterra equations, sustainable coexistence necessitates nonzero determinant of the interaction matrix. Here we show that this requirement is equivalent to demanding that each species be part of a non-overlapping pairing, which substantially constrains the food web structure. We demonstrate that a stable food web can always be obtained if a non-overlapping pairing exists. If it does not, the matrix rank can be used to quantify the lack of niches, corresponding to unpaired species. For the species richness at each trophic level, we derive the food web assembly rules, which specify sustainable combinations. In neighboring levels, these rules allow the higher level to avert competitive exclusion at the lower, thereby incorporating apparent competition. In agreement with data, the assembly rules predict high species numbers at intermediate levels and thinning at the top and bottom. Using comprehensive food web data, we demonstrate how omnivores or parasites with hosts at multiple trophic levels can loosen the constraints and help obtain coexistence in food webs. Hence, omnivory may be the glue that keeps communities intact even under extinction or ecological release of species.

AB - In food webs, many interacting species coexist despite the restrictions imposed by the competitive exclusion principle and apparent competition. For the generalized Lotka-Volterra equations, sustainable coexistence necessitates nonzero determinant of the interaction matrix. Here we show that this requirement is equivalent to demanding that each species be part of a non-overlapping pairing, which substantially constrains the food web structure. We demonstrate that a stable food web can always be obtained if a non-overlapping pairing exists. If it does not, the matrix rank can be used to quantify the lack of niches, corresponding to unpaired species. For the species richness at each trophic level, we derive the food web assembly rules, which specify sustainable combinations. In neighboring levels, these rules allow the higher level to avert competitive exclusion at the lower, thereby incorporating apparent competition. In agreement with data, the assembly rules predict high species numbers at intermediate levels and thinning at the top and bottom. Using comprehensive food web data, we demonstrate how omnivores or parasites with hosts at multiple trophic levels can loosen the constraints and help obtain coexistence in food webs. Hence, omnivory may be the glue that keeps communities intact even under extinction or ecological release of species.

U2 - 10.1371/journal.pcbi.1004727

DO - 10.1371/journal.pcbi.1004727

M3 - Journal article

VL - 12

JO - P L o S Computational Biology (Online)

JF - P L o S Computational Biology (Online)

SN - 1553-7358

IS - 2

M1 - e1004727

ER -

ID: 162181236