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Global structural stability and the role of cooperation in mutualistic systems

Dynamical systems on graphs allow to describe multiple phenomena from different areas of Science. In particular, many complex systems in Ecology are studied by this approach. In this paper we analize the mathematical framework for the study of the structural stability of each stationary point, feasi...

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Autores principales: Portillo, José R., Soler-Toscano, Fernando, Langa, José A.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Public Library of Science 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9017889/
https://www.ncbi.nlm.nih.gov/pubmed/35439272
http://dx.doi.org/10.1371/journal.pone.0267404
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author Portillo, José R.
Soler-Toscano, Fernando
Langa, José A.
author_facet Portillo, José R.
Soler-Toscano, Fernando
Langa, José A.
author_sort Portillo, José R.
collection PubMed
description Dynamical systems on graphs allow to describe multiple phenomena from different areas of Science. In particular, many complex systems in Ecology are studied by this approach. In this paper we analize the mathematical framework for the study of the structural stability of each stationary point, feasible or not, introducing a generalization for this concept, defined as Global Structural Stability. This approach would fit with the proper mathematical concept of structural stability, in which we find a full description of the complex dynamics on the phase space due to nonlinear dynamics. This fact can be analyzed as an informational field grounded in a global attractor whose structure can be completely characterized. These attractors are stable under perturbation and suppose the minimal structurally stable sets. We also study in detail, mathematically and computationally, the zones characterizing different levels of biodiversity in bipartite graphs describing mutualistic antagonistic systems of population dynamics. In particular, we investigate the dependence of the region of maximal biodiversity of a system on its connectivity matrix. On the other hand, as the network topology does not completely determine the robustness of the dynamics of a complex network, we study the correlation between structural stability and several graph measures. A systematic study on synthetic and biological graphs is presented, including 10 mutualistic networks of plants and seed-dispersal and 1000 random synthetic networks. We compare the role of centrality measures and modularity, concluding the importance of just cooperation strength among nodes when describing areas of maximal biodiversity. Indeed, we show that cooperation parameters are the central role for biodiversity while other measures act as secondary supporting functions.
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spelling pubmed-90178892022-04-20 Global structural stability and the role of cooperation in mutualistic systems Portillo, José R. Soler-Toscano, Fernando Langa, José A. PLoS One Research Article Dynamical systems on graphs allow to describe multiple phenomena from different areas of Science. In particular, many complex systems in Ecology are studied by this approach. In this paper we analize the mathematical framework for the study of the structural stability of each stationary point, feasible or not, introducing a generalization for this concept, defined as Global Structural Stability. This approach would fit with the proper mathematical concept of structural stability, in which we find a full description of the complex dynamics on the phase space due to nonlinear dynamics. This fact can be analyzed as an informational field grounded in a global attractor whose structure can be completely characterized. These attractors are stable under perturbation and suppose the minimal structurally stable sets. We also study in detail, mathematically and computationally, the zones characterizing different levels of biodiversity in bipartite graphs describing mutualistic antagonistic systems of population dynamics. In particular, we investigate the dependence of the region of maximal biodiversity of a system on its connectivity matrix. On the other hand, as the network topology does not completely determine the robustness of the dynamics of a complex network, we study the correlation between structural stability and several graph measures. A systematic study on synthetic and biological graphs is presented, including 10 mutualistic networks of plants and seed-dispersal and 1000 random synthetic networks. We compare the role of centrality measures and modularity, concluding the importance of just cooperation strength among nodes when describing areas of maximal biodiversity. Indeed, we show that cooperation parameters are the central role for biodiversity while other measures act as secondary supporting functions. Public Library of Science 2022-04-19 /pmc/articles/PMC9017889/ /pubmed/35439272 http://dx.doi.org/10.1371/journal.pone.0267404 Text en © 2022 Portillo et al https://creativecommons.org/licenses/by/4.0/This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
spellingShingle Research Article
Portillo, José R.
Soler-Toscano, Fernando
Langa, José A.
Global structural stability and the role of cooperation in mutualistic systems
title Global structural stability and the role of cooperation in mutualistic systems
title_full Global structural stability and the role of cooperation in mutualistic systems
title_fullStr Global structural stability and the role of cooperation in mutualistic systems
title_full_unstemmed Global structural stability and the role of cooperation in mutualistic systems
title_short Global structural stability and the role of cooperation in mutualistic systems
title_sort global structural stability and the role of cooperation in mutualistic systems
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9017889/
https://www.ncbi.nlm.nih.gov/pubmed/35439272
http://dx.doi.org/10.1371/journal.pone.0267404
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