Dataset.
About ghost transients in spatial continuous media: Supplementary material
Digital.CSIC. Repositorio Institucional del CSIC
oai:digital.csic.es:10261/347732
Digital.CSIC. Repositorio Institucional del CSIC
- Calsina, Àngel
- Cuadrado, Sílvia
- Vidiella, Blai
- Sardanyés, Josep
List of Figures: S1 Graph of the half-period of the center (p. 2).-- S2 Time series for different diffusion values and distances to the bifurcation point (p. 3).-- S3 Transient times for initial populations with growing spatial regions below the ghost bottleneck (p. 4).-- S4 Effect of the different initial spatial distribution of cooperators on extinction times (p. 5).-- S5 Time to extinction from an initial spatial distribution with random gaps depending on gap frequency close to the bifurcation (p. 6).-- S6 Time to extinction from random gap distribution far from the bifurcation (p. 7).-- S7 Phase portraits for different values of diffusion before the bifurcation in the two-patch model (p. 8).-- S8 Phase portraits depending on diffusion after the bifurcation in the two-patch model (p. 9).-- S9 Times to extinction dependence on initial conditions in the two-patch model: homogeneous and heterogeneous extinctions (p. 10).-- S10 Comparison of ghost phenomena depending on diffusion in the two-patch model (p. 11)., No
DOI: http://hdl.handle.net/10261/347732
Digital.CSIC. Repositorio Institucional del CSIC
oai:digital.csic.es:10261/347732
HANDLE: http://hdl.handle.net/10261/347732
Digital.CSIC. Repositorio Institucional del CSIC
oai:digital.csic.es:10261/347732
Ver en: http://hdl.handle.net/10261/347732
Digital.CSIC. Repositorio Institucional del CSIC
oai:digital.csic.es:10261/347732
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2 Documentos relacionados
2 Documentos relacionados
Dipòsit Digital de Documents de la UAB
oai:ddd.uab.cat:283133
Artículo científico (article). 2023
ABOUT GHOST TRANSIENTS IN SPATIAL CONTINUOUS MEDIA
Dipòsit Digital de Documents de la UAB
- Calsina i Ballesta, Àngel|||0000-0003-2585-0039
- Cuadrado Gavilán, Sílvia|||0000-0003-2051-2030
- Vidiella, Blai|||0000-0002-4819-7047
- Sardanyés, Josep|||0000-0001-7225-5158
The impact of space on ecosystem dynamics has been a matter of debate since the dawn of theoretical ecology. Several studies have revealed that space usually involves an increase in transients' times, promoting the so-called supertransients. However, the effect of space and diffusion in transients close to bifurcations has not been thoroughly investigated. In non-spatial deterministic models such as those given by ordinary differential equations transients become extremely long in the vicinity of bifurcations. Specifically, for the saddle-node (s-n) bifurcation the time delay, τ, follows τ∼|μ−μ|; μ and μ being the bifurcation parameter and the bifurcation value, respectively. Such long transients are labeled delayed transitions and are governed by the so-called ghosts. Here, we explore a simple model with intra-specific cooperation (autocatalysis) and habitat loss undergoing a s-n bifurcation using a partial differential equations (PDE) approach. We focus on the effects of diffusion in the ghost extinction transients right after the tipping point found at a critical habitat loss threshold. Our results show that the bifurcation value does not depend on diffusion. Despite transients' length typically increase close to the bifurcation, we have observed that at extreme values of diffusion, both small and large, extinction times remain long and close to the well-mixed results. However, ghosts lose influence at intermediate diffusion rates, leading to a dramatic reduction of transients' length. These results, which strongly depend on the initial size of the population, are shown to remain robust for different initial spatial distributions of cooperators. A simple two-patch metapopulation model gathering the main results obtained from the PDEs approach is also introduced and discussed. Finally, we provide analytical results of the passage times and the scaling for the model under study transformed into a normal form. Our findings are discussed within the framework of ecological transients.
Digital.CSIC. Repositorio Institucional del CSIC
oai:digital.csic.es:10261/347729
Artículo científico (article). 2023
ABOUT GHOST TRANSIENTS IN SPATIAL CONTINUOUS MEDIA
Digital.CSIC. Repositorio Institucional del CSIC
- Calsina, Àngel
- Cuadrado, Sílvia
- Vidiella, Blai
- Sardanyés, Josep
© 2022 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)., The impact of space on ecosystem dynamics has been a matter of debate since the dawn of theoretical ecology. Several studies have revealed that space usually involves an increase in transients’ times, promoting the socalled supertransients. However, the effect of space and diffusion in transients close to bifurcations has not been thoroughly investigated. In non-spatial deterministic models such as those given by ordinary differential equations transients become extremely long in the vicinity of bifurcations. Specifically, for the saddle–node(s–n) bifurcation the time delay, 𝜏, follows 𝜏 ∼ |𝜇 − 𝜇𝑐|−1∕2; 𝜇 and 𝜇𝑐 being the bifurcation parameter and the bifurcation value, respectively. Such long transients are labeled delayed transitions and are governed by the so-called ghosts. Here, we explore a simple model with intra-specific cooperation (autocatalysis) and habitat loss undergoing a s–n bifurcation using a partial differential equations (PDE) approach. We focus on the effects of diffusion in the ghost extinction transients right after the tipping point found at a critical habitat loss threshold. Our results show that the bifurcation value does not depend on diffusion. Despite transients’ length typically increase close to the bifurcation, we have observed that at extreme values of diffusion, both small and large, extinction times remain long and close to the well-mixed results. However, ghosts lose influence at intermediate diffusion rates, leading to a dramatic reduction of transients’ length. These results, which strongly depend on the initial size of the population, are shown to remain robust for different initial spatial distributions of cooperators. A simple two-patch metapopulation model gathering the main results obtained from the PDEs approach is also introduced and discussed. Finally, we provide analytical results of the passage times and the scaling for the model under study transformed into a normal form. Our findings are discussed within the framework of ecological transients., This research has been funded through the 2020–2021 Biodiversa and Water JPI joint call under the BiodivRestore ERA-NET Cofund (GA N°101003777) project MPA4Sustainability with funding organizations: Innovation Fund Denmark (IFD), Agence Nationale de la Recherche (ANR), Fundação para a Ciência e a Tecnologia (FCT), Swedish Environmental Protection Agency (SEPA) and grant PCI2022-132926 funded by MCIN/AEI/10.13039/501100011033 and by the European Union NextGenerationEU/PRTR (J.S. and B.V). This work is also supported by the Spanish State Research Agency, through the Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D (CEX2020-001084-M). We thank CERCA Programme/Generalitat de Catalunya for institutional support. J.S. has been also supported by the Ramón y Cajal grant RYC-2017-22243 funded by MCIN/AEI/10.13039/501100011033 “FSE invests in your future”, as well as by grant PID2021-127896OB-I00 funded by MCIN/AEI/10.13039/501100011033 “ERDF A way of making Europe”. B.V. has been also funded by grant RYC-2017-22243, whose PI is J.S. A.C. and S.C. have been supported by grants MTM2017-84214-C2-2-P, RED2018-102650-T, and PID2021-123733NB-I00 funded by MCIN/AEI/10.13039/501100011033 “ERDF A way of making Europe”., With funding from the Spanish government through the ‘María de Maeztu Unit of Excelence’ accreditation (CEX2020-001084-M)., Peer reviewed
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Digital.CSIC. Repositorio Institucional del CSIC
oai:digital.csic.es:10261/347732
Dataset. 2023
ABOUT GHOST TRANSIENTS IN SPATIAL CONTINUOUS MEDIA: SUPPLEMENTARY MATERIAL
Digital.CSIC. Repositorio Institucional del CSIC
- Calsina, Àngel
- Cuadrado, Sílvia
- Vidiella, Blai
- Sardanyés, Josep
List of Figures: S1 Graph of the half-period of the center (p. 2).-- S2 Time series for different diffusion values and distances to the bifurcation point (p. 3).-- S3 Transient times for initial populations with growing spatial regions below the ghost bottleneck (p. 4).-- S4 Effect of the different initial spatial distribution of cooperators on extinction times (p. 5).-- S5 Time to extinction from an initial spatial distribution with random gaps depending on gap frequency close to the bifurcation (p. 6).-- S6 Time to extinction from random gap distribution far from the bifurcation (p. 7).-- S7 Phase portraits for different values of diffusion before the bifurcation in the two-patch model (p. 8).-- S8 Phase portraits depending on diffusion after the bifurcation in the two-patch model (p. 9).-- S9 Times to extinction dependence on initial conditions in the two-patch model: homogeneous and heterogeneous extinctions (p. 10).-- S10 Comparison of ghost phenomena depending on diffusion in the two-patch model (p. 11)., No
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