About ghost transients in spatial continuous media
Calsina i Ballesta, Àngel (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Cuadrado Gavilán, Sílvia (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Vidiella, Blai (Centre de Recerca Matemàtica)
Sardanyés, Josep (Centre de Recerca Matemàtica)

Date:	2023
Abstract:	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.
Grants:	European Commission 101003777 Agencia Estatal de Investigación PCI2022-132926 Agencia Estatal de Investigación MTM2017-84214-C2-2-P Agencia Estatal de Investigación PID2021-123733NB-I00 Agencia Estatal de Investigación RED2018-102650-T Agencia Estatal de Investigación CEX2020-001084-M Agencia Estatal de Investigación PID2021-127896OB-I00 Agencia Estatal de Investigación RYC-2017-22243
Note:	Altres ajuts: acords transformatius de la UAB
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Published in:	Chaos, solitons and fractals, Vol. 166 (January 2023) , art. 112915, ISSN 0960-0779

DOI: 10.1016/j.chaos.2022.112915

13 p, 3.3 MB

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