Examinando por Autor "Rebolledo, Rolando"

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  • Miniatura
    Ítem
    Coexistence, dispersal and spatial structure in metacommunities: a stochastic model approach
    (Springer, 2021) Tejo, Mauricio; Quiñinao, Cristóbal; Rebolledo, Rolando; Marquet, Pablo A.
    We propose a stochastic model for interacting species in a metacommunity in order to study the factors affecting the intensity of the competition/colonization trade-off as a coexistence mechanism in metacommunities. We particularly focus on the role of the number of local communities and the number of refuges for the inferior competitor. The stochastic component is associated with the dispersal process and is represented by Poisson random measures. Thus, this stochastic model includes two dynamic scales: a continuous one, which refers to the interactions among species, and a low frequency one, referring to dispersal following a Poisson scheme. We show the well-posedness of the model and that it is possible to study its long-term behavior using Lyapunov exponents; the extinction of a species is associated with a negative slope in the time trajectory of the Lyapunov exponent, otherwise, it is equal to zero. We show that the competition/colonization trade-off is a function of the dispersal rate of the inferior competitor, and that it becomes less intense as the number of local communities increases, while the opposite is true with an increase in the number of refuges for the inferior competitor. We also show that under a priority effect type of scenario, dispersal can reverse priority effects and generate coexistence. Our results emphasize the importance of coexistence mechanisms related to the topology of the system of local communities, and its relationship with dispersal, in affecting the result of competition in local communities.
  • Miniatura
    Ítem
    Evolving Systems of Stochastic Differential Equations
    (Springer, 2022) Videla, Leonardo; Rebolledo, Rolando
    We introduce Evolving Systems of Stochastic Differential Equations. This model generalizes the well-known stochastic differential equations with Markovian switching, enabling the countably many local systems to have solutions in regime-dependent dimension. We provide two constructions, the first one based upon general results on measure-valued processes and the second one partially inspired by recent developments of the theory of concatenation of right processes. We prove the Feller property under very mild assumptions, provide some extensions to the basic model, and show applications of our general framework to a biological model.