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Modeling Competition in Motionless Populations

In: Trends in Biomathematics: Stability and Oscillations in Environmental, Social, and Biological Models

Author

Listed:
  • Hamlet Castillo Alvino

    (Escuela de Ciencias Naturales y Exactas, Pontificia Universidad Católica “Madre y Maestra”, STI Facultad Ciencias e Ingenierías)

  • Marcos Marvá

    (Universidad de Alcalá, Departamento de Física y Matemáticas)

  • Ezio Venturino

    (Università di Torino, Dipartimento di Matematica “Giuseppe Peano”)

Abstract

In this work we consider interference competition of motionless (sessile) populations, whose interactions are definitely different form mobile individuals population. Indeed, intraspecific competition in a sessile population takes place only with the closest individuals, those on its “vital surroundings”. When a sessile population competes with a mobile population, we assume that both populations are well mixed. The outcomes of the classical competition model are possible and, in addition, a conditional bi-stable scenario arises, where one semi trivial equilibrium and a coexistence equilibrium are both simultaneously locally asymptotically stable. In the competing parameter space, this bi-stability region reduces the domain in which the mobile population out-competes the motionless one. When two sessile populations compete, we assume that they are mainly separated and interact only through their common boundary. In this scenario the competitive outcomes are reduced to competitive exclusion due to the system’s initial conditions or tri-stable conditional coexistence, for which populations can either coexist or either one of them goes extinct, due to the system’s initial conditions.

Suggested Citation

  • Hamlet Castillo Alvino & Marcos Marvá & Ezio Venturino, 2022. "Modeling Competition in Motionless Populations," Springer Books, in: Rubem P. Mondaini (ed.), Trends in Biomathematics: Stability and Oscillations in Environmental, Social, and Biological Models, pages 183-209, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-12515-7_10
    DOI: 10.1007/978-3-031-12515-7_10
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