El Instituto de Ingeniería Matemática y Computacional (IMC) los saluda atentamente y los invita al seminario que se dictará la próxima semana.
Cristóbal Quiñinao, Facultad de Ciencias Biológicas, Pontificia Universidad Católica de Chile.
Miércoles 16 de octubre de 2024, 13:40 hrs. (Presencial en auditorio Edificio San Agustín; link Zoom disponible escribiendo a Esta dirección de correo electrónico está siendo protegida contra los robots de spam. Necesita tener JavaScript habilitado para poder verlo.)
ABSTRACT
We study the large-time behavior of an ensemble of entities obeying replicator-like stochastic dynamics with mean-field interactions as a model for a primordial ecology. We prove the propagation-of-chaos property and establish conditions for the strong persistence of the N -replicator system and the existence of invariant distributions for a class of associated McKean-Vlasov dynamics. In particular, our results show that, unlike typical models of neutral ecology, fitness equivalence does not need to be assumed but emerges as a condition for the persistence of the system. Further, neutrality is associated with a unique Dirichlet invariant probability measure. We illustrate our findings with some simple case studies, provide numerical results, and discuss our conclusions in the light of Neutral Theory in ecology.
