8 June 2020, 14.30
Duccio Fanelli (Univ. Firenze)
“Endogenous noise and emerging regularity in stochastic population dynamics”
Complex systems are systems composed of many microscopic entities, subject to mutual interactions. Starting from the microscopic rules of interaction, systems self-organize in time and in space, yielding ordered macroscopic patterns which are needed for implementing dedicated functions.
The classical approach to population dynamics relies indeed on characterizing the densities of species through a system of ordinary differential equations, which incorporates the interactions being at play. In other words, pure competition, predator-prey interactions, or even cooperative effects could be translated into specific interaction terms. Noise and other disturbances can be eventually hypothesized to alter the ideal deterministic dynamics but always acting as a macroscopic bias.
As opposed to this formulation, a different level of modeling can be invoked by focusing instead on the individual-based description, which is intrinsically stochastic. Individuals entities interact when e.g.
they happen to meet and the ensuing reactions might occur with a given success rate. The system becomes probabilistic and the idealized deterministic picture can be solely recovered when considering very large populations of interacting units.
For finite size populations, demographic noise, as the probabilistic contributions are customarily referred to, acts as a source of endogenous perturbation, shaking the system from the inside. In this talk I will discuss, in simple terms and building on examples, how the noisy component of the dynamics, as stemming from the discreteness of the scrutinized sample, can yield the emergence of quasi-regular patterns. Microscopic disorder can hence materialize in macroscopic order, a counterintruitive mechanism which could be exploited by living systems to orchestrate a multitude of different functions.
