Stochastic processes with complex behaviour in population biology

Luogo: Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Sala Seminari "-1"
Ore: 11:00

Relatore:

• Nico Stollenwerk (Universidade de Lisboa)

Abstract:

We review some predator-prey systems with complex bifurcation structures, where stochastic versions can be given easily. Namely, the Rosenzweig-MacArthur model with seasonal forcing shows Hopf and torus bifurcations, and then also bifurcations into chaotic attractors with positive Lyapunov exponents.
Stochastic versions can be obtained by disentagling the time scale separation leading to the classical Rosenzweig-MacArthur model, where searching and handling predators as well as resource limitations for the prey via birth-death processes are considered.
Markov processes and Fokker-Planck equations leading to stochastic differential equations are given and compared in their numerical performance.
Then we show some recently investigated mutator-replicator dynamics, with global or local trait specific resource limitation, in a similar way as done in the predator-prey systems mentioned above.
Dynamics for local expectation values and Fokker-Planck equations can be derived in a similar way as above, and in limiting cases of continuous trait space, functional Fokker-Planck equations show up.
These mutator-replicator systems are closely related to well known processes in evolutionary contexts.
Finally we will give some implications for the investigation of dynamic multi-strain epidemiological systems, i.e. where no explicit static fitness functions have to be given, with discrete or continuous trait space.
Further implications will be given for data analysis of empirical systems, since we have readly the stochastic formulations obtained.

Referente: Andrea Pugliese