Contributed talk in Evolution 3, Aug. 2, 2019, 4:30 p.m. in room USB.2.022

From abstract objects via Darwinian evolution to species in dynamical systems

Martin Biehl and Ryota Kanai

watch We sketch a speculative way of deriving the instances of the individuals forming a species inside a dynamical system by searching a for a set of abstract objects whose induced population dynamics exhibit features of Darwinian evolution. For this we use a construction of macroscopic variables that can be interpreted to count the number of instances of a (purely spatial) abstract object present in a given state of the dynamical system. By normalizing the resulting counts of a set of abstract objects we can then obtain ``population'' densities that are themselves macrostates of the system. These population densities obey dynamics induced by the microscopic law of the dynamical system. From an artificial life point of view the interesting sets of abstract objects are those whose induced population dynamics show features of Darwinian evolution. We then call abstract objects that are part of such sets species and the instances of those abstract objects are instances of the individuals forming these species. In order to search for species among abstract objects we then need formal definitions of such features / criteria. One possibility might be to check whether the population densities obey the replicator equation, a formalization of natural selection. The main purpose of this work is to contribute to efforts of formally defining individuals and agents within dynamical systems.