Physics of Evolution: Selection without Fitness

Traditionally evolution is seen as a process where from a pool of possible variations of a population (e.g. biological species or industrial goods) a few variations get selected which survive and proliferate, whereas the others vanish. Survival probability is typically associated with the ’fitness’ of a particular variation. In this paper we argue that the notion of fitness is an a posteriori concept, in the sense that one can assign higher fitness to species that survive but one can generally not derive or even measure fitness – or fitness landscapes – per se. For this reason we think that in a ’physical’ theory of evolution such notions should be avoided. In this spirit, here we propose a random matrix model of evolution where selection mechanisms are encoded in the interaction matrices of species. We are able to recover some key facts of evolution dynamics, such as punctuated equilibrium, i.e. the existence of intrinsic large extinctions events, and, at the same time, periods of dramatic diversification, as known e.g. from fossil records. Further, we comment on two fundamental technical problems of a ’physics of evolution’, the non-closedness of its phase space and the problem of co-evolving boundary conditions, apparent in all systems subject to evolution.