Natural selection is said to be able to explain the complex diversity of life. Although not in contradiction with this statement, most, if not all of our mathematical theories fail to provide support for it. Limitations largely come from failing to understand the causes and the mechanisms for innovations. Population genetics have been developed mainly to understand the fate of micro-mutations and how they affect existing traits, but understanding the origin of complexity requires a richer source of combinatorial search. Amongst other kinds of mechanisms, symbiosis can facilitate continuous change, allowing for the possibility of ongoing evolution, even on environments that are stable. This is in essence the hypothesis of the Red Queen (RQ). I present and discuss some models that explore the evolutionary genetics of two species that interact though complex genotypes. An interesting aspect is that even if the phenotypic space is unbounded, species might not necessarily wander on a RQ fashion. However, different conditions allow this RQ dynamics. For example, if selection is asymmetric amongst the species and acts on trait correlations, genetic drift might facilitate RQ. The same holds for weak symmetric interactions where species directly determine a single optimum. However, even if interactions are symmetric but these are stronger than drift, then stasis is a stable outcome. These results show conditions for open-ended evolution. However, the models behind are still “uncreative” in that a fixed set of traits change only in a quantitative way. An alternative to address innovations with true open endedness is presented by using stochastic computational methods borrowed from combinatorial chemistry (Gillespie algorithm). This approach which is consistent with Darwinian models of evolution, but can describe arbitrary increases in complexity.
Harold P. de Vladar has been a research fellow at Parmenides Foundation (Pullach/Munich) since 2013. He originally studied Cell Biology and Statistical Physics in Venezuela. In 2009 he completed his PhD at the University of Groningen, The Netherlands under the direction of Ido Pen. Afterwards, he was a postdoc in IST Austria with Nick Barton, with whom he worked on evolutionary genetics developing a theory to understand the evolution of quantitative traits based on principles of statistical physics. His main research subject is on the origin and evolution complexity, and its relation to the Major Evolutionary Transitions. He employs mathematical and computational methods, often relying on analogies or techniques from physics.