Evolutionary dynamics, topological disease structures, and genetic machine learning

Abstract

Topological evolution is a new dynamical systems model of biological evolution occurring within a genomic state space. It can be modeled equivalently as a stochastic dynamical system, a stochastic differential equation, or a partial differential equation drift-diffusion model. An application of this approach is a model of disease evolution tracing diseases in ways similar to standard functional traits (e.g., organ evolution). Genetically embedded diseases become evolving functional components of species-level genomes. The competition between species-level evolution (which tends to maintain diseases) and individual evolution (which acts to eliminate them), yields a novel structural topology for the stochastic dynamics involved. In particular, an unlimited set of dynamical time scales emerges as a means of timing different levels of evolution: from individual to group to species and larger units. These scales exhibit a dynamical tension between individual and group evolutions, which are modeled on very different (fast and slow, respectively) time scales. This is analyzed in the context of a potentially major constraint on evolution: the species-level enforcement of lifespan via (topological) barriers to genomic longevity. This species-enforced behavior is analogous to certain types of evolutionary altruism, but it is denoted here as extreme altruism based on its potential shaping through mass extinctions. We give examples of biological mechanisms implementing some of the topological barriers discussed and provide mathematical models for them. This picture also introduces an explicit basis for lifespan-limiting evolutionary pressures. This involves a species-level need to maintain flux in its genome via a paced turnover of its biomass. This is necessitated by the need for phenomic characteristics to keep pace with genomic changes through evolution. Put briefly, the phenome must keep up with the genome, which occurs with an optimized limited lifespan. An important consequence of this model is a new role for diseases in evolution. Rather than their commonly recognized role as accidental side-effects, they play a central functional role in the shaping of an optimal lifespan for a species implemented through the topology of their embedding into the genome state space. This includes cancers, which are known to be embedded into the genome in complex and sometimes hair-triggered ways arising from DNA damage. Such cancers are known also to act in engineered and teleological ways that have been difficult to explain using currently very popular theories of intra-organismic cancer evolution. This alternative inter-organismic picture presents cancer evolution as occurring over much longer (evolutionary) time scales rather than very shortened organic evolutions that occur in individual cancers. This in turn may explain some evolved, intricate, and seemingly engineered properties of cancer. This dynamical evolutionary model is framed in a multiscaled picture in which different time scales are almost independently active in the evolutionary process acting on semi-independent parts of the genome. We additionally move from natural evolution to artificial implementations of evolutionary algorithms. We study genetic programming for the structured construction of machine learning features in a new structural risk minimization environment. While genetic programming in feature engineering is not new, we propose a Lagrangian optimization criterion for defining new feature sets inspired by structural risk minimization in statistical learning. We bifurcate the optimization of this Lagrangian into two exhaustive categories involving local and global search. The former is accomplished through local descent with given basins of attraction while the latter is done through a combinatorial search for new basins via an evolution algorithm