Organization of Evolutionary Populations through Graph Theory
https://www.wired.com/story/this-mutation-math-shows-how-life-keeps-on-evolving/
A team of scientists in Australia and the United States have mapped the evolution and natural selection of species through construction of large population graphs. From their analyses, they’ve concluded that because of the randomness that occurs naturally in evolution, it isn’t certain whether advantageous mutations in individuals will contribute to the evolution of their species. They investigate “amplifier” structures in networks, which are designed to guarantee selection of advantageous mutations in such a lineage. These structures are naturally rare, but this team demonstrates how to construct them, so they may be of use in optimization of biomolecules and in diagnosis.
The method organizes the evolutionary representation as a graph with individual organisms as vertices and edges to vertices their offspring will replace. The edges are weighted with a probability representing risk of replacing another individual in the next generation. Evolution is represented by randomly selecting organisms in a generation and repeatedly allowing them to reproduce into the next (by selecting connected vertices with likelihood according to edge weights). They observe network topologies with “weak ties” between organisms are more likely to suppress selection of advantageous mutations from a single vertex. On the other hand, star topologies in which all vertex pairs are connected through a path of “strong ties” will promote spread of such a mutation as a strong amplifier.