Topological Scaling Laws and the Mathematics of Evolution

Explore a comprehensive lecture on the mathematical aspects of evolutionary biology, focusing on topological scaling laws and their implications. Delve into the scale-invariant topology of phylogenetic trees and the bursty pattern of diversification observed across evolutionary timescales. Examine a coarse-grained statistical mechanics model that couples ecological niche construction with speciation, and learn how renormalization group arguments explain the statistical scaling properties of phylogenetic trees. Discover the potential of simplistic, minimal arguments in understanding large-scale aspects of evolutionary biology, including the emergence of open-ended complexity growth and the response of evolving systems to perturbations. Gain insights into how mathematical reasoning can lead to new understanding of living systems, despite the complexity and exceptions in biology. The lecture also touches on future challenges in the field and the need for significant mathematical advances to address key biological questions.