Title: Thermodynamic duality in growing populations
Abstract: Two fundamental quantities in population biology, the reproductive number R₀ and the growth rate, are intimately linked, but the exact nature of their relationship is somewhat obscure. Models of microbial growth typically have R₀=2, but estimating their growth rate, and hence fitness, requires solving the famous Euler-Lotka equation. Conversely, in epidemiology one typically measures how quickly the infected population grows, but it is the reproductive number R₀ that sets the threshold for an epidemic breakout and for herd immunity. In this talk, we use thermodynamics to clarify how exactly the population growth rate and R₀ are connected. We show that the long-term behaviour of a population is encoded in a single convex function that relates growth rate, R₀, and the statistics of intergeneration times in lineages. As an application, we derive a general formulation of the Euler-Lotka equation and explain why it is almost always appears as an implicit equation.