MPIDS Colloquium: Population growth and extinction on a changing landscape

We explore the combined roles of varying fitness (environment) and migration on sim-ple models of distributed populations. Within a mean-field approach, we find that var-iations in fitness lead to broad (power-law) distributions in local population size, somewhat smoothened by migration. This leads to novel critical behavior for a popula-tion going extinct, as well as “Richards-like growth” for an expanding popula-tion. Initially proposed as an empirical rule over half a century ago, the Richards equa-tion has been frequently invoked in population modeling and pandemic forecasting. Central to this model is the introduction of a fractional exponent, typically fitted to the data. While various motivations for this non-analytical form have been proposed, it is still considered foremost an empirical fitting procedure. Our justification of the Richards growth law thus provides a testable connection to the distribution of constit-uents of the distributed population. If time permits, I shall discuss growth and extinc-tion of competing bacteria at the front of an expanding colony.