Survival Probabilities in a Simple Model of Branching Populations

Cells growing in branching structures are observed in many biological contexts, ranging from
the tissue of kidney and lung ducts, to the branched growth of some microbial colonies. It is of
interest to understand how strains of cells compete within these structures because the geometry
of the population strongly influences the evolutionary dynamics. We study a simple model of a
branching population as an initially uniform tube (i.e., cylinder), which then bifurcates into two
identical tubes. These tubes may then continue bifurcating, generating a network. Using simulations
and some insights from the theory of random walks, we calculate the survival probability of a
strain within the population (e.g., some particular mutant) that competes with the other cells with a
selective advantage s ≥ 0. We find that the branching significantly enhances the survival probability
of the strain relative to growth in a non-branching population.