Title: Competing evolutionary paths in growing populations with applications to multidrug resistance,
Abstract: Investigating the emergence of a particular cell type is a recurring theme in
models of growing cellular populations. The evolution of resistance to therapy
is a classic example. Common questions are: when does the cell type first
occur, and via which sequence of steps is it most likely to emerge? For growing
populations, these questions can be formulated in a general framework of
branching processes spreading through a graph from a root to a target vertex.
Cells have a particular fitness value on each vertex and can transition along
edges at specific rates. Vertices represents cell states, say \mic{genotypes
}or physical locations, while possible transitions are acquiring a mutation or
cell migration. We focus on the setting where cells at the root vertex have the
highest fitness and transition rates are small. Simple formulas are derived for
the time to reach the target vertex and for the probability that it is reached
along a given path in the graph. We demonstrate our results on \mic{several
scenarios relevant to the emergence of drug resistance}, including: the
orderings of resistance-conferring mutations in bacteria and the impact of
imperfect drug penetration in cancer.