Abstract
Increasingly, predicting and even controlling evolutionary processes is
a sought after goal in fields ranging from agriculture, artificial
intelligence, synthetic biology, oncology, and infectious diseases.
However, our ability to predict evolution and plan such interventions in
real populations is limited in part by our understanding of how spatial
structure modulates evolutionary dynamics. Among current clinical assays
applied to predict drug response in infectious diseases, for instance,
many do not explicitly consider spatial structure and its influence on
phenotypic heterogeneity, despite it being an inextricable
characteristic of real populations. As spatially structured populations
are subject to increased interference of beneficial mutants compared to
their well-mixed counter-parts, among other effects, this population
heterogeneity and structure may non-trivially impact drug response. In
spatially-structured populations, the extent of this mutant interference
is density dependent and thus varies with relative position within a
meta-population in a manner modulated by mutant frequency, selection
strength, migration speed, and habitat length, among other factors. In
this study, we examine beneficial mutant fixation dynamics along the
front of an asexual population expanding its range. We observe that
multiple distinct evolutionary regimes of beneficial mutant
origin-fixation dynamics are maintained at characteristic length scales
along the front of the population expansion. Using an agent-based
simulation of range expansion with mutation and selection in one
dimension, we measure these length scales across a range of population
sizes, selection strengths, and mutation rates. Furthermore, using
simple scaling arguments to adapt theory from well-mixed populations, we
find that the length scale at the tip of the front within which ‘local’
mutant fixation occurs in a successive mode decreases with increasing
mutation rate, as well as population size in a manner predicted by our
derived analytic expression. Finally, we discuss the relevance of our
findings to real cellular populations, arguing that this conserved
region of successive mutant fixation dynamics at the wave tip can be
exploited by emerging evolutionary control strategies.