Benjamin Allen

Evolutionary graph theory is a mathematical framework for
studying evolution in spatially structured populations.  Despite a
decade of active research, some fundamental questions remain open.  I
will discuss recent results regarding neutral drift and weak selection
on graphs.  Under neutral drift, mutations have no phenotypic effect
and accrue at a rate known as the ``molecular clock”.  I will show
that, surprisingly, spatial structure can either accelerate or slow a
population’s molecular clock.  Weak constant selection refers to the
case that a mutation confers a small fitness advantage relative to the
wild-type population.  Spatial structure can either amplify or
suppress the mutation’s fixation probability.  I will discuss a
conjecture, motivated by recent numerical results, that amplification
is impossible under the process known as death-Birth updating.