  Mutation and drift play opposite roles in genetics. While mutation creates
diversity, drift can cause gene variants to disappear, especially when they are
rare. In the absence of natural selection and migration, the balance between
the drift and mutation in a well-mixed population defines its diversity. The
Moran model captures the effects of these two evolutionary forces and has a
counterpart in social dynamics, known as the Voter model with external opinion
influencers. Two extreme outcomes of the Voter model dynamics are consensus and
polarization, which correspond to low and high diversity in the Moran model.
Here we use a Shannon's information-theoretic approach to characterize the
smooth transition between the ordered and disordered states of consensus and
polarization in the Voter model. Mapping the Moran into the Voter model we
extend the results to the mutation-drift balance and characterize the
transition between low and high diversity in finite populations. Describing the
population as a network of connected individuals we show that the transition
between the two regimes depends on the geographic structure of the population
and on the possible asymmetries in the mutation rates.
