  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
coexistence of opinions, 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 states of consensus and
coexistence of opinions 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 network topology of the population and
on the possible asymmetries in the mutation rates.
