  Population diversity is crucial in evolutionary algorithms as it helps with
global exploration and facilitates the use of crossover. Despite many runtime
analyses showing advantages of population diversity, we have no clear picture
of how diversity evolves over time. We study how population diversity of
$(\mu+1)$ algorithms, measured by the sum of pairwise Hamming distances,
evolves in a fitness-neutral environment. We give an exact formula for the
drift of population diversity and show that it is driven towards an equilibrium
state. Moreover, we bound the expected time for getting close to the
equilibrium state. We find that these dynamics, including the location of the
equilibrium, are unaffected by surprisingly many algorithmic choices. All
unbiased mutation operators with the same expected number of bit flips have the
same effect on the expected diversity. Many crossover operators have no effect
at all, including all binary unbiased, respectful operators. We review
crossover operators from the literature and identify crossovers that are
neutral towards the evolution of diversity and crossovers that are not.
