  We study the population genetics of two neutral alleles under reversible
mutation in the \Lambda-processes, a population model that features a skewed
offspring distribution. We describe the shape of the equilibrium allele
frequency distribution as a function of the model parameters. We show that the
mutation rates can be uniquely identified from the equilibrium distribution,
but that the form of the offspring distribution itself cannot be uniquely
identified. We also introduce an infinite-sites version of the \Lambda-process,
and we use it to study how reproductive skew influences standing genetic
diversity in a population. We derive asymptotic formulae for the expected
number of segregating sizes as a function of sample size. We find that the
Wright-Fisher model minimizes the equilibrium genetic diversity, for a given
mutation rate and variance effective population size, compared to all other
\Lambda-processes.
