With the multiallelic parent-independent mutation-drift model, the
equilibrium proportions of alleles are known to be Dirichlet distributed. A
special case is the biallelic model, in which the proportions are beta
distributed. A sample taken from these models is then Dirichlet-multinomially
or beta-binomially distributed, respectively. Maximum likelihood (ML)
estimators for the mutation parameters of the biallelic parent-independent
mutation model are available via an expectation maximization algorithm.
Assuming small scaled mutation rates, the distribution of a sample of size M
can be expanded in a Taylor series of first order. Then the ML estimators for
the two parameters in the biallelic model can be expressed using the site
frequency spectrum. In this article, we go beyond parent-independent mutation
and analyse a strand-symmetric mutation model with six scaled mutation
parameters that deviates from parent independent mutation and, generally, from
detailed balance. We derive ML estimators for these six parameters assuming
mutation-drift equilibrium and small scaled mutation rates. This is the first
time that ML estimators are provided for a mutation model more complex than
parent-independent mutation
