When subpopulations are at genetic equilibrium, the migration rate is
related to 
such that
and
since the number of subpopulations sampled is already incorporated in
the estimation of 
(see the formulae in Weir and Cockerham, 1984).
Through a simulation of the TPM, Slatkin (1995) investigated
the performance of 
and 
in their estimation of Nm. This
simulation involved 10 subpopulations among which migration was equally
probable, and the mutational process at the microsatellites was
modelled via the TPM. In separate runs the migration rate and the
proportion of multi-step mutations were varied (Nm = .1, 1, 10; p =
.75, .95, 1). The simulations were continued until an equilibrium was
reached. In all cases 
performed as good or better than 
at
estimating the true Nm values. This result is not surprising as
was developed to fit the SMM.
An alternative method for estimating Nm was also developed by Slatkin
(1985). He noted that there exists a linear relationship between the
average frequency of alleles found only in a single subpopulation 
(i.e. private alleles) and Nm. This relationship used to estimate
Nm is given by the general formula,
where a and b are variables which depend on the number of individuals sampled per subpopulation.
Allen et al. (1995) used this
relationship along with 
and 
to estimate Nm between
two populations of grey seals. Although it is unlikely that the
populations are at an equilibrium, they found estimates of Nm of 
41
for 
, 13.8 for 
, and 5.6 for 
. The intriguing question arising
from these results is why does the private allele estimate give the
lowest value? Since homoplasies will lead to an underestimation of
, and thus an overestimation of Nm, it is clear why the value
estimated from 
is larger then 
. The private allele
method, on the other hand, is not concerned with the amount of
homoplasy, rather only with the rate at which novel mutations are
derived. As the rate of migration increases, the time that these
alleles exist in a private state decreases. As it decreases the
proportion of private alleles in the subpopulations increases until an
equilibrium is reached. Although this method underestimates the actual
amount of mutations, it is less sensitive to the problems of back
mutations or homoplasy.
As long as the rate of generation of private alleles remains constant, this method may prove effective at measuring Nm. It is clear, however, that the properties of this method need to be tested with both the SMM and the TPM. In particular it would be interesting to see how the two models affect the estimate. For instance, multi-step mutations will more often lead to novel mutations than single step mutations. Further, it is important to determine how an increase in the number of alleles at a locus affects the results. An increase in number of alleles may decrease the rate at which novel mutations are produced with the SMM. Finally, it is also important to address how the imposition of a size constraint alters the estimate. A size constraint may also change the rate of novel mutations.