The question of loss of genetic diversity in spatially structured
populations has been considered by
many authors, who have either assumed symmetric migration between subpopulations
or restricted
the analysis to two subpopulations and allowed asymmetric migration. In
this paper we briefly
discuss the two-subpopulation case that has been dealt with by other authors
and then find a
general formula for fixation probabilities for a population divided into
three and four
subpopulations. The number of individuals in the subpopulations
can be different, but the size of
each subpopulation is constant over time. Migration between the subpopulations
may be
asymmetric, that is the number of migrants moving from subpopulation
i to subpopulation j is not
the same as the number of migrants moving from subpopulation j
to
subpopulation i. When
migration is symmetric, the results of previous authors are
confirmed. The result for asymmetric
migration shows that the influence a subpopulation has on the
fixation probability for the whole
population is determined by its size and the net amount of gene flow out
of the subpopulation,
directly and indirectly, to the whole population. The position
of a subpopulation relative to the
other subpopulations (that is, edge versus centre) is only
important in that it can determine the
amount of net gene flow from a subpopulation. Some examples are given of
how this result can be
applied, and of applications to conservation genetics. We conclude that
when considering a
management plan with the intention of maintaining genetic diversity, the
relative strength and
direction of migration must be considered.