Table 1.

Notation used in the single locus process model.

Parameter	Definition
A	Number of alleles
S	Number of populations in each geographical region
k	Number of geographical regions
P	Total number of populations. P = kS
V	An A × A matrix of mutation rates. v rs is the mutation rate from the rth allele to the sth allele
M	A P × P matrix of backward migration rates. m ij is the probability that an allele in population i came from population j in the preceding generation
B	The Kronecker product of M and V
N ij	Number of individuals in population j of geographical region i
${\mathrm{p}}_{\mathrm{ij}}^{\left(\mathrm{t}\right)}$	The vector of allele frequencies in population j of geographical region i at time t. $p_{\mathit{ij},r}^{\left(t\right)}$ is the frequency of the rth allele.
Properties when the process has reached stationarity.
uij	The mean vector of allele frequencies in population j of geographical region i.
Σij,ij	The variance-covariance of allele frequencies within population j of geographical region i.
Σij,i′j′	The covariance of allele frequencies between population j of geographical region i and popogulation j′ of geographical region i′.
Finite island model
m 0	Probability that an allele came from the same population in the preceding generation.
m 1	Probability that an allele came from a different population in the same geographical region in the preceding generation.
m 2	Probability that an allele came from a different geographical region in the preceding generation.
F-statistics
$F_{ST}=\frac{{\sigma }_p^2}{{\mu }_p(1-{\mu }_p)}$	Wright's F ST, where ${\sigma }_p^2$ is the variance of allele frequencies and μp is the mean allele frequency.
θ	An interpretation of F ST that arises when μp is taken as the mean allele frequency and ${\sigma }_p^2$ is taken as the allele frequency variance in a single population over time.
$\theta (p_{11}^{\left(t\right)},\dots ,p_{\mathit{kS}}^{\left(t\right)})$	An interpretation of F ST that arises when μp is taken as the mean allele frequency and ${\sigma }_p^2$ is taken as the allele frequency variance across populations at a single time.