12 Computing the effective size

The eigenvalue variance effective size determining the asymptotic rate of convergence of a subdivided population is determined by eigenvalue of the transition matrix in the recurrence equation for the variances and covariances rearragned into $n(n+1)/2$ column vectors. For details, see Tufto and Hindar (2002). The function effectpop returns the effective size based on this approach and takes two arguments: a migration matrix $\b M$ and a vector of effective population sizes of each subpopulations. For example, the effective size of population with migration following a stepping stone pattern can be computed as follows:

   > M <- steppingstone(c(0,.1),n=4)
   > M
   [,1] [,2] [,3] [,4]
   [1,] 0.95 0.05 0.00 0.00
   [2,] 0.05 0.90 0.05 0.00
   [3,] 0.00 0.05 0.90 0.05
   [4,] 0.00 0.00 0.05 0.95
   > N <- rep(100,4)
   > N
   [1] 100 100 100 100
   > effectpop(M,N)
   [1] 413.0410