Island Population Model

The Island Population Model

The island population model is characterised by constant population sizes, and constant birth and migration rates. The island model takes as input the effective population sizes (Ne) of each deme and the rates of migration with demes. The birth (F) and migration (G) rates array components are defined by the following formulas.

The value of x_F does not affect the value of the structured tree likelihood.

A PhyDyn XML island model takes as input:

• demes: Deme names.
• Ne: Effective population sizes.
• migRates: A vector denoting the migration rates matrix (from the point of view of the coalescent process). Note that this rates correspond to values in the matrix M in the formula above (backward rates), as opposed to G, which correspond to the forward migration rates of the population process.
  Rates are entered row-wise, skipping the diagonal since M_ll=0.
• t0: Trajectory start time.
• t1 (optional): Trajectory end time. t1 must be specified if the population model is not associated with a tree (in which case t1 takes the value of the date of the tip furthest from the root). If the migration matrix is symmetric, we need only enter the values of the upper triangle.

<model spec='PopModelIsland' id='<ID>' demes="<ID>+"
   Ne = "<DOUBLE>+" migRates="<DOUBLE>+" xF="100"
   t0="<DOUBLE>" t1="<DOUBLE>" >
</model>