  We consider a population of agents that are heterogeneous with respect to (i)
their strategy when interacting $n_{g}$ times with other agents in an iterated
prisoners dilemma game, (ii) their spatial location on $K$ different islands.
After each generation, agents adopt strategies proportional to their average
payoff received. Assuming a mix of two cooperating and two defecting
strategies, we first investigate for isolated islands the conditions for an
exclusive domination of each of these strategies and their possible
coexistence. This allows to define a threshold frequency for cooperation that,
dependent on $n_{g}$ and the initial mix of strategies, describes the outbreak
of cooperation in the absense of migration. We then allow migration of a fixed
fraction of the population after each generation. Assuming a worst case
scenario where all islands are occupied by defecting strategies, whereas only
one island is occupied by cooperators at the threshold frequency, we determine
the optimal migration rate that allows the outbreak of cooperation on
\emph{all} islands. We further find that the threshold frequency divided by the
number of islands, i.e. the relative effort for invading defecting islands with
cooperators decreeses with the number of islands. We also show that there is
only a small bandwidth of migration rates, to allow the outbreak of
cooperation. Larger migration rates destroy cooperation.
