Analytical Solution of Metapopulation Dynamics in Stochastic Environment
  We study a stochastic linear discrete metapolulation model to understand the effect of risk spreading by dispersion. We calculate analytically the stable distribution of populations that live in different habitats. The result shows that the simultaneous distribution of the populations has a complicated self-similar structure, but a population at each habitat follows a log-normal distribution. 
Satoru Morita and Jin Yoshimura
q-bio.PE physics.soc-ph