  We consider a fitness-structured population model with competition and
migration between nearest neighbors. Under a combination of large population
and rare migration limits we are particularly interested in the asymptotic
behavior of the total population partition on supporting trait sites. For the
population without mutation on a finite trait space we obtain the equilibrium
configuration and characterize the right time scale for fixation. For the model
with mutation on an infinite trait space a jump process-trait substitution tree
model is established on a rarer mutation time scale against the rare migration
constrained in terms of a large population limit. Due to a change of the
fitness landscape provoked by a new mutant, some temporarily unfit types can be
recovered from time to time. In the end we shed light to illustrate sexual
reproduction in a diploid population on the genetic level.
