  The problem of natural selection in dispersal-structured populations
consisting of individuals characterized by different diffusion coefficients is
studied. The competition between the organisms is taken into account through
the assumption that the reproduction and/or death probability of an individual
is influenced by the number of other individuals within a neighborhood with
radius R. It is observed that for a wide range of parameters the competition
advantage is given to the individuals whose motion is characterized by
intermediate values of diffusion coefficient, instead of the most or least
motile ones. The optimal level of the dispersal is determined by the interplay
between various factors such as cluster formation, temporal fluctuations,
initial conditions, and carrying capacity of the system. The dynamics and the
time evolution of the system are investigated in detail revealing the winning
mechanism and process of the natural selection in such dispersal-structured
populations. Furthermore, the rescaling of the results is discussed for
different values of the interaction radius R of the organisms.
