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The dynamics of natural selection in dispersal-structured populations

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.