Effects of random migration in population dynamics

We study the influence of random migration of a species (may be insects) in the population dynamics when initially all the individuals live in a primordial site (their habitats may be trees). We assume (i) a finite number of sites, (ii) that migration occurs randomly to nearest neighbors, and (iii) an on-site age-structured population whose size varies according to Ricker's map. We find that even for a very small migration rate, the population density becomes appreciably affected. If migration is not allowed, depending on the value of the characteristic parameters, the population may display a chaotic oscillation; however, with migration permitted, the chaos is reduced or even suppressed, and the population density will oscillate with period 2 or period 4. We examined the effects of migration through higher-order iterations of the map, entropy, and time correlation function. We also considered a long chain, analyzing (a) the spatial correlation between sites, noting the occurrence of a transition in the correlation function between sites separated by odd and even units of distance and (b) the fluctuations in time of the populations when initially all sites are populated.