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Updated: Aug 8, 2026

Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling
Published on: July 4, 2007
Effects of random migration in population dynamics
1Departamento de Física, CCET, Universidade Federal de São Carlos, Rodovia Washington Luiz km 235, São Carlos, 13565-905, SP, Brazil. colato@ifsc.sc.usp.br
Abstract:
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.
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