Random Perturbations and Lattice Effects in Chaotic Population Dynamics

Lattice Effects in Chaotic Population Dynamics Henson et al. (1) illustrated that populations consisting of integer numbers of individuals cannot be modeled as a continuum without paying attention to the discrepancy between the dynamics of discrete and continuous systems. The inverse of this problem (i.e., discrete models for continuous dynamical systems) has been well investigated since the work of Ulam (2), and several fundamental results in that area (3– 5) can be applied to the questions raised by Henson et al. One interesting issue is whether the refinement of the lattice (i.e., considering increasingly large habitat size) justifies, in the limit, using continuum models. As opposed to the ambiguous comments of Henson et al., we believe that there is no evidence at hand that discrete models converge in this sense. On the contrary, even on fine lattices, short cycles can be observed (4, 6). The discretized (lattice) Ricker model investigated by Henson et al. is no exception: xt 1 F xt int bxtexp c V xt (1)