How does stochasticity in colonization accelerate the speed of invasion in a cellular automaton model?

Abstract

We investigate the speed of invasion waves for a single species generated by stochastic short-and/or long-distance colonizations in a time-continuous cellular automaton (CA) model on a two-dimensional homogenous landscape. By simulating the CA models, we demonstrate that stochasticity can dramatically increase the speed of invasion compared to the corresponding deterministic CA model or the corresponding onedimensional stochastic CA model. To explain this phenomenon, we first develop a mathematical model for the invasion involving only short-distance colonization (i.e., colonization only occurs from the eight adjacent cells), and present several approximation methods for solving the model. Our analyses show that the increased wave speed in the stochastic model is due to irregularity in the shape of the wavefront. Further extension of this model to include long-distance colonization demonstrates that stochasticity influences speeds to even greater extents in this case. Using dimension analysis, we deduced a semiempirical formula for the speed as a function of three parameters intrinsic to short-and long-distance colonization, which agrees well with simulation results. Based on these results, we discuss how important stochasticity in colonization and spatial dimensionality are in the acceleration of invasion speed.

Effects of Demographic Stochasticity on Population Persistence in Advective Media

“…Complementary studies on the effects of demographic stochasticity on invasion speeds have been done in Kawasaki et al (2006), Kot et al (2004), Lewis (2000), Mollison (1977), Snyder (2003. For linear systems on an infinite domain, it was shown that stochasticity does not generally slow invasions.…”

“…For linear systems on an infinite domain, it was shown that stochasticity does not generally slow invasions. For nonlinear systems, variability in production and movement typically slows invasions, however, see Kawasaki et al (2006) for an example where it speeds them up. It was noted in that the asymptotic velocity above which no population can survive on any length of domain is equivalent to the critical speed in which an invasion front switches from advancing upstream to retreated downstream.…”

An integrodifference model for biological invasions in a periodically fragmented environment

“…Earlier studies of invasion used reaction-diffusion equations on a homogeneous one-dimensional space, in which reproduction and movement are assumed to occur continuously and the movement is subject to random dispersal (Fisher [8], Skellam [38], Okubo [29], Bramson [4], Okubo and Levin [30]). Recently, newer models in various mathematical frameworks including integral kernel-based models (van den Bosch et al [3], Mollison [26], Slatkin [39], Weinberger [42], Kot et al [20], Metz et al [25]), stratified diffusion model (Shigesada et al [36], Shigesada and Kawasaki [34], [35]), cell-automata model (Shaw [33], Hastings [12], Ellner et al [7], Kawasaki et al [16]), and individual-based model (Higgins et al [15]) have been developed in order to accommodate complex features in real ecosystems such as long distance dispersal, life-history of organisms, spatiotemporal heterogeneity, or demographic stochasticity (Hastings et al [13]). Among them, the integrodifference model has been gaining growing attention for its ease in incorporating the life history of organisms with nonoverlapping generations and various types of dispersal kernel (Kot et al.…”

Hierarchical Bayesian modelling of early detection surveillance for plant pest invasions

“…It is also common for species to have multiple dispersal mechanisms that operate at quite different scales (Hastings et al 2005). Short and long distance natural dispersal, as well as human assisted modes, may be present in both insects and pathogens (Kawasaki et al 2006). Pests of interest to early detection surveillance programs almost always have a human assisted pathway, either on propagating material, produce, or as hitchhikers.…”