Stochastic dynamics in exotic and native blowflies: an analysis combining laboratory experiments and a two-patch metapopulation model

In this study we explored the stochastic population dynamics of three exotic blowfly species, Chrysomya albiceps, Chrysomya megacephala and Chrysomya putoria, and two native species, Cochliomyia macellaria and Lucilia eximia, by combining a density-dependent growth model with a two-patch metapopulation model. Stochastic fecundity, survival and migration were investigated by permitting random variations between predetermined demographic boundary values based on experimental data. Lucilia eximia and Chrysomya albiceps were the species most susceptible to the risk of local extinction. Cochliomyia macellaria, C. megacephala and C. putoria exhibited lower risks of extinction when compared to the other species. The simultaneous analysis of stochastic fecundity and survival revealed an increase in the extinction risk for all species. When stochastic fecundity, survival and migration were simulated together, the coupled populations were synchronized in the five species. These results are discussed, emphasizing biological invasion and interspecific interaction dynamics.

Basic ingredients for mathematical modeling of tumor growth in vitro: Cooperative effects and search for space

Based on the literature data from HT-29 cell monolayers, we develop a model for its growth, analogous to an epidemic model, mixing local and global interactions. First, we propose and solve a deterministic equation for the progress of these colonies. Thus, we add a stochastic (local) interaction and simulate the evolution of an Eden-like aggregate by using dynamical Monte Carlo methods. The growth curves of both deterministic and stochastic models are in excellent agreement with the experimental observations. The waiting times distributions, generated via our stochastic model, allowed us to analyze the role of mesoscopic events. We obtain log-normal distributions in the initial stages of the growth and Gaussians at long times. We interpret these outcomes in the light of cellular division events: in the early stages, the phenomena are dependent each other in a multiplicative geometric-based process, and they are independent at long times. We conclude that the main ingredients for a good minimalist model of tumor growth, at mesoscopic level, are intrinsic cooperative mechanisms and competitive search for space. © 2013 Elsevier Ltd.