Individual-based modelling of population growth and diffusion in discrete time.

Individual-based models (IBMs) of human populations capture spatio-temporal dynamics using rules that govern the birth, behavior, and death of individuals. We explore a stochastic IBM of logistic growth-diffusion with constant time steps and independent, simultaneous actions of birth, death, and movement that approaches the Fisher-Kolmogorov model in the continuum limit. This model is well-suited to parallelization on high-performance computers. We explore its emergent properties with analytical approximations and numerical simulations in parameter ranges relevant to human population dynamics and ecology, and reproduce continuous-time results in the limit of small transition probabilities. Our model prediction indicates that the population density and dispersal speed are affected by fluctuations in the number of individuals. The discrete-time model displays novel properties owing to the binomial character of the fluctuations: in certain regimes of the growth model, a decrease in time step size drives the system away from the continuum limit. These effects are especially important at local population sizes of <50 individuals, which largely correspond to group sizes of hunter-gatherers. As an application scenario, we model the late Pleistocene dispersal of Homo sapiens into the Americas, and discuss the agreement of model-based estimates of first-arrival dates with archaeological dates in dependence of IBM model parameter settings.

Habitability in different Milky Way stellar environments: a stellar interaction dynamical approach.

Every Galactic environment is characterized by a stellar density and a velocity dispersion. With this information from literature, we simulated flyby encounters for several Galactic regions, numerically calculating stellar trajectories as well as orbits for particles in disks; our aim was to understand the effect of typical stellar flybys on planetary (debris) disks in the Milky Way Galaxy. For the solar neighborhood, we examined nearby stars with known distance, proper motions, and radial velocities. We found occurrence of a disturbing impact to the solar planetary disk within the next 8 Myr to be highly unlikely; perturbations to the Oort cloud seem unlikely as well. Current knowledge of the full phase space of stars in the solar neighborhood, however, is rather poor; thus we cannot rule out the existence of a star that is more likely to approach than those for which we have complete kinematic information. We studied the effect of stellar encounters on planetary orbits within the habitable zones of stars in more crowded stellar environments, such as stellar clusters. We found that in open clusters habitable zones are not readily disrupted; this is true if they evaporate in less than 10(8) yr. For older clusters the results may not be the same. We specifically studied the case of Messier 67, one of the oldest open clusters known, and show the effect of this environment on debris disks. We also considered the conditions in globular clusters, the Galactic nucleus, and the Galactic bulge-bar. We calculated the probability of whether Oort clouds exist in these Galactic environments.