Hierarchical population model with a carrying capacity distribution for bacterial biofilms.

In order to describe biological colonies with a conspicuous hierarchical structure, a time- and space-discrete model for the growth of a rapidly saturating local biological population N(x,t) is derived from a hierarchical random deposition process previously studied in statistical physics. Two biologically relevant parameters, the probabilities of birth, B, and of death, D, determine the carrying capacity K. Due to the randomness the population depends strongly on position x and there is a distribution of carrying capacities, Pi(K). This distribution has self-similar character owing to the exponential slowing down of the growth, assumed in this hierarchical model. The most probable carrying capacity and its probability are studied as a function of B and D. The effective growth rate decreases with time, roughly as in a Verhulst process. The model is possibly applicable, for example, to bacteria forming a "towering pillar" biofilm, a structure poorly described by standard Eden or diffusion-limited-aggregation models. The bacteria divide on randomly distributed nutrient-rich regions and are exposed to a random local bactericidal agent (antibiotic spray). A gradual overall temperature or chemical change away from optimal growth conditions reduces bacterial reproduction, while biofilm development degrades antimicrobial susceptibility, causing stagnation into a stationary state.

Controlling simple dynamics by a disagreement function.

We introduce a formula for the disagreement function which is used to control a recently proposed dynamics of the Ising spin system. This leads to four different phases of the Ising spin chain at zero temperature. One of these phases is doubly degenerated (antiferromagnetic and ferromagnetic states are equally probable). On the borders between the phases two types of transitions are observed: infinite degeneration and instability lines. The relaxation of the system depends strongly on the phase.

Population dynamics with and without selection.

A model describing population dynamics is presented. We study the effect of selection pressure and inbreeding on the time evolution of the population and the chances of survival. We find that the selection is in general beneficial, enabling survival of a population whose size is declining. Inbreeding reduces the survival chances since it leads to clustering of individuals. We have also found, in agreement with biological data, that there is a threshold value of the initial size of the population, as well as of the habitat, below which the population will almost certainly become extinct. We present analytical and computer simulation approaches.