Identifying fitness and optimal life-history strategies for an asexual filamentous fungus.

Filamentous fungi are ubiquitous and ecologically important organisms with rich and varied life histories, however, there is no consensus on how to identify or measure their fitness. In the first part of this study we adapt a general epidemiological model to identify the appropriate fitness metric for a saprophytic filamentous fungus. We find that fungal fitness is inversely proportional to the equilibrium density of uncolonized fungal resource patches which, in turn, is a function of the expected spore production of a fungus.

Numerical study of stress distribution in sheared granular material in two dimensions.

We simulate the response of dense granular material to shear. Our simulations use a micromechanical model which includes realistic material models for each deformable grain, and a Coulomb friction model for interactions between grains. We measure the probability density function (PDF) governing the volume distribution of stress for monodisperse and polydisperse samples, circular and polygonal grains, and various values of microscopic friction coefficients, yield stresses, and packing fractions.

Numerical solution of structured population models. I. Age structure.

Numerical methods are presented for a general age-structured population model with demographic rates depending on age and the total population size. The accuracy of these methods is established by solving problems for which alternate solution techniques are available and are used for comparison. The methods reliably solve test problems with a variety of dynamic behavior.

Time delays in age-structured populations.

A combination of analytical and computational techniques is employed to investigate age-structured populations in which the life cycle consists of two sequential demographic phases. Individuals within each phase have identical demographic rates that are functions of population size, but these rates may differ between phases. A model consisting of a system of delay ordinary differential equations is derived, and existence and stability of equilibria are discussed.

A model of cell sorting.

Voronoi polygons are introduced as a suitable representation for a two-dimensional cell sheet. These polygons are defined in terms of a finite number of points, making numerical simulations tractable and yet allowing cells to change neighbors and their shape in response to deforming forces without leaving gaps in the tissue. Using this geometry and an extension of the equilibrium theory proposed by Steinberg to drive the motion, simulations of rounding of uneven tissue and engulfment of two intact tissues are carried out.