On habit and habitat

Scientific theories based on mathematical models are frequently used in sciences to reveal natural behaviour of systems and eventually to be able in predicting such behaviour once the system's parameters and relevant conditions are known and can be specified. The integration of accumulated theoretical as well as experimental knowledge allows us to present such a unifying theory underlying the equivalence between habit and habitat in population growth. While the focus of the initial development was derived from microorganisms, the theory is extended to other population types too. The biological interpretation of ‘inertia’ or ‘habit’-based processes is provided as a consequence of this theory, and its relationship to the population ‘resource utilization’ available in the ‘habitat’ is derived. This paper focuses on the link between the ‘resource utilization’, which is related to the ‘habitat’, and ‘biological inertia’, which is related to population ‘habit’. This link extends the context of population growth and predictive modelling of microorganisms.

WEAK NONLINEAR ANALYSIS OF THE NEOCLASSICAL GROWTH MODEL AT SPATIALLY HOMOGENEOUS CONDITIONS

The neoclassical growth model is being analyzed subject to spatially homogeneous perturbations by using the weak nonlinear method of solution and comparing its results to the numerical solution. The latter expands the analytical tools beyond the investigation of Turing instability. The results identify a Hopf bifurcation at a critical value of a controlling parameter, and their comparison to direct numerical solutions show an excellent match in the neighborhood of this critical value and for amplitudes of oscillations that are not too large.

Theoretical and experimental evidence of extinction and coexistence of killer and sensitive strains of yeast grown as a mixed culture in water

Theoretical and experimental evidences of extinction and coexistence during batch interaction of killer and sensitive strains of Saccharomyces cerevisiae grown as a mixed culture in pure water are provided. The experimental results show that in the limited nutrient conditions of growth in pure water, the killer yeast is subject to extinction when the initial concentration ratio of killer to sensitive yeast is 1:100. However, if the initial concentration ratio of killer to sensitive yeast is 1:1, both strains coexist. Substantial damped oscillations are associated with the growth process in the mixed culture. A new theoretical model that was originally developed for recovering the growth of single species in isolation is extended and applied to two species competing over a common ecological niche. The solutions of the model are shown to recover all the qualitative features captured in the experiments.