Modelling eco-behavioral systems (Q1074529)

The work of the psychologist Roger Barker and his followers on characterization of communities with the aid of ''behavior settings'' inspired the author of this paper to try some mathematical formalization and modeling. He quotes the original ideas of Barker and applies different mathematical concepts to formalize them. So dynamic aspects of interaction are described with the aid of Markov chains (mainly the linear and logistic form of birth-and-death processes). Stochastic modeling of interdependence between two groups of settings enables to come to the problem of short-term and long-run time scales. The concept of variety of behaviour is studied using probability distribution functions and Lorenz curves and some elements of utility functions are used, too. This type of argumentation has led as far as linear programming. To measure globally people's participation in different settings a general richness index was defined; the author calls the measured characteristic ''diversity''. Here the reader finds a typical example of construction of numerical scales summing ranks on several rank scales. The problem of optimal diversity is studied by means of quadratic forms. A similar way has been used to measure ''efficiency'' derived from Baker's concept of interdependence. In this case correlation coefficients are used and operated with the aid of quadratic forms again. Elements of the theory of games are used, too. At the end the author discusses in short further possibilities of modeling eco-behavioral systems.