From Population Monitoring to a Mathematical Model: A New Paradigm of Population Research
Dmitrii O. Logofet, Nina G. Ulanova
Abstract
The new paradigm of population research means formulating traditional and innovative themes of population theory in terms of a matrix model of the dynamics of the studied population with a discrete (age, stage, or other kind of) structure, analyzing the relevant properties of this model, interpreting them in biological terms, and obtaining objective quantitative characteristics. Our knowledge of the species biology and the method of population monitoring determine the life cycle graph of organisms, which, in turn, generates the pattern of the population projection matrix (PPM), the core of the matrix model, according to the standard rule of matrix theory and predetermines its further properties. Calibration of the PPM according to empirical data gives quantitative certainty to its elements, the population vital rates., whereby the needed properties and quantitative indicators of the population are obtained by the appropriate methods of matrix algebra. The survey gives an overview of the wide range of problems studied within the framework of the new paradigm and the broad abilities the matrix population models possess to solve those problems. The task and methodological difficulties of assessing the population viability based on data from long-term monitoring are considered in the greatest detail. Noted are some current directions in the development and application of the mathematical apparatus of matrix population models.