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Reference:

The Variation Approach to Model Medieval Distribution of Population (the Example of Derevskaya Pyatina of Novgorodskaya Land in the Late 15th Century)

Shpirko Sergey

Associate Professor, Moscow State Historical Archives Institute, Russian State University for the Humanities

119313, Russia, g. Moscow, ul. Leninskii Prospekt, 88 korpus 3, kv. 122

shpirkos@mail.ru
Другие публикации этого автора
 

 

DOI:

10.7256/2585-7797.2018.4.28287

Review date:

06-12-2018


Publish date:

07-01-2019


Abstract: Mathematical modeling is increasingly popular to study spatial distribution of population. This trend is determined by the necessity to study the dynamics of population quantity and density, reconstruct lacking data, search for population displacement factors and evaluate their influence on this process. The current study develops the model describing the system of centers distribution (the settlement structure) of the one-level hierarchy. Such a modeling aims at searching for basic factors and evaluating their influence on the process, associating optimum parameters which characterize the system of centers distribution. The model developed by the author is based on the innovative approach of S.M. Gusein-Zade which makes it possible to describe the regularities in the location (distribution) of heterogeneous settlements and other centers on the territories. The variations calculus methods applied as well as the concept of Pareto optimality allows one to find parameters of the existing systems of centers location and quantitatively describe the phenomena occurring in them. The model has been tested to study a medieval rural settlement and has proven adequate and correct.
It has been demonstrated that the process of free population displacement was caused by two counterbalancing factors: a centripetal one (concentration of settlements around their centers) and a centrifugal one (displacement of population near the farmland).


Keywords: Pareto equilibrium, calculus of variations, human settlement system, scribe book, central location theory, Poisson distribution, Mathematical modelling, population density function, functional, linear regression
This article written in Russian. You can find full text of article in Russian here .

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