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VARIATIONAL PRINCIPLES AND CONSERVATION CONDITIONS IN VOLTERRA'S ECOLOGY AND IN URBAN RELATIVE DYNAMICS *
Author(s) -
Dendrinos Dimitrios S.,
Sonis Michael
Publication year - 1986
Publication title -
journal of regional science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.171
H-Index - 79
eISSN - 1467-9787
pISSN - 0022-4146
DOI - 10.1111/j.1467-9787.1986.tb00825.x
Subject(s) - dynamics (music) , population , kullback–leibler divergence , mathematics , mathematical economics , mathematical optimization , statistical physics , statistics , physics , sociology , demography , acoustics
. Relative spatial population dynamics are analyzed in this paper under Volterra‐Lotka specifications. At first, the Volterra conservation conditions under absolute growth and their variational principles are reviewed, extended, and interpreted. Then, the relative dynamics are presented which demonstrate the presence of competitive exclusion. The main aim is to derive the variational principles underlying relative population dynamics. It is found that these principles produce an integrand, the stationary value of its integral being the cumulative entropy of the population distribution over a time horizon. Substantive interpretation of these results in accordance with optimization principles in economic theory is presented.