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The Distribution of Species Numbers in a Controlled Environment
Author(s) -
Whittle Peter
Publication year - 2004
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2004.00308.x
Subject(s) - mathematics , liapunov function , convergence (economics) , distribution (mathematics) , interpretation (philosophy) , function (biology) , mathematical optimization , population , mathematical analysis , computer science , nonlinear system , physics , demography , quantum mechanics , evolutionary biology , sociology , economics , biology , programming language , economic growth
Summary A model is proposed in which a population of projects is induced to distribute itself optimally over a number of modes (‘species’), consistently with resource constraints, by manipulation of a price vector. A control rule for the price vector is suggested which is shown by the use of a Liapunov function to achieve convergence to the optimum. For a stochastic version of the problem this Liapunov function has a distributional interpretation, leading to the conclusion that the numbers in the various surviving modes are distributed as independent gamma variables in an open model.