maisМоделирование и анализ информационных системModeling and Analysis of Information Systems1818-10152313-5417Yaroslavl State University10.18255/1818-1015-2023-3-234-245mais-1801Research ArticleTheory of ComputingРаспределение Больцмана в проблеме рационального выбора популяцией участка при неполной информации о его ресурсахThe Boltzmann distribution in the problem of rational choice by population of a patch under an imperfect information about its resourceshttps://orcid.org/0000-0002-3356-1846КирилловАлександр НиколаевичKirillovAlexander N.krllv1812@yandex.ruhttps://orcid.org/0000-0001-7031-4580ДаниловаИнна ВладимировнаDanilovaInna V.danilovainna1987@mail.ruКарельский научный центр Российской академии наукРоссияKarelian Research Centre of the Russian Academy of SciencesRussian FederationПетрозаводский государственнй университетРоссияPetrozavodsk State UniversityRussian Federation202317092023303234245Copyright © Кириллов А.Н., Данилова И.В., 20232023Кириллов А.Н., Данилова И.В.Kirillov A.N., Danilova I.V.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.mais-journal.ru/jour/article/view/1801

Рассматривается задача рационального выбора популяцией участка, содержащего энергетические (пищевые) ресурсы. Рассматриваемая задача относится к теории оптимального фуражирования, которая в свою очередь изучает вопросы, касающиеся поведения популяции, когда она покидает участок или выбирает наиболее подходящий. Для определения оптимального для популяции выбора участка предлагается вариационный подход, основанный на идее распределения Больцмана. Для построения распределения Больцмана вводятся функции полезности, которые учитывают факторы, способные повлиять на выбор популяции: имеющаяся информация о качестве участков, энергетическая полезность участков, затраты на перемещение к участку, стоимость информации о качестве участков. Основная цель статьи – исследовать влияние имеющейся информации о количестве ресурсов, содержащихся в участках, на процесс принятия решений, генерируемых популяцией при выборе подходящего участка. Оптимальная рациональность определяется с учетом стоимости информации, средней энергетической ценности всех участков, рациональности, зависящей от качества участка. Получены условия, при которых популяция при недостатке информации выбирает «бедный» участок в смысле энергетической ценности (ресурсов). Последнее дает теоретическое обоснование экспериментальным наблюдениям, согласно которым, популяция может выбрать участок худшего качества. Полученные результаты носят общий характер и могут быть использованы не только в поведенческой экологии, но и при построении любых процессов принятия решений.

The problem of rational choice by the population of a patch containing energy (nutritive) resources is considered. This problem belongs to the theory of optimal foraging, which, in turn of, studies issues related to the behavior of the population when it leaves the patch or chooses the most suitable one. In order to define the optimal patch choice for population, a variational approach, based on the idea of the Boltzmann distribution is proposed. To construct the probability distribution the utility functions are used, that take into account factors that can influence the patch choice of a population: available information about the quality of patches, the energy utility of patches, the cost of moving to the patch, the cost of information about the quality of patches. The main goal of the paper is to investigate the influence of available information about the amount of resources, contained in patches, on a decision-making process generated by the foragers while a suitable patch choosing. The optimal rationality is determined in the cases taking into account the information cost, the average energy utility of all patches, the rationality depending on the patch. The conditions under which the population, with the lack of information, select the “poor” patch, in sense of its resources, are obtained. The latter provides a theoretical justification of experimental observations, according to which a population can choose a patch with worse quality. The obtained results have a general character and may be used not only in behavioral ecology but when constructing any decision making processes.

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The authors declare that there are no conflicts of interest present.