Stochastic Growth Model of Pollack  Gadus chalcogrammus  (Pallas, 1814)

V. V. Sukhanov; Суханов В. В.

doi:10.31857/S0134347523020080

Stochastic Growth Model of Pollack Gadus chalcogrammus (Pallas, 1814)

Authors: Sukhanov V.V.¹^,2
Affiliations:
1. Zhirmunsky National Scientific Center of Marine Biology, Far Eastern Branch, Russian Academy of Sciences
2. Far-Eastern Federal University
Issue: Vol 49, No 2 (2023)
Pages: 127-134
Section: ОРИГИНАЛЬНЫЕ СТАТЬИ
Published: 01.03.2023
URL: https://ruspoj.com/0134-3475/article/view/670273
DOI: https://doi.org/10.31857/S0134347523020080
EDN: https://elibrary.ru/DVWGFD
ID: 670273

Cite item

Full Text

Open Access
Restricted Access

Access granted
Restricted Access

Subscription Access

Abstract
About the authors
References
Supplementary files
Statistics

Abstract

A mathematical model is proposed that describes the age-related dynamics of the vector of means and the covariance matrix of characters of individuals in the Sakhalin pollock population Gadus chalcogrammus (Pallas, 1814). The model is based on the Bertalanffy and Gompertz equations. The covariance matrix is composed of two parts: noise (caused by rapid random fluctuations in environmental conditions) and structural (due to intrapopulation variability of the parameters included in the growth equations). The model well reproduces the age dynamics of the distribution of fish according to the quantitative characters of individuals. The age-related increase, the passing through a maximum at a young age, the subsequent decrease in dispersions and their stabilization at low levels in the length and mass of the body of adult fish have been described. The age-related decrease in the correlation between length and body mass has been explained.

Keywords

Fokker-Planck-Kolmogorov equation, Bertalanffy-Gompertz model, body length and mass covariance matrix, noise and structural variability of characters

About the authors

V. V. Sukhanov

Zhirmunsky National Scientific Center of Marine Biology, Far Eastern Branch,
Russian Academy of Sciences; Far-Eastern Federal University

Author for correspondence.
Email: vsukhan@mail.ru
Russia, 690041, Vladivostok; Russia, 690001, Vladivostok

References

Бард Й. Нелинейное оценивание параметров. М.: Статистика. 1979. 349 с.
Животовский Л.А. Интеграция полигенных систем в популяциях. М.: Наука. 1984. 182 с.
Коздоба Л.А. Методы решения нелинейных задач теплопроводности. М.: Наука. 1975. 227 с.
Мина М.В., Клевезаль Г.А. Рост животных. М.: Наука. 1976. 291 с.
Суханов В.В. Стохастическая модель роста рыб // Вопр. ихтиологии. 1980. Т. 20. № 4. С. 615−624.
Суханов В.В., Лопатин О.Е. Математическое моделирование роста и развития Chironomus thummi // Деп. в ВИНИТИ 30.06.88 № 5244-В88. Владивосток. 1988. 57 с.
Суханов В.В., Селин Н.И. Модель стохастического многомерного роста Mizuhopecten yessoensis (Jay, 1857) (Bivalvia: Pectinidae) // Биол. моря. 2018. Т. 44. № 5. С. 1−8.
Тихонов В.И., Миронов М.А. Марковские процессы. М.: Сов. радио. 1977. 488 с.
Томович Р., Вукобратович М. Общая теория чувствительности. Серия “Библиотека технической кибернетики”. М.: Сов. радио. 1972. 240 с.
Шмальгаузен И.И. Определение основных понятий и методика исследования роста. Л.: Биомедгиз. 1935. 53 с.
Sukhanov V.V. Generalization of Bertalanffy-Gompertz model for multidimensional stochastic growth of organisms // Marine Biodiversity for a Healthy Ocean – Biodiversity, Functional Groups and Ocean Health. Proc. of the Russia-China Bilateral Workshop. October 10−11, 2019. Vladivostok. Russia. P. 130−132.