Yoshioka Hidekazu, Yaegashi Yuta
Faculty of Life and Environmental Science, Shimane University, Nishikawatsu-cho 1060, Matsue, Shimane, 690-8504, Japan.
Graduate School of Agriculture, Kyoto University, Kitashirakawa-oiwake-cho, Sakyo-ku, Kyoto, 606-8502, Japan.
Theory Biosci. 2018 Nov;137(2):99-116. doi: 10.1007/s12064-018-0263-8. Epub 2018 May 2.
Comprehending life history of migratory fish, onset of migration in particular, is a key biological and ecological research topic that still has not been clarified. In this paper, we propose a simple mathematical model for the onset of fish migration in the context of a stochastic optimal stopping theory, which is a new attempt to our knowledge. Finding the criteria of the onset of migration reduces to solving a variational inequality of a degenerate elliptic type. As a first step of the new mathematical modeling, mathematical and numerical analyses with particular emphasis on whether the model is consistent with the past observation results of fish migration are examined, demonstrating reasonable agreement between the theory and observation results. The present mathematical model thus potentially serves as a simple basis for analyzing onset of fish migration.
了解洄游鱼类的生活史，尤其是洄游的开始，是一个关键的生物学和生态学研究课题，目前仍未得到明确。在本文中，我们在随机最优停止理论的背景下提出了一个简单的鱼类洄游开始的数学模型，据我们所知，这是一项新的尝试。寻找洄游开始的标准归结为求解一个退化椭圆型的变分不等式。作为新数学建模的第一步，我们对数学和数值分析进行了研究，特别强调该模型是否与过去鱼类洄游的观测结果一致，结果表明理论与观测结果之间具有合理的一致性。因此，目前的数学模型有可能作为分析鱼类洄游开始的一个简单基础。
