Theoretical Study of Diadrmous Migration Evolution in Fish Species.

在大约3万种鱼类中，约有130种在生活史上在淡水和海洋之间迁徙。江河鱼类包括两类截然不同的鱼类：(I)鲑鱼(鲑科)和七鳃鳗(七鳃鳗科)，它们出生在淡水中，迁徙到海洋，然后回到淡水产卵(逆行迁徙)；以及(Ii)一些鳗鱼(鳗鱼科)和乌鱼(梭鱼科)，它们出生在海洋，迁徙到淡水，然后回到海洋产卵(迁徙)。长期以来，这些截然不同的移民方向的存在一直令人困惑。当鱼类在不同类型的媒介之间迁徙时，维持动态平衡是鱼类迁徙最严重的生理障碍。离子和渗透调节是必不可少的，并在进化过程中被很好地安排。我将生长(db/dt)和生存(dl/dt)分别表示为与栖息地类型(河流或海洋)和体型(B)有关的函数。进一步假定dL/dt为分配给离子和渗透调节的能量比例(u(T))的函数。用庞特里亚金极大值原理分析了鱼类如何选择能量分配给离子和渗透报复，以及如何选择栖息地以最大化B(T)L(T)，其中T是考虑的终点时间。最优栖息地选择调度在无序物种中表现为最优的出海调度，通过数学模型得到的最有趣的结果是，大卵出生的个体比小卵出生的个体更早下海。几个实验和观察显示了相同的模式。因此，应该得出结论，通过数学模型获得的结果是启发式稳健的。

Of roughly thirty thousand fish species, about 130 species are diadrmous that migrate between freshwater and the ocean in their life history. Diadromous fishes include two distinctly different groups ; (i) such as salmon (Salmonidae) and lamprey (Petromyzonidae) , which are born in freshwater, migrate to the ocean, and return to freshwater to spawn (anadrmous migration) ; and (ii) such as some eels (Anguillidae) and mullets (Mugilidae) , which are born in the ocean, migrate to freshwater, and return to the ocean to spawn (catadrmous migration). The existence of these contrasting directions of migration has long been perplexing. The most serous physiological barrier of diadrmous migration is maintenance of homeostasis, when fish migrate between different types of mediums. Ionic and osmotic regulation is essential, and it is well scheduled in the course of evolutionary process.I represented growth (dB/dt) and survival (dL/dt) as functions with respective to habitat type (river or sea) and body size (B). Further dL/dt was assumed as function with proportion of energy allocated (u (t)) to ionic and osmotic regulation. How fish choose energy allocating to ionic and osmotic retaliation, and how it choose habitat so as to maximize B (T) L (T) were analyzed by the Pontryagin's maximum principle, where T is a terminal time considered. Optimal habitat choice schedule exhibits optimal sea-run schedule in anadrmous species.The most interesting result acquired by the mathematical model is that individual born from large egg goes down sea earlier than that born from small egg. Several experiments and observations exhibit the same pattern. Thus it should be concluded that the result acquired by the mathematical model is heuristically robust.