|Budget Amount *help
¥2,100,000 (Direct Cost : ¥2,100,000)
Fiscal Year 1997 : ¥300,000 (Direct Cost : ¥300,000)
Fiscal Year 1996 : ¥1,800,000 (Direct Cost : ¥1,800,000)
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.