International Journal of Biomathematics Vol. 12, No. 2 (2019) 1950023 (22 pages) c  World Scientific Publishing Company DOI: 10.1142/S1793524519500232 Interplay between reproduction and age selective harvesting: A case study of Hilsa (Tenualosa ilisha ) fish at Sundarban estuary of northern Bay of Bengal, India Debaldev Jana ∗,§ , Sachinandan Dutta †,¶ and G. P. Samanta ‡,‖ ∗ Department of Mathematics & SRM Research Institute SRM Institute of Science and Technology Kattankulathur 603 203, Tamil Nadu, India † Aquatic Bioresource Research Laboratory Department of Zoology, University of Calcutta 35 Ballygunge Circular Road, Kolkata 700 019, India ‡ Department of Mathematics Indian Institute of Engineering Science and Technology Shibpur, Howrah 711103, India § debaldevjana.jana@gmail.com ¶ duttasachi@gmail.com ‖ g p samanta@yahoo.co.uk; gpsamanta@math.iiests.ac.in Received 20 February 2018 Revised 2 January 2019 Accepted 9 January 2019 Published 8 February 2019 New offspring due to sexual reproduction is not an instantaneous process from its birth, it takes time to be sexually mature. On the other hand, harvesting of commercially profitable fish population before the perfect size or weight is reached is not only a commercial loss but also risks the extinction of the population. Now, we discuss the issue of Ganges-Brahmaputra-Meghna basin, northern Bay of Bengal for the age-selective harvesting of Hilsa shad (Tenualosa ilisha) which lays eggs after its sexual maturation. Harvesting of hilsa before its sexual maturation risks its extinction and due to lamer body weight, it is not a commercially profitable policy. This is a reality of Sundarban estuary for hilsa fish harvesting, therefore, biologically and economically both India and Bangladesh are facing several problems. Empirical data of Frasergunje Fishing Harbor shows a clear picture as the supporting document of this mathematical problem. Keywords : Maturation delay; age selective harvesting; extinction risk; MSY; bionomic equilibrium; optimal harvesting. Mathematics Subject Classification 2010: 92D25, 92D30, 92D40, 93D20, 34C23 § Corresponding author. 1950023-1