<p>  This paper develops a simple mathematical model for determining an optimal installation timing of the overhead lines (Tegusu) to reduce predation from piscivorous birds, such as Phalacrocorax carbo (Kawau), to Plecoglossus altivelis (Ayu) taking into account of its decaying protection effect. Temporal dynamics of the total number and the individual body weight of P. altivelis are described with the system of ordinary differential equations for non-renewable population. Then, this paper formulates and numerically solves the governing equation of the optimal installation timing to simultaneously minimize the total predated P. altivelis and the cost to install and maintain the overhead lines. Extensive comparative statics of the optimal installation timing against model parameters is carried out to investigate its dependence on river environment and attitudes of decision makers. </p>