Models in fish population dynamics

The use of population dynamics models is essential to provide assessment of the fish abundance and advice on management and strategies for the fisheries. The stock-recruitment curve define the relationship between the spawning stock and the subsequent recruitment, describing nature's regulation of population size, whether or not the populations are being exploited. The two classical relations, established by Ricker and Shepherd, are: R (S) = b1S e-b2S , b1, b2 > 0 (4) R (S) = S b1 + b2Sb3 , b1, b2, b3 > 0 where S is the spawning stock and R is the recruitment, i.e. the amount of offspring coming in the fishing exploitable phase. We present a mathematical model for studying the evolution of an age-structured population living in a bounded domain Ohm ? R. Under suitable assumptions, which are biologically consistent, we prove the well posedness of the system, using a semigroup approach. Numerical methods for the approximation of the solution are under development. This is joint work with Gabriela Marinoschi from Institute of Mathematical Statistics and Applied Mathematics, Romanian Academy, Buchare