Fish populations dynamics with nonlinear stock-recruitment renewal conditions

The dynamics of a fish population with age-structure and space diffusion is studied under a renewal condition represented by various nonlocal nonlinear stock-recruitment functions, instead of the standard linear birth condition. This population dynamics model is approached as a Cauchy problem for an evolution equation with an unbounded nonlinear operator in a Hilbert space. The domain of the operator contains specific restrictions induced by the definition of the stock-recruitment function which make not possible the proof of the m-accretiveness property. Its lack is compensated by some other essential properties proved in the paper, which allow the proof of the existence and uniqueness of the solution. The semigroup formulation of the problem ensures the convergence of a time-difference scheme used for providing some numerical simulations which can give information about the stock, recruitment and fishing strategy.