Equilibrium, transient dynamics and sustainable reference points under age-specific natural mortality rates and varying levels of population productivity: The case of the Northern cod stock.

Scientific advisory bodies provide scientific advice for sustainable fisheries management based on the precautionary approach and maximum sustainable yield (MSY) reference points, such as spawning stock biomass (SSB) value B, and fishing mortality giving MSY, F. The lack of a stock-recruitment function (SRF) to identify a clear breakpoint B has recently emerged in important stock collapses. It also precludes the use of equilibrium-based methods to analyze the sustainability of F.

A contraction approach to dynamic optimization problems.

An infinite-horizon, multidimensional optimization problem with arbitrary yet finite periodicity in discrete time is considered. The problem can be posed as a set of coupled equations. It is shown that the problem is a special case of a more general class of contraction problems that have unique solutions.