Several traps in size-dependent population models published in fisheries journals

Abstract

In this note, I explain why, in the deterministic context, an age-dependent population model is equivalent to a size-dependent one, and discuss several other related issues that must be understood, in order to implement, correctly, a size-dependent population model. Several conclusions are in order. The age-based instantaneous rates of fishing and natural mortalities must be used in an age-dependent model, whereas size-based ones must be used in a size-dependent model. Their huge differences both in value and in dimension imply that any use of an age-based instantaneous rate of natural mortality in place of a size-based one in a size-dependent model for a fish population is equivalent to assuming that its population is far more dynamic than real, the size of its population is far smaller than real, its recruitment strength is far greater than real, and its population (if depleted) recovers much faster than real. Thus, such a mis-specified size-dependent model will produce a far more optimistic picture than real. Also, both size- and age-dependent population models apply to the populations of animals that can or cannot be aged. Any attempt at constructing, from a set of conventional tagging data, a growth function or a size-transition matrix that can account for the incremental change in the size of a crustacean as a function of its age is doomed to failure, unless data are available on the moult number and the duration of the stages of individual animals. Moreover, for logical consistency, the stochasticity in the quantities of interest in a population model must be introduced into the underlying differential equations to yield stochastic differential equations or by formulating new stochastic processes, but must not be introduced into an existing population model as the solution of some deterministic differential equations. It is high time to follow examples of the work before the 1990s on size- and age-dependent population models and move forward.