the sea. This layer responds most readily to the wind, so possibly the fish can navigate
shoreward by surfacing when the skin of the sea is carried toward the shelf.
Dynamic Methods
(^) Models for stock management are designed in a variety of ways. Most emphasize
some aspect of the following general input–output relationships. A catchable fish
population, or unit stock, can be considered to have some total mass, B. This mass can
be changed by four processes as represented in the following diagram:
If A is a general age-structure variable, X is fishing pressure, and Y is fishery yield,
then:
(^) (Eqn. 17.1)
(^) Or, in words:
(^) Parentheses in the symbolic statement indicate “function of” in the usual way. For
example, fishing mortality, Y, must be some function of fishing effort, stock size, and
stock age structure.
(^) The objective of fishery dynamics is to replace R, G, M, and Y by a system of
explicit functions (a model) that realistically mimics the behavior of the stock, thus
enabling manipulation of X so that Y(X,P,A) can be maximized on a stable, long-term
basis. This has been done with modest success in some fisheries, although the success
of the manipulation is often less than that of the models. There are two reasons for
this last caveat: (i) The models are adjusted to fit data from the past, and so can be
tuned to fit, while manipulation involves prediction of the future, which is more
difficult to tune. Moreover, the models generally assume an unchanging dynamics of
the stock, while both ocean climate and the interaction of the stock with its predators
and prey are nearly certain to shift substantially through time. This point is the main
basis of a recent book by Alan Longhurst (2010 – Mismanagement of Marine
Fisheries). (ii) Managers are often overruled in the politics of fishing (Rosenberg
(2003). In some approaches, R and G are explicitly included. In other, simpler
approaches, the relations among X, B and Y(X,B,A) are the focus. We will consider the
both types briefly. Readers seeking an extensive, fully mathematized treatment could
consult Quinn and Deriso (1998).