for return of a very small fraction of the original tagged lot (the usual case) are
unfavorable (big estimator variances); (iii) the assumption of a closed population is
often violated in the sea; and (iv) tag mortality. Tags kill; there are almost no tags
without some tag-associated mortality. Hence, M < (TL/TR)Y. How much less is
extraordinarily hard to estimate.
(^) Regardless of their practical utility, an instructive value of the equations above is
that Y and M compete for the available stock: N = Y + M. If we don’t eat them,
something else will. Fishers are well aware of this competitive relationship with other
fish consumers. They are sometimes tempted to take such direct actions as shooting
seals.
(^) Tags are also useful for study of population dispersal and migration (see Jennings et
al. 2001). Fish tagged at one site and captured at another have moved by some route
between those points. With sufficient tag returns, it is possible to reconstruct typical
movement patterns. For example, Pacific halibut is a continental-shelf and upper-
slope species whose eastern stock is spread around the perimeter of the Gulf of
Alaska. It usually migrates downslope to spawn, and the larvae are transported north
and west around the Gulf. Recoveries of tags placed in young adult fish show a
general migration back toward the south and east, keeping the population from
removal to the west by larval advection. In recent years, tags have become very
sophisticated, internally recording temperature, pressure, light levels, and other
variables. In some cases, a migration trajectory can be derived from daylength
changes or other data, and understanding of large fish behavior is improving rapidly
thanks to this data.
Yield and Fishery Mortality (ΔB/Δt = ... − Y(X,B,A))
(^) The yield per unit effort relation (Eqn. 17.3) above,
(^)
(Eqn. 17.6)
(^) That function suggests that there should be a parabolic relationship between yield
and effort: the yield versus effort curve (Fig. 17.5b). Such a relationship is what
economists for several hundred years have called a “Law of Diminishing Returns”.
Each section of the curve can be explained verbally as follows:
(^1) The more fishing done at low levels of exploitation, the more fish caught,
but at a declining rate of increase.
2 Maximum sustainable yield, called MSY by everybody.
3 At large X, the population gets so depleted that fish become hard to catch
and yield falls off.