when there are very few spawners. Spawner–recruit relations for several herring
stocks (Fig. 17.9b & c), illustrate this well. The points on the graphs retreated toward
the origin as the stocks were fished down. This is very simply understood; if there are
no parents, there will be no young. The relationship away from the origin often, but
not always (Fig. 17.10) tends to a wild scatter. Intense effort and emotion have gone
into choosing and justifying the best mathematical functions to fit spawner–recruit
curves. There are curves due to Beverton and Holt (same as the Michaelis–Menten
function), Ricker, Cushing, Shepard, and others for fitting these stock–recruitment
relationships. With rare exceptions, the debate is useless, since no one of these
deterministic equations looks better as a representation of the scatter than the rest.
There are several reasons beside competition for a spawner–recruit curve to drop at
the right. For fish with planktonic larvae, it will be rare that larval numbers are so
great that they limit their own resources, since larvae are a minor part of the overall
pelagic ecosystem, but it could happen. Large numbers of larvae could also attract
predator attention, reinforcing successful prey search patterns, raising mortality.
Fig. 17.9 Three examples from herring fisheries of spawner–recruit curves. (a) Zero-
age North Sea herring vs. estimated spawning stock biomass of fish 2 years and older,
fitted by a Ricker curve.
(^) (After Saville & Bailey 1980.)
(b) Icelandic summer-spawning herring (“1-ringers” vs. spawning stock). The data
from 1947–1961 form a quasi-parabolic spawner–recruit curve. (c) Icelandic spring-
spawning herring.
(^) (b & c from data in Jakobsson 1980.)