472 SCHAEFER AND BEVERTON [CHAP. 21 



still fragmentary and is a serious gap in our present understanding of their 

 dynamics. 



There remains for consideration the density-dependence of recruitment. This 

 is of quite a different nature to that of growth or natural mortality, because 

 recruitment is a property not of the contemporary population but of an earlier 

 mature population of which the recruits are the progeny. A study of the density- 

 dependence of recruitment therefore concerns the relations, in effect, between 

 successive generations and involves the analysis, both from data and in the 

 theoretical model, of the long-term dynamics and self-regenerating properties 

 of the population. 



In the simple model formulated by (10), it is assumed that a constant 

 absolute number of fish is recruited annually, although, as has been mentioned 

 earlier, this assumption can be broadened to allow for a fluctuating recruitment 

 without loss of generality, provided the fluctuations have themselves a constant 

 mean value. It could hardly be expected, however, that this assumption could 

 remain valid over very wide ranges of size of parent population. A population 

 of one mature male and one mature female, even with the enormous fecundity 

 which characterizes many species offish, could scarcely be expected to produce 

 the same number of recruits as a population consisting of hundreds of millions 

 of mature fish of each sex, which many do. It may therefore seem rather 

 remarkable that for no major fish population has a clear-cut relation between 

 parent stock and subsequent recruitment yet been established. The reasons for 

 this are not, however, far to seek. The main one is that recruitment usually 

 fluctuates very widely from one year to the next, primarily through the in- 

 fluence of varying environmental conditions on the survival of the young fish, 

 and this range of fluctuation is usually much greater than that of the size of 

 the parent stock which has been encompassed by the available data. In this 

 connection it has to be remembered that the fecundity of most marine teleosts, 

 including the pleuronectids, gadoids, clupeoids and scombroids on which most 

 of the world's largest fisheries are based, is very high ; a mature female of any 

 of these groups might spawn something between a hundred thousand and 

 several million eggs annually. Yet for the adult population to be maintained in 

 a steady state only a very few of these, perhaps only two or three, are needed 

 to survive to maturity — an event which in many cases roughly coincides with 

 recruitment to the commercial fishery. 



With such an enormous mortality intervening between successive adult 

 generations it is hardly surprising to find that recruitment usually fluctuates 

 widely. There are, nevertheless, marked differences in the degree of recruitment 

 fluctuations in various stocks. In the North Sea haddock, for example, the 

 abundance at recruitment of the 30 year-classes which have been sampled since 

 1920 has varied over a 500-fold range ; in contrast, the variation of recruitment 

 to the North Sea plaice population over 26 year-classes has been only six-fold, 

 with an average variation of about 35% above or below the mean (Beverton, 

 1962). Since the range of adult population size of the two species over the 

 periods in question has been of the same order, between about six- and ten-fold 



