Myers and Barrowman; Is fish recruitment related to spawner biomass? 



723 



subsequent recruitment can be rejected. These con- 

 clusions hold for almost every species and family 

 analyzed. These results also help to explain the 

 widely-held belief that spawner abundance and re- 

 cruitment are not related. When there is little varia- 

 tion in spawner abundance, no practical relation be- 

 tween spawners and subsequent recruitment may 

 seem to be the case; however, wider ranges of spawner 

 data reveal that the relationship holds. Sadly, many 

 of the populations for which wide ranges of spawner 

 data are available are those that have been fished to 

 low levels, perhaps due, in part, to a rejection of 

 spawner- recruitment relationships. 



Our results are robust. We have considered three 

 different approaches to our general question, and in 

 each case the results are consistent with the hypoth- 

 esis that recruitment is indeed linked to abundance 

 of spawners. Errors in estimation of spawner abun- 

 dance should have the effect of reducing the signifi- 

 cance of our tests (Judge et al., 1984, chapter 5). For 

 example, for our third question, errors in estimating 

 spawner abundance would result in misclassifying 

 observations and would reduce the magnitude of 



All stocks 



Salmonidae 



i ' '"""I r 



1 10 100 1000 



Gadidae 



Clupeidae 



5 10 50 



Max(spawners)/min(spawners) 



Figure 5 



Test of the hypothesis that our results are caused by 

 autocorrelation of recruitment. This scatterplot repeats the 

 analysis shown in Figure 2 (the relative rank of spawner 

 abundance for the highest recruitment versus the ratio 

 ^max^m,n^' exce Pt that populations with an autocorrelation 

 in recruitment of 0.4 or greater are eliminated. Data points 

 from series with fewer than 10 pairs of observations are 

 shown as open circles. If spawner abundance and recruit- 

 ment were independent, the distributions would be expected 

 to have a median of 0.5. To help summarize the data, curves 

 representing cumulative (from the right) weighted means 

 are superimposed on the plots in each figure. 



R aboiJ R below A second potential source of bias 

 arises in the statistical analysis of spawner-recruit- 

 ment relationships because the "independent" vari- 

 able, spawners, is not independent of the interannual 

 variation in the spawner-recruitment relationship. 

 For a given spawning population, above-average re- 

 cruitment tends to result in higher spawning popula- 

 tions, whereas below-average recruitment tends to re- 

 sult in lower spawning populations. This is called "time 

 series bias" and causes the density-dependent mortal- 

 ity to be overestimated (Walters 1985, 1990; Myers and 

 Barrowman, 1995). If this source of bias is important 

 in our problem it will cause our conclusions to be con- 

 servative because the importance of density-dependent 

 mortality will be overestimated, and thus recruitment 

 would appear to be less positively related to spawners. 

 Some, who are not familiar with the fisheries lit- 

 erature, may consider our analysis unnecessary be- 

 cause the results seem obvious. However, the results 



