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



719 



the weighted mean relative rank is less than or equal 

 to 0.5 can be rejected for all stocks combined and for 

 most of the taxonomic groups considered (Table 2A). 

 In moving from left to right in the figure, the sample 

 size used in the test decreased, whereas the reliabil- 

 ity of the data (as gauged by S max /S m ,„) increased. 

 The tests were performed for all stocks, and sepa- 

 rately for 3 major families. The overall trend of in- 

 crease from left to right was due to the loss of power 

 as the sample size used in the test decreased. 



Hypothesis 2: Does the smallest recruitment 

 occur when spawner abundance is low? 



Next, we examined r,„, n , the relative rank of spawner 

 abundance for the lowest recruitment (Fig. 1A). This 

 time, r m „, = implies that the lowest recruitment 

 occurs for the lowest spawner abundance, whereas 

 /•„,,„ = 1 implies that the lowest recruitment occurs 

 for the highest spawner abundance. As before, cu- 

 mulative weighted means were calculated and a ran- 

 domization test was performed. 



The lowest recruitment tended to occur when 

 spawner abundance was low (Fig. 3). Again, the pat- 

 tern held for all stocks combined and for most of the 

 taxonomic groups considered. The effect for the low- 

 est recruitment appeared to be less than the effect 

 for highest recruitment. The statistical significance 

 of the results is usually less than 0.05, but there is a 

 tendency for the significance to be reduced if the 

 range of spawners is small (Table 2B). 



Hypothesis 3: Is recruitment greater if 

 spawner abundance is above rather than 

 below the median? 



Finally, for each spawner-recruitment series we 

 asked whether the mean recruitment is the same 

 when the spawner abundance is below or above the 

 median. We split each spawner-recruitment series 

 into two sections: the first section at or below the 

 median spawner abundance, and the second section 

 above the median spawner abundance. We then com- 

 puted the mean recruitment for each section, which 

 we denote as R above an ^ R below respectively. When the 

 mean recruitment is identical on both sides of the 

 median spawner abundance, the ratio R aoove l R oe i ow 

 equals 1, or equivalently log( R abov J ' R below) = 0. A 

 distribution-free test of this null hypothesis is the 

 one-sample Wilcoxon signed rank test ( Conover, 1980; 

 Lehmann, 1975). We computed the ranks of the ab- 

 solute values of the log ratios. The test statistic was 

 given by the sum of the ranks of the positive log ra- 

 tios. The logarithm was used because ratios of (for 

 example) 1:2 and 2:1 would result in ties. 



All stocks 



Salmonidae 



1 10 100 1000 



Gadidae 



1 10 100 1000 



Clupeidae 



10 100 1000 



Max(spawners)/min(spawners) 



Figure 3 



Scatter plots of the relative rank of the spawner abundance 

 for the lowest recruitment versus the ratio S IS mm for 

 all stocks and for three major families. See Figure 2 for 

 explanation of data points, axis labels, and lines. 



Our alternative hypothesis was that the median of 

 the distribution of log ratios was greater than 0. For 

 this one-sided test, in order to reject the null hypoth- 

 esis (at the 5% significance level), we required at least 

 5 observations. When there were 25 or fewer log ratios, an 

 exact probability for the test was computed; otherwise a 

 normal approximation was used. Note that there were 

 no ties in the absolute values of the log ratios. 



This test is conservative because errors in the es- 

 timates of the range will bias the estimate of the slope 

 downward (Judge et al., 1984). The ratio of the mean 

 recruitment above the median level of spawners to 

 that below, R above l R be i„ w , is greater than 1 for all 

 families if the range of observed spawners is large 

 (Fig. 4). For narrow ranges of spawner data, the ra- 

 tio is closely clustered. When the data are grouped 

 taxonomically, the pattern holds. The Wilcoxon 

 signed rank test shows that the null hypothesis that 

 the median of the distribution of R abuve / R be i ou , is 1 

 can be rejected for all stocks combined and for most 

 of the taxonomic groups considered. 



Taxonomic variation 



The Clupeidae show strong evidence of greater re- 

 cruitment at large spawner-abundance levels. This 



