Fishery Bulletin 94(4), 1996 



B 



"below 



500 1000 1500 



Spawning stock biomass (thousand tons) 



Figure 1 



Illustration of the three nonparametric methods applied 

 to spawner-recruitment data for Labrador-Newfound- 

 land cod (Cod NAFO 2J3KL, Table 1). Here spawner 

 abundance is measured as spawning stock biomass. (A) 

 The maximum recruitment is R and the correspond- 

 ing spawner abundance is S Rmax . which ranks 26th out 

 of 28. Hence r max = (26-DA28-1) = 0.93. Similarly, the 

 minimum recruitment is R and the corresponding 

 spawner abundance is S Rmln which ranks 8.5 out of 28 

 (since there is a tie). Hence r max = (8.5 -l)/(28 -1) = 

 0.28. (B) The mean recruitment below the median 

 spawner abundance is R below whereas the mean recruit- 

 ment above the median spawner abundance is R t . . 



tested the null hypothesis that the weighted mean rela- 

 tive rank is less than or equal to 0.5 versus the alter- 

 native hypothesis that it is greater than 0.5 . A sampled 

 randomization test (Manly, 1991) of the null hypoth- 

 esis of independence was easily performed. For the zth 

 series, a random rank between 1 and n, was selected, 

 and the corresponding relative rank computed. This 

 was performed for each series, and the weighted mean 

 of the relative ranks was then computed. Repetition of 

 this procedure (10,000 times sampling with replace- 

 ment) gives an empirical null distribution of weighted 

 mean relative ranks. If m of these 10,000 weighted 

 means were greater than or equal to the observed 

 weighted mean, we then assigned a one-sided P-value 

 of njioi- The smallest one-sided P-value is thus u ,',„„. 



All stocks 



Salmonidae 



Clupeidae 



Max(spawners)/min(spawners) 



Figure 2 



Scatter plots of the relative rank of spawner abundance 

 for the highest recruitment versus the ratio S /S for 



° max mm 



all stocks and for three major families. Data points from 

 series with fewer than 10 pairs of observations are shown 

 as open circles. The horizontal axis has a logarithmic scale. 

 If spawner abundance and recruitment were independent, 

 the distributions would be expected to have a median of 

 0.5. To help summarize the data, we superimposed curves 

 representing cumulative (from the right) weighted means 

 on the plots in each figure. 



As with the cumulative weighted means, we took 

 into account the varying reliability of the data based 

 on the range of spawner abundance. Therefore, we 

 performed significance tests beginning with the data 

 having large values of S max /S nu „ and progressively 

 including data with smaller values of S max /S min . 



For each family, the highest recruitment tends to 

 occur when spawner abundance is high (Fig. 2). The 

 cumulative weighted means never fell below 0.5 for 

 any family. The cumulative weighted mean began 

 on the right-hand side and accumulated to the left- 

 hand side because we had greater confidence in the 

 relative ranks obtained from time series having wide 

 ranges of spawner abundance. Consequently, the 

 value of the cumulative weighted mean on the ex- 

 treme left-hand side encompassed all the data shown 

 in the plot. Using the sample size as a weighting fac- 

 tor, we incorporated a greater confidence in the rela- 

 tive ranks obtained from long time series. The ran- 

 domized test showed that the null hypothesis that 



