708 



Fishery Bulletin 94(4). 1996 



We tried to assemble all time series of reliable data 

 on spawner abundance and recruitment. We started 

 with the 477 time series from the most recent ver- 

 sion of the database by Myers et al. ( 1995b). Of these, 

 77 series were eliminated because they had less than 

 5 years of spawner-recruitment data, 5 series were 

 eliminated because they were for invertebrates, 17 

 pink and chum salmon series were eliminated be- 

 cause they were described as less reliable, and 14 

 series were eliminated because they were different 

 versions of other series or because they overlapped 

 other series. We were left with 364 series. Sometimes 

 the same population was included more than once 

 because of incompatible time periods or because dif- 

 ferent life stages were examined. 



For each population, Table 1 lists the method used 

 to estimate spawner abundance and recruitment. For 

 most marine populations, spawning biomass and 

 recruitment had been estimated by sequential popu- 

 lation analysis (SPA) of commercial catch-at-age 

 data. SPA techniques include virtual population 

 analysis (VPA; Gulland 1 ), cohort analysis (Pope, 

 1972), and related methods that reconstruct popula- 

 tion size from catch-at-age data (Deriso et al., 1985, 

 1989; Megrey, 1989; Gavaris, 1988). For some ma- 

 rine populations, accurate commercial catch-at-age 

 data were not available; therefore research vessel (RV) 

 surveys estimates were used. For a few populations, 

 other types of data were used, e.g. spawning stock bio- 

 mass was estimated from SPA and recruitment was 

 estimated from research vessel surveys. We did not 

 include populations for which there was only commer- 

 cial catch-per-unit-of-effort estimates of abundance. 



For populations in the family Salmonidae, series 

 were sometimes available for several different life- 

 stage transitions. The life stages are denoted in Table 

 1 as follows: a = adults (or eggs); f = fry; s = smolts 

 (sea-bound migrating juveniles); and p = parr (juve- 

 niles within the river). 



For most of the Pacific salmonid populations, the 

 numbers of spawners and recruits were reconstructed 

 from commercial catch-at-age data and independent 

 estimates of fishing mortality or from an indepen- 

 dent estimate of escapement from surveys of spawn- 

 ing, or both. In these cases, the method is termed 

 "stock reconstruction," and is denoted as SR in Table 

 1. Some of the estimates were derived from experi- 

 ments in which the number of spawners and recruits, 

 e.g. number of parr produced, are direct counts. We 

 analyzed data by families and species separately if 

 there were at least 6 populations per taxa. 



Methods and results 



In evaluating the relationship between spawners and 

 recruitment, the range of the spawner data will 

 clearly be important. For near constant spawner lev- 

 els, changes in recruitment will reflect only variabil- 

 ity in density-independent mortality. As an index of 

 the range spanned by the spawner data, we used the 

 ratio S ma JS mm , where S max is the maximum observed 

 spawner abundance and S mtn is the minimum ob- 

 served spawner abundance. When this ratio is near 

 1, the spawner level is nearly constant; the larger 

 its value, the greater the range of spawner data. 

 Values of S max /S min for the data series examined in 

 this paper are listed in Table 1. 



Hypothesis 1 : Does the largest recruitment 

 occur when spawner abundance is high? 



For each spawner-recruitment series we asked 

 whether the highest recruitment, R max , occurred 

 when spawner abundance was high. We computed 

 the rank of the spawner abundance that gave rise to 

 the highest recruitment, S Rmai . In order to compare 

 ranks across populations, we computed a "relative 

 rank" r max = (rank(S ftmat ) -l)/(n - 1), where n is the 

 number of observations in the spawner-recruitment 

 series (Fig. 1A). The relative rank therefore lies be- 

 tween and 1, with r max = implying that the high- 

 est recruitment occurs for the lowest spawner abun- 

 dance, and conversely, with r max = 1 implying that 

 the highest recruitment occurs for the highest 

 spawner abundance. 



To help summarize the data and to test hypoth- 

 eses, cumulative weighted means were calculated. 

 The weighted mean of k relative ranks r maxi is 



> n.i 



Hi 



1 



1 Gulland, J. A. 1965. Estimation of mortality rates. Annex 

 to Rep., Arctic Fish. Working Group ICES Council Meeting 

 1965(31.9 p. 



where n, is the number of observations in the iih 

 spawner-recruitment series. The cumulative 

 weighted mean was calculated by starting with the 

 relative rank associated with the largest value of 

 S max /S min and by continuing through the relative 

 rank associated with the smallest value ofS max /S mm . 

 If, for a given population, spawner abundance and 

 highest recruitment were independent, each possible 

 relative rank would be equally likely, i.e. the expected 

 value of r max , would be 0.5. If this were true for each 

 population, then the expected value of the weighted 

 mean relative rank would also be 0.5. Therefore we 



