Gledhill and Lyczkowski-Shultz: Indices of Scomberomorus caval/a abundance in the Gulf of Mexico 687 



series. Annual estimates of mean king mackerel occurrence 

 were more precise than the estimates of larval abundance, 

 and CVs for both king mackerel indices were comparable 

 to CVs of ichthyoplankton-based estimates for other species 

 (Hunter and Lo, 1993). Lai-val abundance of Atlantic bluefin 

 tuna, a species that poses a more intractable sampling prob- 

 lem than does king mackerel, namely an immense spawn- 

 ing area (the open Gulf) and lower overall abundance, has 

 been used as a tuning variable in population assessments 

 by VPA (Scott etal., 1993). 



The use of a simple larval index for monitoring stock 

 size is not unprecedented. Data from larval surveys of 

 Atlantic herring iClupea harengiis harcngus) in the North 

 Sea have been used since 1967 as the sole source of infor- 

 mation on stock size or in combination with catch sta- 

 tistics or acoustic surveys, or both (Heath, 1993). One of 

 the two larval indices for North Sea herring, the larval 

 abundance index, employs only larvae less than 10 mm in 

 length (up to 15 days old ). The correlation between this 

 larval index and stock size became weaker with increasing 

 age of lai-vae owing, it was surmised, to interannual varia- 

 tion in mortality and dispersal. The potential influence of 

 varying mortality rates and dispersal were likewise mini- 

 mized in our study because most king mackerel larvae col- 

 lected during the SEAMAP surveys were less than 5 mm 

 and no more than ten days old. The other larval herring 

 abundance index for the North Sea, the lai-val production 

 estimate, utilizes all size and age gi-oups to estimate the 

 abundance at hatching and requires estimates of growth 

 and mortality rates. Both herring indices are calculated 

 annually; however, the actual use of each in VPA assess- 

 ment is dependent on survey coverage in time and space 

 in relation to spawning events for that year. 



Our attempt to account for differences in larval age com- 

 position among years by adjusting the index for mortality 

 of larvae did not improve the correlation with stock size. 

 There are a number of reasons for this outcome. It is very 

 likely that the limited age-at-length data available for con- 

 version of king mackerel lengths to age probably resulted 

 in imprecise assignment of ages. Overestimation of age by 

 a single day would result in a TOf error in the backcal- 

 culated abundance of age one-day fish, and a 41% error if 

 underestimated. Hauser and Sissenwine (1991) noted that 

 estimates of lai-val production using "back-calculation tech- 

 niques," as we did to estimate the abundance of one-day- 

 old king mackerel larvae, will be biased if the growth rate 

 used is incorrect or if mortality is size dependent, or both 

 conditions transpire. It is also likely that the assumption 

 of constant mortality rate, an integi-al part of catch curve 

 analysis, did not hold for king mackerel larvae. Bailey et 

 al. (1996a; 1996b) found that early mortality rates of wall- 

 eye pollack larvae were not only highly variable among 

 years but declined as larvae became older. Furthermore, 

 the observation that instantaneous mortality rates of king 

 mackerel larvae among years were not significantly differ- 

 ent may be caused by the low number of larvae caught 

 and the small number of age classes represented in col- 

 lections (Comyns, 1997). However, an age-adjusted index 

 calculated with annual estimates of mortality rate had a 

 much poorer correlation with stock size; therefore we did 



< 



£1 

 < 



VPA stock size (number x 10^) 

 Larval abundance index (mean/100 m'^) 

  Larval occurrence (percent) 



1980 



1984 



1988 



1992 



1996 



B 



30 



20 



10 



 Age-adjusted index (mean/1 m^) 



1982-1995 '•=0 65(P=0 011) 

 1986-1995 r=0 78 (PsO 008) 



1980 



1984 



1988 



Year 



1992 



1996 



Figure 1 



(A) King mackerel adult spawning stock size (number x 10'' 

 offish in the 1 through 11-h age groups) estimated by VPA, 

 survey larval index of abundance (mean number under 

 100 m- of sea surface ±SE), and survey larval frequency of 

 occurrence ( percent of stations where larvae were captured 

 ±SE). (Bl Annual age-adjusted larval index of abundance 

 (mean number under 10 m- of sea surface). 



not report these data. Our estimate of mortality (Z=0.53) 

 may be biased high owing to net selectivity, i.e. avoidance 

 of the net by larger larvae. To correct this bias, we trun- 

 cated the upper 20% of the size distribution and recalcu- 

 lated mortality rates and an age-adjusted index. Although 

 the mortality estimate was lower (Z=0.43), the correlation 

 between stock size and the age-adjusted index based on 

 this mortality rate did not differ from the correlations 

 based on nontruncated distributions. 



Another measure of king mackerel stock size was con- 

 sidered, namely the VPA-generated estimate of egg pro- 



