Gledhill and Lyczkowski-Shultz: Indices of Scomberomorus cavalla abundance in the Gulf of Mexico 



685 



quency of occurrence was ultimately accepted as a tuning 

 variable, abundance was not because larval catches had 

 not been adjusted for age. Interannual differences in age 

 composition of sampled larvae could contribute a large 

 amount of variation in estimates of mean annual abun- 

 dance because of the exponential decline in numbers of 

 larvae with age. Furthermore, it was thought that survey 

 estimates of larval abundance would be too variable to 

 be of value as an index of stock size owing to the highly 

 variable nature of larval mortality rates.- In our study, we 

 developed an age-adjusted larval index for king mackerel 

 and evaluated the appropriateness of using larval indices 

 in calibrating the king mackerel VPA. 



regi'ession procedure to fit a single model for all years with 

 test statements that tested for homogeneity of intercepts 

 and of slopes. Instantaneous daily mortality rates and an 

 age-adjusted index of abundance were then calculated. 



The age-adjusted index for king mackerel was based 

 on the abundance of a single age class to eliminate the 

 influence of variable larval age composition among years. 

 We arbitrarily chose one-day-old larvae as the standard 

 age class on which to base the age-adjusted index. We 

 estimated the density of one-day-old larvae at each sta- 

 tion by back-calculating and summing their numbers from 

 older age classes using an estimate of daily instantaneous 

 mortality rate. The density of one-day-old king mackerel 

 larvae at each station was estimated as 



Materials and methods 



King mackerel larvae in the Gulf of Mexico have been col- 

 lected annually since 1982 during Southeast Ai'ea Monitor- 

 ing and Assessment Progi-am (SEAMAP) ichthyoplankton 

 surveys conducted by the states of Florida, Alabama, Mis- 

 sissippi, Louisiana, and by the National Marine Fisheries 

 Service. Larvae were captured in oblique tows from near 

 bottom to the surface with a 61-cm, 0.333-mm-mesh bongo 

 net by following standardized SEAMAP collection proce- 

 dures (Richards et al., 1993). Sui-vey stations were typi- 

 cally located 55.56 km apart in a fixed grid, and sampled 

 at all times of day or night. Collections were taken west 

 of 88°W longitude in June and July from 1982 to 1985. 

 Starting in 1986, gulf-wide samples were also collected in 

 late August, September, and early October Catches of king 

 mackerel larvae were standardized to account for sam- 

 pling effort and expressed as number of larvae under 10 

 m^ of sea surface (no./lO m^). Annual mean abundances, 

 i.e. the indices not adjusted for age composition of larval 

 catches, were based on arithmetic means. LIse of the delta- 

 distribution (Pennington, 1983) did not lower estimates of 

 standard error. 



The age composition of king mackerel larvae captured 

 at each station was estimated by converting lengths to 

 ages with a least squares regression model based on the 

 length and age of larvae (n=47) collected in September 

 1986 from the Gulf of Mexico and Atlantic Ocean and aged 

 by counting otolith gi-owth increments' (DeVries et al., 

 1990). Two additional techniques for assigning larval ages 

 from lengths were considered, namely a probability age- 

 classification matrix (Scott, et al., 1993) and discriminant 

 analysis, but these were found to be ineffective owing to 

 the small number of aged lai-vae. Once ages were assigned, 

 individual catch curves for each year of the time series 

 from 1982 to 1995 were constructed from the descending 

 arm of log^-transformed catch-at-age data (Ricker, 1975) 

 by using the regression procedure of SAS (SAS Institute 

 Inc., 1990). A dummy-variable model was used in the 



^I«,.,., 



where 7^,^ = the number of one-day-old larvae under 



10 m- of sea surface (j=year; s=station); and 



N^,^^ = the number of larvae under 10 m- of sea 



surface of each age class represented in the 



sample (!=age class). 



Annual mean age-adjusted index of larval abundance was 

 estimated as the average of station values. 



Annual estimates of spawning stock size (ages 1 through 

 11-1- years) were obtained from a VPA of king mackerel.^ 

 No king mackerel larval occurrence data from SEAMAP 

 were used to tune this VPA. However, the VPA used for 

 the most recent stock assessment was calibrated with 

 larval occurrence data. Residual plots from regi'essions 

 between the VPA estimate of stock size indices of larval 

 abundance exhibited no particular pattern; therefore data 

 were not transformed for correlation analyses. Correlation 

 between the VPA estimate of spawning stock size and 

 three SEAMAP larval indices were then estimated by 

 using the correlation procedure of SAS (SAS Institute Inc., 

 1990). Larval indices used were 1) frequency of occurrence; 

 2) mean abundance of all larvae captured unadjusted for 

 age; and 3) mean abundance of age one-day larvae. 



Results 



The SEAMAP survey king mackerel larval frequency of 

 occurrence index ranged from 0.02 (SE=0.017, CV=100%) 

 in 1983to0.32(SE=0.038, CV=129nin 1995 (Table D.The 

 survey lai'val abundance index (no./lO m-) ranged from 

 0.23 ("SE=0.228, CV=100'7f) in 1983 to 5.15 (SE=0.924; 

 CV=18'"'f ) in 1995 (Table 1). Mean frequency of occurrence 

 and abundance of king mackerel lai^vae varied more 

 during the first four years of the time series when obser- 

 vations were available from only the early part of the 

 spawning season, i.e. summer months. However, both fre- 

 quency of occurrence and abundance have increased over 



- Powers, J. E. 1996. Personal conimun. Southeast Fisheries 

 Science Center, Miami Laboratory, Miami, FL 33149. 



■' DeVries, D. 1996. Personal comniun. Southeast Fisheries Sci- 

 ence Center, Panama City Laboratory, Panama City, FL 32407. 



Legault, C. 1998. Personal commun. Southeast Fisheries 

 Science Center, Miami Laboratory, Miami, FL 33149. 



