LO ET. AL.: ESTIMATES OF LARVAL MORTALITY 



would be required to attain the same level of 

 precision. 



Application to CalCOFI Surveys 



Three key assumptions underlie the use of the 

 CalCOFI time sei-ies of larval mortality esti- 

 mates for hypothesis testing: 1) a stable age 

 distribution prevails (i.e., abundance of several 

 cohorts of larvae at one moment in time is repre- 

 sentative of one cohort as it ages through time), 

 2) variations in observed mortality rate repre- 

 sent true natural variations and not sampling 

 error, and 3) use of the same larval gi'owth par- 

 ameters for all years does not bias the estimates 

 of mortality rate. 



The first assumption was not addressed in this 

 study. It impHes negligible immigration and 

 emigi'ation of larvae and continuous production 

 of spawn. The CalCOFI surveys are designed to 

 encompass the anchovy spawning habitat and 

 thus minimize inaccuracies caused by transport 

 of larvae in and out of the survey area. For a 

 species with a broad temporal spawning curve 

 and with repeated spawning by individuals 

 (9-16% of the females spawn each night; table 7, 

 Fiedler et al. 1986), unbiased estimates of mor- 

 tality rate may be obtained by poohng plankton 

 tows conducted throughout the spawning season 

 (table 6, Hewitt and Methot 1982). With smaller 

 surveys and shorter time periods, the assump- 

 tion of a stable age distribution may not be suit- 

 able, and estimates of mortahty rates may be 

 biased. 



With regard to the second assumption, our 

 simulations indicate that the time series of daily 

 mortality rate of anchovy larvae represents pre- 

 dominantly real differences owing to biological 

 variation rather than random variation. Recent 

 CalCOFI ichthyoplankton surveys (Table 9) 

 yielded between 36 and 236 positive tows per 

 spawning season. The simulation model indicates 

 that sample sizes >80 are sufficient to detect a 

 difference of 0.5 or more in the mortality coeffi- 

 cient (p) between years (Table 7). When all pos- 

 sible pairs for the eight surveys (1980-87) are 

 compared, 12 of the 28 comparisons had a differ- 

 ence >0.5 (Table 9). Results of our simulation 

 imply that the precision of past surveys was ade- 

 quate, and the interannual variation in mortality 

 rate ((3 ranged from 1.22 in 1980 to 2.14 in 1986) 

 is real. 



Because larval mortality rate is age-depen- 

 dent (IMR = p/0 with high mortality occurring 

 during the onset of feeding and decreasing there- 



after, variations in daily mortality rates can be 

 typified by "large differences concentrated in a 

 short period of time" and thus be easily detect- 

 able (Gulland 1971). The critical issue in compar- 

 ing mortality rates does not appear to be one of 

 precision but rather one of obtaining a represen- 

 tative sample. 



With regard to the third assumption, the 

 simulation also indicated that the risk of intro- 

 ducing a large bias in estimates of mortality 

 rates by using a single family of standard gi'owth 

 curves is relatively low. A large bias would be 

 expected only when the standard gi-owth curves 

 overestimated the actual gi'owth by a factor of 

 two or more. It is unknown how frequently the 

 standard growth curve generates this large bias, 

 for lack of data on variability of larval gi'owth 

 rates from year to year in the field. 



Table 9. — Number of tows 

 positive for anchovy larvae 

 (n) and mortality coeffi- 

 cients (P) for CalCOFI 

 ichithyoplankton surveys 

 conducted during January 

 thiroughi Apnl 1980-87. 



CONCLUSIONS 



These simulations validate the use of CalCOFI 

 survey information to test hypotheses regarding 

 larval survival and recruitment (Butler 1987, 

 Peterman et al. 1988). The sample size required 

 for adequate precision of estimates of mortality 

 rates is modest relative to the one required for 

 adequate representation of the spawning season 

 and habitat of a major marine stock such as the 

 northern anchovy. As stated, the critical issue in 

 comparing mortality rates does not appear to be 

 precision of the estimates but rather how well 

 the sample represents the population. 



ACKNOWLEDGMENTS 



We would like to acknowledge Paul Smith, 

 who outlined the main consideration necessary 



413 



