Precision and Bias of Estimates of Larval Mortality 



Nancy C. H. Lo, John R. Hunter, and Roger P. Hewitt 



ABSTRACT: The results of four ichthyoplankton 

 surveys conducted during January through April 

 1984 off the coast of California were used as the 

 basis for Monte Carlo simulation of populations of 

 northern anchovy, Engraulis mordax, larvae. The 

 simulated populations were sampled and larval 

 mortality rate was calculated, using established 

 analytical procedures. Results may be used to deter- 

 mine the precision of an estimate of larval mortal- 

 ity rate and to determine the number of plankton 

 tows required to detect a difference in mortality 

 rates between two surveys. The estimated mortality 

 rate was found to be biased high when the larval 

 growth rate is overestimated and biased low when 

 the growth rate is underestimated. The bias is 

 asymmetrically distributed and greatest when the 

 assumed growth substantially overestimates the 

 real growth. The results justify interannual com- 

 parisons of lar>'al anchoN-y mortality rates when 

 interannual variation in larval growth is less than 

 twofold. The results also indicate that the sample 

 size required for adequate precision of estimates of 

 mortality rates is modest compared to that required 

 for adequate representation of the spawning season 

 and larval habitat. 



The early life stages of several fish have been 

 extensively studied as they are the Unk between 

 the present adult stock and some future recruit- 

 ment to the adult stock. Frustrated with the 

 apparent lack of a clear relationship between 

 stock and recruitment, fishery scientists have 

 focused attention on events during the larval 

 stage and their ultimate effect on survival to the 

 juvenile and adult stages. Several hypotheses 

 have been proposed (e.g., Hjort 1913); however, 

 an understanding of the precision and accuracy 

 of estimates of larval mortality rates is neces- 

 sary to distinguish among them (GuUand 1971). 

 This paper draws upon our experience with the 

 northern anchovy, Engraulis mordax, to ad- 

 dress this issue. 

 We focus on three questions: 1) What is the 



Nancy C. H. Lo, John R. Hunter, and Roger P. Hewitt: 



Southwest Fisheries Center, National Marine Fisheries 

 Service, NOAA, P.O. Box 271, La JoUa, CA 92038. 



Manscript accepted March 1989. 

 Fishery Bulletin, U.S. 87: 399-416. 



minimum number of plankton tows required to 

 estimate the mortality rate of young larvae (<20 

 days old) for a given coefficient of variation? 2) 

 What is the minimum number of plankton tows 

 required to detect a difference in the mortality 

 rates of young larvae between two surveys? 3) 

 How does violation of the assumption of a con- 

 stant growth model affect the estimate of larval 

 mortality? 



Several biases associated with sampling north- 

 ern anchovy larvae have been identified and 

 quantified. Pelagic ichthyoplankton are caught 

 by lowering a fine-mesh net to a depth below the 

 larval habitat and by steadily retrieving it to the 

 surface of the ocean (Smith and Richardson 

 1977). VariabiUty in the volume of water filtered 

 per unit of depth affects the number of larvae 

 captured; Ahlstrom (1948) formulated the "stan- 

 dard haul factor" to adjust for this bias. Larvae 

 are extruded through the meshes of the sam- 

 pUng gear: retention rates can be expressed as a 

 function of larval length and mesh size (Lenarz 

 1972; Zweifel and Smith 1981; Lo 1983). Larvae 

 also evade capture as evidenced by differences in 

 the night and day catch rates (Ahlstrom 1954; 

 Smith 1981): retention rates can be expressed as 

 a function of larval length and the diurnal time of 

 capture (Hewitt and Methot 1982). The apparent 

 length of larvae is affected by abrasion from the 

 samphng net and by the preservative solution: 

 live larval length may be expressed as a function 

 of preserved larval length and the duration of 

 the plankton tow (Theilacker 1980). 



The application of these corrections yields 

 unbiased estimates of the density of larvae in 

 each of several length categories. Age-specific 

 variations in growth introduce variability in the 

 duration of time that a larva of given length is 

 vulnerable to capture. The density of larvae 

 divided by the duration of growth through each 

 length category yields estimates of the number 

 of larvae of a given age produced per unit sea- 

 surface-area per unit time, which is termed 

 larval production (Hewitt and Methot 1982). 

 Yolk-sac larvae growth has been described as a 

 function of temperature (Zweifel and Lasker 



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