Abstract.- The inverse method 

 for mortality and growth estimation 

 (IMMAGE) is a new approach to 

 obtain unbiased estimates of mortal- 

 ity and growth parameters for lar- 

 val fishes from length-frequency 

 data biased by the size selectivity of 

 plankton nets. The performance of 

 IMMAGE is compared with methods 

 which attempt to eliminate selection 

 bias from sampled length-frequen- 

 cies. Using Monte Carlo simulations, 

 IMMAGE estimates growth and 

 mortality parameters that are more 

 accurate and precise than those pro- 

 duced by other methods. 



Inverse method for mortality 

 and growth estimation: A new 

 method for larval fishes 



David A. Somerton 



Honolulu Laboratory, Southwest Fisheries Science Center 

 National Marine Fisheries Service, NOAA 

 2570 Dole Street, Honolulu, Hawaii 96822-2396 

 Present address: Alaska Fisheries Science Center 



National Marine Fisheries Service, NOAA 



7600 Sand Point Way NE, Seattle, Washington 98 11 5-0070 



Donald R. Kobayashi 



Honolulu Laboratory, Southwest Fisheries Science Center 



National Marine Fisheries Service, NOAA 



2570 Dole Street Honolulu, Hawaii 96822-2396 



Manuscript accepted 9 March 1992. 

 Fishery Bulletin, U.S. 90:368-375 (1992). 



Estimation of the growth and mor- 

 taHty rates of larval fishes is com- 

 plicated by the sampling biases that 

 can result from the size selectivity 

 of plankton nets. Size selectivity due 

 to net avoidance by larvae, for exam- 

 ple, results in an underestimation of 

 larval abundance that progressively 

 increases with increasing larval 

 length. This bias leads to an under- 

 estimation of mean length-at-age and 

 therefore growth rate, because 

 larger larvae in each age-class are 

 underrepresented relative to smaller 

 larvae. Such bias also leads to an 

 overestimation of mortality rate, 

 because older larvae are underrepre- 

 sented relative to younger larvae. 

 Size selectivity due to extrusion of 

 larvae results in an underestimation 

 of larval abundance that progressive- 

 ly decreases with increasing larval 

 length and likewise leads to bias in 

 estimates of growth and mortality 

 rates. 



Grovirth studies rarely address such 

 size selection, and when they do, the 

 approach taken is usually to devise a 

 sampling procedure that provides un- 

 biased length-frequencies (Methot 

 and Kramer 1979, Yoklavich and 

 Bailey 1990). Mortality studies, by 

 comparison, almost always address 



size selection and do so after the fact 

 by taking one of several approaches 

 to eliminate the selection bias from 

 the sampled length-frequencies. One 

 approach taken by mortality studies 

 is to divide the sampled length-fre- 

 quencies by length-specific estimates 

 of capture probability. Such capture 

 probabilities have been obtained from 

 field studies and estimated as (1) 

 catch ratios of large to small mesh 

 nets (Lenarz 1972, Leak and Houde 

 1987), (2) catch ratios of day to night 

 sampling (Houde 1977, Zweifel and 

 Smith 1981, Morse 1989, Somerton 

 and Kobayashi 1989), or (3) catch 

 ratios of plankton nets to purse 

 seines (Murphy and Clutter 1972, 

 Leak and Houde 1987). Capture 

 probabilities have also been based on 

 theoretical escapement models (Ware 

 and Lambert 1985). A second ap- 

 proach taken by mortality studies is 

 to simply eliminate the biased por- 

 tions of the length distribution. Such 

 elimination may exclude only small 

 (Morse 1989) or large larvae (Houde 

 1977, Methot and Kramer 1979) or 

 both (Essig and Cole 1986). Ehmina- 

 tion of biased length-frequencies also 

 has been combined with the use of 

 capture probabilities (Houde 1977, 

 Morse 1989). 



368 



