FISHERY BULLETIN: VOL. 87, NO. 2, 1989 



sizes, all shells encountered in the tagging area (con- 

 tained within the study site) were measured from 

 1980 on. Because of the low number of abalones 

 recovered in the random quadrats in 1981, additional 

 quadrats were selected to increase the sample size 

 for the mortality analysis. A sixth visit was con- 

 ducted in June 1984 to assess the effects of the 

 strong El Nino of 1982-84 (Tegner and Dayton 

 1987) on the growth of the tagged abalones; shells 

 were also collected at this time. 



Mortality Rate 



Total mortality rate was estimated from the 

 length-frequency data using the method of Fournier 

 and Breen (1983; Breen and Fournier 1984). For 

 each year, observed numbers in each 3 mm length 

 interval were converted to proportions of the total 

 sample, then multiplied by the density in the des- 

 truct quadrats. Observations were then summed for 

 all years 1978-82, and then multiplied by 100 as 

 numbers were so small. The Fournier and Breen 



method simultaneously estimates the mean lengths- 

 at-age, the standard deviations of lengths-at-age 

 around their mean, the variance of mean lengths 

 around a von Bertalanffy growth curve, the three 

 von Bertalanffy growth parameters (tf, , asymptotic 

 length L„ , and Brody coefficient K), total instan- 

 taneous mortality rate Z, the population proportions- 

 at-age, and the variance of proportions-at-age 

 around a smooth exponential decay curve. Some of 

 these estimates can be fixed or constrained so that 

 existing knowledge is used in obtaining estimates. 

 The number of age classes and various initial con- 

 ditions must be specified. 



Fournier and Breen (1983) used this method to 

 estimate natural mortality rate by sampling aba- 

 lones in unfished populations. In the population de- 

 scribed here, we can estimate only total mortality 

 rate because the population has been subjected to 

 exploitation. The natural mortality rate must be less 

 than this estimate. The minimum legal size for the 

 commercial fishery is close to the average maximum 

 size, and because this method estimates average 



Table 1.— Parameter values and initial conditions used in estimating mortality rates of red abalones, 

 and ttieir rationale. Parameters wittiout good rationale were varied (see Table 6) to determine ttie sen- 

 sitivity of the estimate. 



316 



