586 



Fishery Bulletin 94(3), 1996 



Discussion 



Two alternative models have been developed for RKC 

 populations. A measurement error model using catch 

 and survey data was developed to smooth out mea- 

 surement errors in abundance estimates oflegal male 

 crabs composed of two groups: recruits and post- 

 recruits (Collie and Kruse, in press; Kruse and Col- 

 lie 2 ; Collie 3 ). The expanded version of the measure- 

 ment error model is a length-based population model 



400 



360- 



320 



.'3D 

 240 

 000 

 160 



80 



40 



64 66 68 70 72 74 76 78 80 82 

 Year 



Figure 9 



Comparison of observed and estimated fishing efforts of 

 the Kodiak red king crab fishery modeled with weighting 

 factor A = 1 and constant M of 0.3 and 0.5 and with weight- 

 ing factor A = 3 and 10 and constant M of 0.3. 



1495 1545 159.5 164 5 169.5 174.5 179.5 184 5 

 Carapace length (mm) 



Figure 10 



Comparisons of length compositions of recruits (e: A=0 and 

 M=0.3, f: A=10 and A/=0.3), molting probabilities during 

 periods 1966-71 and 1973-79 (c: A = l and M=0.2, d: A = l 

 and M=0.5), and during periods 1964-65, 1972, and 1980- 

 82 (a: A=l and M=0.b, b: A=0 and Af=0.3 1 from the two most 

 disparate fits among all model fits for Kodiak red king crab. 



that incorporates stochastic growth and gradual re- 

 cruitment over length and that estimates abundances 

 of mature crabs of both sexes (Zheng et al., 1995). 

 The length-based model also provides a means to 

 study stock-recruitment relationships and can be 

 used to evaluate harvest strategies. The catch-length 

 analysis we developed in this study is a simplified 

 version of the length-based model constructed by 

 Zheng et al. ( 1995 ) and is meant to be applied to crab 

 populations for which no surveys are conducted. The 

 length-based model estimates abundance by produc- 

 ing the best fit to length-frequency data from the 

 survey and the catch-length analysis estimates abun- 

 dance by producing the best fit to length-frequency 

 and fishing-effort data from the commercial fleet. The 

 catch-length analysis generally provides accurate 

 estimates of trends of relative population abundances 

 and gives reasonable estimates of absolute abun- 

 dances provided that M can be approximated. 



The legal male crab abundances estimated from 

 the survey data for both populations were assumed 

 to be absolute and were used to gauge the reliability 

 of the catch-length analysis. A systematic approach 

 was used to survey both populations with complete 

 coverage of areas occupied by large-size crabs 

 (Peterson et al., 1986; Stevens et al. 1 ). The length 

 frequency of crabs caught by the survey gears in 

 Bristol Bay and Kodiak indicated that the selectiv- 

 ity of legal male crabs is about equal to one. 

 Catchability of survey gears is difficult to estimate. 

 Zheng et al. (1995) assumed the catchability of the 

 trawl survey for Bristol Bay legal male RKC to be 

 one, and Collie and Kruse (in press) showed that 

 catchabilities oflegal male RKC for both populations 

 are close to one. Therefore, our assumption of abso- 

 lute crab abundances from the survey estimates is rea- 

 sonable. If this assumption is invalid, the survey abun- 

 dances still represent relative population abundances, 

 but we cannot use them to compare different levels of 

 natural mortality in the catch-length analysis. 



The most important parameter affecting total 

 abundance estimates from the catch-length analysis 

 is M, which has to be estimated separately from the 

 analysis. Published natural mortalities for RKC vary 

 greatly from one study to another and are probably 

 a function of time and length (Schmidt and Pengilly, 

 1993; Zheng et al., 1995). A constant M of 0.3 was 

 assumed for both Bristol Bay and Kodiak legal male 

 RKC (Kruse and Collie 2 ; Collie 3 ; NPFMC 4 ). Our re- 



NPFMC (North Pacific Fishery Management Council). 1990. 

 Environmental assessment for Amendment 1 to the fishery 

 management plan for the commercial king and Tanner crab fish- 

 eries in the Bering Sea/Aleutian Islands. North Pacific Fish- 

 ery Management Council, Anchorage, AK, 27 p. 



