Zheng et al: Catch-length analysis for crab populations 



581 



decades (Stevens et al. 1 ). The abundances peaked in 

 the late 1970s and then declined more than 30-fold 

 during the early 1980s (Fig. 1 ). A moderate recovery 

 occurred in the late 1980's and early 1990s; then 

 abundances decreased again during the last three 

 years. The estimated abundances by different weight- 

 ing factors with natural mortality of 0.3 generally 

 reflected this trend of crab abundance with different 

 accuracies, although modeled estimates were gener- 

 ally lower than the survey abundances (Fig. 1). The 

 commercial CPUE was adjusted to the same scale as 

 abundances to facilitate comparison, but it did not 

 track well with the abundance trend estimated from 

 the trawl surveys. The CPUE's were much higher in 

 1974 and 1975 and much lower in 1977 and 1978 

 than expected from the survey data. The CPUE's from 

 1984 to 1993 fluctuated around a low level, whereas 

 the abundance increased and then decreased during 

 the same period (Fig. 1). The estimated abundances 

 from catch-length analyses with A = and A = 1 were 

 very similar, but the abundances in recent years 

 tended to increase beyond a reasonable level with- 

 out constraints on fishing effort or the recruitment 

 in the terminal year for A= 0. The upper limit of re- 

 cruitment in the terminal year ( 1993) with A = was 

 set to that estimated with A = 1 to stabilize estimates. 

 High weighting factor, A = 3 or A = 10, forced the 

 abundance estimates close to the trend of CPUE. 

 Overall the estimated abundance with A = 1 most closely 

 followed the trend of survey abundances ( Fig. 1 ). 



The estimated abundances with different instan- 

 taneous natural mortality rates followed the trend 

 of survey abundances, and higher natural mortali- 



ties resulted in higher abundance estimates (Fig. 2). 

 Generally, M = 0.4 produced absolute abundance es- 

 timates closer to the trawl survey than other natu- 

 ral mortalities. Variable natural mortality, expressed 

 as three different levels, produced abundance estimates 

 between those with M of 0.2 and 0.5, providing improve- 

 ment in abundance estimates only during the early 

 1980's when high natural mortality occurred (Fig. 2). 



The observed catches by length were compared to 

 estimated catches by length from the model fit with 

 A = 1, with constant M of 0.3 and 0.5, and with three 

 levels of M (Fig. 3). All three fits of the model pro- 

 duced similar catches by length and fit the observed 

 data very well. 



The observed and estimated fishing efforts have a 

 similar overall trend but differed by up to 50% in 

 some years (Fig. 4). As expected, larger weighting 

 factors resulted in estimates of fishing effort closer 

 to the observed level. 



To explore further the effects of parameters A and 

 M on model results, we compared estimated length 

 compositions of recruits and molting probabilities for 

 the two most disparate fits (Fig. 5). There was very 

 little variation in length compositions of recruits 

 among different fits. The difference in molting prob- 

 abilities was less than 15% between any two fits for 

 any given length class within the same time period 

 (Fig. 5) and was less than 5% among most fits for a 

 given length class. The average molting probabili- 

 ties from all fits for the first group of years were simi- 

 lar to the average molting probabilities estimated by 

 Zheng et al. ( 1995) from the survey data with one ex- 

 ception. The molting probabilities for the period 1980- 



74 75 76 77 78 79 80 81 82 83 84 85 86 87 

 Year 



89 90 91 92 93 



Figure 1 



Comparison of estimates of total legal male abundance for 

 Bristol Bay red king crab, with M = 0.3 and with different 

 weighting factors (A). The fishery CPUE (mean catch of 

 legal male crabs per pot lift) was scaled to the same level 

 as abundances. Also shown are NMFS trawl survey esti- 

 mates of abundance. 



60 



50 

 40 

 30 



20 



10 





m 



74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 

 Year 



Figure 2 



Comparison of estimates of total legal male abundance for 

 Bristol Bay red king crab modeled with weighting factor 

 A = 1 and with either constant or variable M at three lev- 

 els: 0.2 for 1974-79 and 1985-93, 0.7 for 1980 and 1983- 

 84, and 1.2 for 1981-82. Trawl survey estimates of abun- 

 dance are also shown for comparison. 



