Zheng etal: Catch-length analysis for crab populations 



587 



suits indicate that a constant M of 0.4 provides popu- 

 lation abundance estimates closest to the abundances 

 estimated by survey data for both RKC populations. 

 Unlike the results from Zheng et al. ( 1995), variable 

 M over time improved only slightly the abundance 

 estimates from catch-length analysis. Because it is 

 difficult to estimate M for crab populations, we sug- 

 gest that a sensitivity study should be conducted to 

 examine the effect of M on estimated abundances. 

 Although M affects absolute abundance greatly, rela- 

 tive abundance is fairly robust to changes in M. Thus, 

 if we are mainly interested in recruitment or popu- 

 lation trends, such as those used in fishery oceanog- 

 raphy, then uncertainty of M is not a big concern. On 

 the other hand, if we wish to manage an unsurveyed 

 crab stock with a fixed exploitation rate strategy, M 

 must be known fairly accurately in order to avoid 

 consistent over- or under-harvest. 



In contrast to M, weighting factor A primarily af- 

 fects the estimated trend of a population. By weight- 

 ing fishing efforts heavily, the population trend most 

 closely resembles the fishery CPUE. The CPUE for 

 crab pots depends not only on exploitable crab abun- 

 dance, but also on many other factors, such as pot 

 size, soak time, bait, tidal cycle, and vessel charac- 

 teristics. Pot size is limited by regulations in Alaska 

 and has not changed much over time. Soak time is 

 probably the most important factor but generally is 

 not collected for crab fisheries. Tidal information is 

 available, but the relationship between tidal condi- 

 tion and CPUE may be too complex to be used for 

 effort standardization. Vessel characteristics can be 

 used to adjust for temporal changes in fleet composi- 

 tion, but Johnson (1991) found that vessel charac- 

 teristics do not effect the relationship between crab 

 density and CPUE for the Kodiak RKC fishery from 

 1969 to 1982. The CPUE defined as catch per pot 

 lift, which is available for most crab fisheries in 

 Alaska, could explain only partial variation in crab 

 densities. Therefore, heavy weighting of fishing ef- 

 fort would distort the true trend of crab abundance, 

 whereas without fishing effort information the abun- 

 dances in recent years have tended to be over-esti- 

 mated. An error-weighting factor of one generally 

 gave a good fit for both RKC populations. 



Red king crab tend to aggregate by forming pods 

 much in the same way that some fishes form schools. 

 When crab abundance decreases, the area of distri- 

 bution shrinks, and crab density in the remaining 

 area is still relatively high. The overall geographic 

 distribution of Bristol Bay RKC has gradually shrunk 

 since crab abundances peaked in the late 1970's. Such 

 aggregate or schooling behavior may produce 

 depensatory catchability (Clark, 1974). When popu- 

 lation abundances are low, depensatory catchability 



can easily result in overestimates of population abun- 

 dances and overfishing if a constant catchability is 

 assumed. On the other hand, when population abun- 

 dances are high, abundances may be underestimated 

 because of gear saturation (Bannerot and Austin, 

 1983). We modified Equation 10 in a manner de- 

 scribed by Bannerot and Austin (1983) to compare 

 the results between constant and density-dependent 

 catchabilities. Overall, both relative and absolute 

 abundances estimated under a constant catchability 

 assumption fitted closer to the survey abundances for 

 both populations than those fitted under an assump- 

 tion of density-dependent catchability. It is conceivable 

 that our fishery CPUE data may not have sufficient 

 information to estimate density-dependent catchability. 



As with conventional catch-age or cohort analy- 

 ses, without auxiliary information there is great 

 uncertainty in estimating the abundance in the ter- 

 minal year by catch-length analyses. The accuracy 

 of estimated absolute abundance in the terminal year 

 depends on how accurately we can estimate fishing 

 mortality. However, by incorporating fishing effort 

 data, even with large measurement errors, it has 

 been possible to estimate relative abundance trends 

 rather well in most recent years. In cases where fish- 

 ing effort is not available, an upper limit should be 

 set for recruitment in the terminal year to avoid bi- 

 asing the trend of relative abundances upward in the 

 most recent years. 



The selectivity coefficient for the first length class 

 was estimated to be less than one for all scenarios; 

 thus legal crabs with sizes close to the size limit ap- 

 pear to have a lower catchability. Legal male crabs 

 have been mature for at least one or two years and 

 theoretically should fully recruit to the fishing gear. 

 But the observed catch-length frequency shows that 

 length compositions of the first length class were 

 smaller than those of the second length class for both 

 fisheries and for all years except 1993. This selectiv- 

 ity may be partially caused by throwing back some 

 barely legal-size crabs that were incorrectly mea- 

 sured by fishermen. The catch-length analysis may 

 sometimes fail to estimate selectivity because selec- 

 tivity coefficients and recruitment parameters may 

 be confounded. A low proportion of recruitment to 

 the first length class of new-shell crabs can cancel 

 the effect of selectivity. We suggest that the selectiv- 

 ity coefficient for the first length class be interac- 

 tively set to different values less than one during 

 estimation until RSS cannot be further minimized. In 

 recent years, observers have been placed on crab catcher 

 and floater processors in Bristol Bay, and length fre- 

 quency of the catch has been measured before sorting. 

 In the future, comparison of the time series of length- 

 frequency data on presorted and retained catches could 



