576 



Abstract. -A catch-length model 

 was constructed to estimate abundance 

 of crab populations for which no sur- 

 vey data are available. The model in- 

 corporates stochastic growth by length 

 and gradual recruitment over length 

 and assumes constant catchability. Re- 

 quired data include catch by length and 

 shell condition, fishing effort, growth 

 increment per molt by length, and an- 

 nual natural mortality rate. Model ap- 

 plication to red king crab populations 

 in Bristol Bay and off Kodiak Island, 

 Alaska, generally provides accurate 

 estimates of trends of relative popula- 

 tion abundances. The accuracy of ab- 

 solute abundance estimates depends on 

 knowledge of natural mortality. The 

 model provided a good fit to the catch 

 by length and shell condition for both 

 populations. In comparison to popula- 

 tion abundances estimated directly 

 from surveys, the catch-length model 

 performed best with instantaneous 

 natural mortality set equal to 0.4 and 

 with fishing effort and catch-length/ 

 shell composition weighted equally in 

 the calculation of residual sum of 

 squares. 



A catch-length analysis for crab 

 populations* 



Jie Zheng 



Margaret C. Murphy 

 Gordon H. Kruse 



Alaska Department of Fish and Game 



Commercial Fisheries Management and Development Division 



PO Box 25526 



Juneau, Alaska 99802-5526 



Manuscript accepted 1 April 1996. 

 Fishery Bulletin 94:576-588 ( 1996i. 



Molting is one of the most impor- 

 tant biological differences between 

 crabs and fishes. The hard structure 

 of crabs is replaced during molting, 

 which makes direct ageing of crabs 

 extremely difficult. The molting pro- 

 cess of an individual crab is short, 

 normally a few days, resulting in 

 punctuated growth. Molting fre- 

 quency of red king crab (RKC, 

 Paralithodes camtschaticus) de- 

 pends on body size and varies over 

 time (Balsiger, 1974). Thus, ability 

 to age crabs indirectly by conven- 

 tional length-frequency analysis is 

 questionable. Without age informa- 

 tion, a conventional catch-age 

 analysis cannot be applied to crab 

 populations. 



An alternative to a catch-age 

 analysis is a catch-length analysis 

 which combines information on fish- 

 ing effort, catch at length, growth, 

 and natural mortality to estimate 

 recruitment and population abun- 

 dance. During the past decade, 

 much progress has been made to 

 improve catch-length analysis. Lai 

 and Gallucci (1988) examined the 

 effects of parameter variation on 

 length-cohort analysis, Fournier 

 and Doonan (1987) developed a 

 length-based production model, and 

 Schnute (1987) derived a general 

 size-structured population model. 

 Sullivan et al. ( 1990) constructed a 

 catch-length analysis which incor- 

 porates stochastic growth and sepa- 

 rates recruitment into year and 



length components. However, most 

 catch-length analyses were devel- 

 oped or applied to fish populations. 

 Some size-frequency analyses have 

 been conducted for decapods (Jones, 

 1979; Caddy, 1987; Fogarty and 

 Idoine, 1988 ), but to our knowledge, 

 few catch-length analyses have 

 been applied to crabs. 



Some commercially important 

 crab populations are assessed an- 

 nually by trawl surveys, and popu- 

 lation abundances can be directly 

 estimated from assessment data. 

 Previously, we developed a length- 

 based population model using such 

 crab survey data to estimate popu- 

 lation parameters and to improve 

 abundance estimates (Zheng et al., 

 1995). However, for many crab 

 populations the only usable data 

 available are fishing effort and 

 catch at length. Thus, a logical 

 choice is to estimate abundance of 

 crab populations using these data. 



Our purpose in this study is to 

 develop a catch-length analysis to 

 estimate population size for unsur- 

 veyed crab populations. We modi- 

 fied the length-based population 

 model developed by Zheng et al. 

 ( 1995) for application to fishing ef- 

 fort and catch-at-length data that 

 are routinely collected from many 



Contribution PP-111 of the Alaska Depart- 

 ment of Fish and Game, Commercial Fish- 

 eries Management and Development Di- 

 vision, Juneau, Alaska. 



