Population Dynamics and Stock Assessment of Red King Crab in Bristol Bay, Alaska Jie Zheng Alaska Department of Fish and Game Juneau, Alaska, USA

Summer Survey Abundance

What occurred during early 80s? Speculation: 1)Completely wiped out by fishing: Directed pot fishery Indirected pot fishery (Tanner crab fishery) Trawl (esp. “red bag” hypothesis) 2)High fishing and natural mortality

Summary of early 1980s High fishing mortality in 1980 and 1981 Bycatch from the Tanner crab fishery Trawl observed and unobserved bycatch Older crabs due to slow growth in late 60s and early 1970s Disease could be an issue with record population density Main predator biomass increased 10 times within a few years and highly concentrated in Bristol Bay

High fishing and natural mortality Natural mortality estimated by LBA was much higher in the early 1980s than the other periods My position: “In summary, our results indicate that high natural mortality coupled with high harvest rates may have contributed to and hastened the collapse of the Bristol Bay RKC population. Low spawning biomass in the early 1980s appears to be responsible for its continued lack of recovery.”  from Zheng, Murphy & Kruse (1995)

If actual M increases greatly and the model uses a fixed M, the model will greatly over-estimate population abundance at critical times

Bristol Bay Red King Crab Models 1.Stock assessment model used since 1994 (Zheng et al. 1995a, 1995b, Zheng and Kruse 2002) 2.Research model developed in 2003 and presented for Red King Crab Stock Assessment Workshop in Catch-length model and catch-survey model (Zheng et al. 1996a, Zheng et al. 1996b)

Stock Assessment Model Since 1994 Parameters Estimated Independently: –Length-weight relationship: Personal comm. from Stevens –Growth increment per Molt: tagging data –Mean length of recruits: 95 mm for females, 102 mm for males Parameters Estimated Conditionally: –Recruits for each year except the first –Total abundance in the first year (1972) –Parameters  (growth variation) &  r (R variation) –M t : 4 levels for females & 3 levels for males –Molting probability parameters  1,  2,  3,  1,  2, and  3 for males Parameters assumed: –Survey catchability for mature crabs to be 1.

Length-based Analysis (LBA) Newshell < i Oldshell < i Newshell i Recruitment i Oldshell i Catch Newshell >i N. Mortality Molt No Molt Molt No Molt

Assessments made during

Bristol Bay red king crab model Eastern Bering Sea snow crab model Historical errors

Bristol Bay Research Model Original intent was to use it to study survey catchability, bycatch and “red bag” issues. More complex and less stable results Used to estimate parameters with a constant M and male molting probability for the work group for data

Male model: N l,t and O l,t are newshell and oldshell crab abundances in length class l and year t, M t is instantaneous natural mortality in year t, m l,t is molting probability for length class l in year t, R l,t is recruitment into length class l in year t, y t is lag in years between assessment survey and the fishery in year t, P l',l is proportion of molting crabs growing from length class l' to l after one molt, and C l,t is catch of length class l in year t.

a and b are constants, & is mid-length of a length group. Mean growth increment per molt is assumed to be a linear function of pre-molt length: Growth increment per molt is assumed to follow a gamma distribution: The expected proportion of molting individuals growing from length class l1 to length class l2 after one molt is equal to the sum of probabilities with length range [i1, i2) of the receiving length class l2 at the beginning of next year; i.e., For the last length class L, P L,L = 1.

The molting probability for a given length class is modeled by an inverse logistic function: a and b are parameters, and i is the mean length of length class l. Recruitment is separated into a time-dependent variable, Rt, and size-dependent variables, Ul, representing the proportion of recruits belonging to each length class. U l is described by a gamma distribution.

i.e., annual lengths at 50% selectivity follow a random walk process Different sets of parameters (β, L 50,t ) are estimated for retained males, pot female bycatch, trawl male bycatch, and trawl female bycatch Retained selectivities, pot female bycatch selectivities, trawl male and females bycatch selectivities

Different sets of parameters (β, L 50 ) are estimated for males and females. A is set to be for females and for males based on Weinberg et al. (2004). Survey selectivities/catchabilities,

Robust likelihood function For length compositions (p l,t,s,sh ): where L is the number of length groups, T is the number of years, and n is sample size.

Objective function Weighted log-likelihood functions: Weighted λs are assumed to be 6 for retained length compositions, 2 for Trawl survey length compositions, 1 for all other length compositions, 3000 for retained catch biomass, 1000 for survey biomass, and 200 for all other biomasses, 0 for recruitment variation, 1 for recruitment sex ratio, and 0.25 for all annual changes in length of 50% selectivity.

Carapace length (mm) Does the model overestimate molting probability? Model estimate is much lower than those from tagging data by Dr. Balsiger

Newshell males Carapace length (mm)

Mean growth increment per molt, Estimated outside of the population model

Thanks