Smith and Jamieson: Movement and mortality of Cancer magister 



141 



121og e [s]. 



(2) 



Consequent to Equations (1 a-g), the expected num- 

 ber of recoveries of tagged crabs released in zone i and 

 recovered in zone j after k months-at-large (E ijk ) is 



E ijk = N ijk qlj 



(3) 



where Ij is monthly fishing intensity (Table 1) in zone 

 j, and q is the catchability coefficient (Ricker 1975). 

 We employed a multinomial negative log-likelihood 

 function, the separation statistic 



f\ = 1 O ijk log e [O ijk /E ijk ], for all O ljk >0 (4) 

 ijk 



of Schnute and Fournier (1980), without their factor 

 2, to evaluate the parameter estimates. In total, the 

 11 Qij's in Equations (la-g), q and S required estima- 

 tion. The model was structured to constrain the Qjj's 

 to values between and 1, and to assure the multi- 

 nomial likelihood condition of 



lo 



ijk 



ijk 



= 1 



ijk 



E 



ijk- 



(5) 



Equation (4) measures the discrepancy between ob- 

 served (O ijk ) and expected (Ejj k ) frequencies over all 

 frequency cells, and yields maximum-likelihood param- 

 eter estimates when f 1 is minimized. We used the 

 SIMPLEX algorithm of Nelder and Mead (1965) as im- 

 plemented by Mittertreiner and Schnute (1985) to 

 minimize f l , while approximate standard errors for 

 the estimates were calculated using the numerical 

 method supplied with Mittertreiner and Schnute (1985). 

 This method uses the matrix of second partial deriva- 

 tives of fi with respect to the parameters (calculated 

 numerically) to generate the asymptotic covariance 

 matrix (Kendall and Stuart 1979). For males we applied 

 the analysis only to recoveries obtained after at least 

 one full month-at-large (k>l), because tagged males 

 were released a short time before fisherman were 

 prepared for the mark-recovery program. Consequent- 

 ly our analysis of male movement and mortality is 

 based on a sample size of 864 recoveries rather than 

 the complete sample of 920 recoveries. 



Acoustic tagging 



Freshly activated acoustic tags (Smith-Root Inc., Van- 

 couver, WA) were attached longitudinally to the cara- 

 pace of recently trap-caught hard-shelled male and 

 female Dungeness crabs using fast-drying epoxy. Care 

 was taken to maintain each crab cool and moist while 



the carapace was allowed to air-dry for a short period 

 prior to attachment of the tag. Once the epoxy set and 

 we were confident the bond was secure (about one-half 

 hour), each crab was placed in a bucket with fresh sea- 

 water to assess its vitality. No crabs appeared to suf- 

 fer an obvious detriment from the tagging procedure, 

 so all crabs released were anticipated to survive and 

 transmit location information. 



Once activated, each 61 x 14 mm capsule-shaped 

 acoustic tag emits an acoustic signal characterized by 

 a unique transmitting frequency and pulse rate. The 

 bulk of the tag structure is a battery with a transmit- 

 ting life of =60-90 days. With our direction-finding 

 equipment we were able to identify a strong signal up 

 to =lkm away and subsequently home-in on the loca- 

 tion of a tag by audibly or electronically evaluating 

 changes in signal strength. In our study site we were 

 generally able to define the location of a tag to within 

 =10-25 m of a chart reference. 



During 7-13 August 1986 two male and three female 

 crabs were tagged with acoustic tags, then released 

 near the mouth of Lemmens Inlet (zone 3, Fig. 1). 

 Similarly on 15 November 1986 two male and three 

 female crabs were again tagged and released in the 

 same area. Following the first series of releases we 

 attempted to monitor the location of each crab at least 

 daily, but other commitments, and occasionally being 

 unable to locate the transmitted signal, resulted in the 

 time between observations often exceeding one day. 

 The same limitations applied to the second series of 

 releases, and additionally we only attempted to monitor 

 each crab every three days. All crabs released pro- 

 vided location information for 21-86 days, with the 

 exception of a 140-mm CW male released on 15 

 November 1986 which was never located after its 

 release. 



Mean daily displacement rates for males and females 

 were estimated under the assumption that movement 

 was random from the point of release. We could not 

 entertain a more sophisticated hypothesis with our 

 limited data. Also because of our limited data, we 

 report our results for males and females, and by series 

 (August-October, November-February), with all data 

 from individual crabs combined. Mean daily displace- 

 ment is the mean expected distance between the loca- 

 tion of a crab at the same time on two consecutive days. 

 The maximum-likelihood estimates for mean daily 

 displacement rates (A) were obtained by minimizing the 

 negative log-likelihood function 



ft = Z {(Di 2 /t,A) + logeftA*] - log e [2Di]}, 



i = l 



for all Dj>0 (6) 



