Smith and Abramson: Leopard shark tag-recovery data from San Francisco Bay 



373 



1976). Prior to the work described here, nothing was 

 known of its movements or the degree of exchange 

 with other leopard shark populations along the Califor- 

 nia coast. 



In 1979, a tagging study was initiated in San Fran- 

 cisco Bay to obtain information on age validation, 

 growth, and movements of this species. Tag recaptui'es 

 were monitored over a 9-year period. This report gives 

 results of movements that were deduced from the tem- 

 poral and geographic distribution of tag recoveries. In 

 addition, although beyond the planned design of this 

 study, we decided to utilize the tag recovery data 

 together with published information to estimate the ef- 

 fect of management by size limit on stock replenish- 

 ment and on yield per recruit. The lack of suitable 

 statistical information on catches, as mentioned previ- 

 ously, prevented us from performing analyses that 

 involve weighting tag recoveries by catch or effort. 

 Results of the age validation segment of the study have 

 been published elsewhere (Smith 1984), and results on 

 age and growth are also being published separately 

 (Kusher et al. In prep.). 



Methods 



All sharks were tagged off Hunters Point in south San 

 Francisco Bay in 1979. Collections were made with a 

 183-m longline rigged with an average of 150 baited 

 hooks fished on the bottom at depths of 15-20 m. Prior 

 to release, total and precaudal lengths were recorded 

 to the nearest centimeter, and each fish was given an 

 intraperitoneal injection of oxytetracycline hydrochlor- 

 ide to mark vertebral centra for age verification pur- 

 poses (Smith 1984). A record was made of the sex and 

 general physical condition of each fish; seriously injured 

 animals were not tagged. Those with minor hook in- 

 juries or with partially everted stomachs were classified 

 as "injured"; the rest were classified as "healthy." A 

 plastic rototag of the type recommended by Kato and 

 Carvallo (1967) was applied to the first dorsal fin and 

 the fish released at the capture point. The fin tags were 

 imprinted with a legend informing the recoverer that 

 a reward (amount unspecified) was offered for return 

 of the tag and the fish or a section of its vertebral col- 

 umn for age verification purposes. The legend also 

 provided an address and phone number to contact to 

 arrange delivery. 



Mortality estimation 



Fishing mortality rates were estimated from the tag- 

 ging data using the concept described by Murphy 

 (1965), Gulland (1965), and Tomlinson (1970), which is 

 now commonly referred to as virtual population anal- 



ysis (VPA), though it differs from the original VPA 

 procedure of Fry (1949). The computer program 

 COHORT, written by John Geibel and Phil Law (Calif. 

 Dep. Fish Game, 411 Burgess Drive, Menlo Park, CA 

 94025) was used to calculate the estimates. The natural 

 mortality estimate was based on Hoenig's (1983) 

 regression equation log (Z) = 1.46-1.01 log (f,„„j:) 

 where Z is the instantaneous annual total mortality 

 coefficient and t,,,,,,. is maximum age attained by the 

 species. If the maximum age was determined from a 

 period when there was virtually no fishing directed at 

 the species, then one could assume the estimated Z 

 approximates the instantaneous annual natural mor- 

 tality coefficient, M. 



The basic procedure involved assuming values of M 

 over each 1-year time interval, taking a trial value of 

 F„ , the instantaneous annual fishing mortality coeffi- 

 cient, for the ultimate interval, and executing the 

 backward VPA computation on the tag recoveries to 

 obtain an estimate of A^o > the number of tagged fish 

 at the beginning of the first interval. Trial values were 

 then iterated until the series converged on N(t . 



Before conducting the VPA, it was necessary to con- 

 sider two additional factors which would cause adjust- 

 ments to the actual observations used in the analysis: 

 (1) the likely rate of tag loss and (2) the level of tag 

 recovery nonreporting. Since the tagging experiment 

 was not designed for this type of analysis, there were 

 no built-in procedures to estimate these factors. We 

 therefore used what we judged to be the best available 

 information from outside sources. 



Yield per recruit 



Yield per recruit was calculated by piecewise integra- 

 tion of the yield curve. The yield in weight at each age 

 was taken to be the product of the annual rate of 

 exploitation, the midpoint between an individual's 

 weights at the beginning and end of the age interval, 

 and the population size at the beginning of the interval. 



Y = exp[-M(^. -I- 1)] [1 - exp(-Z)] (F/Z) 



X X {exp[-Z(t-t,)]}w, 



(1) 



t^i. 



where Y is yield per recruit in weight (kg), t is age, 

 <,. is age at first capture, and w, is the midpoint be- 

 tween the weights at t and t + 1. 



Weight at age was computed by using pi-edicted 

 values from the von Bertalanffy length equation from 

 Kusher (1987) and the weight-length formula in Smith 

 (1984). Note that equation (1) assumes cbnstant M 

 and Z except that natural mortality is doubled during 



