McGarvey: Estimating emigration rates from marine sanctuaries using tag-recovery data 471 



location of the present study (the 1995 northern zone 

 rock lobster season) was estimated to be 26% (Ward et 

 al. 3 ) by using total yearly effort and catches by weight 

 and number and a vector of weights at age. The tag-re- 

 covery rate of 11.3% (Table 2) is the estimated propor- 

 tion of tagged lobsters that were captured and for which 

 tags were reported. Thus the estimated tag-reporting 

 rate (of those recaptured) is 0.113/0.26 = 43%. If tag 

 shedding and natural mortality were also incorporated 

 as additional causes for nonrecovery, the estimate would 

 fall in the neighborhood of a 50% tag-reporting rate. 

 This estimated level of tag-reporting falls within the 

 range considered probable by fishermen. Thus, the re- 

 covery-rate estimate falls within a plausible range of 

 values, adding confidence that the tag-recovery data 

 are consistent with external estimates of exploitation 

 rate. 



Substantial movement of Jasus edwardsii out of a ma- 

 rine sanctuary was previously observed in New Zealand 

 (Kelly and MacDiarmid, 2003) but not in Tasmania 

 (Gardner and Ziegler 4 ). Long-distance movement of 

 this genus was also observed in New Zealand (Booth, 

 1997) but was much less common in Tasmanian Jasus 

 edwardsii populations (Gardner et al., in press). 



Discussion 



The emigration-rate derivation above combined recap- 

 ture-and tag-conditioned movement proportions. Both 

 ways to define a movement rate were used to constrain 

 the range of solutions for both analytic and numerical 

 estimators. Equating these two definitions for movement 

 proportion reduced the degrees of freedom by 1, thereby 

 circumventing the absence of a count of recaptured lob- 

 sters from within the fished zone. 



Previous estimators of movement rates among spatial 

 cells from tag-recovery data have used either tag- or 

 recapture-conditioned approaches. Hilborn (1990: see 

 also Quinn and Deriso, 1999) developed a tag-condi- 

 tioned movement-rate estimator. This estimator gen- 

 erally requires prior knowledge of the tag reporting 

 rate. Schwarz et al. (1993) employed data consisting 

 of simultaneous tag releases and recaptures repeated 

 over a number of years at the same time each year to 

 estimate movement, survival, and recovery rates in 

 each spatial stratum. Schwarz et al. (1993) presented 

 a general formulation for modeling this multiple yearly 



3 Ward, T. M., R. McGarvey. Y. Xiao, and D. J. Brock. 

 2002. Northern zone rock lobster [Jasus edwardsii) fish- 

 ery. South Australian Fisheries Assessment Series Report 

 2002/04b. 109 p. Aquatic Sciences, South Australian 

 Research and Development Institute (SARDI): RO. Box 120, 

 Henley Beach, South Australia 5022. Australia. 



4 Gardner, C, and P. Ziegler. 2001. Are catches of the south- 

 ern rock lobster Jasus edwardsii a true reflection of their 

 abundance underwater? Tasmanian Aquaculture and Fish- 

 eries Institute Final Report. TAFI (Tasmanian Aquaculture 

 and Fisheries Institute), University of Tasmania, Private 

 Bag 49, Hobart TAS 7001, Australia. 



tag-recovery data set, extending a series of estimators 

 for movement and survival (Arnason, 1972, 1973), and 

 estimated the rate of tag recovery. Brownie et al. (1993) 

 generalized the estimator of Schwarz et al. to non-Mar- 

 kovian movement rates. McGarvey and Feenstra (2002), 

 following Hilborn, used the less costly and more com- 

 monly available single tag-recovery data employed in 

 the present study but adopted a recapture-conditioned 

 approach for estimating yearly movement rates. With 

 "numbers recaptured" appearing in both the numerator 

 and denominator, all nonspatially dependent sources of 

 variation (such as tag reporting and shedding, short- 

 and long-term tag-induced mortality, and natural mor- 

 tality) cancel from the predicted recapture-conditioned 

 likelihood proportions. This procedure permits a cor- 

 responding reduction in the prior information required 

 to obtain unbiased movement estimates. 



When recapture times vary, movement estimation is 

 sensitive to spatial differences in mortality rate, no- 

 tably between tag and recapture cells. Assuming that 

 the nonreporting rate is unknown, mortality can be 

 inferred from single tag-release information only impre- 

 cisely, for example by using mean tagged time at large. 

 For this reason externally obtained mortality estimates, 

 typically from stock-assessment models using fishery 

 data, can be usefully combined with single tag recover- 

 ies in movement estimation. Hestbeck (1995) showed, 

 when survival differs by cell, that ignoring the time of 

 movement between yearly samples could bias movement 

 estimates. McGarvey and Feenstra (2002) made explicit 

 the variation in residence time and thus survival in 

 source (tag-release) and destination (recapture) cells for 

 each recaptured animal. By using prior knowledge of a 

 migration season, migration source cell and destination 

 cell residence times can be approximated as the time 

 from the date of tag release to an assumed fixed (yearly) 

 date of movement, and from that date to the date of re- 

 capture. These residence times are used in exponential 

 survival factors that differ spatially given externally- 

 estimated fishing mortality rates in each cell. 



For the data set available from Gleesons Landing, all 

 tagged animals were released during the peak fishing 

 season (mid-summer). Thus recoveries from the fol- 

 lowing fishing season had a mean and mode near the 

 desired one-year-at-large. In future tag-recovery stud- 

 ies, where a yearly movement rate is sought, a similar 

 choice for timing of tag releases, namely during the 

 season of highest fishery catches, should yield a peak in 

 recaptures a year later. Schwarz et al. (1993) employed 

 this strategy with their multiple yearly tag-recovery 

 data sets. 



In the estimator presented above, variations in ex- 

 pected recovery numbers versus time, notably due to sur- 

 vival, were neglected. The small sample (33 recoveries 

 between 0.5 and 1.5 years from the sanctuary) and lack 

 of recaptures from within the sanctuary necessitated 

 more modest estimation goals. Among data classes avail- 

 able for movement analysis, notably 1) multiple yearly 

 tag recaptures by researchers in all cells, 2) multiple 

 yearly tag recoveries where recapture is by fishermen (or 



