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



467 



80 

 60 

 50 

 40 

 20 



12 

 10 

 8 

 6 

 4 

 2 



J 



Fished zone 



M 



}MM) 







1 — JT-Th-n-i ~ 



Sanctuary 



f irm \h 



m 



12 3 4 5 6 



Time at large (years) 



Figure 2 



Histograms over time at large (in monthly bins! of recapture 

 numbers from the fishing zone iMFA blocks 33 and 40 i and from 

 the Gleesons Landing Lobster Sanctuary. The diamond mark- 

 ers indicate divisions between modes at 0.5, 1.5., 2.5, etc. years 

 at large; recaptures from the sanctuary and fishing zone that 

 occurred between 0.5 and 1.5 years after release (between the black 

 diamond markers! identify the subsets of data used to estimate 

 yearly emigration rate from the sanctuary. 



inside and outside the sanctuary. The tag-recovery data 

 provided direct measures for only three of these eight 

 possible numbers of recaptures. 



We define "not recovered" to include both tagged ani- 

 mals that were not recaptured, as well as those that 

 were recaptured by a fisherman but whose tag informa- 

 tion (notably the location of recapture) was not reported 

 back to researchers and therefore was not included in 

 the tag-recovery database. 



The movement-rate estimate is given in terms of the 

 following data inputs: the number of lobsters tagged 

 and released in li fished and 2) protected zones, and 

 the numbers recovered that 3) moved (>3 km) or 4) did 

 not move from the fished zone over one year after tag- 

 ging, and the 5) number that moved (>3 km) from the 

 sanctuary in one year. 



Superscripts 'F' and 'S' denote fished zone and sanc- 

 tuary, respectively, for the location of tag release. Let 

 N^ MR and Nfj R denote the numbers of animals that 

 were recovered after a year and that moved or that did 

 not move in the fished zone. From animals tagged and 

 released inside the sanctuary, only the number that 

 moved and were recovered (A^ ;/? ) is available as an un- 

 biased measure. In addition, we know the total number 

 of animals originally tagged and released in the fished 

 zone and sanctuary, Nj. and N^. Input quantities from 

 the tag-recovery data set will henceforth be indicated by 

 a tilde ("): (iV® R iVf. N$ MiRj N? R _ N% } (Table 1). 



Assumptions 



Three assumptions were used to derive an emigration- 

 rate estimate: 1) The two ways to define an estimate for 

 the proportion that moved within the fished zone, namely 

 as a proportion by using only recapture numbers, and 

 as a proportion over the number originally tagged, can 

 be set equal. 2) Recapture probabilities of animals that 

 were tagged and released inside the sanctuary and that 

 moved are assumed to equal those that were tagged and 

 released into the fished zone and that also moved. (The 

 first two assumptions were employed explicitly in steps 

 2 and 3 below.) 3) A third assumption is implicit in step 

 2, specifically in the recapture-conditioned movement 

 proportion in the fished zone (.Pjtf R , Eq. 2): recapture 

 probabilities of animals tagged and released in the 

 fished zone that moved and of those that did not move 

 are assumed to be equal. Assumptions 2 and 3 would 

 both follow from assuming equal recapture probabilities 

 for all lobsters in the fished zone. 



Emigration rate: derivation of the estimate formula 



In this section, an emigration-rate formula is derived. It 

 provides a closed-form estimate of the yearly proportion 

 of lobsters emigrating out of the sanctuary. 



The proportion of animals moving can be estimated 

 from tag-recovery data in two ways, namely as "tag- 



