Xiao et al.: Instantaneous rate of tag shedding for Galeorhinus galeus and Mustelus antarcticus 



177 



e{i,o,B,t{i)) 



-1 



l-p{i,A)e "•'• 



Mi,A,s)ds 



\Mi.B.s)ds 



e(i,0,0,t{i)) = 



- jXU,A.s)ds 



l-p(i,A)e """ 



p{i,B)e ""• 



- \X(i.B.s)ds 



l-p{i,B)e '""' 



(3) 

 continued 



where h j, and k index fish recaptures with both tags retained, with tag A only, and with tag B only; n,m , and 

 p are the total numbers of fish recaptures with both tags retained, with tag A only, and with tag B only. 



In the estimation, we assumed that fg(;J=0, there was no type-I tag shedding (i.e. p{i,A)-pii,B)=l), and 

 R(iA,B,t(i))=R(i,A,Q,t(i))-R(i,0,B.t(i)). The latter assumption makes Equation 3 independent of probability of 

 reporting at time t(i). We also set the instantaneous shedding rate of tagj (;=A,B) as a function offish total 

 length at release L{i) and time at liberty t(i) of the form Mij,t(i))-P^(j}+fi^(j)L(i}+li./j)t(i}, where fi^ij), p^ij) and 

 /J2C/'' are parameters to be estimated. Thus, k(ij,t(i)) has three terms and seven (2^-1) nested models, since 

 each term can be included or excluded in a nested model and a nested model has at least one term. Under 

 these assumptions. Equation 3 becomes 



ith 



/-/ — ^ / *-*-'9*A-' O) 



(4) 



'-.-n 



e{h,A,Bj(h)) 



_\e{h.A,B,t(h)) + 9{h,A,0,t{h)) + d(h,0,B,t(h)) 



L. n 



e{j,A,o,t{j) 



^/^e(j,A,B,t(j)) + 0(j,A.O,t(j)) + (eij.O,B.t{j)) 



Ls n 



e{k.o,Bj[k)) 



\9{k,A,B,t{k)) + e(k,A,0j(k)) + e{k,0,B,t(k)) 



9(i,A,B,t{i)) = e 2 



e{i,A,0,t(i)) = e^ ' ^ 



-[/JolBl+/J,(BlL(il]/((l — /ijiBl/lil 



1-e 2 



d{i,0,B,t(i)) = 



e(i,o.oj{!))- 



-[/ii,(Al+/J,lA)Z,(()]((i) — /JjlAird)- 



1-e ^ 



-[P„iA) + l3^tA)LU)]tU)--p2^-A)tiit 



1-e ^ 



-[0oiB) + l)i{B)Lui\tU)--P2'-B)Ht)'' 



-|/3„iBl+/3ilB)Z,(i)]((i)-^/32(B)((i) 



1-e 2 



