326 Fishery Bulletin 90(2). 1992 



Appendix: Simulation steps of IVIonte Carlo tests 



Control variables are F,, F2, z,, pt, nu pi2. o,, 02, /^k/ cv[l<], jua^ cv[AJ, cvfqj, cv[C] 



Compute the following once each trial for Kt«T: 



1 If the Ft are variable, Ft~U(Fi, Fg) 



2 If the Zt are variable, Zt~U(zi, Z2) 



3 If a single catch occurs once each period, then 



A probability of unobserved events (z) during yt to Ct is Pr[z']t=l-e"^t(ct-yt), 



B probability of being caught (on date Ct) is Pr[C]t = Ft, 



C probability of unobserved events (z) during q to yt+j is Pr[z']t= l-e"^t(yt+i-Ct)^ or 



4 If catching is continuous, then 



A probability of death during y^ to yt+i is Pr[D]t=l-e"<^+'^t)(yt.i-yt), and 

 B Pr[z]t = Pr[D]tZt-(zt + Ft). 



5 If recruitment is seasonal, then 



A pt~U(l,20) where pt is the proportion recruited during period t, 



t T-l 



B <5t = ^ Pi ^ Pj = the accumulative frequency, 



i=i j=i 



C /Jt~U(p(i, M2). and 

 D ot~U(oi, 02). 



Compute the following once for each fish: 



6 Draw growth parameters k and A such that 

 A k~NU,(MkCv[k]2), 



B A~NOiA, (ma cv[A]2). 



7 Draw a recniitment data, tj , such that 



A if recruitment is uniform, then ti~U(l,20), or 

 B if recruitment is seasonal, 



(1) draw t with probability specified by 6, 



(2) drawti~N(Mt, o2t). 



8 If fishing is continuous, then 



A for the time period of recruitment draw u where u~U(0,l). 



(1) If u<Zti(l-e-<^ti+Ft,)(yt..i-t,)H-(zti + Fti), the fish exited of unobserved causes; STOP. 



(2) If not, but if u<l-e-<^ti+F.i)(y„,,-t,)_ the fish was caught; go to step 8C(2)(a). 



(3) If neither occurred, the fish lived through the time period of recruitment; continue. 



B Add a fish to the abundance matrix. 



(1) t = t+1. 



(2) ti = yt. 



(3) Si = the lower bound of the minimum size-class. 



(4) Compute the size-class from equation (1). 



(5) Nt.s2 = Nt,32+1. 



(6) If t = T, STOP. 



C Draw u where u~U(0,l). 



(1) If u<Pr[z]t, the fish exited dur to unobserved events; STOP. 



(2) If not, but if u<Pr[D]t, the fish was caught. 



(a) Draw u where u~U(0,l). 



(b) t2 = t-t-U. 



(c) Compute the size-class equation (1). 



(d) Add to the catch matrix: Ct,s = Ct,s + l; STOP. 



