FISHERY BULLETIN: VOL 76, NO. 4 



325 525 725 92 5 112 5 132 5 32 5 62 5 72 5 92 5 1125 1325 



SIZE AT RECRUITMENT (cm) 



Figure 13. — Estimates of relative stock fecundity at level of 

 fishing effort at the time of study as a function of size at recruit- 

 ment, fecundity index, and sex ratio hypothesis: (a) high Input F 

 and fecundity index I, (b) high Input F and fecundity index II, (c) 

 low Input F and fecundity index I, and (d) low Input F and 

 fecundity index II. 



specify the nature of movements, locations of re- 

 cruitment, parameters of growth, and natural 

 fishing mortality. 



We crudely represented the eastern Pacific 

 Ocean with the grid of 5° square areas shown in 

 Figure 14. The number offish of a specific age in 

 each cell at time t is given by the vector 



N, = AS,N,_, 



(5) 



where A^, (112 x 1) has elements (n,), equal to the 

 numberof fishincelU attimef, S;(112 x 112) is a 

 diagonal matrix with elements (s,,); equal to the 

 survival rate offish in cell ;' from time ^ - 1 to time 

 t, A (112 X 112) is a probability transfer matrix 

 with elements (Oy) equal to the probability of a fish 

 incellj moving to cell J, and where A'^o^ 112 x l)has 

 elements {n,)^ equal to the number of recruits in 

 cell i. Five consecutive year classes are in the 

 system at a time. 



For our work we specified A, the transfer ma- 

 trix, by the assumption that for any cell the prob- 

 abilities of fish remaining stationary and moving 

 to each of eight adjacent cells is the same, i.e., 1/9. 

 Any other transfer has zero probability. This gen- 

 eral rule is modified as follows: 



1) Probabilities of remaining stationary in cells 

 adjacent to the shore are augmented by the sum of 

 probabilities of those movements which would 

 otherwise put fish on land and the probability of 

 occurrence on land is zero. 



818 



Figure 14. — Representation of eastern Pacific Ocean. Each cell 

 represents a 5° square area. Hatched cells represent land. Col- 

 umn 1 is western boundary and Column 14 is eastern boundary. 

 Row 1 is northern boundary and row 8 is southern boundary. 



2) Probabilities projecting beyond the northern 

 and southern edges are similarly absorbed on the 

 boundaries. 



3) In cells of rows 2 and 7, probabilities of mov- 

 ing toward rows 1 and 8 are decreased by half with 

 the probability of remaining stationary increased 

 by a like amount. This is an attempt to simulate a 

 stock encountering increasingly marginal condi- 

 tions as the northern and southern boundaries are 

 approached. 



4) Probabilities of remaining stationary on the 

 western edge are augmented by the probability of 

 returning from beyond the boundary in a single 

 time interval. The remainder of the fish that move 

 beyond the western boundary are lost to the sys- 

 tem. 



The speed of dispersion is controlled both by A and 

 the time interval. The time interval was 3 mo for 

 this study. The combination of A as defined and 

 time interval of 3 mo allows a fish to travel a 

 maximum of 1,200 mi in a year. Only 1 out of 820 

 surviving fish that begin the year in the center of 

 the grid travel 1,200 mi in a year. These relatively 

 slow random movements seemed reasonable, 

 based on the results shown in Bayliff and 

 Rothschild (1974) and recent results of lATTC 

 tagging studies (Inter- American Tropical Tuna 

 Commission^). 



Two alternative recruitment models were 

 examined. For the first, denoted as inshore re- 



^Cited with permission of M. Clifford Peterson, Acting Direc- 

 tor of the Inter- American Tropical Tuna Commission. From the 

 Inter-American Tropical Tuna Commission Bi-monthly Report, 

 March- April 1976:8-13. 



