140 



Fishery Bulletin 89|l). 1991 



Analysis of movement and mortality 



We simultaneously analyzed crab movement and mor- 

 tality using a model structure that facilitated estima- 

 tion of monthly proportional transfer rates of crabs 

 among the seven geographical zones demarcated in 

 Figure 1. Zone 7 essentially represents the universe 

 outside the study site and provides the option for crabs 

 to vacate the study site. Maximum-likelihood param- 

 eter estimates for the transfer rates and mortality were 

 obtained by minimizing the discrepancy between ob- 

 served and expected number of recoveries in each zone 

 during consecutive one-month intervals of time-at- 

 large. Estimation of expected numbers of recoveries 

 required our fishing-effort survey data. This model 



structure allowed us to search for persistent directional 

 movement patterns and obtain male and female mor- 

 tality estimates that were not confounded by move- 

 ment of tagged crabs from the study site or into a zone 

 where fishing effort was low. 



We organized 920 male and 103 female tag recov- 

 eries by the three fishermen and ourselves who re- 

 corded all tag-recovery information, and whose fishing 

 effort over time was measured, into frequency cells 

 (Oijk) by zone released (i=l,...,7), zone recovered 

 (j = l,...,7), and months-at-large (k = 1,..., 18). 

 Therefore, if the observed number of recoveries in cell 

 04,1.2 = 5, then 5 crabs released in zone 4 were 

 recovered in zone 1 after 2 months (30-60 days)-at- 

 large. We ignored absolute time, so our analysis was 

 not sensitive to seasonal movement patterns. We also 

 assumed an equal number of trap hauls each month. 

 Although the total number of trap hauls peaks in sum- 

 mer due to an increase in the number of part-time 

 fishermen (Fig. 2b), our assumption is reasonable for 

 the three full-time fishermen, and ourselves, whose tag- 

 recovery and trap-haul data are the only trap-haul data 

 incorporated into this analysis. Monthly fishing inten- 

 sity (Ricker 1975) for each zone was calculated by 

 dividing the number of trap hauls each month by the 

 area (km 2 ) of the zone (Table 1). Zone 7 was deliber- 

 ately defined to represent an extremely large area (1 

 million km 2 ) to ensure that we did not underestimate 

 the rate of movement of tagged crabs from the study 

 site. 



The number of tagged crabs initially released in zone 

 i that are present in zone j after k months-at-large 

 (Njj k ) is described by the following series of difference 

 Equations (la-g). 



N n ,k + i = (Nii k (l-<2 12 ) + G 2 iN i2k ) S 



N i2lk+ i = (N i2k (l - 2*i - 2 23 ) + S2i 2 N !lk + S 32 N i3k )s 



N i3 .k + i = (Ni3 k (l-Q3 2 -Q3 5 -Q 36 ) + Q 23 N i2k + ^N^k + G 63 N i6k )s 



N i4 .k + i = (Ni4k(l-2«) + S54N.sk )s 



N i5 .k + i = (N 1Bk (l - Q 53 - Q54) + SisNuk + «35N i3k )s 



N i6 . k+ i = (N i6k (l-Q 63 -Q 67 ) + Q 36 Ni3 k )s 



N i7 ,k + i = (N,7k + SeyNiek ) s 



(la) 



(lb) 

 (lc) 

 (Id) 

 (le) 

 (If) 



dg) 



In these equations, Q l} represents the proportion of 

 tagged crabs in zone i that move to zone j during any 

 one-month interval. Note that when i=j, N ij0 is 

 number of tagged crabs released in zone i (Table 1), 

 and that Qjj's exist only for adjacent zones (Fig. 1). 



The parameter Q 76 could not be estimated because no 

 tagged crabs were released in zone 7. The parameter 

 s is monthly survival rate. The annual instantaneous 

 rate of disappearance of tagged crabs (S) is related to 

 s by 



