FISHERY BULLETIN: VOL. 70, NO. 3 



(1) multiply the estimated average weight at 

 the beginning of each interval by the number 

 estimated for the population by the Murphy 

 method. That is, 



P*ij = Cyu'*ii/.&ij = estimated biomass to be- 

 gin interval j, age i, 



w*ij = estimated average weight for age i at 

 beginning of interval j, 



Cij = estimated number of age i caught dur- 

 ing interval j. 



(2) Multiply the average number of age i alive 

 during interval j by the average weight of age i 

 individuals during this interval. That is, 



Pij = NijiVij = estimated average biomass 



of age i, during j. 

 Wii = average weight in the catch of age i, 

 ^ during interval j. 



Nij = average number alive during interval 



j of age i. 



For this study, the second method was used with 

 average population numbers, Na, being given by 



Nii = Nii{l-e-Yu)/itiZ<}) 

 Nii = Cii/Eij, 



ti = fraction of year elapsed during inter- 

 ^ val j; tj — 1/12 for all intervals. 



Zij = total annual instantaneous mortality 

 coefficient during j. 



Total population biomass for ages I through III 

 was computed as 



Pj = V NijWij — average biomass available 



i = l 



during interval j, and the 

 catchability coefficient from 



qj = ^CijWij/iPjf }); fi is effort expended 

 during interval j. 



Estimates of within-season monthly popula- 

 tion biomass varied from a high of 12.0 million 

 pounds in May 1955 to a low of 3.4 million 

 pounds in October 1964 (Table 7) . Population 

 changes estimated by the Murphy method follow 



trends estimated by the Schaefer model (Figure 

 5), except Schaefer model estimates exhibit con- 

 siderably less within season change. This dif- 

 ference in range of within season change was 

 caused by the different ways in which the two 

 models treat growth and recruitment. The 

 Schaefer model assumes a continuous process 

 for combined growth and recruitment, whereas 

 the Murphy method treats growth as continuous 

 (Figure 3) and recruitment as instantaneous 

 (Table 7). 



Estimates of monthly catchability (q) (Table 

 7) had extreme variation and showed an average 

 within season increase (Figure 6). However, 

 the within season changes were inconsistent and 

 obscured by the variation. Monthly estimates 

 of q varied from 21.3 x 10"^ in June 1968 to 

 3.8 X 10-5 in May 1955. Yearly averages had 

 less variation and appeared to show no long-term 

 trend (Figure 7). Average q over all months 

 was about 9.0 X 10"^ which agreed closely with 

 the value 8.5 x 10-^ used for the Schaefer model. 



Spawning Biomass and Recruitment 



Female spawning biomass consisted of all 

 ages II and III shrimp plus some fraction of 

 age I shrimp. Some data from commercial catch 

 samples on the fraction of age I shrimp func- 



~1— MURPHY METHOD 

 ^ — SCHAEFER METHOD 



55 56 57 58 59 60 61 62 63 6.1 65 66 67 SB 69 70 



YEAR 



Figure 5. — Comparison of annual maximum and min- 

 imum population sizes as estimated by the Schaefer 

 model and the Murphy method. 



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