FISHERY BULLETIN: VOL. 81, NO. 3 



length of the development and an instantaneous dai- 

 ly mortality rate (i) of 0.0788, the mean observed, 

 overall rate of the two sampling years. This mortality 

 was constant over all stages and constant within the 

 molt cycle. The mortality rate was incorporated in a 

 simple exponential decay formula to estimate sur- 

 vival rate over time (N t =N e~ u ). Two hatching- time 

 distributions were used: 1) A standard Normal dis- 

 tribution with 10 6 individuals released over 20 d, and 

 2) a severely peaked distribution with 850,000 of the 

 10 6 released over 5 d around median hatch time. We 

 feel the latter distribution most accurately reflects 

 hatching of P. jordani in the field. 



The population was sampled in the model at various 

 intervals, and the sequence of abundance of suc- 

 cessive stages was determined by summing the abun- 

 dance of each over all samples, just as we have done 

 with the field estimates. These model stage abun- 

 dances were presented in Figure 13. As would be ex- 

 pected, sampling more than once within an intermolt 

 period (every 4 d) tends to overestimate survival to 

 each larval stage. Sampling every 9 d (1.5 times the 

 intermolt period) consistently underestimated larval 

 numbers and survival. The severely peaked distribu- 

 tion of larval hatching times resulted in an oscillating 

 estimate of larval survival. Magnitude of the oscilla- 

 tion was related to the degree of phase agreement 

 between the sampling and molting. In all cases, 

 however, whether the number of larvae was over- or 

 underestimated at any particular stage, the survival 

 rate based on sums of estimates of abundance 

 paralleled the "actual" rate. 



Table 3 summarizes the time between cruises, the 

 estimated surface temperatures for each intercruise 



4 Peaked 



4 Normal 



ly 



9 Normal 



'9 Peaked 



VI VII VIII IX X XI XII XIII Juv 

 Stage of Development 



Figure 13.— The effect of sampling interval and larval hatching dis- 

 tribution on estimates of larval abundance and survival rate. Heavy 

 line indicates "actual" survival rate; 4-normal, sampling standard 

 normal distribution of larval hatch every 4 d; 9-normal, sampling 

 every 9 d; 4-peaked, sampling peaked distribution of larval hatch 

 every 4 d; 9-peaked, sampling peaked distribution every 9 d (see text 

 for further explanation). 



period (taken from Fig. 5), and an estimated inter- 

 molt period based on larval rearing experiments 

 (Rothlisberg 1979). The shortest period between two 

 cruises over the 2-yr sampling period was 8 d (22-30 

 May 1972), while the average was 14.5 d. Surface 

 temperature for the larval period was rarely below 

 8°C (expected intermolt period = 8,08 d) and was 1 0° 

 between 22 and 30 May 1972 (expectation = 7.0 d). 

 The mean ratio of interval between cruises to inter- 

 molt period was 2.1, indicating that the survival es- 

 timates of this study would be low to an extent. 

 Larvae could progress more than two stages between 

 some cruises. 



TABLE 3. — Period between cruises (days), estimated tem- 

 perature for the period (from Fig.5), intermolt period at the 

 temperature (from Rothlisberg 1979), and the ratio be- 

 intercruise (IC) period and intermolt (IM) period. 



Estimates of Larval Survival from 

 Commercial Landings 



Long-range trends in larval survival of P. jordani 

 were sought from Oregon fishery statistics to put the 

 apparent differences in larval survival between 1971 

 and 1972 into perspective. Data on number of ova 

 and of age 1 shrimp were provided by J. Robinson 5 . 

 He estimated ova from adjusted estimates of num- 

 bers of females in samples of the April commercial 

 landings and an empirical length to fecundity 

 relationship (Robinson 1971). Numbers of age 1 



■J. Robinson, Oregon Department of Fisheries and Wildlife, 

 Marine Science Drive, Newport, OR 97365, pers. commun. Feb- 

 ruary 1982. 



468 



