FISHERY BULLETIN: VOL. 87, NO. 3, 1989 



6 . 28 days 



Age (t) 



L = 4.25 (^-f )^"°'^' fortl6.28days 

 L = 27 {^y"'"^ for t > 6 . 28 days 



Where: oc^= a^. exp (bi- x TEMPERATURE) 



= . 11 exp (0 . 1 2 X TEMPERATURE) 



o<„= (a„-b„x MONTH) 



-1 



= (22 48 - . 83 X MONTH)'"" 



Figure 6. — Temperature-dependent and season-dependent larval 

 growth curves (Methot and Hewitt 1980; Lo 1983). Gompertz models 

 are used to describe each gi'owth phase where a^ is the temperature- 

 dependent growth coefficient and a„, is the season-dependent gi-owth 

 coefficient. 



The fraction, p, of larvae extruded through the 

 mesh or avoiding the net was generated by a 

 sample mean of a binomial random variable, ;/, 

 with parameters A'^ and P. The parameter: N 

 was set to 50 and P was the length-specific ex- 

 trusion rate or avoidance rate from the same 

 equations used to construct the population from 

 the 1984 surveys. Thus p equaled ij/50. Although 

 p has a mean of P, it was not necessarily equal to 

 P for each simulation run. The live lengths of 

 larvae were reduced to account for the effects of 

 net abrasion and preservaton effects (Theilacker 

 1980; Fig. 7). A standard haul factor was select- 

 ed from the observed normal distribution of this 

 variate (mean = 4.96, SD = 0..567) and used to 

 index the volume of water filtered per unit of 

 depth sampled. These catches then formed the 

 raw material for the mortality estimation pro- 

 cedure. 



Estimating Mortality Rate 



The larvae in each catch were grouped into 1 

 mm length categories. A weighted negative bi- 

 nomial distribution was fitted to each length 

 category where the original variate was the 

 number of larvae (of a given length category) per 

 station. Using this procedure, each observation 

 was weighted for the effects of sampling biases 

 (extrusion, avoidance, volume of water filtered, 

 gi'owth and shrinkage). The final variate was the 

 number of larvae (of a given age) produced per 

 day per 0.05 m" of sea surface. The rate at which 

 larval production declines with time was defined 

 as the mortality rate. For the Pareto model, the 

 mortality rate was assumed to decline with age 

 and mortality was indexed by the mortahty coef- 

 ficient (p). For the simulations described in this 

 report, (3 was estimated as the slope of the log- 



406 



