FISHERY BULLETIN: VOL. 84, NO. 4 



APPENDIX 



List of symbols used in model development and illustration 



b' 



B 



A X -A A terms used in computation of biomass per 

 recruit (Equation (21)) 



a - multiplicative term in equation linking K x 



and body weight (Equation (3)) 



- intercept of a Type I (multiple) linear re- 

 gression 



a - intercept of a Type II (multiple) linear re- 



gression 



b - slope of a Type I linear regression 



- exponent in equation linking K x and body 

 weight 



b c - slope of a Type I multiple linear regression 



- slope of a Type II linear regression 



- slope of a Type II multiple linear 

 regression 



- biomass (under equilibrium condition) 



- exponent in model linking K x and body 

 weight (Equation (4)) 



- similar to ft, but estimated jointly with 

 #imax (Equation (37)) 



- (-log 10 (l - KJ) 



- same as C, but expressed in standard 

 deviation units 



- rate of food consumption 



- rate of growth in weight 



- trophic efficiency, i.e., production by popu- 

 lation/food consumption by population 



i - counter for number of variables in a multi- 



ple regression 



j - counter for number of multiple regres- 



sions 



K - constant in VBGF 



K x - gross conversion efficienty (Equation (1)) 



■^lmax  hypothetical upper limit for K x (with 



# lmax < 1) (Equation (37)) 

 M - instantaneous rate of natural mortality 



- a dummy variable expressing food type 

 (Equation (27)) 



M' - a dummy variable expressing food type in 

 standard deviation units 



n - number of partial regression coefficient 



used in computing a given value of 6/ 



N - number of fish in population (Equation 



(19)) 



840 



C 



C 



dq/dt 

 dwldt 



Q - food consumption of a population (per unit 



time) 



Q/B - food consumption per unit biomass of an 

 age-structured animal population 



Q c - cumulative food consumed by a single fish 

 between ages t r and t max (Equation (22)) 



R - number of recruits (Equation (19)) 



r - product moment correlation coefficient 



5 - a dummy variable expressing sex 



S' - a dummy variable expressing sex in stan- 



dard deviation units 



t - age 



t c - mean age at first capture (in an exploited 



stock) 



£ - a parameter of the VBGF expressing the 



theoretical age at size zero 



^max  maximum age considered (= longevity) 



t r - mean age at recruitment to the part of the 



population considered when computing 



Q/B 



temperature in °C 



temperature in °C, expressed in standard 

 deviation units (Equation (32)) 



any variable beyond W which affects K x 



the von Bertalanffy growth function 



body weight (in log units in some cases) 



body weight (in log 10 units), expressed in 

 standard deviation units 



weight of a fish egg 

 weight of a fish at hatching (yolk sac ex- 

 cluded) 



body weight corresponding to t max 

 body weight corresponding to t r 

 mean weight at age t 

 yolk sac weight in a newly hatched fish 



asymptotic weight in the VBGF or in new 

 model (Equation (4)) 



an estimate of asymptotic weight obtained 

 indirectly (i.e., from data of a type differ- 

 ent than those in model using value of 

 W 



Y { - any variable included in a multiple regres- 



sion 



Z - instantaneous rate of mortality (= PIB 



ratio) 



T 

 T 



Vi 



VBGF 

 W 



w 



w c 

 w h 



w 



" max 



w r 

 w t 

 w y 



w, 



(oo) 



