HOUDE: ABUNDANCE AND POTENTIAL YIELD OF ROUND HERRING 



Potential Yield to a Fishery 



Alverson and Pereyra (1969) and Gulland 

 (1971, 1972) have proposed that an estimate of 

 potential yield for an unfished stock can be ob- 

 tained if the virgin biomass and natural mortality 

 coefficient are known. The estimator is: 



XMB 



(9) 



where C max = the maximum sustainable yield 



X = a constant, assumed to be 0.5 (Gul- 

 land 1971). 

 M = the natural mortality coefficient. It 

 is equal to Z, the total mortality 

 coefficient, in an unfished stock. 

 B = the virgin biomass. My biomass es- 

 timates of round herring are esti- 

 mates of B because there is no sig- 

 nificant fishing at this time. 



No estimates of M are available for round her- 

 ring. It seems probable that it must lie in the range 

 0.4-1.0, based on literature on other relatively 

 short-lived tropical and warm temperate clupeid 

 stocks (Beverton 1963; Schaaf and Huntsman 

 1972; Dryfoos et al. 1973) and from the empirical 

 relationship of M to life span given by Tanaka 

 (1960). Assuming M is between 0.4 and 1.0, a 

 range of potential yields to a fishery can be pre- 

 dicted. I used this approach for round herring. 



Larval Abundance and Mortality 



As a first step in determining survival rates of 

 round herring larvae for comparisons among 

 years and to determine abundance of larvae by 

 length classes, larval abundance was estimated 

 for each 1-mm length class: 



*«ZaX^-4 



(10) 



;=i 



7 = 1 



where P al = the annual estimate of total larvae in 

 a length class /; this is the estimate if 

 no correction is made for night-day 

 variation in catches 



Cji — the catch of larvae in length class / at 

 station,;' on cruise i 



Zj = the depth of tow (in meters) at station 

 j on cruise i 



Vj = the volume filtered (in cubic meters) 

 at station j on cruise i 



Aj = the area (in square meters) rep- 

 resented by station j on cruise i 

 k = the number of stations sampled dur- 

 ing cruise i 

 Di = the number of days represented by 

 cruise i (for details, see definition 

 under Equation (4)) 

 r = the number of cruises upon which the 

 estimate is based. 



Larval abundance estimates are subject to er- 

 rors due to escapement of small larvae through the 

 meshes and due to avoidance of the gear by larger 

 larvae (Smith and Richardson in press). Avoid- 

 ance usually is greater during daylight than at 

 night. Some of the avoidance error can be cor- 

 rected if the differential between night and day 

 catches of larvae in each length class is evaluated. 

 Catches of round herring larvae were examined 

 from each station for 1971-73 cruises. The ratios of 

 the sum of larvae estimated under 10 m 2 of sea 

 surface caught at night stations to the sum of 

 larvae estimated under 10 m 2 of sea surface 

 caught at day stations were determined for each 

 1-mm length class. These ratios were then used to 

 derive functions that corrected the day-caught 

 larval abundance estimates. Thus, abundance of 

 larvae in each 1-mm length class at stations oc- 

 cupied during daylight was corrected by a factor R : 



c il z i 



p * =-7T* 



(11) 



where P. 



- the number of larvae in length class / 

 in the area represented by station j 

 R = the factor by which the number of 

 larvae in length class / at station j 

 should be multiplied to correct for 

 night-day variation. It equals 1.0 for 

 stations sampled at night. 

 Cji,Zj, Vj, and Aj are defined in Equation (10). 



R is greater than 1.0 if avoidance is more pro- 

 nounced during daylight hours. The corrected sta- 

 tion catches (from Equation (11)) were substituted 

 into Equation (10) for larvae caught at stations 

 occupied during daylight. Corrected larvae abun- 

 dance estimates (P a/ ) were then obtained. 



Larval mortality rates can be determined and 

 expressed in terms of age if the growth rate of 

 larvae is known or if a model of growth during the 

 larval stage can be used to describe growth 

 adequately. Smith and Richardson (in press) 



67 



