Hannah: A new method for indexing spawning stock and recruitment for Pandalus jordani 



483 



egg production (Rothschild and Fogarty, 1989; 

 Hannah et al., 1995). A second objective of this study 

 was to construct, in addition to an improved index of 

 spawning stock, an index of egg production, and 

 evaluate the relationship between recruitment and 

 egg production. One of several challenges in con- 

 structing such an index is that the trawl fishery har- 

 vests egg-bearing female shrimp in late October, just 

 before the fishing season ends, and again in early 

 April, as fishing resumes. It can be argued that be- 

 cause of reduced fishing effort late in the season in 

 most years and because of the high natural mortal- 

 ity rates experienced by ocean shrimp over the win- 

 ter, the harvest of egg-bearing shrimp in October 

 should have a negligible impact on total lar\'al re- 

 lease the next spring. However, in April, when lar- 

 val release is imminent for any shrimp still bearing 

 eggs, the impact of the fishery could be more detri- 

 mental. Also, with much of the larval release taking 

 place before the fishing season opens on 1 April, fish- 

 ery impacts are concentrated on late-release larvae. 

 If, as postulated in the prior study (Hannah, 1993), 

 the timing of the spring transition is critical to lar- 

 val survival or retention in the study area, the fish- 

 ery may be impacting the larvae with the greatest 

 chances for success in a poor environment: those des- 

 tined for release after a late spring transition. A third 

 objective of this study was to estimate the harvest of 

 egg-bearing shrimp in April and examine the impact 

 that April harvest of egg-bearing shrimp may have 

 had on subsequent recruitment. 



Materials and methods 



In my earlier study of ocean shrimp stock and re- 

 cruitment (Hannah, 1993). I used an age-structured 

 index of recruitment calculated by summing two com- 

 ponents. The first component was an estimate of the 

 age-2 shrimp population in April (year t), calculated 

 from the average fishery catch per unit of effort 

 (CPUE) of age-2 shrimp m April and May, divided by 

 an assumed catchability coefficient calculated from 

 data in Geibel and Heimann ( 1976). The second com- 

 ponent was simply a sum of the catch of age- 1 shrimp 

 during the prior year it-l ), with each monthly catch 

 discounted to 1 April of year t by using an assumed 

 monthly natural mortality rate of 0.096 (Gotshall, 

 1972). In essence, this index was a crude estimate of 

 what the age-2 shrimp population would have been 

 in the absence of fishing, on 1 April of the age-2 year 

 (Hannah, 1993). To index the shrimp spawning stock 

 in the earlier study, I used a simple average of Sep- 

 tember-October shrimp fishery CPUE. Both indices 

 depended heavily on an assumption of constant 



catchability. The recruitment index also relied on an 

 assumption of constant natural mortality. 



The relationship between CPUE, population size, 

 geographic stock area, and the catchability coefficient 

 can be described by the equations 



CPUE = paNA-^ 

 q = paA~^, 



(1) 

 (2) 



where p = the proportion of shrimp within the sweep 

 of the gear that will be captured (the el- 

 emental efficiency); 



A = the geographic stock area (stock area); 



a = the area covered by a single sweep of the 

 gear; 



b - a coefficient that describes how q will 

 vary with stock area; 



N= the population size; and 



q = the catchability coefficient (Winters and 

 Wheeler, 1985). 



Accordingly, an assumption of constant catchability 

 is equivalent to assuming that stock area is constant. 

 However, stock area for ocean shrimp has been shown 

 to be roughly proportional to stock abundance and 

 to vary substantially between years (Hannah, 1995; 

 Hannah, 1997). In the present study, I incorporated 

 stock area estimates into both the shrimp recruit- 

 ment and spawner indices, making an assumption 

 of constant catchability unnecessary. I did assume 

 that 6 in the above equation was equal to 1, an as- 

 sumption that has been previously shown to be rea- 

 sonable, according to a roughly linear relationship 

 between stock area and abundance (Hannah, 1995). 

 My approach also assumes that the elemental effi- 

 ciency of shrimp trawl gear, p, is constant. 



Because the assumed rate of natural mortality was 

 used in the prior study (Hannah, 1993) only to dis- 

 count age-1 catches forward in time to 1 April of the 

 age-2 year, the simplest way to reduce the influence 

 of variable natural mortality on the recruitment in- 

 dex is to index the population at an earlier age. This 

 is a useful approach; however, age-1 shrimp must 

 still be fully recruited to the fishery at the time cho- 

 sen. Using data from the early years of the shrimp 

 fishery, Lo ( 1978) showed that age-1 shrimp were in- 

 completely recruited to the California shrimp fish- 

 ery, especially early in the April-October season. A 

 variety of data suggest that, since about 1979, age-1 

 shrimp have been fully recruited to the trawl fishery 

 by June or July of each year Prior to 1974, Oregon 

 required a minimum codend mesh of 34.9-mm ( 1 3/8 

 in) stretch measure. Since this date, minimum 

 codend mesh size has been unregulated in the Or- 



