Somerton and Kikkawa: Population dynamics of Pseudopentaceros wheelen 



761 



and the mean annual biomasses were then estimated as 



B*t = 



qtPf 



(9) 



where Ut and q, are the mean annual CPUE and 

 catchability. Variance of B* was estimated with 

 methods described in the Appendix. 



Period 3 Biomass during Period 3 was estimated 



from the mean catch-per-hour of Japanese trawlers 



(Ut)as 



Ut 

 B*t = — ^, (10) 



qjPf 



where Qj is the mean catchability of Japanese trawlers 

 estimated for Period 2. Variance of B* was estimated 

 with methods described in the Appendix. 



Period 1 Biomass during Period 1 was estimated 

 from longline catch-per-hook (Ut ) as 



B*t 



qi 



(11) 



where Wt is the mean individual weight of armorhead 

 caught during sampling Period t, and qi is the catch- 

 ability of the longlines. Estimation of qi required an 

 independent estimate of B*t for at least one of the 

 sampling periods, and the estimate chosen was the 

 terminal biomass of the 1980 year-class in 1985. Catch- 

 ability was thus estimated as 



qi = 



U85 P80 W: 



85 



B*. 



(12) 



80,85 



where Ugs is the catch-per-hook, Wgs is the mean body 

 weight in 1985, B*8o,85 is the terminal biomass of the 

 survivors of the 1980 year-class at the start of 1985, 

 and Pgo is the proportion of the 1985 population com- 

 posed of the 1980 year-class survivors. Variances of 

 B*t and qi were estimated with the methods described 

 in the Appendix. 



Spawning and recruitment biomasses 



Spawning and recruitment biomasses were estimated 

 for Periods 1 and 2 in which FI information was avail- 

 able. Spawning biomass in each year (St ) was esti- 

 mated as: 



St+i 



B*t - 



Ct 

 2 



M 



Pr.t), 



(13) 



where Prj is the proportion of B* comprised of newly- 

 recruited fish, and all other terms are as previously 

 defined. This formulation assumes that B* was always 

 estimated on 1 July, the midpoint of both the fishing 

 season and the stock-assessment cruise. Natural mor- 

 tality between 1 July and 31 December, the assumed 

 peak of spawning (Bilim et al. 1978), was accounted for 

 by the term e"'^'-, where M is the annual instantan- 

 eous natural mortality rate. P^t was estimated as 

 the proportion of the population (P^) within the modal 

 group with the largest mean FI, or as zero if no model 

 group had a mean FI>0.25. P^t was included in the 

 estimate of spawning biomass because, based on 

 samples collected on the August 1988 stock-assessment 

 cruise (R. Humphreys, NMFS Honolulu Lab., unpubl. 

 data), female armorhead appear to be nonreproductive 

 during the first spawning season after they recruit to 

 the seamounts. Recruitment biomass was estimated as 



R, = |B*t + -^|Pr,f 



(14) 



This formulation assumes that recruitment occurs from 

 March to May (Boehlert and Sasaki 1988) and is com- 

 plete by the time B* is estimated. Since young armor- 

 head recruit to the seamounts at approximately 24-30 

 months of age (Uchiyama and Sampaga 1990), recruit- 

 ment follows spawning by 3 calendar years. Spawner- 

 recruit relationships were therefore examined using a 

 3-year lag between spawning and recruitment. 



Results and discussion 



The armorhead population on SE Hancock Seamount 

 fluctuated tremendously between 1970 and 1990 (Fig. 

 2) and declined steadily after the population high in 

 1972, except for small increases occurring in 1980 and 

 1986. Before the forces producing these changes (i.e., 

 natural mortality, fishing mortality, and recruitment) 

 are examined, the potential biases and the precision of 

 the biomass time-series will be considered. 



Biomass estimates 



Construction of the time-series of biomass estimates 

 required (1) merging two time-series of CPUE data 

 that were non-overlapping in time and were from 

 distinctly different gear types, and (2) the conversion 

 of a relative measure of abundance (CPUE) into the 

 absolute measure of biomass. Since Japanese trawls 

 and research longlines were never used simultaneous- 

 ly, the time-series could not be merged by simply stan- 

 dardizing the catchability of one gear relative to the 

 other. Fortunately, however, the armorhead popula- 



