Somerton and Kikkawa: Population dynamics of Pseudopentaceros wheelen 



759 



1 Nij Ai U: 



N^^ = 



i=l 



Z AiUi 



i=l 



(2) 



where Njj is the number of fish in FI category j and 

 depth stratum i. 



The frequency distributions of FI usually display two 

 or three distinct modes which are similar in appearance 

 to the modes often present in length-frequency distribu- 

 tions of temperate fishes. Since armorhead recruitment 

 to the seamounts is seasonal (Boehlert and Sasaki 

 1988), these modes were assumed to represent annual 

 cohorts of fish. To estimate the proportion of the pop- 

 ulation contributed by each cohort (P^ ) and the mean 

 and variance of its FI distribution, the FI distributions 

 were separated into their component distributions by 

 fitting a distribution mixture model using a procedure 

 developed for length-frequency data (Macdonald and 

 Pitcher 1979). 



Several of the year-class modes in the FI distribu- 

 tions were so distinct that they could be followed 

 through the time-series in an orderly progression from 

 when they were fat (high FI) to when they were lean 

 (low FI). This feature of the FI distributions was used 

 in two ways. First, the rate at which armorhead 

 decrease in fatness was estimated by following the 

 particularly strong year-class recruiting to the sea- 

 mount in 1986. Mean FI of this cohort (jji^) on each 

 cruise was regressed against the time (in months), and 

 the time squared, since the cohort was considered fully 

 recruited to the seamount. Linearity of the relation- 

 ship was determined by the significance of the coeffi- 

 cient of the squared term. 



Second, the instantaneous natural mortality rate (M) 

 of armorhead was estimated by following two cohorts, 

 one composed of armorhead recruiting to the seamount 

 in 1986 and the other composed of all armorhead pres- 

 ent on the seamount during the first cruise in 1985. 

 Relative abundance of each cohort at each time (t) was 

 first estimated as the product of the catch-per-hook and 

 the proportion of the population witWn the appropriate 

 cohort on each cruise; that is, P^ t Uf Instantaneous 

 natural mortality rate was then estimated by regress- 

 ing the natural logarithm of relative abundance against 

 the time (in months) since the cohort was considered 

 fully recruited. Analysis of covariance (ANCOVA) was 

 used to test whether the slopes of the regression lines 

 (i.e., the estimated values of M) differed between 

 cohorts. A best estimate of M was computed as the 

 average of the estimates for the two cohorts weighted 

 by the inverses of their variances. Additionally, M was 

 estimated for each sex separately, considering only the 

 1986 cohort. ANCOVA was again used to test whether 



the estimated values of M differed between sexes. 

 These and all subsequent applications of ANCOVA 

 herein will first test a model with one slope and two 

 intercepts against a model wnth two slopes and two in- 

 tercepts. If such a test is not significant, then a model 

 with one slope and one intercept is tested against a 

 model with one slope and two intercepts. 



Period 2 In the period 1978-84, Japanese trawlers 

 conducted 10 fishing trips to SE Hancock Seamount. 

 For all trips, U.S. observers recorded the weight of 

 armorhead caught and the duration of each trawl-haul. 

 In addition, fork length and body weight were recorded 

 for a random sample of armorhead drawn from each 

 haul. 



The biomass of armorhead at the start of each fishing 

 trip was estimated by using the Leslie method (Leslie 

 and Davis 1939) in which the change in CPUE over 

 time is related to the cumulative catch removed. 

 Algebraically, this is expressed as 



Ud = Bo q-q Kj 



(3) 



where Ud is the daily average catch (in kg) of armor- 

 head per hour of fishing on day d, K<j is the cumulative 

 catch of armorhead up to the beginning of day d, q is 

 the catchability coefficient, and B,, is the initial bio- 

 mass. Two parameters (q. Bo) were estimated by re- 

 gressing Ud on Kd ; variance of Bq was estimated using 

 the equation from Polovina (1986). Mean catchability, 

 qj , and its variance were calculated from the per-trip 

 estimates. 



Frequency distributions of FI were computed the 

 same as for Period 1, except that body depths were not 

 measured but were estimated from body weights and 

 fork lengths using the regression equation previously 

 described. Since the distributions showed apparent 

 cohort modes similar to those observed during Period 

 1, the mean and variance of the FI distribution for each 

 cohort and the proportional contribution of the cohort 

 to the population were again estimated with a distri- 

 bution mixture model. The rate at which FI de- 

 creased with time was estimated by regressing the 

 mean FI of the cohort recruiting in 1980 against the 

 time (in months), since the cohort was considered fully 

 recruited. 



Period 3 In the period 1970-77, Japanese trawlers 

 fished Hancock Seamounts for at least 1 month in every 

 year; however, data from NW and SE Hancock Sea- 

 mounts could not be separated. Soviet trawlers also 

 likely fished the Hancock Seamounts over this period, 

 but the available Soviet data (Borets 1975) were aggre- 

 gated over all seamounts and were not useful for deter- 

 mining the stock dynamics on the Hancock Seamounts. 



