Smith et al.: Distribution and biology of Zaprora silenus 



171 



Frequency distributions of prowfish total length, sepa- 

 rated by sex and region, were calculated as the weighted 

 percent of measurements within 10-cm length intervals. 

 The weighting factors were calculated for each fish mea- 

 surement as the inverse of geographic-stratum sampling 

 (i.e. haul) density, multiplied by the inverse of the indi- 

 vidual haul area that was swept . Also, differences in mean 

 length between sexes or regions were examined by using 

 analysis of variance (ANOVA) 4 to test the significance of 

 statistical differences based on the weighted lengths. Be- 

 cause potential grouping of prowfish by size could affect 

 within-haul variance, source haul (i.e. that in which each 

 measured fish was caught) was included in analyses as 

 a possible random variable affecting length. Variances in 

 length between regions and sexes were each tested for sig- 

 nificance against variance among hauls. The significance 

 of the haul variable was also checked by testing variance 

 among hauls against that among measurements. 



The relationship of body weight (g; W) to total length 

 (cm; L) was assumed to be an exponential function: 



W = e"U\ 



for which the parameters a and ft were estimated from 

 the data by first log-transforming both variables and then 

 calculating the intercept and slope of the least squares 

 linear regression: 



\n(W) = a + p\n(L). 



To determine whether the relationship differed by sex, 

 analysis of covariance ( ANCOVA; Statgraphics Plus, Manu- 

 gistics. Inc., Rockville, MD) was used to compare the fit of 

 a model with two regression lines, each with a sex-specific 

 intercept and slope, to the fit of a two-line model with sex- 

 specific intercepts and a common slope (null hypothesis). 

 If no significant difference was observed, then a second 

 test was performed by testing the latter model against the 

 null hypothesis of a common regression line with single 

 intercept and slope for both sexes combined. The relation- 

 ships in the best-fit model were then transformed back to 

 exponential form. 



Prowfish growth was described by fitting the von Berta- 

 lanffy function to length (L) and age (year; t ) data by using 

 nonlinear least squares. The function is 



L=L (1 



-«'i/-(,ii) 



where L^ = asymptotic maximum length; 



k - a constant (per year) affecting model early 

 growth rate; and 



U 



hypothetical age at length. 



To determine whether parameters differed between prow- 

 fish sexes, we fitted the function separately to the data from 

 each sex as well as to the data for both sexes combined. A 



4 Unless otherwise specified, ANOVA, log-likelihood, and nonlin- 

 ear regression analyses were accomplished by using Systat 10 

 software (Systat 10 Statistics I, SPSS Inc. .Chicago, ID. 



likelihood ratio test was then used to determine whether 

 the separate-sex model fitted the data significantly better 

 than the combined-sex model (Kimura, 1980). Significance 

 of the likelihood ratio was based on the chi-squared sta- 

 tistic with degrees of freedom equal to the difference in 

 number of parameters between the two models. 



The proportion of prowfish females that were mature 

 (P mo( ) at a given length or age was described with logistic 

 functions of the formP ma , = 1/(1 + e" + ' iV ), where X is either 

 length (L) or age in years (f), and a and /3 are function pa- 

 rameters. The models were fitted to the data by using maxi- 

 mum likelihood. After the relationships were estimated, 

 the length and age at which 50% of females were mature 

 were estimated by setting P mat = 0.5 in each function and 

 solving forX The 959r confidence interval for each estimate 

 was calculated by using the delta method (Seber, 1973). 



Results 



Geographic distribution 



Prowfish distribution in the waters off Alaska, as indicated 

 by their presence at 1528 out of a total of 35,159 histori- 

 cal bottom trawl locations, is shown in Figure 2. The total 

 count of individuals in catches was 11,401. Distribution 

 south of approximately 50°N latitude off Vancouver Island 

 is not shown because here 6 of 7442 bottom trawl hauls 

 caught a total of 8 prowfish. The southernmost occurrence 

 was at 34°13.4'N latitude near San Miguel Island, southern 

 California. Prowfish were taken at depths ranging from 24 

 m to 801 m but most frequently appeared in catches close 

 to the break between the continental shelf and upper con- 

 tinental slope near 200 m depth. 



Prowfish CPUE was greater than zero at 64 of 807 haul 

 locations in the Gulf of Alaska in 1996 and at 48 of 408 

 locations in the Aleutian Islands in 1997. Over all areas at 

 the depths fished the range of per-haul CPUE was 0-547.5 

 prowfish/km 2 (average=6.7 prowfish/km 2 ) in the GOA and 

 0-5220.1 prowfish/km- (average=65.1 prowfish/km 2 ) in 

 the AI. The average CPUE within 20-m bottom depth in- 

 tervals in each region indicated that fish tend to be most 

 concentrated at intermediate depths (Fig. 3). Depth at 

 trawl locations ranged from 20 to 479 m for the GOA and 

 from 22 to 474 m for the AI, and prowfish were collected 

 at 34-252 m (GOA) and 89-258 m (AI), respectively. The 

 CPUE-weighted average bottom depth was 163.8 m for the 

 GOA and 150.3 m for the AI. 



The CPUE values within 20-m depth intervals (Fig. 3) 

 indicated that the regional difference in mean density was 

 largely due to differences at the same depth rather than 

 differences between regions in the amount of area available 

 at a given bottom depth. 



Length distribution 



Length-frequency histograms by region and sex for prowfish 

 from the Gulf of Alaska (84 males, 90 females) and Aleutian 

 Islands (396 males, 431 females) are shown in Figure 4. 

 Analysis of variance tests for a difference in mean length 



