12 



Fishery Bulletin 97(1), 1999 



To evaluate whether the test statistic is significant, 

 the observed environmental measurements (.v^^ ) are 

 randomly sampled with replacement and assigned 

 to observed catches with probability W/^/rii^ under the 

 hypothesis that the association between catch and 

 the environmental factor is random. The value of the 

 test statistic (T^l is then computed for this random 

 assignment. The randomization procedure of assign- 

 ing environmental measurements to catches and of 

 computing the value of T^ is repeated a large num- 

 ber of times to generate a distribution of test statis- 

 tics for the null hypothesis of random association 

 between catch and environmental factor. Last, the 

 observed test statistic T is compared to the distribu- 

 tion of test statistics T^ from the randomization pro- 

 cedure to evaluate whether the null hypothesis of 

 random association can be rejected. 



We applied this test to L. pealei and /. illecebrosiis 

 catch, in numbers per tow, using four environmental 

 factors: average depth of tow, time of tow, bottom 

 water temperature, and surface water temperature. 

 A total of 2000 randomizations were performed to 

 provide an empirical distribution based on 2001 test 

 statistics, including the original test statistic. 



Size-specific environmental effects 



Size-specific environmental effects on mean catches 

 were evaluated separately for each species using tows 

 that captured both juveniles and adults to ensure 

 that comparisons were made under the same envi- 

 ronmental conditions and that the ratio of juvenile 

 to adult catch was well defined. Catch numbers of 

 squid were separated into prerecruit (<8 cm ML for 

 L. pealei and <10 cm ML for I. illecebrosus) and re- 

 cruit (>8 cm ML for L. pealei and >10 cm ML for /. 

 illecebrosus) size categories, where prerecruits and 

 recruits roughly corresponded to juvenile and adult 

 squid. In what follows, prerecruit and recruit cat- 

 egories will sometimes be colloquially referred to as 

 juveniles and adults, respectively. However, both L. 

 pealei (Macy, 1980) and /. illecebrosus (Coelho and 

 O'Dor, 1993) exhibit variability in sex-specific size 

 at maturity, and for both species, an unmeasured 

 fraction of smaller individuals within the recruit cat- 

 egory were juveniles. The effect of depth on mean 

 catch was evaluated first. Tow depth was categorized 

 according to the depth zones used to define offshore 

 strata of the NEFSC bottom trawl surveys: depth 

 zone I (27-55 m), zone II (56-110 m), zone III (111- 

 185 m), and zone IV (186-366 m). Similarly time of 

 tow was categorized into three time zones: zone I 

 (night: 20:00-23:59 and 00:00 to 3:59), zone II (dawn 

 and dusk: 4:00-7:59 and 16:00-19:59), and zone III 

 (day: 8:00-15:59). Bottom and surface temperatures 



were grouped into three zones based on the 25th (P.,5) 

 and 75th (P75) percentiles of the empirical tempera- 

 ture distribution of each of these two variables. Tem- 

 perature zone I was Pq to P.^j, zone II was P,,^ to P.^^, 

 and zone III was P.^^ to Pj,,q. Mean catches between 

 zones were compared after applying a logarithmic 

 transformation to stabilize the variance of number 

 per tow. Similarly, mean ratios of juvenile to adult 

 catches were compared between zones after apply- 

 ing a logarithmic transformation to the ratio. Mean 

 logjg-transformed catch per tow values of juveniles 

 and adults and their ratios were tested at the 5% 

 level of significance by using the GT-2 test which is 

 appropriate for unplanned comparisons with unequal 

 sample sizes (Sokal and Rohlf, 1981). Only the ef- 

 fects of individual environmental factors on juvenile 

 and adult catches were evaluated in these univariate 

 tests and the potentially important factors of 

 interannual changes in abundance or of survey strati- 

 fication were subsumed into random variation. 



Diel correction factors 



We analyzed the combined effects of survey design, 

 time of day, and annual squid abundance to deter- 

 mine correction factors for diel differences in 

 catchability of juvenile and adult squid. As in the 

 evaluation of size-specific environmental effects, 

 catches (C) from tows that captured both juveniles 

 and adults were logj^-transformed. A general linear 

 model (Searle, 1987) was applied to estimate the ef- 

 fects of survey stratum (Fig. 1), time of day category, 

 and year on logj,, -transformed catches. Time of day 

 was categorized into three time zones: zone I (night: 

 20:00-23:59 and 00:00-3:59), zone II (dawn and dusk: 

 4:00-7:59 and 16:00-19:59), and zone III (day: 8:00- 

 15:59) so that the time period effect (T) measured 

 diel differences in mean catch. The year effect (Y) 

 provided a measure of the effect of changes in rela- 

 tive annual abundance on mean catch whereas the 

 survey stratum effect (S) accounted for the effects of 

 geographic location and depth. The general linear 

 model (GLM) was 



log C,,^ = log C/fi + log T, + log Yj + log S^ + e,jk , (4 ) 



where C . - mean catch during the i"' time period 

 (T, ) in the/'' year (7, ) within the k"' 

 stratum (S^ ); 

 Uj^ = mean catch in a standard reference cell 

 (where standard time period=day. 

 year=1994, and survey stratum=l ); and 

 c , = an independent and identically distrib- 

 uted normal random variable with zero 

 mean and constant variance d^. 



