576 



Fishery Bulletin 103(4) 



data were collected by midwater trawl, bottom trawl, 

 and Methot trawl (see Honkalehto et al. 1 for details). 

 Pollock length data from trawls were aggregated into 

 analytical strata based on echosign type, geographic 

 proximity of hauls, and similarity in size composition of 

 hauls. Estimates of numbers of pollock by size were de- 

 rived by scaling acoustic measurements with the target 

 strength-to-length relationship described in Traynor 

 (1996). Temperature data were collected with an MBT 

 mounted on the headrope of the trawl, although many 

 of the profiles did not reach bottom because the trawls 

 usually targeted midwater fish aggregations. For that 

 reason, we elected not to use the temperature data 

 collected during the EIT survey. Because both surveys 

 were conducted at approximately the same time of 

 year, we used the mean bottom temperature from the 

 BT survey as an index temperature for the EIT survey. 

 We used EIT data collected in years 1994, 1996, 1997, 

 1999, and 2000. 



Because of the semidemersal nature of pollock (Bailey 

 et al., 1999a) and assuming that pollock do not dive as 

 a boat and trawl approaches, BT data are assumed to 

 describe the demersal part of the pollock stock within 

 3 m of the bottom. EIT data represented the midwa- 

 ter part of the stock from 3 m above the bottom to 

 14 m below the surface. In our calculations, we used 

 two density measures: CPUE in kg/ha for the BT data 

 and biomass (tons) per 20-mile square for EIT data 

 (the term "density" will be used in the present study 

 to refer to both of these measures). Echo integration 

 trawl survey 20-mile squares were centered on the BT 

 survey stations, so that both sets of data could be easily 

 compared (the term "station" will be used here to refer 

 to BT survey stations as well as EIT survey squares). 

 Because of known age-dependent behavioral differences 

 between pollock (e.g., Shuntov et al., 1993; Bailey et al., 

 1999a), we investigated five different length classes of 

 pollock; up to 20 cm (mostly 1-year-old pollock), 21-29 

 cm (mostly 2-year-old pollock), 30-39 cm, 40-49 cm, 

 and pollock >50 cm. Because of differences in the year- 

 class strengths between years, we scaled the data by 

 dividing the density data for each station by the aver- 

 age fish density for each year within each length class. 

 Thus, a station with a density value of 1 has an average 

 density for a given year and a station with a value of 5 

 has a density 5 times larger for a given year. 



If the pollock distribution in the EBS is assumed to 

 be dynamic and related to temperature, the relationship 

 between temperature and pollock density will be differ- 

 ent at each spatial location. This means that if pollock 

 moved from location A to location B over a period of 

 rising temperatures, we expected a negative relation- 

 ship between density and temperature in location A 

 and an offsetting positive relationship in location B. To 

 study these relationships in the EBS, we applied a two- 

 step approach. In the first step, we identified possible 

 locations where pollock density may be changing with 

 temperature. In the second step, we identified locations 

 of most significant biomass changes with temperature 

 and quantified these changes. 



First step— identifying areas of change in fish density 

 with temperature 



For both types of surveys, we calculated the slope of the 

 linear regression of scaled density against bottom tempera- 

 ture for each station over the time series (e.g., a slope value 

 of 1 indicates an increase of 1 unit of density per degree 

 increase of temperature). Slopes in the range between -0.3 

 and 0.3 were ignored because they represented areas of 

 low fish density or areas of no significant changes in fish 

 density between years. Each station slope was then plot- 

 ted on a map to visualize the spatial relationship between 

 these two variables for the BT and EIT surveys. 



To contour areas with similar slopes, we interpolated 

 the data using inverse distance-weighted squared inter- 

 polation (IDW). This method was chosen because IDW 

 is an exact interpolator, where the maximum and mini- 

 mum values in the interpolated surface can occur only 

 at sample points and values at all sampling points are 

 true measured values (ArcGIS, Geostatistical Analyst 

 Help, 2003, ESRI, Redlands, CA). Using these maps, 

 we identified the main spatially correlated clusters of 

 stations with positive or negative slopes of the linear 

 regression of pollock density against temperature (Figs. 

 2 and 3). Stations were assigned to clusters visually by 

 using slope maps that overlapped the stations map. For 

 practical reasons we investigated only clusters with four 

 stations or more. Twenty-eight clusters were identified 

 for BT survey and 17 clusters were identified for EIT 

 survey (Figs. 2 and 3). 



Second step— identifying areas of most significant 

 changes in biomass with temperature and 

 quantifying these changes 



For each cluster, we calculated mean temperature and 

 percentage of total biomass of pollock present in this 

 cluster in each year. Total biomass and biomass within 

 clusters were calculated as outlined in Wakabayashi 

 et al. (1985). The relationship between mean bottom 

 temperature and percentage of pollock biomass within 

 each cluster was then fitted to a linear regression model. 

 Because the error variances for the BT survey were 

 not constant (variance increased with fish density), we 

 weighted the regression by the inverse of the variance 

 (Neter et al., 1996). For the EIT survey, we made no 

 assumptions about the variance that was due to a small 

 number of observations (only five years of data). 



The relative strength of the relationship between the 

 percentage of pollock biomass and temperature within 

 each cluster was characterized by the P-value of the 

 slope (Table 1) (the P-values are not a true measure 

 of statistical significance because the stations were 

 not chosen randomly). Only clusters with the stron- 

 gest relationships were used in the interpretation of 

 results. Because the number of data points (years) in 

 each analysis was equal within the survey (BT sur- 

 veys — 20 points, EIT surveys — 5 points), P-values in- 

 dicate relative strength of the temperature-biomass 

 relationship. We plotted histograms of P-values for 



