SUPPLEMENTAL METHODS
SCUBA-based line transects were sampled during daylight hours in Howe Sound and adjacent Georgia Strait between mid-July 2008 and early September 2009. Maps and further description of the study area are reported in Marliave & Challenger (2009) and the spatial distribution of transects is described in the main text. Relative to chart datum, transects were at least 15 m deep and some reached depths of 27 m. Shallower habitats were excluded because EUHEL, Pandalus and quillback rockfish tend to be absent.
Transect length varied between ca. 20 m in small reefs and ca. 150 m in larger ones.
Although weather and other constraints caused several multiweek gaps in field work, year-round sampling tended to include each reef every 10-14 days.
Data collected during line transects consisted of counts per minute of each taxon, with one diver counting lingcod and rockfish and a second diver counting demersal crustaceans. Divers searched for organisms inside and outside of rocky interstices, and estimated total lengths of organisms with rulers attached to poles or drawn on data slates.
We chose timed counts as measures of relative abundance over density estimates because environmental challenges (e.g. poor visibility, strong currents, limited time during deep dives) sometimes precluded that the full length of long transects be sampled. Sampling was restricted to the length of the line transect but we did not constrain lateral distances for counting animals. Thus, counts made during poor visibility were less accurate, which increased unexplained variability without biases because visibility did not vary consistently between reefs or sampling periods.
Both copper and quillback rockfish have small home ranges and strong site fidelity
(Matthews 1990). In contrast, lingcod make large movements lasting days or weeks away

from preferred reefs (Martell et al.
2000). Spatiotemporal variation in lingcod use of reefs, therefore, serves as a natural experiment in variable predation risk for rockfish.
Counts of demersal crustaceans focused on species known to be major prey items for subadult rockfish (Murie 1995): squat lobsters ( Munida quadraspina ), Pandalus sp. and the three aggregated genera of small-bodied shrimp (EUHEL). (Squat lobsters were excluded from path models because preliminary analyses suggested the two shrimp groups were stronger explanatory variables: see below). Although finer taxonomic distinctions were made in the field, we aggregated all species of Pandalus ; these included primarily P . danae , but P . stenolepis and P . platyceros also were present. Pandalus had minimum total lengths of 2 to 4 cm while total lengths for EUHEL tended to be less than
1 cm. Although analyses aggregated copper and quillback rockfish, quillback rockfish were the more abundant species at the depths sampled.
The structural complexity of transects was indexed with rugosity measurements at points separated by restricted random distances (i.e. 1 to 4 standardized fin kicks).
Depending on transect length, there were 3 to 16 sampling points. At each point, we measured a 2-m straight line distance just above the substrate, and then measured the contoured distance below that straight line (i.e., contouring over the shape of the substrate but not reaching into the interior of interstices). Rugosity was estimated as the ratio of contoured over straight distances (Luckhurst & Luckhurst 1978) and averaged for each transect.
Details on how predictions were generated
Predictions on trophic cascades and apparent competition derived from an a priori framework (e.g. Chaneton & Bonsall 2000; Heithaus et al.
2008). Also, one of us (JM)

had been studying reefs in our study area for >20 years, which facilitated adapting theoretically-based predictions to the natural history of the system almost entirely a priori
. By ‘almost’, we mean the following. First, prior to our study Beaudreau &
Essington (2007) had established that rockfish consumption by lingcod was sizedependent, with small lingcod being incapable of consuming rockfish. That paper, however, did not make it entirely clear where in the 40-50 cm range of total lengths lingcod should be excluded from our analyses (i.e. it would be flawed to include lingcod that are too small to eat rockfish). Early in the study, therefore, we plotted the available data subset from Period 1 (N=39 in October 2008; data for Period 1 reached N=56 by
December 2008) to determine whether analyses should exclude lingcod at total lengths of
<40 cm or <50 cm (we chose the latter). Second, Murie (1995) had established the importance of demersal shrimps in the diet of copper and quillback rockfish, particularly for subadult size classes. From that study we knew that demersal shrimps and squat lobsters were important diet items for copper and quillback rockfish in general, and that rockfish undergo ontogenetic diet shifts (with consumption of fish prey increasing) as they grow in size. That paper, however, did not make it entirely clear whether squat lobsters were important diet items to subadult size classes of rockfish. Early on, therefore, we plotted the available data subset from Period 1 (the same N=39 as for lingcod) to determine whether squat lobsters influenced the relative abundance of subadult rockfish.
There was no indication that this was the case, justifying the exclusion of squat lobsters from analyses, which allowed for a more parsimonious structural equation model.
Our rationale for including in formal analyses the data subsets just described is as follows. First, the theoretical basis for each prediction was a priori (i.e., data were not

mined). Second, results from Periods 3 and 4 were consistent with the principal results from analyses that aggregated non-winter periods (Periods 1, 3 and 4) and for Period 1 alone. Finally, given the nature of SCUBA-based work in cold and relatively deep water
(most data required dives to ≥20 m), each data point was expensive and difficult to obtain; arguably, it would be wasteful to discard the 39 data points used to make two analyses decisions early in the study.
References
Beaudreau A. & Essington T. (2007). Spatial, temporal, and ontogenetic patterns of predation on rockfishes by lingcod. Transactions of the American Fisheries
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Chaneton E.J. & Bonsall M.B. (2000). Enemy-mediated apparent competition: empirical patterns and the evidence. Oikos , 88, 380-394.
Heithaus M., Frid A., Wirsing A. & Worm B. (2008). Predicting ecological consequences of marine top predator declines. Trends in Ecology and Evolution , 23, 202-210.
Luckhurst B.E. & Luckhurst K. (1978). Analysis of influence of substrate variables on coral-reef fish communities. Marine Biology , 49, 317-323.
Marliave J. & Challenger W. (2009). Monitoring and evaluating rockfish conservation areas in British Columbia. Canadian Journal of Fisheries and Aquatic Sciences ,
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Matthews K. (1990). A telemetric study of the home ranges and homing routes of copper and quillback rockfishes on shallow rocky reefs.
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Murie D.J. (1995). Comparative feeding ecology of two sympatric rockfish congeners,
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