Supporting Information Appendix S3. Summary of model selection approach for factors that
may underlie variation in the indirect effect of predators on oyster production. Fitted parameters
include a null model of intercept equal to 1, submergence time of reef by water, the amount of
juvenile oysters available to consumers, the amount of food available to oysters (chl a), the
maximum aerial temperature on reefs during low tide, and the amount of sediment accumulation
on reefs. Below the summary of results, we outline the rationale for how each of these factors
could influence the outcome and/or relative importance of trophic cascades for oyster
production. AICc difference (∆i) is the difference between the AICc of model i and the lowest
AICc observed. Akaike weight (wi) is calculated as the model likelihood, exp(-∆i / 2), normalized
by the sum of all model likelihoods; values close to 1 indicate greater confidence in the selection
of a model. The best candidate model is highlighted in bold.
Candidate models
(∆i)
df
wi
Null model
a
3
4.3
0.05
4
8.4
0.007
Phytoplankton
4
4.9
0.04
Oyster recruitment
4
4.2
0.06
Phytoplankton + Oyster recruitment
5
6.8
0.015
4
8.4
0.007
Physical alteration of predatory-prey dynamic
Reef submergence
Bottom-up controls and supply of oyster larvae
Environmental Stress
Maximum aerial temperature
Sediment accumulation
4
0.0
0.47
Max. aerial temperature + Sediment accumulation
5
5.4
0.03
Reef submergence + Phytoplankton
5
11.8
0.001
Reef submergence + Oyster recruitment
5
9.2
0.004
Reef submergence + Maximum aerial temperature
5
13.3
<0.001
Reef submergence + Sediment accumulation
5
7.6
0.01
Oyster recruitment + Maximum aerial temperature
5
6.3
0.019
Oyster recruitment + Sediment accumulation
5
1.2
0.26
Phytoplankton + Maximum aerial temperature
5
11.0
0.002
Phytoplankton + Sediment accumulation
5
6.3
0.02
Physical alteration & Bottom-up controls
Physical alteration & Environmental Stress
Resource Supply & Environmental Stress
Rationale
Physical alteration of predator-prey interaction: Throughout the SAB, variability in the tidal
submergence of a reef could physically shift the outcome of a trophic cascade. By enhancing the
presence of pelagic predators and the dissemination of their water-borne cues (Smee &
Weissburg 2007), tidal submergence could physically alter the predator-consumer interaction.
The bottom-up influences: Two resources that generally differ along coastlines are the supply of
invertebrate larvae (food for consumers) and phytoplankton (food for oysters). If site differences
in oyster larvae promote spatial variation in recruitment, then high recruitment could reduce the
population-level effect of mud crab foraging at some sites by numerically compensating for any
consumed oysters (Gaines and Roughgarden 1988). In this case, the presence and strength of
indirect predator effects would be irrelevant for oyster population growth. With respect to
phytoplankton, sites rich in pelagic phytoplankton may minimize population-level mortality
oysters in the face of strong consumption by mud crabs if this resource enhances the rate at
which small oysters grow into a size refuge (Kimbro et al. 2009).
The influence of environmental stress: Although tidal inundation could physically alter predatorconsumer encounters, it could also create an environmental stress that affects the direct
interaction between predator and consumer as well as how this outcome cascades to oysters. For
instance, spatial variation in submergence could lead to some reefs with prolonged aerial
exposure during low tide. In this situation, physiological stressors such as desiccation (high
aerial temperature) could create high population-level mortality of oysters regardless of trophic
cascades.