Figure S1.
Residual error plotted against expected values for the best fit model (Incomplete
resource partitioning; equation 2 in text), fit with non-weighted least squares a), and weighted
least squares (b). Weighted least squares was used to fit all models, to account for
heteroscedasticity in the data.
1
Table S1.
Log-likelihood (LL) and Akaike information criterion (AIC) values for the
models presented in the text, fit to the data, using least squares (LS) and weighted least squares
(Weighted LS).
Model
Full Model (Eq. 1)
Niche partitioning removed (Eq. 2)
Facilitation removed (Eq. 2)
Facilitation, Unique niche removed
Facilitation, Niche overlap removed
LS LL
-955.40
-968.26
-956.41
-964.69
-965.81
LS AIC
1936.7
1952.5
1936.8
1945.4
1953.6
2
Weighted LL
-500.8108
-514.9386
-501.3982
-518.7444
-512.096
Weighted LS AIC
1027.6
1045.9
1026.8
1053.5
1046.2
Figure S2.
Natural enemies recovered at the end of the experiment, divided by the number
originally released, summed for true predators in (a) Block 1 and (c) Block 2, and for pupae of
the parasitoid D. rapae in (b) Block 1 and (d) Block 2. Error bars represent means  1 s.e. True
predator reproduction was common in the first trial, which encompassed early summer when
predator reproduction is at its height (e.g., Snyder et al. 2006). Thus, predator densities generally
exceeded the number initially added [Fig. S1(a)]. However, true predator reproduction rarely
occurred in the second trial, conducted well into the summer drought typical for the region, and
thus at a time when activity of most predators naturally declines. Thus, predator densities
declined over the course of the second trial [Fig. S1(c)]. Per capita predator recovery at the end
of Trial 1 generally decreased with increasing predator density, but predator density, predator
diversity, or their interaction did not significantly impact predator densities in either trial [Table
S1(a)]. As with true predators, per capita parasitoid reproduction was higher in Trial 1 than Trial
2 [Fig. S1(b, d); Table S1(b)]. However, parasitoid densities were not significantly impacted by
predator diversity or density, or their interactions, in either trial [Table S1(b)].
Final / initial
30
a) Block 1, predators
18
20
12
10
6
0
0
0.3
2
c) Block 2, predators
b) Block 1, parasitoid
d) Block 2, parasitoid
0.2
1
0.1
0.0
0
4
8
16
4
32
Predator density
Mono
3
Diverse
8
16
32
Table S2.
Three-way ANOVA of the final densities of (a) true predators and (b) the aphid
parasitoid D. rapae.
a. True predators
Source
d.f.
MS
Diversity
1
3.329
Density
3
87.697
Block
1 352.676
Diversity × Density
3
9.047
Diversity × Block
1
3.806
Density × Block
3
87.323
Diversity × Density × Block 3
7.969
Error
48
41.3
F-ratio
0.081
2.123
8.539
0.219
0.092
2.114
0.193
P
0.778
0.110
0.005
0.883
0.763
0.111
0.901
F-ratio
0.005
.490
11.971
1.307
0.081
0.466
1.289
P
0.946
0.695
0.004
0.311
0.780
0.711
0.317
b. Parasitoid
Source
d.f.
MS
Diversity
1
0.073
Density
3
7.511
Block
1 183.659
Diversity × Density
3
20.056
Diversity × Block
1
1.242
Density × Block
3
7.143
Diversity × Density × Block 3
19.784
Error
14 15.342
4