Appendix S1
J. R. Goheen et al.
HGLMs are useful in attributing variance to fixed subplot-level effects (i.e., seed
production, understory cover), fixed plot-level effects (i.e., rodent abundance, occurrence
of cattle, occurrence of native herbivores), and random effects associated with subplots
and plots. Each HGLM incorporated a Poisson (log link) subplot-level sampling model
with an over-dispersion term with a linear, plot-level model. In essence, plot-level models
permit intercepts and slopes within plots to vary as a function of fixed and random plotlevel effects.
Frailty models are useful in accounting for random effects associated with
survival rates. Such random effects or “frailties” correspond to unmeasured covariates;
their incorporation into proportional hazards models permits more accurate estimation of
coefficients, and informs the investigator as to whether non-independence arises within
different units of sampling (i.e., subplot versus plot). In the event that random effects
within these sampling units are negligible, associated frailties are dropped from
subsequent models. Currently, frailty models only permit for a single frailty term (Fox et
al. 2006), so we were unable to assess random effects of subplots and plots
simultaneously. Thus, we evaluated heterogeneity in tree establishment by comparing the
difference in model deviance between our best-fit model for each year to four models
incorporating frailty terms, each of which combined a different random effect (subplot or
plot) with either a Gaussian or gamma distribution for a total of four possible models.
Fox, G.A., Kendall, B.E., Fitzpatrick, J.W. & Woolfenden, G.E. (2006) Consequences of
heterogeneity in survival probability in a population of Florida scrub-jays. Journal of
Animal Ecology, 75, 921-927.
Table S1
J. R. Goheen et al.
Pairwise comparisons for seed production between herbivore treatment x year combinations.
“Wild” denotes plots excluding (0) or accessible to (1) wild herbivores. “Trial” denotes the year
in which the study was conducted: 2004 (1), 2005 (2), or 2006 (3).
native
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
trial
1
1
1
1
1
2
2
2
2
3
3
3
1
1
2
wild
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
trial
2
3
1
2
3
3
1
2
3
1
2
3
2
3
3
est
-772.44
141.73
173.67
-136.08
204.96
914.16
946.10
636.36
977.39
31.93
-277.81
63.22
-309.74
31.28
341.03
SE
120.66
41.87
52.12
140.09
41.81
140.50
140.09
191.13
136.59
41.81
136.59
27.93
120.66
41.87
140.50
DF
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
t
-6.40
3.38
3.33
-0.97
4.90
6.51
6.75
3.33
7.16
0.76
-2.03
2.26
-2.57
0.75
2.43
Pr>|t|
<.0001
0.0070
0.0076
0.354
0.0006
<.0001
<.0001
0.0076
<.0001
0.4627
0.0693
0.0471
0.0280
0.4722
0.0356
Pairwise comparisons for understory vegetation between herbivore treatment x year
combinations. “Cattle” denotes plots excluding (0) or accessible to (1) cattle. “Trial” denotes the
year in which the study was conducted: 2004 (1), 2005 (2), or 2006 (3).
cattle
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
trial
0
0
0
0
0
1
1
1
1
2
2
2
0
0
1
cattle
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
trial
1
2
0
1
2
2
0
1
2
0
1
2
1
2
2
est
-1.45
3.50
4.10
4.24
6.27
4.95
5.55
5.69
7.72
0.60
0.74
2.77
0.13
2.16
2.03
SE
2.13
0.92
1.10
1.79
0.82
1.55
1.79
2.29
1.64
0.82
1.64
0.36
2.13
0.92
1.55
DF
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
t
-0.68
3.78
3.72
2.36
7.64
3.18
3.09
2.48
4.71
0.73
0.45
7.64
0.06
2.34
1.31
Pr>|t|
0.5118
0.0036
0.0040
0.0402
<.0001
0.0098
0.0115
0.0324
0.0008
0.4793
0.6618
<.0001
0.9503
0.0414
0.2210
Pairwise comparisons for Saccostomus mearnsi abundance between herbivore treatment x year
combinations. 0 = all large herbivores excluded; 1 = only cattle permitted; 2 = only wild
herbivores permitted; 3 = both cattle and wild herbivores permitted. “Trial” denotes the year and
month in which small mammal sampling was conducted: June 2004 (1), October 2004 (2),
March 2005 (3), June 2005 (4), September 2005 (5), November 2005 (6), March 2006 (7), and
July 2006 (8).
trt1
0
trial trt2
1
0
trial est
2
6.67
SE
5.04
DF
8
t
1.32
Pr > |t|
0.222
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
6
6
6
6
6
7
7
7
7
8
8
8
1
1
1
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
1
2
3
0
0
0
0
0
1
2
3
0
0
0
0
1
2
3
0
0
0
1
2
3
3
3
3
0
0
1
2
3
0
1
2
3
1
2
3
1
1
1
3
4
5
6
7
8
1
1
1
3
4
5
6
7
8
2
2
2
4
5
6
7
8
3
3
3
5
6
7
8
4
4
4
6
7
8
5
5
5
6
7
8
7
8
6
6
6
8
7
7
7
8
8
8
2
3
4
25
13.33
15.33
21.33
37.33
30.67
13
8.67
32
18.33
6.67
8.67
14.67
30.67
24
6.33
5
19.33
-11.67
-9.67
-3.67
12.33
5.67
7
3
13.67
2
8
24
17.33
15
13.67
26.33
6
22
15.33
15.67
16.33
23.67
20.67
31.33
32.67
16
9.33
11.67
12.67
14.67
-6.67
8
7.33
9.33
9
14.67
17.33
0
19
15.33
4.44
3.67
4.66
6.11
3.91
5.23
4.61
4.61
4.61
5.97
4.89
5.73
5.08
4.56
5.52
6.58
6.58
6.58
5.05
6.46
6.45
5.01
6.24
6.17
6.17
6.17
4.57
4.52
4.03
4.97
4.73
4.73
4.73
5.5
3.75
6.12
6.59
6.59
6.59
6.56
4.96
5.2
4.16
5.29
6.52
6.52
6.52
2.77
2.39
2.39
2.39
3.27
3.27
3.27
5.04
4.44
3.67
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
5.63
3.64
3.29
3.49
9.56
5.87
2.82
1.88
6.95
3.07
1.36
1.51
2.89
6.73
4.35
0.96
0.76
2.94
-2.31
-1.5
-0.57
2.46
0.91
1.13
0.49
2.22
0.44
1.77
5.95
3.49
3.17
2.89
5.57
1.09
5.87
2.5
2.38
2.48
3.59
3.15
6.32
6.28
3.84
1.76
1.79
1.94
2.25
-2.4
3.34
3.07
3.9
2.76
4.49
5.31
0
4.28
4.18
0.001
0.007
0.011
0.008
<.0001
0
0.022
0.097
0
0.015
0.21
0.169
0.02
0
0.003
0.364
0.469
0.019
0.05
0.173
0.586
0.039
0.39
0.289
0.64
0.058
0.674
0.115
0
0.008
0.013
0.02
0.001
0.307
0
0.037
0.045
0.038
0.007
0.014
0
0
0.005
0.116
0.112
0.088
0.055
0.043
0.01
0.016
0.005
0.025
0.002
0.001
1
0.003
0.003
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
2
1
1
1
1
1
1
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
5
5
5
5
5
6
6
6
6
7
7
7
8
8
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
3
1
1
1
1
1
1
2
3
1
1
1
1
1
2
3
3
3
3
3
3
1
1
1
1
2
3
1
1
1
2
3
1
1
2
3
1
2
3
2
3
2
2
2
2
2
2
2
3
2
2
2
5
6
7
8
1
1
3
4
5
6
7
8
2
2
4
5
6
7
8
3
3
4
5
6
7
8
5
6
7
8
4
4
6
7
8
5
5
7
8
6
6
8
7
7
8
8
2
3
4
5
6
7
8
1
3
4
5
18
20
32.33
26.67
-4.33
19
19
15.33
18
20
32.33
26.67
-1.33
13
-3.67
-1
1
13.33
7.67
-4
6.67
7.67
7
4
14.67
16
2.67
4.67
17
11.33
-1.33
11.33
2
14.33
8.67
0.67
8
12.33
6.67
1
3
-5.67
-0.67
1.33
5.67
8.33
3
19.33
18.33
23
25.33
36
36.67
23.33
16.33
15.33
20
4.66
6.11
3.91
5.23
4.61
4.61
5.97
4.89
5.73
5.08
4.56
5.52
6.58
6.58
5.05
6.46
6.45
5.01
6.24
6.17
6.17
5.49
6.38
6.35
4.68
4.94
4.57
4.52
4.03
4.97
4.73
4.73
5.5
3.75
6.12
6.59
6.59
4.16
5.29
6.52
6.52
2.77
2.39
2.39
3.27
3.27
5.04
4.44
3.67
4.66
6.11
3.91
5.23
4.61
5.97
4.89
5.73
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
3.86
3.27
8.28
5.1
-0.94
4.12
3.19
3.13
3.14
3.94
7.1
4.83
-0.2
1.98
-0.73
-0.15
0.15
2.66
1.23
-0.65
1.08
1.4
1.1
0.63
3.13
3.24
0.58
1.03
4.21
2.28
-0.28
2.4
0.36
3.82
1.42
0.1
1.21
2.96
1.26
0.15
0.46
-2.04
-0.28
0.56
1.74
2.55
0.6
4.35
5
4.94
4.15
9.22
7.01
5.07
2.74
3.13
3.49
0.005
0.011
<.0001
0.001
0.374
0.003
0.013
0.014
0.014
0.004
0
0.001
0.844
0.084
0.488
0.881
0.881
0.029
0.254
0.535
0.311
0.201
0.305
0.546
0.014
0.012
0.576
0.333
0.003
0.052
0.785
0.043
0.726
0.005
0.195
0.922
0.26
0.018
0.243
0.882
0.658
0.075
0.788
0.593
0.121
0.034
0.568
0.002
0.001
0.001
0.003
<.0001
0
0.001
0.026
0.014
0.008
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
2
2
2
2
3
3
3
3
3
3
4
4
4
4
4
5
5
5
5
6
6
6
7
7
8
1
1
1
1
1
1
1
2
2
2
2
2
2
3
3
3
3
3
4
4
4
4
5
5
5
6
6
7
2
2
2
3
2
2
2
2
2
3
2
2
2
2
3
2
2
2
3
2
2
3
2
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
6
7
8
2
4
5
6
7
8
3
5
6
7
8
4
6
7
8
5
7
8
6
8
7
8
2
3
4
5
6
7
8
3
4
5
6
7
8
4
5
6
7
8
5
6
7
8
6
7
8
7
8
8
22.33
33
33.67
14.33
-1
3.67
6
16.67
17.33
10.67
4.67
7
17.67
18.33
12.67
2.33
13
13.67
7.33
10.67
11.33
2
0.67
2
2.67
-6
6.67
7.67
7
4
14.67
16
12.67
13.67
13
10
20.67
22
1
0.33
-2.67
8
9.33
-0.67
-3.67
7
8.33
-3
7.67
9
10.67
12
1.33
5.08
4.56
5.52
6.58
5.05
6.46
6.45
5.01
6.24
6.17
4.57
4.52
4.03
4.97
4.73
5.5
3.75
6.12
6.59
4.16
5.29
6.52
2.77
2.39
3.27
5.04
4.44
3.67
4.66
6.11
3.91
5.23
5.97
4.89
5.73
5.08
4.56
5.52
5.05
6.46
6.45
5.01
6.24
4.57
4.52
4.03
4.97
5.5
3.75
6.12
4.16
5.29
2.77
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
4.4
7.24
6.1
2.18
-0.2
0.57
0.93
3.33
2.78
1.73
1.02
1.55
4.38
3.69
2.68
0.42
3.47
2.23
1.11
2.56
2.14
0.31
0.24
0.84
0.82
-1.19
1.5
2.09
1.5
0.65
3.76
3.06
2.12
2.79
2.27
1.97
4.54
3.99
0.2
0.05
-0.41
1.6
1.5
-0.15
-0.81
1.74
1.68
-0.55
2.04
1.47
2.56
2.27
0.48
0.002
<.0001
0
0.061
0.848
0.586
0.38
0.01
0.024
0.122
0.337
0.16
0.002
0.006
0.028
0.683
0.009
0.056
0.298
0.034
0.065
0.767
0.816
0.427
0.438
0.268
0.172
0.07
0.171
0.531
0.006
0.016
0.067
0.024
0.053
0.085
0.002
0.004
0.848
0.96
0.69
0.149
0.173
0.888
0.441
0.121
0.132
0.601
0.075
0.18
0.034
0.053
0.644
Table S2
J. R. Goheen et al.
Results for selection of Poisson regression models for the number of seedlings germinating using subplot-level predictors, used to
formulate hierarchical generalized linear models. Predictors include seed production (SEED), exclosure type (EXC; total, rodent+bird,
bird, control), and understory cover (VEG). Models with strong levels of support (Δi < 2) are presented. Akaike weights (wi) represent
the relative likelihood that a model is “best”, given the data and a candidate set of models. Estimates of coefficients (β) represent the
natural log of the difference in the additional number of germinants in exclosures inaccessible to rodents (rodent+bird and total
exclosures), as compared to bird exclosures and controls (P < 0.001 for all). In no year did germination differ between controls and
bird exclosures (P > 0.10), and in no year did germination differ between rodent+bird and total exclosures (P > 0.10).
Model
2004
EXC + SEED + VEG + EXC*SEED
EXC + SEED + VEG + EXC*SEED + EXC*VEG
# Parameters ΔQAICc
wi
Coefficient Estimates
β
SE
9
12
0
0.92
0.47
0.30
2.50
2.45
0.56
0.82
2005
EXC + SEED + VEG + EXC*SEED
9
0
0.85
1.84
0.27
2006
SEED
VEG
SEED + VEG
2
2
3
0
0.02
1.05
0.30
0.30
0.18
NA
NA
NA
NA
NA
NA
Table S3
J.R. Goheen et al.
Coefficient estimates for hierarchical generalized linear models (HGLM) fit to seedling
production in 3 years. Each HGLM contains tree-level predictors from the best-fit model for
seedling production. Data in parentheses represent seedlings germinating from seeds
protected from rodents. Seedling production is modeled as exp(β0j+ β1j*seed number+
β2j*understory cover). Initially, β0j was modeled as a linear function with an intercept and
three plot-level predictors (γ0j’s): rodent abundance, an indicator variable for occurrence of
cattle, and an indicator variable for occurrence of wild herbivores. Initially, we included
random effects of plots (u0j and uqi’s) on β0j and βqj’s. When γ0j’s, u0j, or uqi’s were not
statistically significant (P>0.10) they were excluded from the HGLM. “NS” = nonsignificant (P>0.10).
Tree-level predictor
Plot-level predictor Coefficient
2004
Intercept β0j
Intercept γ00
1.51(-0.980)
Rodents γ01
-0.120(NS)
Seeds β1j
Intercept γ10
NS(0.013)
Understory β2j
Intercept γ20
-0.130(-0.059)
2005
Intercept β0j
Intercept γ00
Rodents γ01
Seeds β1j
Intercept γ10
Understory β2j
Intercept γ20
2006
Intercept β0j
Intercept γ00
Seeds β1j
Intercept γ10
Understory β2j
Intercept γ20
SE
d.f.
3.180(0.470) 10(11)
0.030(NS)
10(NS)
T
P
0.03(-2.09)
-3.29(NS)
0.98(0.06)
0.01(NS)
NS(189)
NS(12.07)
NS(<0.001)
0.040(0.030) 188(11)
-2.85(-1.97)
0.01(0.08)
NS(0.001)
2.770(1.629) 0.848(0.250) 10(11)
-0.160(NS)
0.022(NS)
10(NS)
3.27(6.5)
-7.10(NS)
0.01(<0.001)
<0.001(NS)
0.004(0.002) 0.001(0.001) 11(185)
2.90(12.11)
0.02(<0.001)
-0.058(-0.023) 0.029(0.010) 11(185)
-2.00(-2.21)
0.07(0.03)
-0.96
0.65
11
-1.48
0.17
0.011
0.010
381
3.78
<0.001
-0.170
0.071
381
-2.39
0.02
Table S4
J. R. Goheen et al.
Results for selection of Cox proportional hazards models for seedling survival using subplot-level predictors, used to
formulate frailty models. Level-one predictors include exclosure type (EXC; total, rodent+bird, bird, control), understory
cover (VEG), and time to emergence (EMERGE). Models with strong levels of support (Δi < 2) are presented. Akaike
weights (wi) represent the relative likelihood that a model is “best”, given the data and a candidate set of models. Estimates
of coefficients (β) represent the natural log of the risk ratio between weekly seedling mortality in bird exclosures and
controls, as compared to exclosures inaccessible to rodents (rodent+bird and total cages). In no year did seedling survival
differ between control subplots and bird cages (P > 0.10), and in no year did germination differ between rodent+bird and
total cages (P > 0.10).
Model
2004
EXC + VEG
EXC + VEG + EMERGE
# Parameters ΔAICc
wi
Coefficient Estimates
β
SE
3
4
0
1.25
0.50
0.27
-0.75
-0.78
0.32
0.32
2005
VEG + EMERGE
3
0
0.61
NA
NA
2006
EMERGE
EMERGE + VEG
EMERGE + EXC
2
3
3
0
1.11
1.95
0.41
0.23
0.15
NA
NA
-0.16
NA
NA
0.47
Fig. S1
J.R. Goheen et al.
Schematic of experimental design. Plot labels within block denote treatments with wild
herbivores and cattle (MWC), wild herbivores only (MW), cattle only (C), or no large
herbivores (0). Subplot labels within trees denote control (C), bird exclusion cages (B), rodent +
bird exclusion cages (RB), or total (bird + rodent + insect; IRB) exclusion cages. Seeds from
each tree were divided and distributed equitably between subplots. Following germination,
seedlings within subplots were monitored for 24 weeks.
Fig. S2
J.R. Goheen et al.
Hazard functions for probabilities of tree establishment, 2004-2006. In 2004, functions are
stratified by rodent access because caged seedlings survived longer than open seedlings. In 2004
and in 2005, functions are stratified by cattle access because seedlings survived longer where
levels of understory cover (driven by cattle) were low.