Appendix S1. View of seed traps used to sample the seed rain of wild chiltepin peppers in
the dessert grasslands of Tumacacori, southern Arizona, USA. In the the fall of 2005 we
placed 182 traps, 265 in 2006, and 221 in 2007. Approximately equal numbers of traps
were placed under fleshy-fruited trees (mostly Celtis pallida, top left panel) and Prosopis
vellutina (top right panel). A metal meshed (bottom left) protected the screen nets that
collected seeds (bottom right).
1
Appendix S2. Distribution of adult wild chiltepin pepper plants at the Chilies Reserve in
Tumacacori, Arizona. Yellow triangle indicates the location of the peak of Tumacacori
mountain. Red dots show the location of plants in the four local populations (A-D). Green
dots show the location of the seed traps (A-D). Site C is 2.3 Km west of I-19 interstate
highway.
A.
Tumacacori peak (1575 m)
(31°33'59.65"N, 111° 4'55.41"W)
D.
C.
B.
0.1 Km
0.5 Km
A.
D.
B.
0.1 Km
C.
0.1 Km
0.1 Km
!
2
Appendix S3. We performed a separate Zero Inflated Negative Binomial regression
analysis (ZINB) for each year because both sampling effort (i.e., number of trays & sites
sampled) and Capsicum phenology were not exactly the same between years. The ZINB
models assume that two processes are at work producing two count populations (Hall
2000). One population is always zero while the other one is distributed as a negative
binomial, which includes zeroes as well (Bolker 2008). A characteristic of ZINB models is
that it is possible for both populations (i.e., zero-inflated & negative binomial) to have
separate parameter estimates for the same predictor variable. For example, the model may
estimate a parameter for the effects of NF trees for both the zero-inflated and the negative
binomial part. We used Maximum Likelihood to estimate parameters in Proc CountReg,
and for optimization we used the Newton-Raphson and Quasi-Newton methods.
To build the most adequate ZINB model for each of the three years we did the
following. First we fitted a full model including all predictor variables and two-way
interactions for both the zero-inflated and negative binomial parts. However, the models not
always could produce stable parameter estimates for all predictor variables, particularly the
zero-inflated part. Thus, having estimated as many stable parameter estimates as possible in
a full model, we proceeded to compare them to progressively reduced models by manually
stepped out the non-significant parameters, and re-running reduced models (Crawley 2007).
During the stepping procedure, priority was given to step out high order interaction terms
first. Final models were selected based on the lowest values of AIC (Akaike Information
Criterion) and SBC (Schwartz's Bayesian Information Criterion). Because SAS allows
several methods to calculate the estimates of the parameters’ covariance matrix, during
model selection we used HISSIAN, Outer Product of Gradient, and/or QML.
3
Zero-Inflated Negative Binomial Regression Model Year 2005:
Fit summary: ZI Link Function = Logistic; Log Likelihood = -268.8; Maximum Absolute Gradient
= 2.84E-5; Iterations = 52; Optimization = Quasi-Newton; AIC = 555.64; SBC = 584.5
DF
Estimate
Error
Approx. t
P > t 
(NB) Intercept
1
0.80
0.67
1.20
0.231
(NB) Site A
1
4.13
0.90
4.57
< 0.0001
(NB) NF trees
1
-3.34
0.73
-4.59
< 0.0001
(NB) neighborhood
1
1.08
0.86
1.25
0.210
(NB) Site A * neighborhood
1
-1.27
0.88
-1.44
0.149
(NB) NF * neighborhood
1
0.30
0.06
4.87
< 0.0001
(ZI) Intercept
1
0.70
0.46
1.51
0.132
(ZI) neighborhood
1
-0.35
0.14
-2.53
0.011
Alpha
1
3.98
1.41
2.82
0.005
Parameters
(NB = negative binomial,
ZI = zero inflated)
4
Zero-Inflated Negative Binomial Regression Model Year 2006:
Fit summary: ZI Link Function = Logistic; Log Likelihood = -326.7; Maximum Absolute Gradient
= 2.50E-6; Iterations = 17; Optimization = Newton-Raphson; AIC = 679.5; SBC = 721.1
Parameters
DF
Estimate
Error
Approx. t
P > t 
(NB) Intercept
1
3.65
0.39
9.39
<0.0001
(NB) Site A
1
0.96
0.48
2.00
0.045
(NB) Site B
1
-0.22
0.57
-0.40
0.691
(NB) Site D
1
-1.64
0.55
-2.96
0.003
(NB) NF trees
1
-1.67
0.57
-2.94
0.003
(NB) Site A * NF trees
1
1.43
0.68
2.09
0.036
(NB) Site B * NF trees
1
0.44
0.81
0.54
0.587
(NB) Site D * NF trees
1
2.98
0.91
3.29
0.001
(NB) neighborhood
1
0.007
0.03
0.23
0.815
(ZI) Intercept
1
-1.34
0.77
-1.76
0.078
(ZI) Site A
1
0.64
0.86
0.74
0.457
(ZI) Site B
1
1.60
0.77
2.07
0.039
(ZI) Site C
1
1.68
0.73
2.30
0.021
(ZI) NF trees
1
1.07
0.49
2.18
0.029
(ZI) Site A* NF trees
1
-1.07
0.84
-1.27
0.204
(ZI) neighborhood
1
-0.30
0.19
-1.61
0.107
(ZI) NF trees * neighborhood
1
-0.61
0.60
-1.02
0.308
5
(ZI) Alpha
2.28
0.37
6.04
<0.0001
Zero-Inflated Negative Binomial Regression Model Year 2007:
Fit summary: ZI Link Function = Logistic; Log Likelihood = -326.7; Maximum Absolute Gradient
= 2.50E-6; Iterations = 17; Optimization = Newton-Raphson; AIC = 679.5; SBC = 721.1
Parameters
DF
Estimate
Error
Approx. t
P > t 
(NB) Intercept
1
0.31
1.29
0.24
0.809
(NB) Site A
1
3.42
1.28
2.64
0.008
(NB) Site B
1
2.98
1.52
1.95
0.051
(NB) NF trees
1
-3.07
0.64
-4.83
< 0.0001
(NB) neighborhood
1
0.29
0.23
1.25
0.212
(NB) NF * neighborhood
1
0.15
0-12
1.28
0.200
(NB) Site A * neighborhood
1
-0.26
0.23
-1.11
0.266
(NB) Site B * neighborhood
1
-0.60
0.33
-1.79
0.072
(ZI) Intercept
1
-0.81
2.30
-0.35
0.725
(ZI) neighborhood
1
-0.70
0.51
-1.39
0.164
(ZI) Site A
1
0.51
2.39
0.22
0.827
(ZI) Site B
1
2.03
2.35
0.86
0.389
Alpha
1
3.55
0.92
3.85
0.0001
6
Appendix S4. Values of correlation coefficients of scatter-plots between the counts of birddispersed chili seeds of seed traps vs. the number of fruiting chili plants within a given
radius (x axis) from traps. Filled symbols represent significant correlation coefficient values
(Bonferroni corrected:  = 0.05 / 21). Correlation values positively peaked for all years at a
radius between 10-15 meters, thus we used the number of chilies within 10 meters as a
“neighborhood” covariate in ZINB regression models (Appendix C).
7
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Appendix S5. Spatial layout of the 16 transects established for the seed-addition
experiment of wild chiltepin peppers (Capsicum annuum var. glabrusculum). The yellow
triangle marks the location and coordinates of Tumacacori peak for reference. Transects
were at least 500 meters away from the nearest natural population of chiltepin peppers. In
each transect we selected fourteen trees: seven Celtis pallida trees and seven Prosopis
vellutina trees. The purpose of the experiment was to examine how seed emergence and
seedling survival and growth were affected by three factors: nurse tree type (Celtis vs.
Prosopis), density of seed addition (0 seeds (neg. control), 10 seeds, 50 seeds, or 500 seeds)
8
and addition mode (added all at once, or gradually over time). Seeds were added
underneath trees nest to a blue marker flag located in the most shaded area underneath
trees. Seeds were added in November-December of 2006. Germination, growth, and
survival was measured starting in late July of 2007 through January of 2008. We found that
significantly more seeds emerged under Celtis than under Prosopis, that seed density did
not have any effect on germination and growth, and that whether seeds were added
gradually or all at once explained most of the variance in seedlings emergence under trees.
9