Species Richness Compared
to Neutral (Ratio)
1
2
3
4
Defense Trait
Dispersion (Landscape)
-2 -1 0 1 2 3 4
(b)
(c)
0.1
Mean Dist. to Center
of Chem. Space
0.2
0.3
0.4
Defense Trait
Dispersion (Neighborhood)
0.0 0.1 0.2 0.3 0.4
(a)
=5
=5
R =0
(d)
J-C 0.05 0.10 0.15 0.20 0.25 0.33 0.50 0.67 1.00 1.50 2.00 3.00 4.00 5.00 6.67 10.0 20.0 Gen Neut
Defense Trait Shape Parameter s
Fig. S1. Model results when the probability that an offspring of species i survives at
location x is: Pi(H) = 1/( 1+NH) and the establishment threshold distance R = 0.
Species richness (a), landscape defense trait structure compared to random species
assembly (b), neighborhood mean trait distance (MTD; c), and mean distance to the
center of two-dimensional defense trait space (d) is shown as a function of the shape
parameter relating enemy-overlap to trait distance between plant species. MTD was
measured between focal individuals and all individuals within 5 m of each focal
individual in the simulation landscape. Results shown pertain to an offspring () and
enemy () dispersal distance of 5 m and  = 25. Each point represents the result of one
simulation of 400,000 adult deaths.
(a)
Defense Trait
Dispersion (Landscape)
-2
0
2
4
Species Richness Compared
to Neutral (Ratio)
0.5 1.0 1.5 2.0 2.5 3.0
=5
= 15
R =3
Defense Trait
Dispersion (Neighborhood)
0.1 0.2 0.3 0.4 0.5
(c)
Mean Dist. to Center
of Chem. Space
0.1
0.2
0.3
0.4
(b)
(d)
J-C 0.05 0.10 0.15 0.20 0.25 0.33 0.50 0.67 1.00 1.50 2.00 3.00 4.00 5.00 6.67 10.0 20.0 Gen Neut
Defense Trait Shape Parameter s
Fig. S2. Model results when the probability that an offspring of species i survives at
location x is: Pi(H) = 1/( 1+NH) the establishment threshold distance R = 3, and enemy
dispersal distance is long relative to seed dispersal distance ( = 15,  = 5). Species
richness (a), landscape defense trait structure compared to random species assembly (b),
neighborhood mean trait distance (MTD; c), and mean distance to the center of twodimensional defense trait space (d) is shown as a function of the shape parameter relating
enemy-overlap to trait distance between plant species. MTD was measured between
focal individuals and all individuals within 5 m of each focal individual in the simulation
landscape. Results shown pertain to  = 25. Each point represents the result of one
simulation of 400,000 adult deaths.
Species Richness Compared
to Neutral (Ratio)
0.5 1.0 1.5 2.0 2.5
Defense Trait
Dispersion (Landscape)
-2 -1 0 1 2 3 4
(b)
Mean Dist. to Center
of Chem. Space
0.20
0.30
0.40
Defense Trait
Dispersion (Neighborhood)
0.05
0.15
0.25
0.35
(a)
=5
=5
R =3
(c)
(d)
J-C 0.05 0.10 0.15 0.20 0.25 0.33 0.50 0.67 1.00 1.50 2.00 3.00 4.00 5.00 6.67 10.0 20.0 Gen Neut
Defense Trait Shape Parameter s
Fig. S3. Model results when the probability that an offspring of species i survives at
location x is: Pi(H) = 1/(N*log(1+H)). Species richness (a), landscape defense trait
structure compared to random species assembly (b), neighborhood mean trait distance
(MTD; c), and mean distance to the center of two-dimensional defense trait space (d) is
shown as a function of the shape parameter relating enemy-overlap to trait distance
between plant species. MTD was measured between focal individuals and all individuals
within 5 m of each focal individual in the simulation landscape. Results shown pertain to
an offspring () and enemy () dispersal distance of 5 m, an establishment threshold
distance (R) of 3 m, and  = 2.5. Each point represents the result of one simulation of
400,000 adult deaths.
Species Richness Compared
to Neutral (Ratio)
0.5 1.0 1.5 2.0 2.5
(a)
Defense Trait
Dispersion (Landscape)
-2 -1 0 1 2 3 4
(b)
Defense Trait
Dispersion (Neighborhood)
0.1
0.2
0.3
0.4
(c)
0.1
Mean Dist. to Center
of Chem. Space
0.2
0.3
0.4
=5
=5
R =3
(d)
J-C 0.05 0.10 0.15 0.20 0.25 0.33 0.50 0.67 1.00 1.50 2.00 3.00 4.00 5.00 6.67 10.0 20.0 Gen Neut
Defense Trait Shape Parameter s
Fig. S4. Model results when the probability that an offspring of species i survives at
location x is: Pi(H) = 1/(1+NH2)). Species richness (a), landscape defense trait structure
compared to random species assembly (b), neighborhood mean trait distance (MTD; c),
and mean distance to the center of two-dimensional defense trait space (d) is shown as a
function of the shape parameter relating enemy-overlap to trait distance between plant
species. MTD was measured between focal individuals and all individuals within 5 m of
each focal individual in the simulation landscape. Results shown pertain to an offspring
() and enemy () dispersal distance of 5 m, an establishment threshold distance (R) of 3
m, and  = 2.5. Each point represents the result of one simulation of 400,000 adult
deaths.
0.25
s = 0.10
s = 0.15
s = 0.20
s = 0.25
s = 0.33
s = 0.50
s = 0.67
0.10
0.05
0.20
0.05
0.10
0.15
Probability of Offspring Survival
0.15
0.20
s = 0.05
0
20 40 60 80 100
0
20 40 60 80 100
0
20 40 60 80 100
Abundance of Focal Species
0
20 40 60 80 100 120
Abundance
Fig. S5. Probability of offspring recruitment as a function of abundance of the focal
species for eight values of s. The rare-species advantage conferred by the J-C mechanism
is sensitive to the value of s. Lines described by the equation y = b - xa were fit to
simulated offspring recruitment trials using non-linear least squares.
An examination of probability of offspring survival as a function of the
abundance of adults of the focal species indicates a strong rare-species advantage in
models in which s is small (Fig. S5). In fact, the strength of this advantage, as indicated
by the value of m in the curve y = b - xm, is strongly associated with the species richness
maintained in the model.
Probability of Successful Immigration Relative toProbability
Mean of Successful Immigration
s = 0.05
(a)
(b)
s = 0.10
(c)
s = 0.20
Chemical Distance from Most Abund. Species
(d)
s = 0.33
(e)
s = 0.50
(f)
s = 1.00
(g)
s = 2.00
(h)
s = 5.00
(i)
s = 10.0
0
0.10
0.20
0.30
0.40
0.50
0.10
0.20
0.30
0.40
0.50
0.10
0.20
0.30
0.40
0.50
Defense Trait Distance of Immigrant from Most Abundant Species
Fig. S6. Probability of immigration success as a function of defense trait distance to the
most abundant species on the landscape for nine values of the shape parameter s. All yaxes are on the same scale in which one tick equals 2 units, but each plot is centered
about the mean. The mean immigration success for each value of s is indicated by a
dashed line. Maximum immigration success is attained by immigrant species with
intermediate trait distances from the most locally abundant species in panels a-e.
In order to better understand the demographic influence of the shape parameter s
on species richness and trait community structure, we measured both the probability of
offspring recruitment as a function of abundance of each focal species in the landscape as
well as the probability of successful immigration as a function of the defense trait
distance between the potential immigrant species and the most abundant species in the
landscape. The later was conducted by selecting 1000 random points on each of 50 arcs
described by radii from 0.01 to 0.50 units of defense trait distance from the location of
the most abundant species in defense space. For each point, 1000 uniformly random
locations were chosen on the community landscape and the success of the immigration
attempt recorded, thus providing a probability of successful immigration.
In models in which s is small and species richness is enhanced relative to the
neutral case, the probability of immigration is low for potential immigrant species that are
defensively similar to the most abundant resident, but increases sharply only a small trait
distance from the abundant resident (Fig. S6a-e). The probability of successful
immigration then declines as potential immigrants approach other abundant residents in
trait space. In models in which species richness is suppressed relative to neutral (1.00 ≤ s
≤ 5.00), it is advantageous for a potential immigrant to be defensively similar to the most
abundant resident (Fig. S6f-h).