Caughlin T.T., Ferguson J.M., Lichstein J.W., Zuidema P.A., Bunyavejchewin S., Levey D.J.
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Text S2: Overview, Design concepts and Details for individual-based model (IBM)
The model description follows the ODD (Overview, Design concepts, Details) protocol for
describing individual- and agent-based models [1,2]
1. Purpose
The purpose of the IBM was to model population dynamics of a tropical tree species, Miliusa
horsfieldii, including spatially-explicit seed dispersal and negative density dependence (NDD),
and quantify the importance of animal-mediated seed dispersal for population viability.
2. Entities, state variables, and scales
The entities in the IBM are individual trees. Trees are classified by three state variables: life
stage, size and location. Life stage includes three categories seeds, seedlings (< 1 cm DBH) and
trees (> 1 cm DBH). Within seedling and tree life stages, we used size as a continuous state
variable, with seedling size classified in terms of height (cm) and tree size classified in terms of
DBH (cm). Throughout the life cycle, attributes of each individual also included x and y
coordinates. Due to the finite size of the simulated area (4 ha), we assumed a toroidal surface
with wrap-around edges.
3. Process overview and scheduling
One time step (a single year) in the IBM includes the following steps:
1. The tree neighborhood for each tree individual is calculated and used in conjunction
with tree size to simulate growth and survival (Eq. 1 and 2).
2. The tree neighborhood and conspecific seedling density is calculated for seedling
growth and survival, using location and size of individuals from the previous time
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Caughlin T.T., Ferguson J.M., Lichstein J.W., Zuidema P.A., Bunyavejchewin S., Levey D.J.
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step (before current year tree growth and survival), and used to simulate seedling
growth and survival (Eq. 3 and Eq 4).
3. After seedling growth and survival is determined in Step 2, we use seedling heightDBH allometry to determine the probability of seedlings switching life stages to
become trees (Eq. 5).
4. For the seedlings that have transitioned to become trees, an additional seedling-height
DBH allometry relationship is used to translate seedling height to DBH (Eq. 6).
5. Next, seed production is estimated as a function of tree DBH (Eq. 7).
6. Following seed production, the distance each seed is dispersed from the parent tree is
simulated using (Eq. 8-11).
7. Following seed dispersal, the tree neighborhood and conspecific seedling density
around each individual seed is determined and seed germination is simulated (Eq. 12).
8. Surviving seedlings, following germination (Step 7), are then assigned an initial
height (Eq. 13).
9.
Germination and initial height of new seedlings occur three months after seed
dispersal, leaving a gap of nine months between these processes and the next time
step of the IBM. Thus, we simulate survival and growth of newly germinated
seedlings for nine months using the submodels for seedling survival and growth (Eq.
3 and 4). After simulating new seedling establishment, the IBM begins the next time
step, starting with adult survival and growth (Step 1).
4. Design concepts
Basic principles:
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Caughlin T.T., Ferguson J.M., Lichstein J.W., Zuidema P.A., Bunyavejchewin S., Levey D.J.

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Interaction Trees interact with one another as a result of decreased growth and survival in
a neighborhood radius for neighboring trees and density in 1 x 1 m2 plots for neighboring
seedlings. Tree neighbors that are bigger and nearer to target individuals have larger
negative effects on growth, survival and germination.

IBM model is linked to empirical data All parameters in the IBM were estimated using
empirical data in a hierarchical Bayesian framework. For each of the 44 parameters in the
IBM we are able to draw from posterior samples of parameters and propagate uncertainty
through to IBM output (Table S2). This is a key design concept, because our simulation
results can be considered robust to variability in data collection and parameter estimation
[3].

Emergent properties: Emergent properties of the IBM include total population size as a
measure of population density, basal area as a measure of biomass, and spatial
aggregation.

Observations We quantified spatial aggregation as the average density of neighbors in a
10 m radius of each tree (Ω) divided by mean population density in the 4 ha area (see
[4,5]. Ω>1 indicates spatial aggregation, Ω=1 indicates random spacing, and Ω<1
indicates regular spacing. These three observations were recorded at each time step of the
IBM.

Stochasticity All demographic processes in the IBM were stochastically simulated by
drawing from the appropriate probability distribution. Consequently, all processes in the
IBM include demographic stochasticity. While we parameterized submodels for tree
growth and survival with a random effect for year, we lacked multiyear data for other
submodels and so did not include environmental stochasticity (year-to-year variation in
demographic processes) in the IBM.
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Caughlin T.T., Ferguson J.M., Lichstein J.W., Zuidema P.A., Bunyavejchewin S., Levey D.J.
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5. Initialization
Each run of the IBM was initialized with the size and location of trees in one of the eight 4 ha
subplots from the 1994 census of the 50 ha Forest Dynamics Plot. During the first eight years of
simulation, growth and survival of trees>1 cm DBH is held constant, while seed production,
dispersal, germination and seedling growth and survival are simulated (Eq 3-13), in order to
approximate the initial distribution of seedlings in the plot. After the first eight years of
simulation, one time step in the IBM begins with tree growth and survival (Step 1 in Scheduling
section).
6. Input data
The model does not use input data to represent time-varying processes.
7. Submodels
One time step in the IBM begins with tree growth and survival (Eq. 1 and 2). In these equations,
DBH𝑖 represents the DBH of the ith individual, with DBH. neighbor𝑗 and Distance. neighborj
representing the size and distance of neighbor tree j in a 25 m radius around the target individual.
Note that because tree census data was collected on a 5 year interval and the IBM runs on an
annual time step, we scale survival and growth to an annual time step by raising the probability
1
of survival to the power of 5, and divide centimeters of growth by 5.
1
5
Tree survival ~Bernoulli ([θ𝑎𝑠
𝑖 ] )
logit(θ𝑎𝑠
𝑖 )=
2 × 𝐺. 𝑠 × DBH𝑖
2
2+
DBH
(𝐺. 𝑠 + 𝑃. 𝑠𝑖 )
DBH. neighbor𝑗
𝛼 𝑎𝑠
×∑
DBH𝑖
Distance. neighborj 𝑑𝑖𝑠.𝑎𝑠
(1)
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Caughlin T.T., Ferguson J.M., Lichstein J.W., Zuidema P.A., Bunyavejchewin S., Levey D.J.
𝑎𝑔
𝑎𝑔
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𝑎𝑔
Skew Normal(μ𝑖 , 𝑠ℎ𝑎𝑝𝑒𝑖 , 𝑠𝑐𝑎𝑙𝑒𝑖 )
Tree growth𝑖 ~
5
𝑎𝑔
μ𝑖 =
2 × 𝐺. 𝑔 × DBH𝑖
DBH 2
(𝐺. 𝑔 + 𝑃. 𝑔𝑖 )
2 × exp (
𝑎𝑔
𝑠ℎ𝑎𝑝𝑒𝑖
DBH. neighborj
𝛼 𝑎𝑔
×∑
)
DBH𝑖,𝑗
Distance. neighborj 𝑑𝑖𝑠.𝑎𝑔
(2)
= 𝑏𝑠ℎ𝑎𝑝𝑒 × exp( DBH𝑖 × 𝑎𝑠ℎ𝑎𝑝𝑒 )
𝑎𝑔
𝑠𝑐𝑎𝑙𝑒𝑖
= √𝑎𝑠𝑐𝑎𝑙𝑒 × DBH𝑖 𝑏𝑠𝑐𝑎𝑙𝑒
The next step in the IBM is simulating seedling growth and survival. Eq. 3 and 4 show
the submodels for seedling growth and survival. In these equations, Size𝑖 indicates the height (in
cm) of the ith seedling and Con. seedlings𝑖 represents the density of conspecific seedlings in 1 m
x 1m2 plots.
Seedling survival 𝑖 ~Bernoulli(θ𝑖𝑠𝑠 )
logit(θ𝑖𝑠𝑠 ) = 𝜇0𝑠𝑠 + 𝑠𝑖𝑧𝑒 𝑠𝑠 × Size𝑖 + 𝛽 𝑠𝑠 × Con. seedlings𝑖
(3)
𝑠𝑔
Seedling growth𝑖 ~Skew Normal(μ𝑖 , 𝑠ℎ𝑎𝑝𝑒 𝑠𝑔 , 𝑠𝑐𝑎𝑙𝑒 𝑠𝑔 )
𝑠𝑔
𝑠𝑔
μ𝑖 = (𝜇0 + 𝑠𝑖𝑧𝑒 𝑠𝑔 × Size𝑖 ) × exp(𝛽 𝑠𝑔 × Con. seedlings𝑖 )
DBH. neighborj
𝛼 𝑠𝑔
× exp (
×∑
)
Size𝑖
Distance. neighborj 𝑑𝑖𝑠.𝑠𝑔
(4)
After seedling growth and survival, the probability of seedlings reaching 1 cm DBH and
the size of new individuals in the tree life stage is simulated using equations for seedling heightDBH allometry.
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Caughlin T.T., Ferguson J.M., Lichstein J.W., Zuidema P.A., Bunyavejchewin S., Levey D.J.
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Tree switch𝑖 ~Bernoulli(θ𝑖𝑠𝑤𝑖𝑡𝑐ℎ )
logit(θ𝑖𝑠𝑤𝑖𝑡𝑐ℎ ) = 𝑎 𝑠𝑤𝑖𝑡𝑐ℎ + 𝑏 𝑠𝑤𝑖𝑡𝑐ℎ × Size𝑖
(5)
ℎ𝑡
Tree DBH𝑖 ~Normal(μℎ𝑡
𝑖 ,𝜎 )
ℎ𝑡
ℎ𝑡
μℎ𝑡
× Size𝑖
𝑖 =𝑎 +𝑏
(6)
The next step in the IBM is to simulate the production of new seedlings, beginning with
seed production. Seed production for the ith tree is drawn from a Poisson distribution, with λ a
sigmoid function of tree DBH:
𝑓𝑟
Seeds𝑖 ~Poisson(λ𝑖 )
𝑓𝑟
λ𝑖
=
𝑓𝑟
𝛽0
+
(7)
1
𝑓𝑟
𝑓𝑟
𝑓𝑟
𝛽1 +exp(𝛽2 ×DBH𝑖 )
For IBM simulations with natural dispersal, the distance each seed is dispersed from the
parent tree is drawn from a two-dimensional Student’s T distribution, with a single free
parameter, u.dispersal:
𝑑𝑖𝑠𝑝𝑒𝑟𝑠𝑎𝑙
P(distance𝑊𝑖𝑡ℎ
) = 2 × distance𝑖 ×
𝑖
1
(𝑢. 𝑑𝑖𝑠𝑝𝑒𝑟𝑠𝑎𝑙)
2
distance𝑖 2
(1 +
)
𝑢. 𝑑𝑖𝑠𝑝𝑒𝑟𝑠𝑎𝑙 ]
[
(8)
In addition to seeds arriving from trees within the IBM plot, we also had a term for seeds
arriving outside the plot, 𝐵𝑎𝑡ℎ. We do not refer to the Bath term as “long distance dispersal,”
because the Bath term refers to dispersal from seed sources from outside the plot, regardless of
distance (thus a seed arriving from a tree 1 m outside the plot would still be included in the Bath
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Caughlin T.T., Ferguson J.M., Lichstein J.W., Zuidema P.A., Bunyavejchewin S., Levey D.J.
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term). For each of the 40,000 1 x 1 m quadrats in the 200 x 200 m simulated area, the number of
Bath seeds arriving in each quadrat is drawn from a Poisson distribution:
Bath seeds𝑖 ~Poisson( λ𝑏𝑎𝑡ℎ
)
𝑖
(9)
λ𝑏𝑎𝑡ℎ
= 𝐵𝑎𝑡ℎ
𝑖
The IBM scenario with no animal dispersal assumes that all seeds are dispersed beneath
parent tree canopies and does not include a bath term. In this version of the IBM, seed
production remains identical to Eq 7, but dispersal distance of seed i from parent tree j, is drawn
from a Uniform distribution with a minimum value equal to the radius of the tree trunk and a
maximum value equal to the tree’s canopy radius:
𝑑𝑖𝑠𝑝𝑒𝑟𝑠𝑎𝑙
distance𝑁𝑜
~Uniform (Trunk𝑗 , Radius𝑗 )
𝑖
(10)
The canopy radius is drawn from a submodel for canopy allometry, which assumes that
canopy radius is a power law of tree DBH:
𝑐𝑎𝑛𝑜𝑝𝑦
Radius𝑗 ~Normal(μ𝑗
𝑐𝑎𝑛𝑜𝑝𝑦
μ𝑗
=𝑎
𝑐𝑎𝑛𝑜𝑝𝑦
, 𝜎 𝑐𝑎𝑛𝑜𝑝𝑦 )
× DBH𝑗
𝑏 𝑐𝑎𝑛𝑜𝑝𝑦
(11)
After seed dispersal, the tree neighborhood in a 20 m radius and conspecific seedling
density in 1 m x 1 m quadrats around each individual seed is determined from the distribution of
trees and seedlings from the previous time step of the IBM. Next, seed germination of the ith
seed is determined as:
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Caughlin T.T., Ferguson J.M., Lichstein J.W., Zuidema P.A., Bunyavejchewin S., Levey D.J.
𝑔𝑒𝑟
Germination𝑖 ~Bernoulli(θ𝑖
𝑔𝑒𝑟
logit(θ𝑖
𝑔𝑒𝑟
) = 𝜇0
+ 𝛽 𝑔𝑒𝑟 × Con. seedlings𝑖 + 𝛼 𝑔𝑒𝑟 × ∑
8
)
DBH. neighbori
Distance. neighbori 𝑑𝑖𝑠.𝑔𝑒𝑟
(12)
The germination submodel determines whether or not a seed survives to become a
seedling. Surviving seedlings must then be assigned an initial height, which for the ith seedling is
drawn stochastically from a skew normal distribution with an expectation, shape and scale:
Initial height 𝑖 ~Skew Normal(μ𝑖𝑛.ℎ𝑡 , 𝑠ℎ𝑎𝑝𝑒 𝑖𝑛.ℎ𝑡 , 𝑠𝑐𝑎𝑙𝑒 𝑖𝑛.ℎ𝑡 )
(13)
8. Simulation experiments and analysis
We analyzed output from the IBM with observed rates of seed dispersal using a global sensitivity
analysis (see Text S3 for more details). We also conducted simulation experiments to compare a
scenario with observed rates of seed dispersal to a scenario in which animal seed dispersers were
hunted to extinction. We then compared total population size, spatial aggregation and basal area
between the two scenarios.
References
1. Grimm, V. et al. 2006 A standard protocol for describing individual-based and agent-based
models. Ecol. Model. 198, 115–126.
2. Grimm, V., Berger, U., DeAngelis, D. L., Polhill, J. G., Giske, J. & Railsback, S. F. 2010 The
ODD protocol: a review and first update. Ecol. Model. 221, 2760–2768.
3. Ellner, S. P. & Fieberg, J. 2003 Using PVA for management despite uncertainty: effects of
habitat, hatcheries, and harvest on salmon. Ecology 84, 1359–1369.
4. Condit, R. et al. 2000 Spatial patterns in the distribution of tropical tree species. Science 288,
1414–1418.
5. Flügge, A. J., Olhede, S. C. & Murrell, D. J. 2012 The memory of spatial patterns: changes in
local abundance and aggregation in a tropical forest. Ecology 93, 1540–1549.
(doi:10.1890/11-1004.1)
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