Journal of Ecology 2012, 100, 862–873
doi: 10.1111/j.1365-2745.2012.01978.x
The interacting effects of clumped seed dispersal and
distance- and density-dependent mortality on seedling
recruitment patterns
Noelle G. Beckman1*†, Claudia Neuhauser2 and Helene C. Muller-Landau3
1
Ecology, Evolution, and Behavior, University of Minnesota-Twin Cities, 100 Ecology, 1987 Upper Buford Circle, Saint
Paul, MN 55108, USA; 2Biomedical Informatics and Computational Biology, University of Minnesota-Rochester, 300
University Square, 111 S Broadway, Rochester, MN 55904, USA; and 3Smithsonian Tropical Research Institute, Unit
9100 Box 0948, DPO, AA 34002-9948, Ecology, Evolution, and Behavior, University of Minnesota-Twin Cities, 100
Ecology, 1987 Upper Buford Circle, Saint Paul, MN 55108, USA
Summary
1. Seed dispersal and natural enemies both influence spatial patterns of seedlings, which in turn
influence future abiotic and biotic interactions, with consequences for plant populations, distributions and diversity. Clumped seed deposition is common, especially for vertebrate-dispersed seeds,
and has the potential to significantly affect interactions with density-responsive enemies, yet has
received relatively little attention.
2. We used spatially explicit simulation models to examine how different patterns of seed dispersal
and natural enemy attack structure seedling spatial patterns. We simulated clumped seed dispersal
by combining a two-dimensional Student’s T dispersal kernel for expected seed rain with a negative
binomial distribution for seed deposition. We based our models for seed mortality on published
data reflecting differing life histories of insect seed predators and soil-borne pathogens. We varied
dispersal distance, degree of clumping, type of enemy, enemy dispersal distance and fecundity
among simulations.
3. Under insect seed predation, seeds escaped predation by dispersing longer distances than insects,
resulting in ‘Janzen–Connell’ patterns in which seedling recruitment peaks at intermediate distances. When insects dispersed longer distances than seeds, higher seed densities near the tree satiated insects, resulting in ‘McCanny’ patterns in which seed deposition, survivorship and seedling
establishment all decrease with distance from the parent tree. Total seedling establishment was lowest when insects and seeds dispersed similar distances.
4. Under pathogen attack, Janzen–Connell patterns predominated except when seedling survival
was virtually zero or one everywhere, or in the case where pathogen dispersal distances exceeded
seed dispersal distances, producing ‘Hubbell’ patterns in which seed deposition and seedling establishment decrease with distance, though survivorship increases.
5. Clumped seed deposition increased the probability of seedling establishment under both insect
seed predation and pathogen attack as it led to local satiation of insect seed predators and made it
harder for pathogen distributions to track seeds.
6. Synthesis. Our modelling study suggests that the relative dispersal distances of seeds and natural
enemies are crucial to determining establishment rates and spatial patterns of seedlings. Better characterization of the movement and natural histories of natural enemies is critical to improving our
understanding of seedling distributions and plant–enemy interactions.
Key-words: aggregated distributions, Bruchidae, dispersal, diversity maintenance, early plant
recruitment, Janzen–Connell, oomycetes, plant–herbivore interactions, spatial patterns, vertebrate-dispersed seeds
Introduction
*Correspondence author. E-mail: [email protected]
†Present address: School of Biological Sciences, University of
Nebraska-Lincoln, 348 Manter Hall, Lincoln, NE 68588, USA.
Forty years ago, Janzen (1970) and Connell (1971) hypothesized that specialized natural enemies are critically important
2012 The Authors. Journal of Ecology 2012 British Ecological Society
Clumped seed dispersal and natural enemy attack 863
predators on seedling establishment patterns (Nathan &
Casagrandi 2004; Mari et al. 2008; Mari, Gatto & Casagrandi
2009). None of these previous studies have addressed the
influence of seed and seedling pathogens on seedling recruitment, even though soil-borne pathogens have been found to
play a critical role in seedling survival with great potential to
contribute to seedling recruitment patterns (e.g. Augspurger
1983, 1984; Augspurger & Kelly 1984; Packer & Clay 2000).
Pathogens have very different life histories from invertebrate
and vertebrate natural enemies, and these differences would
be expected to influence survivorship and recruitment patterns. For example, soil-borne pathogens have fast generation
times, short dispersal distances, high fecundity, and the ability
to remain dormant or switch foraging strategy in the soil for
several years, while insect seed predators are able to search
larger areas and have longer generation times. It is not known
how these distinct characteristics of pathogens might alter
seedling recruitment patterns compared with those of invertebrates or vertebrates.
Following Nathan & Casagrandi (2004), we distinguish five
classes of seedling recruitment patterns, each of which represents a different combination of patterns in seed density, seedto-seedling survivorship and seedling density (McCanny 1985;
Nathan & Casagrandi 2004). The Janzen–Connell pattern
(henceforth denoted JC), first described by Janzen (1970), is
characterized by a monotonic decrease in seed deposition with
distance from the source tree, a monotonic increase in survivorship and thus a unimodal seedling establishment curve
with a peak outside of the tree crown (Fig. 1a; Janzen 1970;
Connell 1971). In the Hubbell pattern (H), seed deposition
decreases and survivorship increases as in the Janzen–Connell
(a)
(b)
1
1
0.8
32
0.6
24
3545
0.4
1418
8
0.2
709
0
0
(c)
1
12
0.8
9
0.6
6
0.4
3
0.2
0
0
50
100
0.6
2127
16
15
0.8
2836
0.4
0.2
0
3972
0
(d)
1
3310
0.8
2648
0.6
1986
0.4
1324
0.2
662
0
0
Survivorship
40
Density of seeds & seedlings
for shaping spatial patterns of plant communities and maintaining plant diversity. Since then, many empirical studies have
examined spatial patterns of seedling recruitment, survival
and ⁄ or growth, and drawn conclusions regarding the role of
natural enemies (Wills et al. 1997, 2006; Wills & Condit 1999;
Harms et al. 2000). Theoretical studies also provide strong
support for the potential of specialized natural enemies to
maintain plant diversity (Becker et al. 1985; Armstrong 1989;
Adler & Muller-Landau 2005; Muller-Landau & Adler 2007).
Yet there is a dearth of theoretical work that examines
expected spatial patterns of plant recruitment and natural
enemy attack under different combinations of enemy and plant
life histories and dispersal patterns, work that would better
guide interpretation of spatial patterns. The little work on this
subject to date focuses on vertebrate and invertebrate enemies
(Nathan & Casagrandi 2004; Mari et al. 2008; Mari, Gatto &
Casagrandi 2009).
Seed dispersal patterns clearly contribute directly to spatial
patterns of recruitment and natural enemy mortality (Nathan
& Muller-Landau 2000). Patterns of seed dispersal are typically characterized by dispersal kernels – probability density
functions for the expected seed density as a function of position
relative to the source tree – which almost invariably show seed
densities decreasing with distance from the nearest reproductive adult (e.g. Janzen 1970). Often overlooked is the variation
in seed deposition around these expected densities and, in particular, the spatial aggregation of seeds into clumps (but see
Schupp, Milleron & Russo 2002; Muller-Landau & Hardesty
2005; Potthoff et al. 2006). Seed dispersal by vertebrates often
results in highly clumped seed deposition, with high seed
densities in some locations far away from the parent tree in
areas used preferentially by dispersers (Schupp, Milleron &
Russo 2002). For example, spider monkeys disperse 92% of
Virola calophylla seeds and deposit approximately half of these
in clumps under their sleeping sites (Russo, Portnoy &
Augspurger 2006). Clumped distributions of seeds resulting
from animal dispersal are common, as approximately 80% of
tropical woody plants are dispersed primarily by vertebrates
(Willson, Irvine & Walsh 1989; Muller-Landau & Hardesty
2005), and a full 56% of all angiosperm species are dispersed
by biotic means (Tiffney & Mazer 1995). Incorporating
clumped seed dispersal by vertebrates in models may significantly alter predictions of subsequent interactions with natural
enemies, spatial patterns of seedling establishment and seedling
diversity.
Natural enemy life history and movement capacity determine the degree to which natural enemies can track seeds and
seedlings in space and time. In his conceptual model, Janzen
(1970) distinguished between distance- and density-responsive
specialized natural enemies and hypothesized how both
would respond to different patterns of seed dispersal. This
seminal work is a starting point for a more complete mechanistic framework that incorporates natural enemy dispersal
abilities, fecundity and dormancy potential, as well as how
seed and seedling survival probability relates to local enemy
densities. Theoretical studies to date have focused on the
influence of vertebrate and invertebrate seed and seedling
0
5
10
0
Distance (m)
Seed dispersal
Survivorship
Seedling establishment
Tree edge
Fig. 1. Recruitment patterns resulting from natural enemy attack:
(a) Janzen–Connell, (b) Hubbell, (c) Invariant Survival and
(d) McCanny. Parameter values are (a) insect seed predators with
a = 7.5, binsect = 400, qinsect = 10, (b) pathogens with a = 2.3,
bpathogen =1000, qpathogen = 10, (c) pathogens with j = 0.1,
a = 8.75, bpathogen = 1000, qpathogen = 10 and (d) insect seed
predators with j = 0.1, a = 2.3, binsect = 180, qinsect = 10.
2012 The Authors. Journal of Ecology 2012 British Ecological Society, Journal of Ecology, 100, 862–873
864 N. G. Beckman, C. Neuhauser & H. C. Muller-Landau
pattern, but the survivorship increase is insufficient to offset
the decrease in seed deposition, and thus seedling establishment decreases (Fig. 1b; Hubbell 1980). In the McCanny
pattern (M), seed deposition, survivorship and seedling establishment all decrease with distance from the parent tree
(Fig. 1d; McCanny 1985); the decrease in survivorship is
predicted to occur because of predator satiation near the seed
source (Nathan & Casagrandi 2004). The Exact Compensation pattern (EC) is identified as a transitional type between
the Janzen–Connell and Hubbell recruitment patterns in
which seed dispersal declines at the same rate as survivorship
increases, resulting in a constant seedling establishment curve
(Nathan & Casagrandi 2004). Invariant Survival (IS) is a transitional type between the Hubbell and McCanny curve and
has constant survivorship with distance, resulting in seedling
densities that decline with distance from the tree in exactly the
same way that seed densities decline (Fig. 1c; Nathan &
Casagrandi 2004). All of these recruitment patterns have
varying degrees of empirical support in the literature, with the
Janzen–Connell pattern being the most cited (summarized in
Mari et al. 2008).
Here, we explore how different seed dispersal patterns and
natural enemy dispersal and life histories affect seedling
recruitment patterns. Unlike past conceptual and mathematical models (Nathan & Casagrandi 2004; Mari et al. 2008;
Mari, Gatto & Casagrandi 2009), we specifically incorporate
aggregated seed deposition and base our model structure and
parameter values on empirical data on the differing life histories of insect seed predators and soil-borne pathogens. We
focus on insect seed predators and soil-borne pathogens
because they are expected to be fairly specialized and thus to
have greater impacts in areas of high conspecific density (and
thereby greater contributions to the maintenance of plant
diversity). We employ spatially explicit simulation models in
which we vary seed dispersal and natural enemy attack to
model different seed dispersers and natural enemies, and
explore the resulting seedling spatial patterns around an isolated tree. This model predicts characteristics of seedling spatial patterns resulting from natural enemies acting on seed
distributions derived from different dispersal modes. By
exploring a range of parameter values, we investigate what
parameter combinations are compatible with different empirically observed spatial patterns of seedlings.
Materials and methods
within one tree crown (Janzen 1980). Little is known about adult bruchid behaviour when hosts are unavailable; they may aestivate or feed
on pollen and nectar of flowers (Southgate 1979; Janzen 1980; Bell
1994). A few agricultural studies show that bruchids use chemical
cues emitted from seeds to find hosts (Ignacimuthu, Wackers & Dorn
2000; Babu, Hern & Dorn 2003; Nazzi, Vidoni & Frilli 2008). Bruchid
seed predators of agricultural crops may delay sexual maturity
through diapause to match the life cycle of their host; environmental
cues, such as photoperiod, temperature or pollen feeding, can terminate diapause (Bell 1994). Life spans and number of generations per
season vary among species (Janzen 1980; Bell 1994).
PATHOGEN MODEL ORGANISM
Our model organisms for plant pathogens that influence recruitment
patterns are oomycetes. A number of oomycetes, including Pythium
and Phytophthora, cause damping-off disease, a major cause of seedling mortality (Hendrix & Campbell 1973). Oomycetes infect both
roots of adult plants and hypocotyls of seedlings after emergence
(Gilligan 1985b). Oomycetes produce both oospores (sexual spores)
and sporangia (asexual reproductive structures; Martin & Loper
1999; Judelson & Blanco 2005). Oospores of some species can survive
up to several years in the soil and have constitutive dormancy, in
which some spores remain dormant even when conditions are suitable
for germination. Zoospores produced by sporangia are motile spores
that can move towards a host in the presence of water and have shortterm viability (on the order of days). Infections arising from soil inoculum are referred to as primary infections, while infections spread
from other infected plants are referred to as secondary (Gilligan
1985a).
MODEL DEVELOPMENT
In nature, individuals are discrete, as are certain events in space and
time, yet ecological models often deal in continuous densities and
rates. Discrete and continuous models can have very different outcomes (Durrett & Levin 1994). Previous theoretical studies of the
influence of natural enemy attack on seedling spatial patterns have all
employed continuous models (Nathan & Casagrandi 2004; Mari
et al. 2008; Mari, Gatto & Casagrandi 2009). In contrast, we use discrete time and space to model dynamics of seeds and enemies. Assuming that trees release seeds discretely over time is realistic for trees that
have a distinct fruiting season that occupies a small subset of the year,
which is typical for many tropical and temperate plants. With discrete
time, we can also model natural enemies as having discrete, non-overlapping generations, matching the life histories of many insect seed
predators. Additionally, the influence of clumped seed deposition can
best be explored in a model such as ours in which seed numbers are
tracked discretely.
INSECT MODEL ORGANISM
MODEL LANDSCAPE
Our model organisms for insect natural enemies affecting plant
recruitment patterns are bruchid beetles. Bruchids are a major class
of seed predators (Southgate 1979; Janzen 1980) and tend to be highly
host specific (Janzen 1980; Tuda 2007). Female adult beetles typically
attach a single egg to the fruit and ⁄ or seed surface, the larvae drill into
the seed, and one or more larvae feed on one seed (Southgate 1979;
Janzen 1980; Tuda 2007). Larvae pupate within the seed, outside of
the seed in cocoons, or in the soil before emerging as adults several
weeks to months later, depending on the species (Southgate 1979;
Janzen 1980; Tuda 2007). Adults have been observed remaining
Model processes occur on a square grid of cells with one reproductive
tree located in the centre of the landscape (Fig. 2a). Each cell may or
may not contain a portion of a tree crown and may contain any number of seeds, seedlings, juvenile plants and natural enemies. The numbers of seeds, seedlings, juvenile plants and natural enemies are
tracked within each cell. Seeds and natural enemy propagules that
disperse off the grid edge are lost (i.e. absorbing boundaries). Simulations occur on a landscape of 90 000 (300 · 300) grid cells, where
each cell represents an area of 1 m2, and therefore, the simulated
landscape as a whole represents 9 ha.
2012 The Authors. Journal of Ecology 2012 British Ecological Society, Journal of Ecology, 100, 862–873
Clumped seed dispersal and natural enemy attack 865
(a)
(b)
1. Seeds disperse into
cells
2. Natural enemies
disperse into cells
3. Seeds die or recruit
into seedlings
Tree Crown
Seed
Enemy
Seedling
Events occur within cells of the landscape.
The tree crown is located in the centre of the
landscape. Seeds and natural enemies
disperse from the tree crown.
4. Natural enemies
reproduce and survive
until next year
5. A fraction of seedlings
(> 1 yr. old) and dormant
spores die each year
Mortality
Fig. 2. Illustration of the events that occur within each year of the simulation. See text for more details.
MODEL PROCESSES
fðrÞ ¼
The simulations are done in discrete time, with each time step being
equivalent to a year. Each year, seeds and natural enemies first disperse; then, natural enemies attack and kill seeds, surviving seeds germinate, and finally natural enemies and juvenile plants are subject to
stochastic mortality (Fig. 2b). Details of each of these processes are
given below, with parameter descriptions and values in Table 1 and
justifications in Appendix S1 in Supporting Information.
Dispersal of seeds and natural enemies
Dispersal of seeds and natural enemies follows functional forms that
have an empirical basis. Seeds disperse from each cell (1 · 1 m) of a
tree crown (5 · 5 m) according to a two-dimensional T distribution
(Clark et al. 1999) in which the degrees of freedom parameter was set
to three (Clark, LaDeau & Ibanez 2004). Specifically, the probability
density function of seed arrival per unit area depends on the distance
to the seed source, r, as:
1
2
2
p expðaÞ 1 þ expr ðaÞ
eqn 1
where a is the dispersal distance parameter for seeds. This has been
shown to fit many tropical tree species (Muller-Landau et al. 2008).
The mean dispersal distance is calculated as p2 exp a2 (Muller-Landau
et al. 2008).
Natural enemy propagule dispersal follows a negative exponential
density function, g(r), a model that fits pathogens well (Fitt et al.
1987):
2
2r
gðrÞ ¼ 2 exp eqn 2
pq
q
where q is the mean dispersal distance for natural enemies. This
function describes the final resting place of insect seed predator
eggs or oomycete pathogen spores following dispersal. Natural
enemies are assumed to disperse from each cell under the tree
crown and, in the case of pathogens, from dead seeds as well.
Table 1. Parameter descriptions and values
Model organism
Parameters
Values
Plant
Crown area
a, Seed dispersal distance parameter*
j, Dispersion parameter for seed deposition
g, Tree fecundity
x, Annual seedling mortality
qinsect, Mean dispersal distance†
binsect, Fecundity
minsect, Infectivity
Dispersal events within a fruiting season
qpathogen, Mean dispersal distance†
bpathogen, fecundity
mpathogen, infectivity
c, Probability of encountering one seed
l, Annual mortality of dormant spores
25 m2
2.3 (5, 4.7), 7.5 (67, 49), 8.75 (125, 72) m
0.1
10 000 m)2
0.5
1 (1.1), 10 (9.7), 40 (39), 50 (48), 100 (76) m
40, 180, 400, 1000, 4500, 10 000 eggs
0.2
4
0.1 (0.14), 1 (1.1), 10 (9.7) m
1000, 10 000,100 000, 200 000 spores
0.01
0.0001
0.9
Insect
Pathogen
*Theoretical and realized mean dispersal distances from the centre of a 1-m2 cell are given in parentheses.
†Realized mean dispersal distances from the centre of a 1-m2 cell are given in parentheses (see Materials and methods).
2012 The Authors. Journal of Ecology 2012 British Ecological Society, Journal of Ecology, 100, 862–873
866 N. G. Beckman, C. Neuhauser & H. C. Muller-Landau
Dispersal of both seeds and natural enemies is assumed to be isotropic (equally likely in all directions). The number of propagules
arriving per cell is drawn from a Poisson distribution with mean equal
to the sum of the expected number of arrivals from all contributing
source cells. The expected number of arrivals is the product of the
number of propagules produced in a source cell and the probability
of arriving in a destination cell given the dispersal kernel. We approximate this probability by integrating the dispersal kernel over each
destination cell using recursive adaptive Simpson quadrature. To simulate clumping in seed deposition, we draw the number of seeds arriving in each cell from a negative binomial distribution, with dispersion
parameter j, and expectation equal to the sum of expected seed arrival from each source cell. Because the variance is greater than the
mean, the negative binomial distribution is useful for simulating
aggregated distributions; as the dispersion parameter goes to zero, it
approaches the Poisson distribution, in which the mean equals the
variance.
Some seeds and propagules are lost from the landscape, especially
at longer dispersal distances, because we are using absorbing boundaries. We ensure that the same total number of propagules is retained
in the model landscape, no matter what the dispersal parameter, by
dividing fecundity by a rescaling factor that varies with the dispersal
parameter. The rescaling factor is calculated by summing overall
probabilities of arriving in each destination cell from all contributing
source cells divided by the sum of all dispersal kernels from each contributing source cell (equal to 25 for seeds and natural enemies dispersing from the tree crown).
Applying continuous dispersal kernels to models in discrete space
is challenging (Chesson & Lee 2005), especially when mean dispersal
distances are on the same order as the cell size (O’Sullivan & Perry
2009), as is the case for some of the natural enemy dispersal distances.
In cases where mean dispersal distances were less than the cell
width, we simulate propagules dispersing from the centre of 100
0.1 · 0.1 grid cells within a 1 · 1 cell and then sum over these 100
cells to calculate dispersal probabilities. When mean dispersal is
greater than or equal to the cell size, we assume propagules disperse
from the centre of cells. Realized dispersal distances are reported in
Table 1.
Pathogens
Pathogens disperse multiple times during a fruiting season, which
incorporates dynamics resulting from their short life spans as well as
primary and secondary infection. Spores attack seedlings within the
first several weeks after germinating. Spores disperse from the adult
root system (assumed equal in area to the crown) and from dead seedlings. We assume that the number of spores dispersing from one
pathogen-killed seedling is equal to the number dispersing from 1 m2
of the adult root system and denote this pathogen fecundity as
bpathogen. The probability of seedling survival is a negative exponential function of the local density of spores, the probability that a spore
encounters a seedling, and its infectivity:
PrðSurvÞ ¼ exp cmpathogen P
eqn 4
where P is local density of spores (determined from the natural
enemy dispersal functions and the relative locations and sizes of
spore sources). The probability c of encountering a seedling is the
probability that a spore will land close enough to a seedling to
germinate (Table 1). In other words, c is the probability of one
spore encountering one seed within the same cell; this is equal to
the area around the seed in which the spore germinates divided
by the area of the cell. Pathogen infectivity mpathogen incorporates
the probability of spores germinating and infecting a seedling. In
this model, we assume that spores only germinate if in the vicinity of seedlings. The number of spores that do not encounter
seedlings and remain dormant in the soil depends on the probability of encountering a seedling c and the number of seeds N.
Assuming that the probabilities of avoiding multiple seedlings are
independent, we have:
Ptþ1 ¼ Pt ð1 cÞN
eqn 5
where t is the spore dispersal season. Dormant spores undergo
annual mortality with probability l between the end of one
(plant) fruiting season and the beginning of the next. In the first
dispersal season of the first year of pathogen simulations, spores
only disperse from roots as no seeds have been killed at this
stage, and the initial number of spores is equal to 25*bpathogen
(because there are 25 m2 of adult root system).
Insect seed predators
Insect seed predators tend to congregate in the adult tree crown
between fruiting seasons, and thus, we model insect dispersal as originating in the tree crown. Because most insect seed predators require
much of the fruiting season to mature into reproductive adults (Janzen 1980), we model insect egg dispersal as occurring once each year.
We model the probability that a seed will survive insect seed predation as a function of the number of insect eggs in the same grid cell
and their infectivity relative to the number of seeds in the grid cell:
I
PrðSurvÞ ¼ exp minsect
eqn 3
N
where minsect is infectivity, I is the number of insect eggs in the cell,
and N is the number of seeds in the cell. Infectivity for insect seed
predators essentially incorporates the probability an egg is laid on
a seed and the probability that a laid egg results in a larva that kills
a seed. We assume one adult female insect seed predator emerges
from every two dead seeds. The number of reproductive female
seed predators produced the following year depends on the number
of seeds killed and insect fecundity, binsect. Adult insects survive
1 year. The initial number of insects is equal to binsect dispersing
from each square metre of tree crown.
Plant survival
Plant survival from the seed to seedling stage depends on local natural
enemy density as specified earlier. The number of seeds that survive
to seedlings in each grid cell is drawn from a binomial distribution
with the probability of survival based on local natural enemy density
according to the previously specified functions. Seedlings that survive
their first year recruit into juvenile plants. At the end of each year, surviving juvenile plants are drawn from a binomial distribution with
probability of mortality x. All seeds germinate in the year that they
are produced, as typical of most tropical tree species (Garwood 1983;
Sautu et al. 2006).
SIMULATIONS
The dispersal parameters of seeds and natural enemies, as well as the
fecundity parameters of the natural enemies, were varied factorially
among simulations to evaluate their relative importance to recruitment patterns. Dynamically, the enemy infectivity parameters have
almost the exact same effect as the enemy fecundity parameters, so
only the fecundity parameters were varied. Ten independent simulations were run for each parameter combination to capture stochastic
2012 The Authors. Journal of Ecology 2012 British Ecological Society, Journal of Ecology, 100, 862–873
Clumped seed dispersal and natural enemy attack 867
variability. Each simulation was run at least 50 years after the number of seeds, seedlings and enemies plateau (which typically occurred
at 100–200 years). The number of seeds, seedlings, juvenile plants
and natural enemies was summed per 1-m annulus, and statistics were
averaged over the last 50 years, after population abundances of seedlings, juvenile plants and natural enemies have all reached equilibrium. The density of seeds, seedlings and natural enemies per square
metre for each 1-m annulus of distance from the parent tree was
obtained by dividing the total number of seeds and seedlings in each
annulus by the total area of cells in the annulus. Survivorship was calculated for each 1-m annulus by dividing the number of seedlings per
square metre by the number of seeds. Equilibrium distributions of
seedlings and survivorship were averaged across replicates and
~ and PðrÞ,
~
denoted by SðrÞ
respectively.
IDENTIFYING RECRUITMENT PATTERNS
Recruitment patterns are identified based on the shape of the curves
relating survivorship and seedling establishment to distance to the
parent tree. Seedling establishment per area and seed-to-seedling
survivorship were calculated for each 1-m annulus of distance from
the source tree, for distances between 0 and rfar, the distance that
encompasses 99% of the cumulative density of seeds (calculated separately for each parameter set) or 130 m, whichever is smaller (the
130-m cut-off is chosen to avoid edge effects). Seedling establishment curves (seedling density vs. distance) were categorized as constant (EC), increasing (JC) or decreasing with distance from parent
~
(H, M or IS). We classify seedling establishment, SðrÞ,
as following
the EC pattern if the absolute difference of the maximum and minimum seedling densities at different distances is less than or equal to
a relative difference of 10%. We identify a Janzen–Connell pattern if
the maximum seedling density is outside of the tree crown (and is
more than 10% higher than the minimum). If the maximum occurs
within the crown (and is more than 10% greater than the minimum),
we categorize recruitment patterns as Hubbell, McCanny or IS,
~
based on the shape of the survivorship curve PðrÞ,
similar to Nathan
& Casagrandi (2004). Following Nathan & Casagrandi (2004), a
pattern of increasing survivorship with distance from the tree is categorized as the Hubbell pattern if the increase is >10%, decreasing
survivorship as McCanny if the decrease is greater than 10%, and
no change or change of <10% as IS.
Attributes important for identifying recruitment patterns were
classified with decision trees (Tan, Steinbach & Kumar 2006). Mean
seed dispersal distance, mean enemy dispersal distance, the ratio
between mean seed and enemy dispersal distances, enemy fecundity
and clumping were included as classification attributes in the classification analyses of recruitment patterns. All attributes were treated as
continuous variables, in which the ordering of the values was
retained, except for clumping, which was treated as a categorical variable. Under visual inspection of the factors influencing recruitment
patterns (Figs S1 and S2), absolute and relative dispersal distances of
seeds and enemies seemed important, thus both were included in analyses; inclusion of highly correlated variables in classification trees
does not negatively affect their accuracy (Tan, Steinbach & Kumar
2006).
Results
INSECT SEED PREDATION AND RECRUITMENT
PATTERNS
Under insect seed predation, the relative dispersal distances
between seeds and insects, clumping and insect fecundity were
important for classifying seedling recruitment patterns
(Fig. 3) with absolute dispersal distances in and of themselves
making little difference (Fig. S1). Generally, Janzen–Connell
patterns emerged when seeds dispersed longer distances than
insect seed predators, while McCanny patterns emerged when
insects dispersed longer distances (Figs 3 and S1). This can be
explained by predator satiation near the source when seeds
dispersed shorter distances. Clumping was an important classifying factor in the decision tree when relative dispersal distances between seeds and insects were relatively matched
(0.3 £ d:qinsect < 2.8; Fig. 3). Clumped seed deposition
decreased the probability that insects encountered seeds,
allowing more seeds to escape insect seed predation near the
source (Fig. 4). With high insect fecundity, this resulted in
more cases of Janzen–Connell patterns, whereas no seedlings
emerged under even seed deposition when seed and insect dispersal distances were relatively matched (IS0; Figs 3 and S1).
When insects with low-to-intermediate fecundity dispersed
only a little further than seeds deposited evenly or in clumps
(0.3 £ d:qinsect <1), seed densities near the tree satiated insect
Fig. 3. Decision tree classifying recruitment
patterns based on mean dispersal distance of
seeds (d) and insects (qinsect), the ratio of
mean dispersal distances of seeds and insects
(d:qinsect), insect fecundity (binsect) and
clumping. Ovals are internal or root nodes,
and squares are terminal nodes depicting
recruitment
patterns:
Janzen–Connell,
McCanny (M) and Invariant Survival. IS1
indicates an average of at least 99% of seeds
survived; IS0 indicates no seedlings survived.
2012 The Authors. Journal of Ecology 2012 British Ecological Society, Journal of Ecology, 100, 862–873
868 N. G. Beckman, C. Neuhauser & H. C. Muller-Landau
(a)
(b)
Fig. 4. Probability of seeds surviving to the
seedling stage with insect seed predation
under (a) even and (b) clumped seed deposition.
SOIL-BORNE PATHOGENS AND RECRUITMENT
PATTERNS
Fig. 5. Decision tree classifying recruitment patterns based on mean
dispersal distance of seeds (d) and pathogens (qpathogen), relative dispersal distances of seeds and pathogens (d:qpathogen), pathogen fecundity (bpathogen) and clumping.
seed predators resulting in McCanny recruitment patterns.
The majority of seedlings survived (IS1) when insects with low
fecundity dispersed further than seeds (d:qinsect < 0.3), and
seed densities satiated insect seed predators when insect fecundity increased (Figs 3 and S1).
The average probability of seeds surviving to seedlings
depended on insect fecundity, dispersal distances of insects relative to seeds and the pattern of seed deposition. Seed survivorship was higher at lower insect fecundities and when seed and
insect dispersal patterns were discordant (either insects dispersing further than seeds or seeds dispersing further than insects;
Fig. 4). Survivorship was lowest when seed and insect dispersal
distances were similar (Fig. 4), and again, the absolute
dispersal distances had little additional explanatory power.
Seeds were more likely to escape insect seed predators under
clumped seed deposition as evidenced by the overall higher survivorship of clumped compared with even seed deposition,
especially at low insect fecundity (Fig. 4). Under even seed
deposition, very few seeds escaped insect seed predation when
mean insect dispersal distance was effectively global (mean dispersal distances = 100 m) and seed dispersal distances were
intermediate to high (Figs 4a and S1a).
Pathogen fecundity and the absolute and relative dispersal distances between pathogens and seeds were important in classifying Janzen–Connell and Invariant Survival (IS1, IS0)
recruitment patterns (Fig. 5). Low pathogen fecundity and
moderate-to-high seed dispersal resulted in IS in which most
seedlings survived (IS1) by escaping pathogens (Fig. 5). In one
instance under clumped seed deposition, spores out-dispersed
seeds resulting in IS1 (Fig. S2d). As pathogen fecundity
increased, Janzen–Connell patterns became more prevalent
(Fig. S2). At these higher fecundities, the ratio of dispersal distances between seeds and pathogens was an important attribute for classifying the parameter region where no seedlings
emerged (IS0) – no seedlings emerged when pathogens dispersed further than seeds (Fig. 5). Mean pathogen dispersal
distances were important in defining regions of high seedling
survival when pathogen fecundity was intermediate (IS1,
Fig. 5). The Hubbell recruitment pattern only occurred once
under even seed deposition with high spore dispersal distance,
low seed dispersal distance and low pathogen fecundity
(Fig. S2).
Seed survivorship was near 100% for medium-to-long seed
dispersal distances combined with low-to-medium pathogen
fecundity (Fig. 6). In general, survivorship increased with
mean seed dispersal distance (Fig. 6). At the lowest seed dispersal distance and lowest pathogen fecundity, survivorship
increased with pathogen dispersal under both even and
clumped seed deposition, as spores out-dispersed seeds
(Fig. 6a,e). At intermediate pathogen fecundity, survivorship
did not depend on spore dispersal (Fig. 6b,f). At the lowest
seed dispersal distance and intermediate to high fecundity,
spores were able to track seeds and caused the highest mortality from pathogen attack (Fig. 6b–d,f–h). For high pathogen
fecundity under clumped seed deposition, survivorship
decreased with mean spore dispersal distances (Fig. 6c–d,g–h).
Overall, seeds tended to have higher survivorship under pathogen attack than insect seed predation for the parameter values
explored in this study (Figs 4 and 6).
Spores tracked seeds in their density patterns with respect
to the parent tree in cases where pathogen fecundity was
sufficiently high and pathogen dispersal was not too short
2012 The Authors. Journal of Ecology 2012 British Ecological Society, Journal of Ecology, 100, 862–873
Clumped seed dispersal and natural enemy attack 869
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
Fig. 6. Survivorship resulting from factorial
combinations of parameters for pathogen
attack under (a–d) even and (e–h) clumped
seed deposition and fecundity equal to (a, e)
1000, (b, f) 10 000, (c, g) 100 000 and (d, h)
200 000 spores.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
Fig. 7. Mean distance of spores from the
parent tree under (a–d) even and (e–h)
clumped seed deposition with pathogen
fecundity (a, e) 1000, (b, f) 10 000, (c, g)
100 000 and (d, h) 200 000 spores.
(Fig. 7). This reflects the dispersal of pathogens not only
from parent trees but also from killed seedlings and their
ability to remain dormant in the soil. Mean distances of
spores from the parent tree increased with spore dispersal
distances and pathogen fecundity (Fig. 7). Mean distances
from spores to the parent tree were highest when pathogen
fecundity and seed dispersal were both high, with pathogen
dispersal having only a relatively minor effect under even
seed deposition (Fig. 7c–d). At the lowest pathogen fecundity, spores were not able to track seeds and the mean distance at which spores were found reflected the expected
mean distance of spores dispersing from the parent tree
(Fig. 7a,e). At intermediate pathogen fecundity, spores were
found at higher distances from the source tree than
expected based on dispersal from the tree alone, with the
highest mean distances at intermediate seed dispersal distances (Fig. 7b,f). At higher pathogen fecundity, the distance of spores increased with seed dispersal distances
(Fig. 7c–d,g–h). With clumped seed deposition and the
highest pathogen fecundities (Fig. 7c–d,g–h), spores were
not able to track seeds with the highest seed dispersal as
well as under even seed deposition. Spores in the soil
tended to be distributed at further distances from the parent
tree under even compared with clumped seed deposition
(Fig. 7).
Discussion
In this study, we use empirically derived relationships and
parameter values to explore how seed dispersal patterns,
including clumped seed deposition, interact with insect seed
predators or soil-borne pathogens to determine seedling
recruitment patterns. We found that recruitment patterns are
sensitive to the type of natural enemy attack and the movement
distances of natural enemies, as well as to seed dispersal distances and the aggregation of seed deposition. The seedling
recruitment patterns observed in the model reproduced the
range of patterns observed empirically. Under insect seed predation, the mean seed dispersal distance relative to mean insect
dispersal distance is the critical parameter for determining
seedling recruitment patterns. Mortality of seeds due to pathogen infection was determined by the ability of spores to track
seeds. Under both insect seed predation and pathogen attack,
clumping decreased seed mortality.
INSECT INFLUENCES ON SEEDLING RECRUITMENT
PATTERNS
Insects produced both Janzen–Connell and McCanny recruitment patterns for different parameter combinations. Similar to
Nathan & Casagrandi (2004) and Mari et al. (2008), we found
2012 The Authors. Journal of Ecology 2012 British Ecological Society, Journal of Ecology, 100, 862–873
870 N. G. Beckman, C. Neuhauser & H. C. Muller-Landau
that Janzen–Connell patterns occurred when seeds dispersed
longer distances than enemies, and McCanny recruitment patterns occurred when enemies dispersed further and insect
fecundity was low. Under insect seed predation, the processes
that resulted in different seedling recruitment patterns are
qualitatively similar to previous studies that assume continuous seed dispersal and predation in continuous space, except
that we found fewer cases of Hubbell recruitment patterns
(Nathan & Casagrandi 2004; Mari et al. 2008).
In our model, insects are distance responsive and cannot
respond quickly to high local densities of seeds near the source
or in clumped seed dispersal, resulting in more frequent satiation at low seed dispersal distances relative to insect dispersal
distances. Although females produce a limited number of eggs
and larvae are limited by the time period of development
(Southgate 1979; Janzen 1980; Tuda 2007), the degree to which
insects are limited by movement is key to the outcome of our
results as well as past studies that assume limited movement
after insect dispersal (Nathan & Casagrandi 2004). If insect
seed predators respond purely to densities of seeds, they are
unlikely to produce Janzen–Connell patterns (Mari et al.
2008). Realistically, it is likely insects respond to both distances
of seeds from the parent tree and local seed densities. To date,
the movement and behavioural responses of insect seed predators to seed densities have been little studied (Lewis & Gripenberg 2008), making it difficult to ascertain which part of the
parameter space is most relevant to insect seed predators. Field
studies documenting the life histories and movement of insect
seed predators are therefore critical to determining the role of
insects in seedling spatial patterns.
PATHOGEN INFLUENCES ON SEEDLING RECRUITMENT
PATTERNS
Less mobile predators are hypothesized to result in a higher
frequency of Janzen–Connell patterns (Nathan & Casagrandi
2004). In our pathogen model, the recruitment patterns resulting from pathogens include Janzen–Connell, Hubbell and IS.
The mechanisms that resulted in these patterns differed from
those involved with insect seed predators and depended on the
interplay between pathogen fecundity, seed dispersal and spore
dispersal that determined whether spores were able to effectively track seeds. Even though their dispersal distances were
short, pathogens were able to track seeds by dispersing from
nearby killed seedlings and were found at higher distances
from the parent tree than expected from mean dispersal distances. In the real world, pathogens may disperse even greater
distances through spore dispersal by water or by animals (e.g.
on feet or invertebrate activity; Ristaino & Gumpertz 2000),
which we did not include in this model. Dispersal by water
could occur during heavy rain events, and long-distance dispersal by animals could be a regular albeit fairly rare event.
These possibilities could be further explored in future studies.
In this study, we employed simple assumptions that incorporate some of the major differences between pathogen and
invertebrate natural enemies. More detailed models of plant
pathogen infection and spread include such factors as both
primary and secondary infection (Kleczkowski, Gilligan &
Bailey 1997), pathozone behaviour (Gilligan & Bailey 1997)
and pathogen production based on plant growth (Gilligan
1995). These models could be extended to explore the role of
more realistic assumptions of pathogen demography and
infection in seedling spatial patterns, such as the contribution
of different sources of inoculum or the influence of host
susceptibility on pathogen infection. Empirical studies that
characterize pathogen life history and movement focus on
plant diseases that have large economic impacts in agricultural
systems (e.g. Timmer et al. 2000; Granke et al. 2009; Widmer
2009). Similar studies in natural systems are lacking but
critical in determining the impact of pathogens on plant
recruitment patterns. Future studies on pathogen life histories
in natural systems that describe the range of pathogen fecundity and patterns of spore dispersal are needed to better determine the influence of soil-borne pathogens on seedling
recruitment patterns.
CLUMPED SEED DEPOSITION
Our results highlighted the importance of clumped seed deposition to patterns of seedling survivorship and recruitment. In
our insect seed predation model, clumping considerably
increased average seedling survival and was important in discriminating between recruitment patterns. Increased survival
resulted from lower encounter probabilities between insects
and seeds near the source as well as local satiation of insect
enemies. Higher survivorship due to clumping resulted in more
cases of IS when insects dispersed further than seeds and
Hubbell recruitment curves when seed dispersal distances were
approximately 10–40 times higher than insect dispersal
distances. At much higher insect fecundities, no seedlings
survived if dispersal distances were equivalent unless seed
deposition was clumped, and then either Janzen–Connell or
McCanny patterns emerged depending on insect fecundity. A
more realistic model of insect attack would capture the possibility of changes in insect arrival depending on seeds present,
as insects respond to the scents of seeds or fruits (Ignacimuthu,
Wackers & Dorn 2000; Babu, Hern & Dorn 2003; Nazzi,
Vidoni & Frilli 2008); such movement could be incorporated
via biased random walks in which insects orient themselves to
areas of higher seed densities (Codling, Plank & Benhamou
2008). In such a model, and in the real world, clumping could
conceivably have the opposite effect of decreasing seed survival
if it disproportionately increases insect arrival and thus insect
attack. The effect of aggregated seed arrival on mortality due
to insect seed predators depends critically on whether areas of
higher local seed densities attract more insect seed predators
than areas with lower densities at the same distance, and if so,
on the degree to which insect arrival tracks seed densities.
Clumping also increased seed survival in our pathogen
model in most parameter combinations, although this effect
was generally smaller than for insect seed predators and was
not important in classifying recruitment patterns in the decision tree analysis. This increased survival can be understood as
a consequence of the lack of correlation between patches
2012 The Authors. Journal of Ecology 2012 British Ecological Society, Journal of Ecology, 100, 862–873
Clumped seed dispersal and natural enemy attack 871
receiving seeds from 1 year to the next, leading to a discordance between patches of spores and seeds. In reality, some
spatial patterns of seed aggregation are expected to persist for
multiple years; this could reflect vertebrate dispersers
favouring the same sleeping, roosting and ⁄ or nesting sites over
multiple years (Wenny & Levey 1998; Russo, Portnoy &
Augspurger 2006). Long-lived clumps away from the parent
tree might increase the local densities of pathogens at these
locations and thereby decrease survivorship. Thus, the impact
of aggregated seed deposition on survivorship and recruitment
curves for pathogens with dormant spores depends critically
on the degree to which deposition is aggregated in the same
areas from year to year.
PLANT STRATEGIES FOR REDUCING SEED MORTALITY
To reduce the cost of predation, plants may escape from predation by dispersing seeds long distances or by satiating predators (Howe & Smallwood 1982; McCanny 1985; Nathan &
Casagrandi 2004). Theoretically, it has been shown that locally
dispersing specialized natural enemies select for increasing dispersal distances of seeds (Muller-Landau, Levin & Keymer
2003). With aggregated seed deposition, plants could employ
both strategies simultaneously. Dispersing seeds in clumps can
be viewed as a way of both escaping predators in space and
satiating seed predators locally and not necessarily at the
source.
The best strategy to reduce seed mortality depends on the
mobility and life history of the relevant natural enemies.
Insect seed predators could select for both longer seed
dispersal distances to escape predation and increased local
densities to satiate insects at the source or in clumps at
further distances from the tree. However, this depends on the
behavioural response of insect seed predators to clumps of
seeds. If insects are attracted to these higher densities of
seeds, clumped seed deposition may be disadvantageous.
Pathogens, on the other hand, are more localized, have faster
generation times and remain dormant in the soil. Aggregated
seed deposition may not be as advantageous against soilborne pathogens compared with insect seed predators for several possibilities. With dormant spores, pathogens may build
up a reservoir in the soil over time increasing the likelihood
of patchy seed distributions encountering enemies. In addition, because of their faster generation times, once pathogens
disperse into an area with a seed clump, they could respond
quickly to these locally abundant resources. Pathogens are
predicted then to select for longer dispersal distances and
more frequently result in Janzen–Connell patterns than insect
seed predators.
are important in exploring what parameter combinations can
result in observed patterns and aid in designing experiments
and formulating predictions. In our study, we find a large area
of parameter space resulting in Janzen–Connell recruitment
patterns. Seedling recruitment patterns depended on the type
of natural enemy, enemy fecundity, and the dispersal distances
of seeds and natural enemies. Although the movement patterns
of natural enemies are critical for determining the outcome of
seedling spatial patterns, the spatial scales across which natural
enemies respond to seed densities are virtually unknown in natural systems (Lewis & Gripenberg 2008). Based on these
results, we recommend field studies that identify relevant natural enemies and better characterize their life histories and
movement patterns.
The interaction between seed arrival and natural enemy
attack influences not only spatial patterns of recruitment, but
also the strength of associated contributions to stabilizing
coexistence through population-level density-dependent mortality (Chesson 2000). How seedling spatial patterns relate to
diversity maintenance has been little explored. Previous studies
examining the effects of the dispersal distances of seeds and
natural enemies on the strength of stabilization find contrasting results depending on the scales of competitive interactions
among plants (Adler & Muller-Landau 2005; Muller-Landau
& Adler 2007). One general result, however, is that for realistic
seed dispersal scales, longer enemy dispersal distances are associated with stronger contributions to the maintenance of diversity (Adler & Muller-Landau 2005; Muller-Landau & Adler
2007). Our results here show that Janzen–Connell seedling
recruitment patterns are less likely to emerge as enemy dispersal distances increase relative to seed dispersal distances.
Future studies should examine how seedling spatial patterns
relate to stabilizing influences when jointly investigated in realistic models.
Although vertebrates, insects and microbes have substantial
influences on the pattern of plant survival and the distribution
of seeds over the landscape, the relative contributions of these
organisms to plant spatial patterns and plant coexistence
remains unknown. The initial template of seed deposition may
alter the contribution of natural enemies to population-level
density dependence and species coexistence of plant communities. A basic understanding of how animals and microbes affect
plant community spatial patterns and diversity is essential as
seed dispersal, seed predation and fungal diseases are expected
to change in the face of increasing anthropogenic pressures on
ecosystems, including hunting, air pollution and global warming (Mitchell et al. 2003; Bearchell et al. 2005; Beckman &
Muller-Landau 2007; Lewis & Gripenberg 2008).
Acknowledgements
CONCLUSIONS AND FUTURE DIRECTIONS
To gain a better understanding of the mechanisms behind seedling recruitment patterns requires better characterization of
natural enemy life histories for model parameterization. As
large-scale field studies are difficult to implement to test questions over large spatial and temporal scales, theoretical studies
We thank Jim Dalling, Linda Kinkel, George Heimpel and David Tilman for
insightful discussions and two anonymous reviewers for helpful suggestions in
revising the manuscript. We gratefully acknowledge the support of a National
Science Foundation Graduate Research Fellowship (N.G.B.), UMN Graduate
School Doctoral Dissertation Fellowship (N.G.B.), UMN EEB Block Grant
(N.G.B.), Packard Fellowship in Science and Engineering (H.C.M.) and the
HSBC Climate Partnership (H.C.M.).
2012 The Authors. Journal of Ecology 2012 British Ecological Society, Journal of Ecology, 100, 862–873
872 N. G. Beckman, C. Neuhauser & H. C. Muller-Landau
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Supporting Information
Additional Supporting Information may be found in the online version of this article:
Appendix S1. Justification of parameter estimates.
Figure S1. Recruitment patterns from insect seed predation.
Figure S2. Recruitment patterns from pathogen attack.
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Received 18 September 2011; accepted 22 March 2012
Handling Editor: Kyle Harms
2012 The Authors. Journal of Ecology 2012 British Ecological Society, Journal of Ecology, 100, 862–873