THE EFFECTS OF TREE SIZE, NUTRIENT AVAILABILITY, INTERACTIONS WITH
NEIGHBORS, AND MASTING SYNCHRONY ON FRUIT PRODUCTION IN
TROPICAL AND TEMPERATE FORESTS
By
David Michael Minor

A THESIS
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Plant Biology - Master of Science
2014

ABSTRACT
THE EFFECTS OF TREE SIZE, NUTRIENT AVAILABILITY,
INTERACTIONS WITH NEIGHBORS, AND MASTING SYNCHRONY ON
FRUIT PRODUCTION IN TROPICAL AND TEMPERATE FORESTS
By
David Michael Minor
Tree regeneration can be limited by the number of fruit produced by mature trees. Fruit
production may influenced by tree size, soil nutrient availability, and competition with neighbors. In addition, synchronized reproduction in masting events may increase reproductive
success of individuals. Differences in soil characteristics and biotic communities in tropical
versus temperate regions may affect fruit production. Fruit production was individually measured for ∼3600 trees of 17 tropical species in La Selva, Costa Rica, and 10 temperate species
in the Manistee National Forest, Michigan, USA. In both regions, tree size was the dominant
influence on fruit production, with larger trees producing more. Soil nutrient availability had
little effect on fruit production in both regions. In tropical species, the presence of larger
neighboring trees reduced fruit production. This effect is consistent with competition for
light, and may suggest that carbon balance is important for reproduction in these species.
In temperate species, I combined individual fruit production measurements with long
term seed and seedling density data to assess the synchrony of individuals during masting
events. In two species, Acer saccharum and Fagus grandifolia, I found that a small subset of
individuals fruited more often and were responsible for a large proportion of fruit production
in their populations. In contrast, in Tila americana different subsets of individuals were
responsible for different masting events. These results highlight the importance of considering
individual trees in studies of masting and environmental effects on reproduction.

ACKNOWLEDGMENTS

I would like to thank Richard Kobe, Andrew Finley, Katherine Gross, Tom Baribault, Ellen
Holste, Andrea Maguire, Benedicte Bachelot, Yoshiko Ida, and Scott Stark for their helpful
comments and expertise during the execution and writing of this thesis. This research was
made possible by EPA Star fellowship FP - 91714201 - 0.

iii

TABLE OF CONTENTS

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

vi

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

vii

Chapter 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

Chapter 2 Fruit Production is Influenced by Tree Size and Size-asymmetric
Competition in a Wet Tropical Forest . . . . . . . . . . . . . . . .
2.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Study site . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.2 Fruit production measurements . . . . . . . . . . . . . . . . . . . . .
2.3.3 Soil resource measurements . . . . . . . . . . . . . . . . . . . . . . .
2.3.4 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.5 Neighborhood competition index . . . . . . . . . . . . . . . . . . . .
2.3.6 Binomial regression . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.7 Multinomial regression . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.8 Plot level analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6
7
7
10
10
10
11
12
13
13
14
16
16
18

Chapter 3 Masting synchrony in northern hardwood forests: super-producers
dominate population fruit production . . . . . . . . . . . . . . . . 24
3.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3.1 Site description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3.2 Fruit estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3.3 Soil nutrient measurements . . . . . . . . . . . . . . . . . . . . . . . 31
3.3.4 Fertilization experiment . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3.5 Individual fruit production modeling . . . . . . . . . . . . . . . . . . 32
3.3.6 Relative size at onset of maturity . . . . . . . . . . . . . . . . . . . . 35
3.3.7 Synchrony in masting cycles . . . . . . . . . . . . . . . . . . . . . . . 36
3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Chapter 4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

iv

44
45

APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Appendix A Tables and figures for Chapter 2 . . . . . . . . . . . . . .
Appendix B Tables and figures for Chapter 3 . . . . . . . . . . . . . .
Appendix C Model Evaluation for Chapter 2 . . . . . . . . . . . . . .
Appendix D Site level fruit production relationships for Chapter 2

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48
49
59
72
77

BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

94

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LIST OF TABLES
Table 1:

Study species at La Selva, Costa Rica. . . . . . . . . . . . . . . . . .

49

Table 2:

Fruit production categories. . . . . . . . . . . . . . . . . . . . . . . .

50

Table 3:

Model evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51

Table 4:

Study species in Manistee National Forest, MI. . . . . . . . . . . . .

59

Table 5:

Fertilizer application rates. . . . . . . . . . . . . . . . . . . . . . . .

60

Table 6:

Model evaluation for the zero-inflated regression on number of fruits
produced using AIC. . . . . . . . . . . . . . . . . . . . . . . . . . .

61

Table 7:

Correlation between seed and newly germinated seedling density. . .

62

Table 8:

Pearson’s correlation of annual average fruit production from direct
counts with annual seed or seedling density. . . . . . . . . . . . . . .

63

Table 9:

Degree of masting synchrony within species. . . . . . . . . . . . . .

64

Table 10:

Model evaluation for the binomial regression. . . . . . . . . . . . . .

74

Table 11:

Model evaluation for the multinomial regression fit to all individuals.

75

Table 12:

Model evaluation for the multinomial regression fit to only reproductive individuals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

76

vi

LIST OF FIGURES
Figure 1:

2-dimensional histogram of fruit production, divided by category and
DBH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

52

Multinomial relationship between DBH and probability of fruit production for each species. . . . . . . . . . . . . . . . . . . . . . . . .

54

Figure 3:

Probability of reproducing as a function of tree diameter. . . . . . .

56

Figure 4:

Conspecific basal area vs. average maximum fruiting category by plot
for two species. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

58

Figure 5:

Probability of reproducing as a function of tree diameter. . . . . . .

65

Figure 6:

Maximum number of fruit produced by each individual in relation to
stem diameter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

66

Figure 7:

Size at onset of maturity. . . . . . . . . . . . . . . . . . . . . . . . .

67

Figure 8:

Time series of fruit production. . . . . . . . . . . . . . . . . . . . . .

68

Figure 9:

Annual density of fruit production.

. . . . . . . . . . . . . . . . . .

70

Figure 10:

Conspecific basal area vs. average maximum fruiting category by plot
for each species. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

78

Conspecific basal area vs. probability of fruit production by plot for
each species. Each point represents one plot. . . . . . . . . . . . . .

80

Nitrogen mineralization rate vs. average maximum fruiting category
by plot for each species. . . . . . . . . . . . . . . . . . . . . . . . . .

82

Nitrogen mineralization rate vs. probability of fruit production by
plot for each species. . . . . . . . . . . . . . . . . . . . . . . . . . .

84

Phosphorus availability vs. average maximum fruiting category by
plot for each species. . . . . . . . . . . . . . . . . . . . . . . . . . .

86

Phosphorus availability vs. probability of fruit production by plot for
each species. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

88

Sum of base cation availability vs. average maximum fruiting category
by plot for each species. . . . . . . . . . . . . . . . . . . . . . . . . .

90

Figure 2:

Figure 11:

Figure 12:

Figure 13:

Figure 14:

Figure 15:

Figure 16:

vii

Figure 17:

Sum of base cation availability vs. probability of fruit production by
plot for each species. . . . . . . . . . . . . . . . . . . . . . . . . . .

viii

92

Chapter 1
Introduction

1

Tree reproduction has long-lasting effects on the forest community. Future canopy composition depends on the reproductive success of adult trees. Often, seedling recruitment is
limited by seed availability, acting as a bottleneck to species’ presence in the future forest community (Caspersen and Saprunoff 2005, De Steven and Wright 2002, Svenning and
Wright 2005). Fruit abundance influences the animal community, affecting frugivore survival
and causing cascading trophic effects which can influence human health (Wright et al. 1999,
Milton et al. 2005, Ostfeld et al. 1996, Jensen et al. 2012).
Climate change and nitrogen deposition may alter tree species’ reproduction in varied and
unpredictable ways, and responses may differ between temperate and tropical forests (Ibanez
et al. 2007, HilleRisLambers et al. 2009). By improving our understanding of individual
reproduction in multiple species and biomes, we can better understand how the environment
influences allocation to reproduction, and improve our ability to predict how global change
will influence reproduction and the future of forest communities.
Fruit production occurs at the individual level and must be measured at this scale in or˙
der to answer certain questions (Zywiec
et al. 2012, LaMontagne and Boutin 2007, Herrera
1998). Many tree species exhibit interannual masting cycles, where peaks in reproduction
are synchronized for a population in a given year (Silvertown 1980, Kelly 1994, Kelly and
Sork 2002). However, population cycles are the cumulative result of individual reproductive
cycles, and the degree of synchrony can only be assessed with individual data. Individual measurements of reproduction are also necessary for understanding how environmental
factors such as soil nutrient availability or competition from neighboring trees affect fruit
production.
In many tree populations reproductive success is highly unequal among individuals, with
a small portion of the population parenting most of the offspring (Moran and Clark 2012,
2

Herrera and Jovani 2010, Gonz´alez-Mart´ınez et al. 2006). Some of the disparity among individuals is due to tree size. Trees must reach a certain size before reaching reproductive
maturity, which varies among species, even relative to their maximum size (Owens 1995,
Thomas 1996b, Wright et al. 2005). The relative size at which species become mature may
be related to other life history traits like shade tolerance, with fast-growing shade intolerant
species reproducing earlier in their life than slower-growing shade tolerant species. After
reaching a reproductive size, larger trees may be able to acquire and store more resources,
leading to more fruit production (Greene and Johnson 1994, Snook et al. 2005, Han et al.
2008, Carbone et al. 2013). Although differences in size may account for some of the reproductive variation in a population, environmental factors such as nutrient availability and
competition are also likely to affect fruit production.
The availability of soil nutrients may cause unequal fruit production among individuals
(Satake and Bjørnstad 2008). The soil nutrients that limit fruit production may vary by
species and location, with nitrogen typically being limiting in temperate forests and phosphorus in tropical forests (Vitousek and Howarth 1991b, Vitousek et al. 2010). However,
this presumed difference between temperate and tropical forests may be over-emphasized.
Nitrogen can increase fruit production in both temperate and tropical forests (Kaspari et al.
2008, Callahan et al. 2008, Lovett et al. 2013), and phosphorus is also important in temperate areas (Gradowski and Thomas 2008). In addition, there is increasing evidence for
the importance of base cations such as calcium, magnesium and potassium for growth and
reproduction in both regions (Gradowski and Thomas 2008, Kaspari et al. 2008, Holste 2010,
Baribault et al. 2010; 2012). However, much of the previous research on nutrient limitation
has focused on the population or community reproductive response, averaging across species
and individuals. By measuring species separately, at the individual level, we can investigate
3

differences in species nutrient requirements and how nutrient availability affects maturation
and fecundity.
Competition from neighboring trees may restrict individual access to soil nutrients and
light. Light availability tends to increase fruit production, likely because recently produced
carbohydrates are used for reproduction (Greene et al. 2002, Ichie et al. 2013). Shading
from larger neighbors may decrease the amount of fruit produced by an individual or delay
maturation (Wright et al. 2005). The incorporation of competition extends the possible
effects of resource limitation to biotic interactions.
In this thesis, I compared fruit production in tropical and temperate forests in two parallel studies. In both forest types, I investigated how fruit production is influenced by tree
size, nutrient availability, and neighborhood competition at the individual level in common
tree species. I used fruiting measurements across a natural range of soil nutrient availability
to determine how these species varied in their reproductive nutrient requirements. Variation in forest community structure was used to assess how competition may decrease fruit
production.
In Chapter 2, I examined the effects of environmental factors on fruit production in
tropical trees. I also determined whether fruit production is associated with community
composition. Greater conspecific density increases pollen availability and may increase fruit
production in pollen-limited species (Knight et al. 2005). In Chapter 3, using long-term
measurements of population seed availability in conjunction with individual measurements
of fruit production, I examine fruit production and masting synchrony in temperate species.
The research presented in this thesis expands upon previous studies of tree reproduction
by using individual measurements to examine nutrient limitation, rather than data collected
at the population or community level. Ascertaining the effects that size, nutrient limitation,
4

and competition have on fruit production can lead to increased understanding of the causes
of reproductive inequality among individuals and better prediction of forest community regeneration.

5

Chapter 2
Fruit Production is Influenced by
Tree Size and Size-asymmetric
Competition in a Wet Tropical Forest

6

2.1

Abstract

In tropical forest communities seedling recruitment can be limited by the number of fruit
produced by adults. Fruit production may be affected by physiological constraints, such as
tree size; local environmental factors, such as soil nutrient availability; and biotic factors,
such as competition. The number of fruit produced was observed for ∼2000 trees of 17 species
across three years in a wet tropical forest in Costa Rica. Fruit production was modeled as
a function of tree size, nutrient availability and neighborhood competition. In all species,
larger trees were more likely to produce fruit, and more of it. In addition, fruit production
was negatively related to presence of larger neighboring trees in 13 species. Soil nutrient
availability (sum of base cations) was positively associated with fruit production in only
two species. I also examined site-level effects, where average fruit production increased with
conspecific basal area for two palm species. This pattern indicates a community constraint
to individual fecundity and is consistent with pollen limitation. Nitrogen and phosphorus
availability were positively related to fruit production in two species at the site level. Overall,
these results suggest that direct influences on fruit production tend to be biotic, through
tree size, competition from neighboring trees, or facilitation by pollination from conspecifics.
Nutrient availability influenced fruit production little, but may operate indirectly through
the dominant effect of tree size.

2.2

Introduction

Tree reproduction affects species composition of the forest understory, as well as future
canopy composition, having long-lasting effects on the forest community. Regeneration is
often limited by seed availability in tropical tree species, with the abundance of suitable sites
7

for germination being greater than the number of seeds that reach these sites (De Steven and
Wright 2002, Svenning and Wright 2005, Hubbell et al. 1999). Fruit is also a vital food source
for frugivore populations in tropical forests, which often have high mortality rates during
periods of low fruit production (Fleming et al. 1987, Wright et al. 1999, Milton et al. 2005).
While fruit is necessary for survival of plant and animal populations, its production represents
a major resource investment for trees (Bazzaz et al. 1987). Allocation to reproduction may
reduce allocation to growth (Charlesworth and Morgan 1991). Allocation in response to
environmental factors is particularly important to understanding carbon cycling in forests.
Fruit production by individual trees is influenced by multiple factors, including tree size,
soil nutrient availability, and crowding from neighboring trees. Tree size affects reproductive
output in at least two ways. First, a tree must reach a certain developmental stage or size
before reaching reproductive maturity, although the size at which this stage occurs varies
based on an individual’s physiology and environment (Owens 1995). The size at which trees
reach maturity also varies among species, even relative to their maximum size (Wright et al.
2005, Thomas 1996b). Second, after reaching maturity, larger trees are likely to produce
more fruit (Greene and Johnson 1994, Snook et al. 2005), possibly due to greater access to
resources (Carbone et al. 2013, Han et al. 2008). However, even among large, potentially
reproductive individuals of the same species, reproduction tends to be very unequal, with
most of the fruit being produced by a few individuals (Gonz´alez-Mart´ınez et al. 2006, Herrera
and Jovani 2010, Moran and Clark 2012). This variation among individuals indicates that
there are additional factors that influence fruit production in trees.
Soil nutrient availability may limit fruit production in some species, and explain some
intraspecific variability in fruit output. The effect of nutrients on fruit production has been
extensively studied in crop species (Dordas 2006, Bishnoi et al. 2007, Burton et al. 2000), but
8

less is known about nutrient requirements in naturally established forests. Fertilization with
nitrogen (N) and phosphorus (P) increased reproductive litter in a tropical forest community,
but it is unknown how these responses vary among species (Wright et al. 2011, Kaspari
et al. 2008). In addition, high concentrations of N, P, and base cations (calcium (Ca),
potassium (K) and magnesium (Mg)) in fruits (Chidumayo 1997, Pregitzer and Burton
¨
1991, Karlsson and Orlander
2002) could indicate high demand for these nutrients by trees
for fruit production, or may simply indicate high availability in the environment.
The surrounding forest community also could influence fruit production. Neighboring
trees may cast shade and compete for soil nutrients (Baribault and Kobe 2011, Canham
et al. 2006). Competition among neighbors may be size-asymmetric, with larger neighbors
being stronger competitors, limiting the light and nutrients available to smaller trees for
reproduction (Wright et al. 2005). In addition, pollination success may increase with greater
conspecific density, subsequently increasing fruit set and production, and resulting in an
Allee effect (Knight et al. 2005).
The goal of this study was to investigate how size, soil nutrients, and neighborhood
crowding influence fruit production in tropical tree species. I estimated fruit production
for 17 common species in a wet tropical forest. By measuring reproduction of trees across
locations with a range of nutrient availability, I aimed to determine which nutrients limit
reproduction in these species, and how competition among neighboring individuals interacts
with nutrient limitations. I predict that for all species fruit production would 1) be positively
correlated with tree size, 2) increase with nutrient availability, 3) decrease with greater
neighborhood crowding, but 4) be positively correlated with stand density of conspecifics.

9

2.3

Methods

2.3.1

Study site

This study was conducted at La Selva Biological Station, Costa Rica (longitude, latitude).
La Selva is located in a wet tropical forest, receiving approximately 4000 cm of precipitation
annually. Fruit production measurements and soil samples were taken from five 41 m x 240
m plots which varied in N, P, and base cation availability. The large variation in soil characteristics at La Selva allowed me to sample areas with differing nutrient availability within a
relatively small area. Three of these plots are located on older, lower-fertility, volcanic soils,
and two are on younger, richer soils deposited by rivers (McDade and Hartshorn 1994). All
trees 5 cm or greater in diameter at breast height (DBH) within each plot have been mapped
and DBH was measured approximately annually.

2.3.2

Fruit production measurements

In order to get direct, individual-level estimates and to avoid potential confounding with
˙
animal predation, fruit production was estimated while fruit was still on the tree (Zywiec
et al. 2012, LaMontagne and Boutin 2007, Herrera 1998). The majority of studies of tree
fruit production utilize litter traps. This approach provides a population-level estimate of
the number of fruit produced, but does not account for losses due to predation and requires
modeling of dispersal or incorporating genetic data in order to detect intraspecific variation
in reproductive output (Clark et al. 2010; 2004, Moran and Clark 2011). It was important
to have measurements at the individual level in order to understand the factors controlling
the amount of fruit produced.
At each plot, fruit production of 17 common canopy and subcanopy tree species was
10

estimated for all mapped individuals. These species were chosen because there were at least
50 individuals of the species present across the five plots, for a total of approximately 2,200
trees (Table 1). I will refer to species by genus throughout the paper. Species tended to be
well represented across their size range, although some species’ size distributions were skewed
toward an abundance of smaller individuals (Figure 1). Fruit production was estimated for
each individual three times: September–November 2007, April–June 2008, and November
2009–May 2010. At each observation, the number of fruit was visually estimated and placed
into one of six categories (Table 2). Visual estimates were made from the ground using
binoculars with 10X magnification.
Categories were used instead of full counts in order to increase the speed of data collection.
In order to assess the accuracy of this method, a more detailed count was performed in March
2010 on a subset of 675 individuals using a more powerful telescope (20X–60X magnification).
This estimate was performed by counting the number of fruit on three reproductive branches
dispersed throughout the crown. The average of these three counts was multiplied by the
total number of reproductive branches on the tree to gain an estimate of the total number
of fruit. These count estimates were compared to categorical estimates taken within two
weeks of each other. The two estimates agreed for >80% of individuals and were positively
correlated (R = 0.53 for all comparisons; R = 0.71 for 56 comparisons where both estimates
were greater than zero), supporting the use of the much faster categorical method.

2.3.3

Soil resource measurements

Soil samples were taken at a relatively fine spatial scale at each plot. Three subsamples were
taken from the upper 20 cm of soil and composited from each meter of a 200-m transect
down the center of the plot. In addition, samples were taken in a lattice structure in the
11

rest of the plot with 10 m spacing between samples (Holste 2010). Samples were measured
+
+
for nitrate (NO−
3 ), ammonium (NH4 ), total extractable phosphorus (P), potassium (K ),

calcium (Ca2+ ), and magnesium (Mg2+ ). To estimate the potential nitrogen mineralization
rate (NMin), nitrate and ammonium were also measured after 30-day incubations. NMin
was used in the analyses here because it better represents nitrogen availability over time
+
than NO−
3 or NH4 (Pastor et al. 1984). Also, because K, Ca, and Mg availabilities strongly

covaried, they were added and used in these analyses as the sum of base cation availability
(SBC). Nutrient availability for each tree was calculated as a distance-weighted average of
the five closest soil sample points, using the R package yaImpute (Crookston and Finley
2008).

2.3.4

Data analysis

Fruit production was modeled as a function of tree size, soil nutrients, and neighborhood
crowding. The dataset was analyzed in three ways with different data subsets to test the
effects of these factors. First, a binomial logistic regression was used to isolate which factors
influence the probability of being reproductive in each species, ignoring variation in the
amount of fruit produced. Second, including all individuals, I modeled fruit production in
each species with a multinomial logistic regression. Third, a multinomial regression including
only reproductive individuals (with fruit observed at least once during the study) was used
to determine which of the factors measured are important for the amount of fruit produced
following reproductive maturity. These models were fit in a hierarchical Bayesian framework
(Clark et al. 2010; 2004), using R and WinBUGS statistical software (R Core Team 2013,
Lunn et al. 2000).

12

2.3.5

Neighborhood competition index

Following Baribault and Kobe (2011) and Canham et al. (2006), the neighborhood competition index (NCI) was defined as:
n

NCI =

αj

−νj /disti
)

(DBHi exp

(1)

i=1

where α and ν are random variables controlling the influence of neighbor DBH and distance
to focal tree, respectively. Both of these variables were drawn from Gamma(1.0, 1.0) distributions. The effect is summed for i = 1, . . . , n neighbors within a 10-m radius of the focal
tree. Two sets of neighbors were tested: 1) all trees within 10 m, and 2) only individuals
that were larger DBH than the focal tree, in order to test for asymmetric neighborhood
competition (ANCI). To keep the number of estimated variables manageable, α and ν were
unique for each focal species j, but assumed to be equal for all neighbor species.

2.3.6

Binomial regression

I used binomial regression to characterize the probability of reproduction, as a function of tree
size, nutrient availability, and neighborhood competition. If fruit production observations
were >0 for an individual, its reproductive success was set to 1. Reproductive status of
individual i of species j (Rij ) was distributed as:

Rij ∼ Bernoulli(πij )

(2)

logit πij = X j β j + i

(3)

13

where π is the probability of being reproductive, X j is the matrix of covariate values for
individuals of species j, and β j is a vector of species-specific coefficients drawn from:

β j ∼ MVNormal(µ, Σ)

(4)

Individual random effects were included such that: i ∼ Normal(0.0, τ ). Random variables
µ, Σ, and τ were drawn from vague prior distributions. There was no effect of plot, so it was
not included explicitly in the model.
Six alternative models were considered for reproductive status (Table 3). Models were fit
via the Markov Chain Monte Carlo (MCMC) technique. The models were run for three chains
of 50,000 iterations each, following a burn-in of at least 10,000 iterations to reach convergence
based on Gelman and Rubin’s convergence criterion (Gelman and Rubin 1992). Therefore,
conclusions were drawn from a posterior distribution of 3 ∗ 50, 000 = 150, 000 samples.
I compared models using deviance information criterion (DIC) and proper scoring rules.
DIC is smaller for better fitting models and includes a penalty for additional parameters
(Spiegelhalter et al. 2002). For an explanation of proper scoring rules, see the Appendix
(Table 10).

2.3.7

Multinomial regression

Although the binomial regression can provide useful information about the factors that
are associated with reproductive status, it does not reveal how these factors influence the
quantity of fruit produced. Therefore, I used a multinomial regression. Because data were
collected in ordered categories, I used an ordinal multinomial regression to investigate how
tree size, nutrient availability, and neighborhood competition influenced the number of fruit.
14

Observations in some fruit production categories were rare so the categories were collapsed
(see Table 2). Because trees reproduce in mast cycles, fruit output, Fij was defined as the
maximum fruiting category observed for each individual i of species j. This model was fit
as an ordinal logistic regression such that:

Fij ∼ Multinomial(πijk )

(5)

πijk = Qijk − Qijk−1

(6)

logit Qijk = γk − (X j β j + i )

(7)

where k is the fruit number category, πk is the probability of producing k fruit, Qk is the
cumulative probability of producing k fruit, and γk is the cut point (or boundary) between
categories k and k + 1. A total of K = 4 categories were used, as described above, with
K − 1 ordered cut points such that:

γ1 = 0 < γ2 < γ3

β and

(8)

were given the same vague priors as in the binomial regression.

The same six alternative sets of covariates were considered for the multinomial regression
as in the binomial model (Table 3). Alternative models were compared with DIC and proper
scoring rules. The model was run for three chains of 100,000 iterations each, following a
burn-in of at least 10,000 iterations to reach convergence based on Gelman and Rubin’s convergence criterion (Gelman and Rubin 1992). Chains were thinned to every tenth iteration,
so conclusions were drawn from a posterior distribution of 3 ∗ 100, 000/10 = 30, 000 samples.
The same multinomial model was used to examine fruit production in the subset of

15

individuals that were reproductive. The same alternative sets of covariates were used (Table
3). I again compared models using DIC and proper scoring rules (Tables 11–12).

2.3.8

Plot level analysis

Because the effects of nutrient availability and crowding may operate at a coarser spatial
scale than the individual tree, I also tested for plot-level trends in fruit production. For each
plot p and species j, mean fruit production category (Fjp ) and mean reproductive status
(Rjp ) were calculated. Simple linear regressions of Fjp and Rjp on plot-level NMin, P, SBC,
and total conspecific basal area were considered for each species.

2.4

Results

Although fruit production was observed for all 17 species, many individuals did not produce
any fruit (Table 1). Virola was excluded from analyses because only one individual of this
species produced fruit during the study. Across all species, fruit production was observed in
each category, with fruit production being more rare in higher categories (Figure 1), which
may be partly attributed to the relative scarcity of larger individuals.
In all species, larger individuals were more likely to produce fruit, and more of it (Figures
2–3). However, the rate at which fruit production increased varied among species. For
example, among the three canopy species Goethalsia, Laetia, and Pentaclethra, I saw a drastic
difference in how rapidly fruit production increased with tree size (Figure 2). In Goethalsia,
moderate levels of fruit production were rare; if an individual was reproductive, it was likely
to be capable of producing more than 1,000 fruits. Laetia individuals were likely to become
reproductive at a similar size as Goethalsia individuals, but had a larger size range where

16

moderate levels of fruit production were likely. Finally, even large individuals of Pentaclethra
produced relatively few fruit.
Competition from larger neighbors was negatively associated with fruit production. The
number of fruit produced was negatively related to ANCI in 13 species, and inclusion of DBH
and ANCI had the strongest support among the multinomial models (Table 11). Based on
DIC, there was also support for the influence of competition from the total neighborhood
(NCI) on the probability of fruiting and fruit production (Tables 10, 12), but this relationship
was not statistically significant for any species.
In the plot level analysis, significant relationships between fruit production and community composition were most common in palm species (Arecaceae). Two palm species
(Cryosophila and Welfia) showed positive relationships between conspecific basal area and
both probability of fruiting (Rjs ), and amount of fruit produced (Fjp ; Figure 4). These positive relationships may indicate pollination limitation in these species, or that these species
generally perform better at certain sites leading to both higher densities and higher reproductive output. In addition, one palm species (Euterpe) had a negative relationship between
Fjp and heterospecific basal area. There were also negative relationships between Rjp and
heterospecific basal area in two canopy species: Laetia and the nitrogen-fixing Pentaclethra.
SBC had a positive relationship with fruit production in the subcanopy species Prestoea
and Rinorea, suggesting base cation limitation. No other nutrients were associated with
individual fruit production (see Appendix).
In contrast, I found that multiple nutrients were related to fruit production at the plot
level, mostly affecting subcanopy species (Figures 12–17). Coussarea and Faramea had
positive relationships between number of fruit (Fjp ) and NMin. In Coussarea only, NMin
was also positively related to reproductive status (Rjp ). In Faramea only, P availability
17

positively affected reproductive status and number of fruit produced. On the other hand,
there was a negative relationship between reproductive status and NMin in the palm species
Euterpe. In palm species Iriartea and Socratea, reproductive status and number of fruit were
negatively related to SBC availability. Canopy nitrogen-fixer Pentaclethra had a negative
relationship between reproductive status and P availability.

2.5

Discussion

The goal in this study was to determine if there was a relationship between resources in a
tree’s environment and fruit production. Species differences in reproductive requirements
may influence their reproductive output, affecting seed availability and ultimately future
forest composition. Trees also must split their resources between reproduction and growth
(Primack and Kang 1989), so allocation priorities could affect forest carbon balance. Reproduction occurs at the individual level, so fruit production data collected at this level are
necessary to assess how environmental factors affect allocation to fruit production.
Tree size was the primary predictor of individual fruit production in all species. Smaller
trees are unable to reproduce until they reach a certain size, which depends on the species
of the individual (Figure 3; Wright et al. 2005, Thomas 1996b). Larger trees may have a
greater ability to acquire and store nutrients and carbohydrates, and they tend to produce
more fruit (Figure 2; Han et al. 2008, Carbone et al. 2013, Greene and Johnson 1994).
Even after accounting for this trend, reproduction tends to be unequal among conspecifics
(Moran and Clark 2012, Herrera and Jovani 2010, Gonz´alez-Mart´ınez et al. 2006), with many
individuals not producing fruit at all (Figure 1).
The negative association between fruit production and the competition from larger neigh-

18

bors, as opposed to all neighbors, may indicate that competition for light affects reproduction
more than competition for soil resources. Carbohydrates which were recently produced from
photosynthesis are important for fruit production (Ichie et al. 2013), and decreased light
availability decreases fruit production (Greene et al. 2002, Wright et al. 2005). In contrast,
competition negatively affected growth of individuals in only 3 out of 15 species examined at
these same plots (Baribault et al. 2012), versus 13 out of 17 species for fruit production. If
competition decreases fruit production, but not growth, there may be preferential allocation
of carbohydrates to growth in these species. An important caveat is that the competition
index in Baribault et al. (2012) included all neighbors instead of only larger neighbors, and
a larger neighborhood area.
The effects of soil nutrients on fruit production varied among species. At the individual
tree level, there were no significant relationships between number of fruit produced and
nutrient availability. High spatial and temporal variability in fruit production can make it
difficult to detect the effects of nutrient availability (Wright et al. 2011). However, base
cations were positively associated with reproductive status at the individual tree scale in
Prestoea and Rinorea. At the plot level, N and P availability was positively associated
with fruit production for Coussarea and Faramea, suggesting that these nutrients may limit
fruit production in these species, and that soil nutrient availability is important at a larger
spatial range for some species. Adult trees may be less affected by fine scale variations in
soil resources than seedlings and saplings due to a larger root network. In addition, the
forest floor is composed of a network of mycorrhyzal fungi and fine roots, which provides
soil nutrients to trees (Hertel et al. 2003). The extent of the root and mycorrhyzal fungal
networks suggest that some species can access nutrients from a much greater surrounding
area, potentially averaging nutrient availability over this area, and decreasing the apparent
19

affect of nutrient availability in the few meters immediately surrounding the stem. This
greater access to resources, mediated by tree size, may increase fruit production.
Similarly, larger trees may be averaging nutrient availability across time. Trees are able
to store nutrients, and in some species storage of N or P may control interannual fruit
production cycles (e.g. masting) (Han et al. 2011; 2008, Ichie and Nakagawa 2011). If soil
nutrients are stored for use in periodic masting events, or if the amount of resources used by
annual fruit production is small compared to the amount stored, fruit production may be
decoupled from environmental nutrient availability.
Larger trees may have a larger storage capacity, contributing to the positive effect of tree
size on fruit production. Alternatively, effects of tree size on fruit production may result
indirectly from nutrient availability; i.e., larger trees grew to that size as a result of higher
nutrient availability (e.g. Baribault et al. 2012), and because of their size are able to produce
more fruit.
Although I did observe some direct influence of soil nutrient availability on fruit production, these effects occurred in relatively few species, and were inconsistent. Despite an
apparent lack of influence of soil nutrient availability on fruit production, it seems unlikely
to be completely unimportant. Plants invest on average more N in reproductive structures
than any other structure (Bazzaz et al. 1987), and fertilization with N (Kaspari et al. 2008)
or a suite of nutrients (Li et al. 2006) increases the biomass of reproductive structures in
tropical forests. I surprisingly found some negative relationships of fruit production with soil
nutrient availability, which may indicate that some species are less able to acquire nutrients
for fruit production in high resource, competitive environments. Nutrient availability also
could have an effect on fruit quality, which was not measured in this study. A trade-off
between the number of fruit produced and the amount of nutrients invested in an individual
20

fruit would allow trees in different nutrient environments to produce similar numbers of fruit
by adjusting the fruit quality (Primack and Kang 1989, Venable 1992). Future research
combining individual estimates of fruit production over time, and fertilization across a range
of spatial scales may help to clarify how soil nutrient availability influences reproduction in
tropical forests.
There were also broader scale community effects on individual tree fruit production, with
fruit production increasing with conspecific basal area in two species. This pattern may be
due to an unobserved factor which increases both survival and fruit production, but is also
consistent with pollen limitation (Knight et al. 2005). A greater density of large, mature
individuals increases the probability of pollination and subsequently fruit production. In
this study, palm species may be especially affected by pollen limitation, accounting for both
species for which this effect was observed. Both species are insect pollinated, which was not
unique among the species studied (insects pollinate 15 out of the 17 species; Chazdon et al.
2003).
Despite accounting for physiological factors (tree size and nutrient availability) and community factors (neighborhood crowding and conspecific density), there was substantial uncertainty in predicting the reproductive status of an individual (Table 10). The contribution
to overall seed availability is highly unequal among individuals, with many not producing
fruit during the study (Figure 1). Even during mast fruiting events it is common for trees
to not produce fruit, even among individuals of reproductive size (Herrera and Jovani 2010).
Lack of reproduction may be due to insufficient nutrient storage by the tree (Han et al. 2008)
or a trade-off with investment in growth (Charlesworth and Morgan 1991). The three-year
timespan of this study, may not have included a mast year for all species. During a mast
year, I would expect the peak in fruit production to make resource limitation more apparent
21

than in other years. Without a longer time series of reproductive data, it is difficult to determine if this study included a peak in fruit production for all species. There are also many
environmental and stochastic factors that influence the reproductive status of an individual
tree, including liana competition/parasitism (Wright et al. 2005), tree health (Silvertown
et al. 2001), weather events (Wright et al. 1999), and location within the species’ geographical range (Hampe 2005, Garcia et al. 2000, Pigott and Huntley 1981). Although this pattern
of unequal fruit production may be exaggerated by the short duration of this study relative
to the lifetime of a tree, it may persist in the long term, with most individuals producing
low or moderate amounts of fruit (Moran and Clark 2012, Herrera and Jovani 2010).
Although it is not surprising that larger trees are likely to produce more fruit, species
differences in the size at which fruit production first occurs, and the rate at which fruit
production increases, provide insight into how seed availability may vary over time. Greater
nutrient availability may increase reproduction and seed availability in certain species (Kaspari et al. 2008, Callahan et al. 2008), but variability in fruit production makes this effect
difficult to assess (Wright et al. 2011). However, competition for light and nutrients from
larger trees can delay reproductive maturity (Wright et al. 2005), and decrease reproductive
output of an individual. This delay in maturation may be caused by resource allocation to
growth being prioritized over reproduction in some species, as competition has less influence
on growth in these species (Baribault et al. 2012).
In many cases, seedling abundance of a species is limited by the number of seeds that reach
the forest floor, with seedling recruitment being higher following greater fruit production (De
Steven and Wright 2002, Turnbull et al. 2000). The number of seeds that reach suitable sites
is limited by the number of fruit produced, dispersal ability, and seed predation (Svenning
and Wright 2005, Hubbell et al. 1999). In species that quickly reach high levels of fruit
22

production, reproductive individuals may have the advantage of greater numbers of offspring
reaching suitable locations over their lifetime.

23

Chapter 3
Masting synchrony in northern
hardwood forests: super-producers
dominate population fruit production

24

3.1

Abstract

Peaks in fruit production via interannual masting cycles are a common phenomena in tree
populations. Masting cycles require some level of synchronization in fruit production among
individuals. The level of synchrony is largely unknown because most studies of masting
measure fruit production at a population level, rather than for individuals. By measuring
individual fruit production, I investigated the degree to which individuals were synchronized,
and how much fruit each individual contributed to a mast event. Through direct canopy
counts, I estimated the number of fruit produced by 1635 individuals of 10 temperate tree
species across 4 years in northern lower Michigan. I also used a longterm dataset of seed and
seedling density on the forest floor to place the individual tree data into a broader context
of population mast cycles. Three species had mast events during the 4-year period of the
study, in addition to some minor peaks in fruit production in these and other species. In
Acer saccharum and Fagus grandifolia, which had multiple peaks in reproduction, a small
subset of the population reproduced more often and was responsible for a large portion of
the total number of fruit produced in the population. In Tilia americana, different subsets
of individuals were responsible for multiple peaks in reproduction. This suggests that it is
important to incorporate individual measures of fruit production when investigating mast
cycles, as small subsets of trees may dominate population patterns. The large amount of
variation in the number of fruit produced suggests that other environmental or biotic factors
may be affecting tree reproduction. Larger trees tended to produce more fruit in all species
and were more likely to be reproductively mature, although even large trees often produced
zero or few fruit. There were no direct effects of nutrient availability or competition on fruit
production. Although the cause is unclear, in some species a small number of trees dominate

25

the number of fruit produced and the frequency of mast cycles. By producing more fruit,
more often than their conspecifics, these individuals increase their chance of successfully
producing offspring over time.

3.2

Introduction

Tree reproduction has long-lasting effects on the forest community. Seedling recruitment
is often limited by seed production, placing a bottleneck on the species available to make
up the future canopy (Caspersen and Saprunoff 2005). Seed availability also affects animal
population sizes, causing trophic cascades that can affect disease prevalence in humans (Ostfeld et al. 1996, Jensen et al. 2012). Tree regeneration may respond in unpredictable ways
to climate change and nitrogen deposition, with responses varying by species (Ibanez et al.
2007, HilleRisLambers et al. 2009). Understanding fruit production in individual trees, and
in the entire forest community, will improve our ability to predict how global change may
influence reproduction and the forest community in the future.
Many temperate tree species have interannual cycles in fruit production (masting), with
synchronized high fruit production across a population in certain years (Silvertown 1980,
Kelly 1994, Kelly and Sork 2002). Drastic increases in fruit availability during mast years
can increase seedling recruitment (Caspersen and Saprunoff 2005) and animal population
sizes, causing trophic cascades that can affect disease prevalence in humans (Ostfeld et al.
1996, Jensen et al. 2012). Much of the research on fruit production in temperate tree species
focuses on masting, and usually fruit production at the population scale (Herrera 1998,
Monks and Kelly 2006). Although masting is a population-level phenomenon, reproduction
occurs at the individual level.

26

Masting is the cumulative result of individual reproductive cycles. By definition, individual cycles must be synchronized to some extent for masting to occur. Fruit production
is typically low between masting events, although some individuals may produce fruit out
of sync with the rest of the population (LaMontagne and Boutin 2007, Koenig et al. 2003).
Even if mast years are observed in a population, it is difficult to tell how synchronized individual trees actually are. Peaks in population-level reproduction could be caused by multiple
scenarios, including:
1) Completely synchronized: all individuals produce large amounts of fruit in mast years
and very little in non-mast years;
2) Somewhat synchronized: Majority of individuals reproduce together and a few individuals
with high fruit output reproduce in other years;
3) Frequent fruiters: A few individuals with high fruit output consistently reproduce together, more frequently than the rest of the population;
The latter scenarios are possible because within a population the number of fruit produced
tends to be highly unequal among individuals, with some individuals producing far more
fruit than their conspecifics (Moran and Clark 2012, Herrera and Jovani 2010, Gonz´alezMart´ınez et al. 2006). However, I do not know how well these high fruit producing trees
are synchronized with the rest of the population. For this reason, I have used individual
fruit production to assess synchrony in temperate tree populations, and to determine how
individual variation in fruit production contributes to masting events.
Because variation in fruit production among individuals determines the extent of masting
synchrony in a population, it is also important to understand the cause of this variation.
Inequality in fruit production by individual trees may be influenced by several factors, including tree size, soil nutrient availability, and competition from neighboring trees. Size may
27

have two effects on reproduction. First, there is a minimum size a tree must reach before
it becomes reproductively mature (Owens 1995). This size threshold tends to vary among
species, even relative to their maximum size (Thomas 1996b, Wright et al. 2005). Although
trees continue to grow following maturation, after this point allocation is divided between
growth and reproduction (Wesselingh et al. 1997). Second, once a tree is mature, the number of fruit produced may increase with size (Greene and Johnson 1994). Larger trees may
have greater access to resources, and greater nutrient and carbohydrate storage capability
(Carbone et al. 2013, Han et al. 2008).
Resources in the local environment may also limit fruit production (Satake and Bjørnstad
2008) In temperate forests, nitrogen (N) is typically considered to be the most important
nutrient that limits growth and productivity (Vitousek and Howarth 1991a). Other nutrients
that limit growth and potentially fruit production include phosphorus (P) and base cations
such as calcium (Ca), potassium (K), and magnesium (Mg) (Vitousek et al. 2010, Baribault
et al. 2010, Gradowski and Thomas 2008). Although fertilization has shown a positive
relationship between nutrient availability and reproduction for some species (Lovett et al.
2013, Callahan et al. 2008, Drenovsky and Richards 2005), the strength of this relationship
may vary based on site conditions and tree species (HilleRisLambers et al. 2009, Magill
et al. 2000). In addition, neighboring trees may indirectly influence fruit production through
competition for resources (Baribault and Kobe 2011, Canham et al. 2006). Larger neighbors
may present stronger competition by casting shade and limiting nutrient uptake by smaller
trees (Greene et al. 2002, Wright et al. 2005).
The goal of this study was to investigate how individual fruit production in temperate tree species contributes to masting events. Specifically, I assessed masting synchrony
among individuals, and the effect of tree size, soil nutrient availability, and neighborhood
28

competition on individual fecundity. I measured fruit production in 10 common species in a
northern hardwood forest in Michigan, USA. I investigated how individual trees contribute
to masting events using individual fruit production data in conjunction with longterm seed
and seedling census data. By observing fruit production across a natural range of nutrient
availability, and experimentally fertilizing, I determined how nutrients may influence reproduction in these species. I also used the variation in tree density across sites to assess how
neighborhood crowding may inhibit fruit production. I predicted that more fruit would be
produced in larger trees, with greater nutrient availability, and with lower competition.

3.3
3.3.1

Methods
Site description

This study was conducted at 12 sites in the Manistee National Forest in the lower peninsula
of Michigan, USA. Each site was located in a mixed hardwood stand ranging from 80–100
years old (Host et al. 1988). These sites were located on a variety of glacial landforms,
and have differences in soil fertility and forest community composition corresponding to the
landform (Zak et al. 1989, Host and Pregitzer 1992). Soil fertility is lowest at outwash
sites and highest at moraine sites, with N, Ca, and water availability increasing along this
gradient (Baribault et al. 2010). I measured fruit production for 10 common species at these
sites (Table 4). Community composition shifts along the fertility gradient, with the lowest
fertility sites being dominated by Quercus alba and Quercus velutina and the highest fertility
being dominated by Acer saccharum. Where possible, site dimensions were 41 m x 240 m.
However, one site was split into two 41 m x 120 m areas and another was 21 m x 240 m. All
trees greater than 10 cm in diameter at breast height (DBH) were mapped and measured for
29

DBH. Along the center axis of each site I established a 200 m x 1 m seedling transect, that was
censused for newly germinated seedlings annually from 1998–2013. Positioned next to the
seedling transect at 10 m intervals were 1 m x 1 m seed traps, which were collected annually
from 2001–2012. Seeds were sorted by species and viability (based on seed development),
and counted.

3.3.2

Fruit estimation

At each site, the number of fruit was estimated for all trees within a 41 m x 41 m area
(21 m x 41 m at one site). For uncommon species, fruit production was estimated for
all trees within the full 41 m x 240 m area in order to obtain a sufficient sample size.
The number of fruit was estimated from direct counts in tree canopies because an estimate
of pre-dispersal, pre-predation fruit production more accurately reflects a tree’s resource
investment. This method also obtains an estimate of individual fruit production, while
avoiding the uncertainty associated with modeling dispersal to seed traps (Clark et al. 2010;
2004, Moran and Clark 2011). For each tree, fruit production was estimated by counting
the number of fruit on each of three fruiting branches. Branches were chosen haphazardly,
with an effort to disperse samples vertically in the crown when possible. Counting was done
from the ground using a telescope with 20–60x magnification. All counts were performed
by a single observer, in order to eliminate inter-observer variation (Chapman et al. 1992).
The average number of fruit from these three branches was multiplied by the number of
fruiting branches to obtain a whole tree estimate of fruit production. The number of fruit
was estimated for each individual annually from 2008–2011 (2009–2011 for A. rubrum and
P. grandidentata).

30

3.3.3

Soil nutrient measurements

Soil nutrient analyses were performed on composite samples, each consisting of three soil
cores from each sampling location. Samples were taken from the central 200-m transect
of each site in a lattice plus fill-in design (Diggle and Lophaven 2006), and from parallel
transects located 5 and 15 m to either side of the central transect at 20-m intervals. Samples were analyzed for ammonium, nitrate, phosphorus, calcium, potassium, and magnesium
concentrations. Potential net N mineralization (NMin) was measured through aerobic mineralization (see Baribault et al. 2010, for details). NMin was used in analyses to better
estimate nitrogen availability over time (Pastor et al. 1984). Because of collinearity among
them, calcium, potassium, and magnesium were combined as the sum of base cations (SBC)
for analyses. To obtain nutrient availability estimates for each tree I used distance-weighted
averages of each nutrient from the five nearest soil samples using the R package yaImpute
(Crookston and Finley 2008).

3.3.4

Fertilization experiment

At 11 of the sites I also fertilized trees outside of the main plot area to determine if fruit
production was limited by specific nutrients. The four most common species were fertilized
(Acer rubrum, Acer saccharum, Quercus alba, and Quercus rubra). Approximately 100
individuals of each species were included, divided evenly among five treatments: control,
N only, Ca only, N and Ca, and a complete nutrient treatment consisting of N, P, K, Ca,
and micronutrients. Fertilizer was applied 2008–2011 in mid-May and mid-June within a
4-m radius around each tree (Table 5), and was effective at increasing nutrient availability
(Baribault 2011). Fruit production was estimated 2009–2011 for all fertilized trees in the

31

same way as the trees in the main plot. I tested for differences in the number of fruit
produced among treatments using an analysis of covariance (ANCOVA), with DBH as a
covariate.

3.3.5

Individual fruit production modeling

Fruit production was modeled as a combination of tree maturity and number of fruit produced. A hierarchical Bayesian approach was used so that my inferences could draw upon
information from the entire community, while also ascertaining species differences (Clark
et al. 2004). In all analyses, Q. rubra and Q. velutina were analyzed as one species. These
two species commonly hybridize (Moran et al. 2012) and could not always be distinguished.
Analyses were performed using the rstan package in R statistical software (R Core Team
2013, Stan Development Team 2013).
To model maturity each tree was assumed to have an underlying reproductive status, Ri ,
and an observed status ri . Ri would be zero for individuals that are not yet reproductive, and
one for mature individuals. Because the duration of this study was relatively short (4 years)
relative to the longevity of the trees being studied, I assumed Ri did not change over the
course of the study. If an individual could be identified as reproductive, either by observing
fruit during the study or evidence of previous reproduction (e.g. the previous year’s acorn
caps still attached), it was classified as ri = 1, otherwise, ri = 0. The probability of maturity,

p(Ri ) = Bernoulli(Ri |πi )

(1)

increases with size. This relationship was represented as a logistic regression with diameter

32

(Di ):

ri ∼ Bernoulli(πi )

(2)

logit(πi ) = D i αj

(3)

where αj was a vector of regression coefficients for species j.

αj ∼ MVNormal(αµ , Σα )

(4)

Random variables αµ and Σα were drawn from vague prior distributions.
Observed reproductive staus (ri ) may not exactly reflect the true status (Ri ). While I
can be confident that an individual was actually mature when ri = 1 (i.e. there were no
false positives), there is more uncertainty when ri = 0. If no fruit production was observed,
an individual may have truly been immature (ri = Ri = 0). However, if fruit production
occurred and was not observed due to detection error, or if a mature tree happened to
not reproduce during the study, then the observed status would not reflect the true status
(ri = 0, Ri = 1). To incorporate this uncertainty into the model of number of fruit produced,
estimated status, ρi , was defined as the probability of R1 = 1 based on the value of r1 .
When r1 = 0, the estimated reproductive status (ρi ) is based on a probability of maturity
(πi ) rather than directly on the value of ri .

ρi = p(Ri = 1|ri ) =





1

ri = 1




π i

ri = 0

(5)

Because the data were overdispersed and had a high frequency of zero fruit production, a
33

zero-inflated negative binomial distribution was used (Martin et al. 2005, Joe and Zhu 2005).
The zero-inflation parameter, δi was based on the estimated reproductive status:

δi ∼ Bernoulli(ρi )

(6)

The negative binomial regression was parameterized as a Poisson-gamma mixture:

X β
Fi ∼ Poisson(δi ηi e i j )

(7)

where Fi was the maximum number of fruit produced by tree i. Maximum number of fruit
was used in order to represent the maximum investment capable by an individual. I also
tested the average number of fruit produced by an individual, which had similar results to
the maximum. Random variables in Equation 7 were ηi , the gamma-distributed error; X i ,
the vector of covariates; and β j , the vector of regression coefficients for species j drawn from

β j ∼ MVNormal(β µ , Σβ )

(8)

Random variables β µ , Σβ , and ηi were drawn from vague prior distributions.
Three alternate sets of covariates were tested for the regression in Equation 7 (see Table
6): Covariates included DBH, soil nutrient availability, and neighborhood competition index
(NCI). Following Baribault and Kobe (2011), NCI was defined as:
n

NCIi =

γj

(DBHk exp−1/distk )

(9)

k=1

where γ is a random variable controlling the influence of neighbor DBH, and was drawn from

34

a Gamma(1.0, 1.0) distribution. The effect is summed for k = 1, . . . , n neighbors within a
10-m radius of the focal tree, including only neighbors with a larger DBH than the focal tree.
For approximately 10% of individuals, the 10-m neighborhood was not completely mapped.
Therefore, an estimated NCI (ENCI) was drawn from a normal distribution, with NCI of
the known area as the mean, and variance as a function of the proportion of the area known
(pi ).
ENCIi ∼ N (NCIi , eη−ν∗pi )

(10)

For individuals with the complete neighborhood known, the variance is small, and grows
larger as the known proportion shrinks. The parameters η and ν are random variables with
vague priors. Each alternative model was run for 4 chains of 2000 iterations, following a 2000
iteration burn-in. All parameters reached convergence based on Gelman and Rubin’s convergence criterion (Gelman and Rubin 1992). Alternative sets of parameters were compared
using Akaike Information Criterion (AIC; Burnham and Anderson 2002).

3.3.6

Relative size at onset of maturity

The binomial portion of the zero-inflated regression described above was used to define a
reproductive diameter threshold (Dthres ), at which the probability of being reproductively
mature was 0.5 (Figure 5). Dthres varied among species, but this could be due to differences
in the maximum size of species. Because tree height growth reaches a limit more so than
diameter growth, I used height to calculate the relative size at onset of maturity for each
species (RSOM ) (Thomas 1996b). First, an allometric function was fit using diameter and

35

height measurements of all individuals in the population (Thomas 1996a).

b

H = Hmax (1 − e−aD )

(11)

H and D were height and diameter, respectively. Hmax was the asymptotic maximum height
for the species, and a and b were random variables. This function was then used to compute
Hthres from Dthres , and RSOM = Hthres /Hmax .

3.3.7

Synchrony in masting cycles

To understand individual fruit production in the context of population mast cycles, I used
long-term seed trap and seedling census data. Populus grandidentata was not included in this
analysis because no seeds or seedlings were found of this species during the study period. To
check for consistency among these three data sources, I correlated direct fruit observations
with newly germinated seedling and viable seed density in the 4 year period for which all
data sources were available, accounting for a time lag in seedling density relative to fruit
counts and seed density. The time lag was 0, 1, or 2 years based on which lag maximized
Pearson’s r in a correlation between seed and seedling density in each species. I expected
most species to have a 1-year lag, but seeds could remain in the seed bank for multiple years.
Because mast years require high allocation of resources to fruit production, and trees
are more likely to produce near their maximum capacity, the effects of nutrient limitation
should be most apparent during a mast year. I used the long-term seed density time series
to determine when mast years had occurred for each species, and if they coincided with the
four year window of direct fruit counts used in the model above. Mast years were determined
based on standardized deviates from the long-term mean seed density. The annual deviate of
36

seed density was the deviation from the longterm mean seed density divided by the standard
deviation of seed density (LaMontagne and Boutin 2009). Any years for which the annual
deviate was greater than the absolute value of the minimum annual deviate was designated
as a mast year.
The occurrence of a mast year at the population level does not imply that all individuals
produced fruit in that year. Synchrony among individuals across the 4 years of direct fruit
˙
counts was measured using Spearman’s rank correlation (Zywiec
et al. 2012, Buonaccorsi
et al. 2001). The mean of all pairwise correlations among individuals that reproduced at
least once was used to calculate the mean synchrony for each species (ρs ). For example, 56
Acer saccharum individuals produced fruit during the study. The amount of fruit produced
by a given tree in each year was individually correlated with the amount produced by each
other tree, for a total of 1540 combinations. The mean of all 1540 correlation coefficients was
taken to produce ρs . Spearman’s correlation was used because the data were not normally
distributed. I also calculated the percentage of each reproductive population that produced
fruit in each year, and how much these individuals contributed to total fruit produced in the
reproductive population. The reproductive population was defined as all individuals greater
in size than the reproductive size threshold (Dthresh ) for each species, which accounted for
≥ 90% of the fruit produced in each species.

3.4

Results

Larger trees were more likely to produce fruit (Figure 5) in seven out of nine species; larger
trees also produced more fruit in all species (Figure 6). In P. grandidentata and F. americana,
the failure to detect a relationship between probability of producing fruit and tree size

37

was probably due to the under-representation of smaller trees in the dataset. Consistent
with other forest communities, relative size at onset of maturity (RSOM: height at first
reproduction / maximum height) varied among species (Figure 7, Thomas 1996b, Wright
et al. 2005), although there was no obvious pattern to this variation, such a connection to life
history strategy. No evidence of direct effects of soil nutrients or neighborhood competition
on fruit production were found, and these factors were not included in the best model (Table
6). In addition, there was no effect of fertilization treatment on number of fruit produced
(A. rubrum: F = 0.8, p = 0.5; A. saccharum: F = 0.6, p = 0.7; Q. alba: F = 1.0, p = 0.4;
Q. rubra: F = 0.9, p = 0.5). However, a longer time period may be required for a fertilization
effect to be observed in mature trees.
In the longterm dataset, there was a 1-year time lag between the number of seeds produced and number of newly germinated seedlings, with the exception of F. americana which
had a 2-year lag (Table 7). Low correlations between seed and seedling density in some
species suggest a low germination rate, high seed predation, or that seeds are remaining in
the seed bank for a longer time period. The average annual fruit production from canopy
counts in 2008–2011 corresponded well to density of seeds and seedlings found at each site,
with the number of seeds having a stronger correlation (Table 8). In the longer time series dataset for seed density (2001–2011), A. saccharum, F. americana, and T. americana
experienced a mast year during the four years of canopy counts (Figure 8). In addition,
F. grandifolia, P. serotina, and Q. rubra/velutina had at least a moderate (minor mast) fruit
production year.
Synchronization also varied among species. Based on Spearman’s rank correlation (ρs ),
synchrony was low in A. rubrum, P. grandidentata, and Q. rubra/velutina; moderate in
F. grandifolia, P. serotina, Q. alba, and T. americana; and high in A. saccharum, and
38

F. americana (Table 9). In A. rubrum and F. americana, very few individuals produced
fruit in non-mast years. In A. saccharum, F. grandifolia, P. serotina, and T. americana,
there were years with zero or near-zero fruit production, but also minor mast years when
10–18% of reproductively mature individuals produced fruit.
In the three species that had both a mast year and a minor mast year, or two minor mast
years (A. saccharum, F. grandifolia, and T. americana), 3–8% of the population reproduced
in both years (Figure 9). In A. saccharum and F. grandifolia the individuals that reproduced
in both mast years account for approximately 40–70% of fruit produced in a single event,
suggesting that a small subset of individuals are responsible for a large proportion of the
fruit production in these populations. In A. saccharum, this subset included the largest tree
measured, which by itself accounted for 20% of the fruit produced in the 2008 mast year. The
other high fruit producing A. saccharum trees were not extraordinarily large, but the high
fruit producing F. grandifolia trees were all in the 80th percentile for size in this species. The
highly reproductive trees in both of these species did not have extraordinarily high nutrient
availability or low neighborhood index. On the other hand, the T. americana individual
that reproduced in both events accounted for <10% of the fruit produced in a given event,
suggesting that in this species different subsets of trees are likely to be reproductive in
different events.

3.5

Discussion

Tree size was the key factor for predicting individual fruit production in most of the nine
species sampled in this study, and the probability of an individual being reproductively mature increased with size. Species varied in relative size at the onset of maturity (RSOM),

39

possibly indicating different allocation strategies among species, although there was no obvious connection to life history traits, such as shade tolerance. A smaller RSOM allows trees
to reproduce for a longer portion of their life, but if there is a trade-off between growth and
reproduction (Charlesworth and Morgan 1991), then becoming mature at a small size may
be at the expense of lifetime growth rate (Wright et al. 2005, Thomas 1996b, Wesselingh
et al. 1997). However, in high resource environments, individuals may be able to allocate to
both growth and reproduction (Moran and Clark 2012).
Highly unequal reproduction among individuals is typical for many tree species (Moran
and Clark 2012, Herrera and Jovani 2010, Gonz´alez-Mart´ınez et al. 2006), and this variation
suggests that environmental factors influence individual fruit production.Fruit production
requires a large investment of carbohydrate and mineral nutrients. Plants invest more nitrogen in reproductive parts than any other structure (Bazzaz et al. 1987). Therefore, it
is surprising that I found no effect of the availability of nitrogen or other soil nutrients on
fruit production, neither across a natural soil nutrient gradient, nor following experimental
fertilization. Nitrogen fertilization has previously increased seed production in multiple temperate species (Lovett et al. 2013, Callahan et al. 2008). A longer time period of fertilization
may be necessary before a fruit production response can be observed. Also, none of the
four species which were part of the fertilizer experiment were observed during a mast year,
when nutrient limitation may be more apparent. Alternatively, previous studies which have
observed an increase in seed production following fertilization have quantified seed biomass
rather than number, possibly combining changes in fruit quantity and quality into one effect.
Although I found no direct effects of soil nutrient availability on fruit production, there
may have been unobserved indirect effects mediated through tree size. Tree growth is influenced by nitrogen and base cation availability (Baribault et al. 2010), so larger trees may
40

have grown to that size because of the locally available soil nutrients, eventually translating
into greater fruit production. Additionally, large trees may have a greater capacity to store
nutrients (Han et al. 2008), allowing them to produce more fruit.
Carbohydrates are also heavily invested in reproduction, so increased light availability
would be expected to increase fruit production (Ichie et al. 2013, Greene et al. 2002, Wright
et al. 2005), but I found no evidence of a negative effect of competition from larger neighboring trees. This is in contrast to findings in some tropical species, which had a negative fruit
production response to asymmetric competition (See Chapter 2). Competition may be more
intense in tropical forests, or fruit production may be a lower priority for tropical species
when light is limiting. Also, productivity at these temperate sites is negatively related to
competition (Baribault and Kobe 2011), suggesting that resource allocation to reproduction
may be higher priority than growth. However, the high variability in fruit production across
years and individuals makes it difficult to compare with growth over the relatively short
time period in this study. The lack of evidence for resource limitation from soil nutrients
or carbohydrates may indicate that other factors such as disease, insect attack, or genetics
may explain some of the reproductive inequality among individuals.
Species differed in the extent to which variation in individual reproduction contributed
to masting. Some species were almost completely synchronized, with very little fruit production occurring outside of mast years. Other species had minor mast years in addition
to full mast years. The minor mast years were due to a subset of individuals reproducing
more often than their conspecifics, or by different groups of trees reproducing in different
years. Consistent with other studies, not more than 40% of the reproductive-size trees in
a population reproduced in a given mast year, and very few contributed to multiple peak
˙
reproduction years (Zywiec
et al. 2012).
41

The lack of synchrony in T. americana and unequal fruit production among individuals in
A. saccharum and F. grandifolia could have consequences for reproductive success at both the
population and individual level. One of the possible benefits of masting is predator satiation
(Kelly 1994). This benefit relies on seed predator populations being reduced in non-mast
years, and producing more seeds than the predator population can consume in mast years.
If different subsets of the population reproduce in consecutive years (as in T. americana), a
large predator population could be maintained. Fruits produced by individuals in the second
year may be completely consumed, and if this pattern continued the reproductive success
˙
of the entire tree population could decrease (Zywiec
et al. 2012). Similarly, if an individual
tree reproduces out of sync with the rest of the rest of the population, its seeds may be
consumed, reducing its reproductive success. However, if peak years are intermittent (as in
A. saccharum and F. grandifolia), and there is a subset of the population which produces
more often and makes a disproportionately large amount of fruit, then these super-producers
will have higher relative fitness without sacrificing the reproductive success of the population.
If the reproductive inequality observed in all species (Figure 6 persists, it may influence
future forest composition. In some tree species, seedling recruitment is limited by the number
of seeds (Caspersen and Saprunoff 2005), and if seeds are only consistently produced by a
few individuals (Table 9, Figure 8), then spatial heterogeneity of seed availability may be
high (Moran and Clark 2012). This could lead to greater seedling competition and mortality
near highly reproductive individuals, decreasing their reproductive success relative to the
number of seeds they produce (Venable 1992, Moran and Clark 2012). In addition, there
may be a trade-off between number of fruit produced and the quality of fruit, reducing
germination rates in fruits from highly reproductive individuals (Primack and Kang 1989).
Although fruit production and seed availability tend to be positively correlated with seedling
42

germination and establishment (Venable 1992, Gonz´alez-Mart´ınez et al. 2006, Moran and
Clark 2012), successful transition from fruit to established seedling is uncertain due to the
high mortality at this life stage. Although I have been able to examine the reproductive
efforts of individual trees by estimating individual fruit production, in order to get a full
picture of the reproductive success of individuals, and the resulting changes in the forest
community, established seedlings or saplings must also be observed (Moran and Clark 2012).
In conclusion, individual measurements provide key insights into tree reproduction that
would have been obscured by population level sampling. I was able to detect differences
in maturation schedules among species and determine that reproduction is highly unequal
within populations. By combining individual and population data, I was able to examine how
synchrony among individuals contributes to masting, revealing that in some species there
may be individual cycles that are not apparent at the population level due to a lack of synchronization among individuals across years. Individual trees that produce more fruit more
often may have greater lifetime reproductive success and greatly influence the surrounding
forest community.

43

Chapter 4
Conclusion

44

4.1

Conclusion

Future forest composition depends on the reproductive success of individual trees, and
seedling recruitment is often limited by seed availability (Caspersen and Saprunoff 2005,
De Steven and Wright 2002, Svenning and Wright 2005). Allocation to fruit production may
be limited by different resources in temperate and tropical forest species (Greene et al. 2002,
Kaspari et al. 2008, Callahan et al. 2008, Lovett et al. 2013, Ichie et al. 2013). The goal
of the studies in this thesis was to gain a better understanding of how tree size, nutrient
availability, and competition affect an individual tree’s production of fruit.
Among both tropical and temperate species, there was a consistent positive effect of
tree size on maturation and fruit production. The size at which trees became reproductive
differed among species in both tropical and temperate forests (Thomas 1996b, Wright et al.
2005). In temperate species, the relative size of maturation also varied among species. The
relative size at which species become mature may reflect species differences in allocation
to growth versus reproduction, but was not related to shade tolerance. Future research is
necessary to determine if relative size at the onset of maturity is consistently related to other
life history traits.
Among reproductive individuals, the distribution of fruit production was skewed. Consistent with previous studies, most of the fruit was produced by a small number of individuals,
while many trees produces few or no fruits (Moran and Clark 2012, LaMontagne and Boutin
2007, Herrera 1998). In addition, some highly reproductive individuals in temperate species
˙
reproduce more frequently than the rest of the population (Zywiec
et al. 2012). These
individuals produce a large portion of the fruit in the population, dominating population reproductive cycles, and underscoring the importance of individual measurements for assessing

45

synchrony. This inequality in fruit production among individuals may cause spatial heterogeneity in seed arrival and seedling recruitment in the environment, leading to increased
competition among seedlings (Moran and Clark 2012).
Nutrient availability had less influence on fruit production than expected. Soil nutrients
had no association with fruit production in temperate species, and varied effects in tropical
species. Reproduction in four tropical species was affected by nutrients, with different species
being limited by nitrogen, phosphorus, and base cations. The relative lack of effects of soil
nutrients and consistent effect of tree size may be caused by soil nutrients acting indirectly
through tree size. Large trees may have grown to their present size because of greater access
to nutrients, and larger trees may be able to acquire and store more nutrients (Han et al.
2008, Baribault et al. 2010; 2012).
The influence of competition on fruit production was the starkest difference between
temperate and tropical species. The number of fruit produced was negatively associated
with neighborhood competition in the majority of tropical species and none of the temperate
species. This may suggest that biotic interactions are more intense in the tropics, leading to
a greater response to competition. Alternatively, tropical and temperate species may differ
in allocation priorities. In some temperate species competition negatively affects growth,
while there is a lack of competitive influence on growth in tropical species (Baribault and
Kobe 2011, Baribault et al. 2012). This may indicate that resources tend to be preferentially
allocated to reproduction in temperate species and growth in tropical species. However, a
study directly comparing fruit production and growth in relation to competition and local
resource environment is necessary to confirm this trend.
This study of reproduction in a broad set of species across tropical and temperate forest types demonstrated that soil nutrients may have less direct effect on fruit production
46

than previously thought, but that tree size and competition influence maturation and the
number of fruit produced. Individual differences in fruit production and reproductive cycles
demonstrate the importance of individual measurements in order to determine population
synchrony, environmental effects on reproduction, and the source of seeds in a population.

47

APPENDICES

48

Appendix A
Tables and figures for Chapter 2
Table 1: Study species at La Selva, Costa Rica. For each speces, the number of
individuals measured and the number of individuals which were observed fruiting at least
once during the study.
Species
Capparis pittieri
Casearia arborea
Coussarea hondensis
Cryosophila warscewiczii
Dendropanax arboreus
Euterpe precatoria
Faramea parvibractea
Goethalsia meiantha
Iriartea deltoidea
Laetia procera
Pentaclethra macroloba
Prestoea decurrens
Rinorea deflexiflora
Socratea exorrhiza
Virola sebifera
Warszewiczia coccinea
Welfia regia
Total

Family
No. trees
Capparaceae
74
Salicaceae
206
Rubiaceae
65
Arecaceae
114
Araliaceae
60
Arecaceae
57
Rubiaceae
85
Malvaceae
55
Arecaceae
374
Salicaceae
48
Fabaceae
367
Arecaceae
112
Violaceae
99
Arecaceae
198
Myristicaceae
51
Rubiaceae
86
Arecaceae
173
2173

49

No. observed fruiting
48
123
28
41
5
16
30
30
32
19
188
44
42
40
1
18
76
780

Table 2: Fruit production categories. The range of number of fruit present on a tree
in each category. Six categories were used in field observations, but were collapsed to four
categories for data analysis.
Category Observed range Collapsed range
1
0
0
2
1–10
1–100
3
11–100
101–1,000
4
101–1,000
>1,000
5
1,001–10,000
6
>10,000

50

Table 3: Model evaluation. Evaluation of the alternative models for the binomial regression (Binom), multinomial regression fit to all individuals (AMulti), and multinomial regression fit to reproductive individuals (RMulti). For each model, DIC is reported. Smaller
values of DIC indicate better model fit.

Covariates
Intercept only
DBH
DBH+ soil
DBH + NCI
DBH + ANCI
DBH + soil + NCI
DBH + soil + ANCI

DIC
Binom AMulti RMulti
2419
3489
993
1703
2749
936
1705
2755
929
1670
2728
884
1674
2718
900
1659
2738
888
1679
2732
910

51

Figure 1: 2-dimensional histogram of fruit production, divided by category and
DBH. Number of trees in each fruit production category (vertical axis) for each species
divided into 5-cm DBH classes. Categories are 1: 0 fruit, 2: 1–100 fruits, 3: 101–1,000 fruits,
and 4: >1,000 fruits. Total number of individuals in each size class are to the right of each
graph. This figure shows the size range for each species, how many individuals were in each
fruiting category, and the size distribution for the individuals in each category.

52

Figure 1 (cont’d)

53

Figure 2: Multinomial relationship between DBH and probability of fruit production for each species. Shaded areas represent the probability of each fruit production
category relative to DBH. Darker shaded areas indicate greater fruit production categories.

54

Figure 2 (cont’d)

55

Figure 3: Probability of reproducing as a function of tree diameter. Posterior mean
probability for individual species are presented with 95% credible intervals indicated with
gray shading. Data points are the observed reproductive status of each individual sampled
(ri ).

56

Figure 3 (cont’d)

57

Figure 4: Conspecific basal area vs. average maximum fruiting category by plot
for two species. Each point represents one plot at La Selva, Costa Rica. The average fruit
category of each plot was normalized by the mean size of individuals (as basal area). Simple
linear regressions were performed for each species. R2 and p-values are reported.

58

Appendix B
Tables and figures for Chapter 3
Table 4: Study species in Manistee National Forest, MI. For each species, the number
of individuals measured over all years and sites, and the number of individuals which were
observed fruiting at least once during the study.
Species
Acer rubrum
Acer saccharum
Fagus grandifolia
Fraxinus americana
Populus grandidentata
Prunus serotina
Quercus alba
Quercus rubra/velutina
Tilia americana
Total

Family
No. trees
Aceraceae
423
Aceraceae
284
Fagaceae
205
Oleaceae
57
Salicaceae
148
Rosaceae
37
Fagaceae
193
Fagaceae
231
Tiliaceae
57
1635

59

No. observed fruiting
173
56
89
25
16
23
91
177
43
699

Table 5: Fertilizer application rates. Amount of fertilizer applied annually (g/yr) in
the four different fertilizer treatments of the fertilization study. Micromax R (The Scotts
Company) is a fertilizer containing a suite of micronutrients, including Ca, Mg, manganese
(Mn), molybdenum (Mo), copper (Cu), iron (Fe), and zinc (Zn).
Treatment
Ca
N
Ca + N
Complete

CaSO4
3000
–
3000
2790

(NH4 )2 SO4
–
1900
1900
–

60

NPK (12-12-12)
–
–
–
3325

Micromax
–
–
–
700

Table 6: Model evaluation for the zero-inflated regression on number of fruits
produced using AIC. Smaller AIC values indicate better model fit.
Covariates
AIC
DBH
10053
DBH+ soil
10134
DBH + NCI 16664

61

Table 7: Correlation between seed and newly germinated seedling density. The
correlation was tested at different time lags (0-2 years), allowing for species differences in
the time spent in the seed bank before germination. Pearson’s r is reported, with the largest
positive correlation in bold for each species.
Species
0 years
A. rubrum
-0.24
A. saccharum
-0.24
F. grandifolia
-0.20
F. americana
-0.33
P. serotina
-0.25
Q. alba
-0.28
Q. rubra/velutina
0.20
T. americana
-0.33

62

1 year
-0.07
0.71
0.80
-0.33
0.20
0.57
0.86
0.16

2 years
-0.23
-0.42
-0.27
0.70
-0.32
-0.25
-0.14
<0.01

Table 8: Pearson’s correlation of annual average fruit production from direct
counts with annual seed or seedling density. The number of fruit observed was correlated with seed density from the same year, and seedling density from the following year. For
Fraxinus americana fruit production was correlated with seedling density from the second
following year (see Table 7).
Species
A. rubrum
A. saccharum
F. grandifolia
F. americana
P. serotina
Q. alba
Q. rubra/velutina
T. americana

63

Seed Seedling
0.96
-0.97
0.94
0.96
0.93
0.94
0.99
0.99
0.87
0.95
0.64
0.34
0.14
0.15
0.94
0.76

Table 9: Degree of masting synchrony within species. Synchrony within each species
as the mean of all pairwise Spearman’s correlations (ρs ). For each year, the percent of the
reproductive population (D > Dthres ) which produced more fruit than the average fruit
production necessary for a mast year is shown. This masting threshold was calculated from
the absolute value of the minimum annual deviate of seed density, and the relationship
between direct counts and seed density. Only species with a strong relationship between
direct counts and seed density were included (see Table 8). Mast events are shown in
bold. For species that had two mast or minor mast events, the percentage of reproductive
individuals that produced fruit in both events is shown (Rtw ), as well as the percentage of
the total fruit production these overlapping individuals contributed to the two events (P1 ,
P2 ).
Species
A. rubrum
A. saccharum
F. grandifolia
F. americana
P. grandidentata
P. serotina
Q. alba
Q. rubra/velutina
T. americana

ρs
2008 2009 2010
0.02
–
0.0
0.0
0.73 35.4 0.0
0.0
0.45 13.6 0.0
3.4
0.90
0.0
0.0
0.0
-0.06
0.39
0.0
3.0
6.1
0.59
0.09
0.50
0.0
0.0 40.0

64

2011
Rtw
P1
P2
0.0
10.4 6.3 (3) 46.6 67.5
14.8 8.0 (7) 38.1 63.2
32.6
18.2

14.0

2.0 (1)

6.6

9.5

Figure 5: Probability of reproducing as a function of tree diameter. Posterior mean
probability for (a) all species and (b–h) individual species. Posterior means for individuals
are presented with 95% credible intervals indicated with gray shading. Data are the observed
reproductive status of each individual sampled (ri ).

65

Figure 6: Maximum number of fruit produced by each individual in relation to
stem diameter. The solid trendline represents the mean value of the negative binomial
regression. The gray area surrounded by dashed lines is the 95% credible interval of each
regression.

66

Figure 7: Size at onset of maturity. (a) Probability density function of P (mature) = 0.5
for all species with legend above. (b) Relative size at onset of maturity. Error bars indicate
the 95% credible intervals.

67

Figure 8: Time series of fruit production. Average fruit production (from direct counts of fruit on trees), seed density, and
seedling density observed each year for nine common species in the Manistee National Forest, Michigan, USA. Seedling density
for year t is displayed at year t − 1 to account for the 1-year lag between fruit production and seed germination, except for
F. americana (d), which is displayed at year t − 2. Vertical dashed lines indicate mast years based on seed density.

68

Figure 8 (cont’d)

69
69

Figure 9: Annual density of fruit production. Vertical dashed lines indicate the average
fruit production in a mast year based on all individuals in the population (left), or only the
individuals above the reproductive size threshold (right).

70

Figure 9 (cont’d)

71

Appendix C
Model Evaluation for Chapter 2
We compared models using deviance information criterion (DIC) for both the binomial and
multinomial models. DIC is smaller for better fitting models and includes a penalty for
additional parameters (Spiegelhalter et al. 2002).
Because I am interested in being able to predict fruit output, I also used proper scoring
rules to compare and assess alternative models. Proper scoring rules are used to evaluate the
quality of predictions made from probabilistic models. They provide a measure of predictive
performance of the model based on observed data and the predictive distribution, π =
{πi , . . . , πK } (Gneiting and Raftery 2007). The scoring rule function S(π, i) was calculated
for each individual i in a holdout set. The holdout set consisted of 100 individuals from the
full dataset which was used in the binomial and complete multinomial models. A holdout
set of 75 individuals was used from the subset of reproductive individuals. It is common
to use multiple scoring rules to evaluate a model, each of which incorporates information
from the observed data and predictive distribution in a different way. Four scoring rules for

72

categorical variables were used:

Zero-one: S(π, i) =





1 if πi = max{π1 , . . . , πK }

(1)




0 if otherwise
K

πk2 − 1

Quadratic: S(π, i) = 2πi −

(2)

k=1

πi

Spherical: S(π, i) =
(

1
K
2) 2
π
k=1 k

Logarithmic: S(π, i) = log πi

(3)

(4)

The zero-one rule (Equation 1) ignores variability in the predictive distribution, returning
zero or one for each individual, resulting in the rate at which the correct category was predicted. The logarithmic rule (Equation 4) also uses a limited amount of information, being
based only on the probability of the category of which individual i is a part. The quadratic
and spherical rules (Equations 2–3) incorporate information from the entire predictive distribution, evaluating the probability of predicting the correct category in relation to the
probability of predicting incorrect categories. Higher scores indicate better predictive performance. For the zero-one and spherical rules this means scores closer to 1, but for the
quadratic and logarithmic rules (which are negative) this means scores closer to zero. The
median and 95% credible intervals were obtained for the posterior mean of each scoring rule.

73

Table 10: Model evaluation for the binomial regression. For each model, DIC and the median and 95% credible intervals
of four proper scoring rules are reported. For DIC, smaller values indicate better model fit. For proper scoring rules, larger
values indicate better predictive performance of the model.
Covariates
Intercept only
DBH
DBH+ soil
DBH + NCI
DBH + ANCI
DBH + soil + NCI
DBH + soil + ANCI

DIC
2419
1703
1705
1670
1674
1659
1679

0.28
0.14
0.15
0.14
0.13
0.16
0.13

Zero-one
0.30 0.34
0.15 0.17
0.21 0.33
0.20 0.33
0.15 0.18
0.21 0.29
0.16 0.19

Quadratic
-0.98 -0.94 -0.90
-1.30 -1.24 -1.19
-1.27 -1.13 -0.95
-1.34 -1.23 -1.01
-1.29 -1.22 -1.16
-1.37 -1.26 -1.12
-1.29 -1.23 -1.17

74

Spherical
0.46 0.47 0.49
0.30 0.32 0.34
0.31 0.37 0.47
0.29 0.33 0.45
0.30 0.33 0.35
0.28 0.33 0.39
0.30 0.32 0.35

Logarithmic
-1.31 -1.22 -1.13
-2.51 -2.21 -2.00
-2.47 -2.05 -1.70
-3.88 -2.32 -1.91
-2.47 -2.17 -1.94
-6.27 -2.76 -2.09
-2.53 -2.25 -2.01

Table 11: Model evaluation for the multinomial regression fit to all individuals. For each model, DIC and the median
and 95% credible intervals of four proper scoring rules are reported. For DIC, smaller values indicate better model fit. For
proper scoring rules, larger values indicate better predictive performance of the model.
Covariates
Intercept only
DBH
DBH+ soil
DBH + NCI
DBH + ANCI
DBH + soil + NCI
DBH + soil + ANCI

DIC
3489
2749
2755
2728
2718
2738
2732

0.63
0.74
0.73
0.74
0.75
0.73
0.74

Zero-one
0.68 0.68
0.77 0.79
0.76 0.79
0.77 0.79
0.77 0.80
0.76 0.79
0.78 0.80

Quadratic
-0.45 -0.43 -0.42
-0.34 -0.32 -0.31
-0.35 -0.33 -0.32
-0.34 -0.32 -0.31
-0.34 -0.33 -0.32
-0.36 -0.34 -0.32
-0.35 -0.33 -0.32

75

Spherical
0.73 0.74 0.75
0.80 0.81 0.82
0.79 0.80 0.81
0.80 0.81 0.82
0.80 0.81 0.82
0.79 0.80 0.81
0.80 0.81 0.82

Logarithmic
-0.79 -0.77 -0.74
-0.60 -0.58 -0.56
-0.63 -0.60 -0.57
-0.61 -0.58 -0.55
-0.62 -0.60 -0.57
-0.63 -0.60 -0.57
-0.63 -0.60 -0.57

Table 12: Model evaluation for the multinomial regression fit to only reproductive individuals. For each model,
DIC and the median and 95% credible intervals of four proper scoring rules are reported. For DIC, smaller values indicate
better model fit. For proper scoring rules, larger values indicate better predictive performance of the model.
Covariates
Intercept only
DBH
DBH+ soil
DBH + NCI
DBH + ANCI
DBH + soil + NCI
DBH + soil + ANCI

DIC
Zero-one
Quadratic
993 0.68 0.71 0.73 -0.42 -0.40 -0.38
936 0.68 0.72 0.75 -0.40 -0.38 -0.36
929 0.68 0.72 0.76 -0.42 -0.39 -0.36
884 0.65 0.71 0.75 -0.42 -0.39 -0.37
900 0.61 0.69 0.75 -0.54 -0.41 -0.37
888 0.67 0.72 0.76 -0.42 -0.39 -0.36
910 0.64 0.71 0.75 -0.49 -0.42 -0.37

76

Spherical
0.75 0.77 0.78
0.77 0.78 0.80
0.76 0.78 0.79
0.75 0.77 0.79
0.69 0.76 0.79
0.76 0.78 0.79
0.72 0.76 0.79

Logarithmic
-0.67 -0.63 -0.60
-0.64 -0.61 -0.58
-0.68 -0.63 -0.58
-0.67 -0.62 0.58
-1.18 -0.68 -0.60
-0.67 -0.62 -0.58
-0.95 -0.67 -0.60

Appendix D
Site level fruit production
relationships for Chapter 2

77

Figure 10: Conspecific basal area vs. average maximum fruiting category by plot
for each species. Each point represents one plot at La Selva, Costa Rica. The average
fruit category of each plot was normalized by the mean size of individuals (as basal area).
Simple linear regressions were performed for each species. R2 and p-values are reported.

78

Figure 10 (cont’d)

79

Figure 11: Conspecific basal area vs. probability of fruit production by plot for
each species. Each point represents one plot. Each point represents one plot at La
Selva, Costa Rica. The probability of fruiting for each plot was normalized by the mean size
of individuals (as basal area). Simple linear regressions were performed for each species. R2
and p-values are reported.

80

Figure 11 (cont’d)

81

Figure 12: Nitrogen mineralization rate vs. average maximum fruiting category
by plot for each species. Each point represents one plot at La Selva, Costa Rica. Simple
linear regressions were performed for each species. R2 and p-values are reported.

82

Figure 12 (cont’d)

83

Figure 13: Nitrogen mineralization rate vs. probability of fruit production by plot
for each species. Each point represents one plot at La Selva, Costa Rica. Simple linear
regressions were performed for each species. R2 and p-values are reported.

84

Figure 13 (cont’d)

85

Figure 14: Phosphorus availability vs. average maximum fruiting category by plot
for each species. Each point represents one plot at La Selva, Costa Rica. Simple linear
regressions were performed for each species. R2 and p-values are reported.

86

Figure 14 (cont’d)

87

Figure 15: Phosphorus availability vs. probability of fruit production by plot for
each species. Each point represents one plot at La Selva, Costa Rica. Simple linear
regressions were performed for each species. R2 and p-values are reported.

88

Figure 15 (cont’d)

89

Figure 16: Sum of base cation availability vs. average maximum fruiting category
by plot for each species. Each point represents one plot at La Selva, Costa Rica. Simple
linear regressions were performed for each species. R2 and p-values are reported.

90

Figure 16 (cont’d)

91

Figure 17: Sum of base cation availability vs. probability of fruit production by
plot for each species. Each point represents one plot at La Selva, Costa Rica. Simple
linear regressions were performed for each species. R2 and p-values are reported.

92

Figure 17 (cont’d)

93

BIBLIOGRAPHY

94

BIBLIOGRAPHY
Baribault, T. and Kobe, R. (2011). Neighbour interactions strengthen with increased soil
resources in a northern hardwood forest. Journal of Ecology, 99:1358–1372.
Baribault, T. W. (2011). Revisiting soil resource limitation: Resource predictors of tree
growth and forest productivity change across ecological gradients. PhD thesis, Michigan
State University.
Baribault, T. W., Kobe, R. K., and Finley, A. O. (2012). Tropical tree growth is correlated
with soil phosphorus , potassium , and calcium , though not for legumes. Ecological
Monographs, 82(2):189–203.
Baribault, T. W., Kobe, R. K., and Rothstein, D. E. (2010). Soil calcium, nitrogen, and
water are correlated with aboveground net primary production in northern hardwood
forests. Forest Ecology and Management, 260:723–733.
Bazzaz, F. A., Chiariello, N. R., Coley, P. D., and Pitelka, L. F. (1987). Allocating resources
to reproduction and defense. BioScience, 37(1):58–67.
Bishnoi, U. R., G, K., and Khan, M. H. (2007). Calcium, Phosphorus, and Harvest Stages
Effects Soybean Seed Production and Quality. Journal of Plant Nutrition, 30:2119–2127.
Buonaccorsi, J. P., Elkinton, J. S., Evans, S. R., and Liebhold, A. M. (2001). Measuring and
testing for spatial synchrony. Ecology, 82(6):1668–1679.
Burnham, K. P. and Anderson, D. R. (2002). Model Selection and Multimodel Inference: A
Practical Information-Theoretic Approach. Springer-Verlag, New York.
Burton, M. G., Laver, M. J., and McDonald, M. B. (2000). Calcium effects on soybean seed
production, Elemental concentration, and seed quality. Crop Science, 40:476–482.
Callahan, H. S., Del Fierro, K., Patterson, A. E., and Zafar, H. (2008). Impacts of elevated
nitrogen inputs on oak reproductive and seed ecology. Global Change Biology, 14(2):285–
293.
Canham, C. D., Papaik, M. J., Uriarte, M., Mcwilliams, W. H., Jenkins, J. C., and Twery,
M. J. (2006). Neighborhood analyses of canopy tree competition along environmental
gradients in New England forests. Ecological Applications, 16(2):540–544.
Carbone, M. S., Czimczik, C. I., Keenan, T. F., Murakami, P. F., Pederson, N., Schaberg,
P. G., Xu, X., and Richardson, A. D. (2013). Age, allocation and availability of nonstructural carbon in mature red maple trees. The New phytologist.

95

Caspersen, J. P. and Saprunoff, M. (2005). Seedling recruitment in a northern temperate
forest : the relative importance of supply and establishment limitation. Canadian Journal
of Forest Research, 35:978–989.
Chapman, C. A., Chapman, L. J., Wangham, R., Hunt, K., Gebo, D., and Gardner, L.
(1992). Estimators of Fruit Abundance of Tropical Trees. Biotropica, 24(4):527–531.
Charlesworth, D. and Morgan, M. T. (1991). Allocation of Resources to Sex Functions in
Flowering Plants. Philosophical Transactions of the Royal Society B: Biological Sciences,
332(1262):91–102.
Chazdon, R. L., Careaga, S., Webb, C., and Vargas, O. (2003). Community and phylogenetic structure of reproductive traits of woody species in wet tropical forests. Ecological
Monographs, 73(3):331–348.
Chidumayo, E. N. (1997). Fruit Production and Seed Predation in Two Miombo Woodland
Trees in Zambia. Biotropica, 29(4):452–458.
Clark, J. S., Bell, D., Chu, C., Courbaud, B., Dietze, M., Hersh, M., HilleRisLambers, J.,
Ib´an
˜ez, I., LaDeau, S., McMahon, S., Metcalf, J., Mohan, J., Moran, E., Pangle, L.,
Pearson, S., Salk, C., Shen, Z., Valle, D., and Wyckoff, P. (2010). High-dimensional
coexistence based on individual variation: a synthesis of evidence. Ecological Monographs,
80(4):569–608.
Clark, J. S., Ladeau, S., and Ibanez, I. (2004). Fecundity of Trees and the ColonizationCompetition Hypothesis. Ecological Monographs, 74(3):415–442.
Crookston, N. L. and Finley, A. O. (2008). yaImpute : An R Package for kNN Imputation.
Journal Of Statistical Software, 23(10):1–16.
De Steven, D. and Wright, S. J. (2002). Consequences of variable reproduction for seedling
recruitment in three neotropical tree species. Ecology, 83(8):2315–2327.
Diggle, P. and Lophaven, S. (2006). Bayesian Geostatistical Design. Scandinavian Journal
of Statistics, 33(1):53–64.
Dordas, C. (2006). Foliar Boron Application Improves Seed Set, Seed Yield, and Seed Quality
of Alfalfa. Agronomy Journal, 98:907–913.
Drenovsky, R. E. and Richards, J. H. (2005). Nitrogen addition increases fecundity in the
desert shrub Sarcobatus vermiculatus. Oecologia, 143:349–356.
Fleming, T. H., Breitwisch, R., and Whitesides, G. H. (1987). Patterns of tropical vertebrate
frugivore diversity. Annual Review of Ecology and Systematics, 18:91–109.
Garcia, D., Zamora, R., Gomez, J. M., Jordano, P., and Hodar, J. A. (2000). Geographical
variation in seed production, predation and abortion in Juniperus communis throughout
its range in Europe. Journal of Ecology, 88:436–446.

96

Gelman, A. and Rubin, D. B. (1992). Inference from Iterative Simulation Using Multiple
Sequences. Statistical Science, 7(4):457–472.
Gneiting, T. and Raftery, A. E. (2007). Strictly Proper Scoring Rules, Prediction, and
Estimation. Journal of the American Statistical Association, 102(477):359–378.
Gonz´alez-Mart´ınez, S. C., Burczyk, J., Nathan, R., Nanos, N., Gil, L., and Al´ıa, R. (2006).
Effective gene dispersal and female reproductive success in Mediterranean maritime pine
(Pinus pinaster Aiton). Molecular ecology, 15(14):4577–88.
Gradowski, T. and Thomas, S. C. (2008). Responses of Acer saccharum canopy trees and
saplings to P, K and lime additions under high N deposition. Tree physiology, 28(2):173–85.
Greene, D. F. and Johnson, E. A. (1994). Estimating the Mean Annual Seed Production of
Trees. Ecology, 75(3):642–647.
Greene, D. F., Messier, C., Asselin, H., and Fortin, M.-J. (2002). The effect of light availability and basal area on cone production in Abies balsamea and Picea glauca. Canadian
Journal of Botany, 80:370–377.
Hampe, A. (2005). Fecundity limits in Frangula alnus (Rhamnaceae) relict populations at
the species’ southern range margin. Oecologia, 143(3):377–86.
Han, Q., Kabeya, D., and Hoch, G. (2011). Leaf traits, shoot growth and seed production in mature Fagus sylvatica trees after 8 years of CO2 enrichment. Annals of botany,
107(8):1405–11.
Han, Q., Kabeya, D., Iio, A., and Kakubari, Y. (2008). Masting in Fagus crenata and its
influence on the nitrogen content and dry mass of winter buds. Tree physiology, 28(8):1269–
76.
Herrera, C. M. (1998). Population-level estimates of interannual variability in seed production : What do they actually tell us ? Oikos, 82(3):612–616.
Herrera, C. M. and Jovani, R. (2010). Lognormal distribution of individual lifetime fecundity:
insights from a 23-year study. Ecology, 91(2):422–30.
Hertel, D., Leuschner, C., and H¨olscher, D. (2003). Size and Structure of Fine Root Systems in Old-growth and Secondary Tropical Montane Forests (Costa Rica). Biotropica,
35(2):143–153.
HilleRisLambers, J., Harpole, W. S., Schnitzer, S., Tilman, D., and Reich, P. B. (2009).
CO2, nitrogen, and diversity differentially affect seed production of prairie plants. Ecology,
90(7):1810–1820.
Holste, E. K. (2010). The effects of spatially heterogeneous irradiance and soil resourcs on
neotropical seedling growth. PhD thesis, Michigan State University.

97

Host, G. E. and Pregitzer, K. S. (1992). Geomorphic influences on ground-flora and overstory
composition in upland forests of northwestern lower Michigan. Canadian Journal of Forest
Research, 22:1547–1555.
Host, G. E., Pregitzer, K. S., Ramm, C. W., Lusch, D. P., and Cleland, D. T. (1988). Variation in overstory biomass among glacial landforms and ecological land units in northwestern Lower Michigan. Canadian Journal of Forest Research, 18:659–668.
Hubbell, S. P., Foster, R. B., O’Brien, S. T., Harms, K. E., Condit, R., Wechsler, B., Wright,
S. J., and Loo de Lao, S. (1999). Light-gap disturbances, recruitment limitation, and tree
diversity in a neotropical forest. Science, 283(5401):554–557.
Ibanez, I., Clark, J. S., LaDeau, S., and Hille Ris Lambers, J. (2007). Exploiting temporal variability to understand tree recruitment response to climate change. Ecological
Monographs, 77(2):163–177.
Ichie, T., Igarashi, S., Yoshida, S., Kenzo, T., Masaki, T., and Tayasu, I. (2013). Are stored
carbohydrates necessary for seed production in temperate deciduous trees? Journal of
Ecology, 101:525–531.
Ichie, T. and Nakagawa, M. (2011). Dynamics of mineral nutrient storage for mast reproduction in the tropical emergent tree Dryobalanops aromatica. Ecological Research,
28(2):151–158.
Jensen, P. G., Demers, C. L., Mcnulty, S. a., Jakubas, W. J., and Humphries, M. M. (2012).
Marten and fisher responses to fluctuations in prey populations and mast crops in the
northern hardwood forest. The Journal of Wildlife Management, 76(3):489–502.
Joe, H. and Zhu, R. (2005). Generalized Poisson distribution: The property of mixture
of Poisson and comparison with Negative Binomial distribution. Biometrical Journal,
47(2):219–229.
¨
Karlsson, C. and Orlander,
G. (2002). Mineral nutrients in needles of Pinus sylvestris seed
trees after release cutting and their correlations with cone production and seed weight.
Forest Ecology and Management, 166(1-3):183–191.
Kaspari, M., Garcia, M. N., Harms, K. E., Santana, M., Wright, S. J., and Yavitt, J. B.
(2008). Multiple nutrients limit litterfall and decomposition in a tropical forest. Ecology
Letters, 11(1):35–43.
Kelly, D. (1994). The evolutionary ecology of mast seeding. Trends in Ecology & Evolution,
9(12):465–470.
Kelly, D. and Sork, V. L. (2002). Mast seeding in perennial plants: Why, how, where?
Annual Review of Ecology and Systematics, 33(1):427–447.
Knight, T. M., Steets, J. a., Vamosi, J. C., Mazer, S. J., Burd, M., Campbell, D. R., Dudash,
M. R., Johnston, M. O., Mitchell, R. J., and Ashman, T.-L. (2005). Pollen limitation of
plant reproduciton: Pattern and Process. Annual Review of Ecology, Evolution, and
Systematics, 36(1):467–497.
98

Koenig, W. D., Kelly, D., Sork, V. L., Duncan, R. P., Elkinton, J. S., Peltonen, M. S.,
and Westfall, R. D. (2003). Dissecting components of population-level variation in seed
production and the evolution of masting behavior. Oikos, 102(3):581–591.
LaMontagne, J. M. and Boutin, S. (2007). Local-scale synchrony in mast seed and variability
production patterns of Picea glauca. Journal of Ecology, 95(5):991–1000.
LaMontagne, J. M. and Boutin, S. (2009). Quantitative methods for defining mast-seeding
years across species and studies. Journal of Vegetation Science, 20:745–753.
Li, Y., Xu, M., and Zou, X. (2006). Effects of nutrient additions on ecosystem carbon cycle
in a Puerto Rican tropical wet forest. Global Change Biology, 12(2):284–293.
Lovett, G. M., Arthur, M. a., Weathers, K. C., Fitzhugh, R. D., and Templer, P. H. (2013).
Nitrogen addition increases carbon storage in soils, but not in trees, in an Eastern U.S.
deciduous forest. Ecosystems, 16(6):980–1001.
Lunn, D. J., Thomas, A., Best, N., and Spiegelhalter, D. (2000). WinBUGS A Bayesian
modelling framework: Concepts, structure, and extensibility. Statistics and Computing,
10:325–337.
Magill, A. H., Aber, J. D., Berntson, G. M., McDowell, W. H., Nadelhoffer, K. J., Melillo,
J. M., and Steudler, P. (2000). Long-Term Nitrogen Additions and Nitrogen Saturation
in Two Temperate Forests. Ecosystems, 3(3):238–253.
Martin, T. G., Wintle, B. a., Rhodes, J. R., Kuhnert, P. M., Field, S. a., Low-Choy, S. J.,
Tyre, A. J., and Possingham, H. P. (2005). Zero tolerance ecology: improving ecological
inference by modelling the source of zero observations. Ecology Letters, 8(11):1235–1246.
McDade, L. A. and Hartshorn, G. S. (1994). La Selva: Ecology and Natural History of
Neotropical Rain Forest. University of Chicago Press, Chicago, Illinois.
Milton, K., Giacalone, J., Wright, S. J., and Stockmayer, G. (2005). Do frugivore population
fluctuations reflect fruit production? Evidence from Panama. In Dew, J. L. and Boubli,
J. P., editors, Tropical Fruits and Frugivores: The Search for Strong Interactors, chapter 2,
pages 5–35. Springer, 2005.
Monks, A. and Kelly, D. (2006). Testing the resource-matching hypothesis in the mast
seeding tree Nothofagus truncata ( Fagaceae ). Austral Ecology, 31:366–375.
Moran, E. V. and Clark, J. S. (2011). Estimating seed and pollen movement in a monoecious
plant: a hierarchical Bayesian approach integrating genetic and ecological data. Molecular
Ecology, 20(6):1248–62.
Moran, E. V. and Clark, J. S. (2012). Causes and consequences of unequal seedling production in forest trees : a case study in red oaks. Ecology, 93(5):1082–1094.
Moran, E. V., Willis, J., and Clark, J. S. (2012). Genetic evidence for hybridization in red
oaks (Quercus sect. Lobatae, Fagaceae). American journal of botany, 99(1):92–100.
99

Ostfeld, R. S., Jones, C. G., and Wolff, J. O. (1996). Of mice and mast. BioScience,
46(5):323–330.
Owens, J. N. (1995). Constraints to seed production: temperate and tropical forest trees.
Tree physiology, 15(7 8):477–484.
Pastor, J., Aber, J. D., McClaugherty, C. A., and Melillo, J. M. (1984). Aboveground
production and N and P cycling along a nitrogen mineralization gradient on Blackhawk
Island, Wisconsin. Ecology, 65(1):256–268.
Pigott, C. D. and Huntley, J. P. (1981). Factors controlling the distribution of Tilia cordata
at the northern limits of its geographical range: III. Nature and causes of seed sterility.
New Phytologist, 87:817–839.
Pregitzer, K. S. and Burton, A. J. (1991). Sugar maple seed production and nitrogen in
litterfall. Canadian Journal of Forest Research, 21:1148–1153.
Primack, R. B. and Kang, H. (1989). Measuring fitness and natural selection in wild plant
populations. Annual Review of Ecology and Systematics, 20:367–396.
R Core Team (2013). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria.
Satake, A. and Bjørnstad, O. N. (2008). A resource budget model to explain intraspecific
variation in mast reproductive dynamics. Ecological Research, 23(1):3–10.
Silvertown, J., Franco, M., and Perez-ishiwara, R. (2001). Evolution of senescence in
iteroparous perennial plants. Evolutionary Ecology Research, 3:393–412.
Silvertown, J. W. (1980). The evolutionary ecology of mast seeding in trees. Biological
Journal of the Linnaean Society, 14:235–250.
Snook, L. K., C´amara-Cabrales, L., and Kelty, M. J. (2005). Six years of fruit production
by mahogany trees (Swietenia macrophylla King): patterns of variation and implications
for sustainability. Forest Ecology and Management, 206(1-3):221–235.
Spiegelhalter, D. J., Best, N. G., Carlin, B. P., and van der Linde, A. (2002). Bayesian
measures of model complexity and fit. Journal of the Royal Statistical Society: Series B
(Statistical Methodology), 64(4):583–639.
Stan Development Team (2013). Stan: A c++ library for probability and sampling, version
2.0.
Svenning, J.-C. and Wright, S. J. (2005). Seed limitation in a Panamanian forest. Journal
of Ecology, 93(5):853–862.
Thomas, S. C. (1996a). Asymptotic height as a predictor of growth and allometric characteristics in Malaysian rain forest trees. American journal of botany, 83(5):556–566.

100

Thomas, S. C. (1996b). Relative size at onset of maturity in rain forest trees : a comparative
analysis of 37 Malaysian species. Oikos, 76(1):145–154.
Turnbull, L. A., Crawley, M. J., and Rees, M. (2000). Are plant populations seed-limited ?
A review of seed sowing experiments. Oikos, 88:225–238.
Venable, D. L. (1992). Size-number trade-offs and the variation of seed size with plant
resource status. The American Naturalist, 140(2):287–304.
Vitousek, P. M. and Howarth, R. W. (1991a). Nitrogen limitation on land and in the sea :
How can it occur ? Biogeochemistry, 13(2):87–115.
Vitousek, P. M. and Howarth, R. W. (1991b). Nitrogen limitation on land and in the sea:
How can it occur ? Biogeochemistry, 13(2):87–115.
Vitousek, P. M., Porder, S., Houlton, B. Z., and Chadwick, O. A. (2010). Terrestrial phosphorus limitation: mechanisms, implications, and nitrogen-phosphorus interactions. Ecological
applications, 20(1):5–15.
Wesselingh, R. A., Klinkhamer, P. G. L., de Jong, T. J., and Boorman, L. A. (1997).
Threshold size for flowering in different habitats: Effects of size-dependent growth and
survival. Ecology, 78(7):2118–2132.
Wright, S. J., Carrasco, C., Calderon, O., and Paton, S. (1999). The El Nino Southern
Oscillation, variable fruit production, and famine in a tropical forest. Ecology, 80(5):1632–
1647.
Wright, S. J., Jaramillo, M. A., Pavon, J., Condit, R., Hubbell, S. P., and Foster, R. B.
(2005). Reproductive size thresholds in tropical trees: variation among individuals, species
and forests. Journal of Tropical Ecology, 21(3):307–315.
Wright, S. J., Yavitt, J. B., Wurzburger, N., Turner, B. L., Tanner, E. V. J., Sayer, E. J.,
Santiago, L. S., Kaspari, M., Hedin, L. O., Harms, K. E., Garcia, M. N., and Corre, M. D.
(2011). Potassium , phosphorus , or nitrogen limit root allocation , tree growth , or litter
production in a lowland tropical forest. Ecology, 92(8):1616–1625.
Zak, D. R., Host, G. E., and Pregitzer, K. S. (1989). Regional variability in nitrogen mineralization, nitrification, and overstory biomass in northern Lower Michigan. Canadian
Journal of Forest Research, 19:1521–1526.
˙
Zywiec,
M., Holeksa, J., and Ledwo, M. (2012). Population and individual level of masting
in a fleshy-fruited tree. Plant Ecology, pages 993–1002.

101