Development of an individual-based model of frugivory to study the effects of defaunation on carbon storage in a tropical forest

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Research Project I

Development of an individual-based model of frugivory to study the effects

of defaunation on carbon storage in a tropical forest

Amalia Llano

42 EC

Contact email: amallanbo@gmail.com Student number: 12162337

Master’s Earth Sciences

Future Planet Ecosystems Science Track

Supervisor / Examiner: dr. rer. nat. Daniel Kissling Assessor: dhr. prof. dr. ir. Willem Bouten

Universiteit van Amsterdam | IBED | BIOMAC June 2019 – January 2020

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Summary

Frugivory is a mutualistic interaction in which frugivorous animals benefit from the nutrition provided by fleshy fruits while the dispersal services they offer favour the establishment and regeneration of plant populations. Frugivory has also been recently found to play an important role in modulating ecosystems services like the carbon storage capacity of tropical forests, since it plays a key role in structuring plant communities, their functional traits, and their dynamics. Here I constructed an individual-based model of an idealised patch of tropical forest to explore how frugivory is related to the carbon storage capacity of this ecosystem. I also used the model to evaluate the consequences of the defaunation of frugivores of different sizes on carbon storage and on the plant community’s functional-trait composition under different scenarios. I found that complete defaunation alone appears to have no qualitative effects on short-term carbon storage capacity in the modelled forest, but that the loss of frugivores could be detrimental to the extent of the plant community’s ability to colonise space (evidenced by a reduced number of trees per hectare). My results also indicate that in scenarios where heavy logging was included, the presence of frugivores seemed to moderately offset the effects of logging on stored carbon and on the mean number of trees per hectare. Although appearing to have relatively slight effects in the short-term, I also found that defaunation, specifically when it targets large frugivores, can change the functional composition of the tree community in the forest favouring fast-growing, light-wooded trees with small fruits. The results I present and my model, although limited and requiring future improvements to make my findings more robust, demonstrate that agent-based models have potential to be used as tools to study the effects of human action on complex, multi-scale processes like frugivory that are essential to ecosystems services.

Introduction

The presence of humans on the planet has had profound consequences. From ocean acidification to landscape fragmentation, biodiversity loss, and climate change, anthropogenic activities have altered the Earth’s ecosystems and geological cycles so significantly that they have come to define a new epoch, the Anthropocene (Otto, 2018; Dirzo, et al., 2014). The Anthropocene is characterised by what is known as ‘global change’, which broadly refers to the biophysical and socioeconomic changes that alter the functioning of the Earth system. Global change involves land use and land cover changes, urbanisation, globalisation, changes in atmospheric composition, climate, and geochemical cycles, biodiversity loss, resource depletion, and pollution, among others. Moreover, most of these changes are complex in nature, interrelated, and show strong nonlinearities (Steffen, Crutzen, & McNeill, 2008).

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5 Global change and human impact have degraded ecosystems and the life-supporting services they provide so extensively, that it is now accepted that life on Earth and the future of contemporary societies are at risk (Steffen, Crutzen, & McNeill, 2008). It has therefore become paramount to understand, predict, and mitigate anthropogenic impacts through the use of a variety of tools, including policy instruments, conservation measures, and scientific research (Harfoot, et al., 2014). Particularly, scientific research needs to address the way in which small-magnitude ecological processes scale up to Earth systems like climate, ocean circulation, and the water cycle (Mace, 2013), while registering the complexity and nonlinearities typical of these processes.

This scenario demands the development, among other things, of mechanistic ecological models that use accessible measurements and parameters to explain and, most importantly, to predict, the effects and outcomes of different global change scenarios on ecosystems and their services. These models, embedded within a systems theory framework, ought to span more than one level of complexity and should also aim to capture how processes at the individual scale, including species interactions, can lead to emergent behaviour at higher levels of complexity (especially at a global scale). Additionally, they should combine the predictive power of process-based models with empirical information and the accuracy of conventional measurement-based models (Landsberg, 2003). Models like these, which explicitly represent the biological, physiological, and ecological mechanisms that underly a system’s functioning, are and will be instrumental to policy and decision-making in the context of global change (Harfoot, et al., 2014).

Individual-based models have been applied in ecology for more than four decades and their use has grown rapidly in recent years as a response to this urgent need for mechanistic models that can capture emergent behaviour, have an empirical component, and are relatively easy to interpret and utilise. These models, also called agent-based models, assume populations and systems of populations that are composed of discrete, individual organisms that have unique sets of state variables (attributes) and behaviours (DeAngelis & Grimm, 2014). The combination and interaction of different individuals gives rise to emergent phenomena at a system-wide scale, allowing these models to capture a rich set of complex behaviours, patterns and interactions, at a scale different to the one in which the modelling rules are defined (Berryman & Angus, 2010). Agent-based modelling is a good complement to the more traditional way of modelling systems using differential equations, because these models can not only incorporate and follow a large range of different types of agents, but they can also capture behaviours and processes that are difficult to include in traditional modelling approaches, such as agent learning or evolution and non-linear interactions between agents (Berryman & Angus, 2010; DeAngelis & Grimm, 2014). These models are also well-suited to

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6 test various hypotheses because they can rule out emergent possibilities given a specific set of rules, and they can provide a platform to generate new hypotheses or falsify predictions (Berryman & Angus, 2010; Popper, 1972).

Given the flexibility of agent-based models, their ability to simulate the behaviour of a large range of agents, and their capacity to capture emergent behaviour through sets of relatively simple rules, they are an appropriate approach for studying ecological processes that directly impact ecosystem services and, therefore, that are linked to the challenges associated with global change. One of these processes is frugivory, a mutualistic relationship in which frugivorous animals benefit from the nutritional content of fleshy fruits, while the dispersal services they offer favour the establishment and regeneration of plant populations. Recent evidence suggests that the defaunation of large frugivores could be indirectly and negatively affecting the carbon storage capacity of tropical forests where animal-dispersed plants are abundant (Bello, et al., 2015; Osuri, et al., 2016). The rationale behind this finding is that eliminating large fruit-eaters limits the recruitment of species with large seeds, which also tend to have denser wood, because large frugivores are the only ones that can handle and disperse their large propagules. This shift in recruitment leads to compositional changes in the plant community that favour small-fruited plants with lower densities. This results in an alteration of the community-aggregated values of wood density and height, and in a reduction in the carbon storage capacity of the forest. Although there is a growing amount of evidence that supports this reasoning in specific simulated scenarios, the magnitudes, spatial extents, and time frames of these compositional changes need to be examined further.

To take a step towards reducing this knowledge gap, in this project I propose a new mechanistic, temporally and spatially explicit individual-based model that uses empirical data and allometric relations and that captures the essential features of frugivory. This model is specifically designed to study the relationship between frugivory, the functional trait composition of the plant community (in terms of traits like diameter, wood density, and growth speed), and selected dynamics of this ecosystem. In addition to proposing the new agent-based model, I use it to perform a preliminary evaluation of the effects that different defaunation scenarios have on both the carbon storage capacity and the functional composition of the plant community of an idealised, one-hectare plot of terra firme moist tropical forest of the Brazilian Central Amazonia.

Methods

To make the agent-based model, I first reviewed relevant literature to identify what processes, agents, and relationships were the most important components of frugivory and its interactions. Subsequently, I wrote an initial outline of the model, in which each of the main

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7 processes and agents were included in a very simple formulation. After analysing this simple model’s behaviour, I expanded some of the modelled procedures to include, for example, tree growth, allometric relations, and calculations of carbon storage. Following the construction of the more detailed version of the model, I crosschecked its parameters and processes with relevant literature to improve its realism and precision. Finally, once the model’s parameters and numbers were as consistent as possible with published literature, I carried out a series of

in-silico experiments to evaluate the effect of defaunation on the carbon storage capacity of a

tropical forest under different scenarios, including different types of defaunation and pressures from heavy logging. The following sections summarise the model and the formulation of the

in-silico experiments, as well as the analysis of their results. Additional details on the model’s

parameters, processes, sub-models, etc. can be found in Appendix I following the ODD Protocol (Grimm, et al., 2010).

Building an individual-based model of tropical forests

The first step taken to make the individual-based model was to identify the relevant processes, relationships, variables, and agents that needed to be included in its formulation. The main goal of the project was to capture how the strategies used by trees to reproduce through frugivore mediation are related to the composition of the plant community and to carbon storage. Therefore, there was a clear need to include in the model a well-structured plant community that differed in functional traits related to carbon storage and to fruit production. Moreover, the model had to be structured to reflect differences in frugivore sizes and movement ranges, so that it could be used to simulate the differential dispersal of large and small fruits and seeds. Finally, it was also important to reflect on how to best implement and write the model. This included deciding on a programming language that would allow me to effectively follow agents or track changes in the composition and traits of the plant community, for example. The following sections summarise the main structure of the individual-based model, and emphasise its basic principles, agents, processes and relations.

NetLogo

I chose to write this model in NetLogo (Wilensky, 1999), a modelling environment specifically designed to build agent-based models. NetLogo has an easily-accessible structure to represent agents, as well as a high-level language composed of less than 500 words, a visual interface, and several extensions that can be used to broaden the language (Bauduin, McIntire, & Chubaty, 2019). This, along with its ease of use and the fact that many actions are already pre-coded in the language, made it an ideal language to implement the frugivory agent-based model.

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Agents and functional groups

The agent-based model considers four types of agents: fruits, trees, seeds, and frugivores. Each of these main categories of agents is divided into functional groups, according to traits that vary between agents (see Figure 1, which summarises all the functional groups for the four types of agents). Trees are divided according to whether they produce fleshy fruits that are dispersed by zoochory (referred to as ‘fruiting’ from here on) or not (referred to as ‘nonfruiting’ from here on). Nonfruiting trees were modelled to represent trees that produce fruits dispersed by other means, here represented as seeds for simplicity, and trees that produce naked seeds.

Each of these categories of trees is further divided according to wood density, into trees with low wood densities (light) and trees with high wood densities (dense). Each of these categories was additionally linked to one of two life strategies, so that trees regarded as light are assumed to be fast-growing, while trees classified as dense are assumed to be slow-growing (see the section on Tree diameter, tree growth rate, and wood density for more detail). Trees are sorted into each wood-density category based on how each tree’s individual wood density compares to a published community mean of a Brazilian rainforest (Cavanaugh, et al., 2014); if the tree’s wood density is less than or equal to the mean, the tree is regarded as light, and if it is above the mean, it is considered to be dense. Finally, each of these is further classified according to fruit size, into trees that produce large fruits, and trees that produce small fruits.

Fruits and frugivores are classified into two qualitative categories: large and small. Small frugivores can only ingest small fruits, and large frugivores have a preference to ingest large fruits but they can also feed on small fruits (Bello, et al., 2015; Jordano, 2000). Seeds are also classified into large and small, and they can come from fruiting or nonfruiting trees.

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9 Figure 1. Agents and functional groups of the agent-based model of frugivory. Refer to main text (Agents and functional groups) for more detail. Simple icons are used to represent agents for simplification and practical purposes. The same graphical representations will be used in all figures. Apples represent fruits, acorns represent seeds, pink trees represent fruiting trees, green trees represent nonfruiting trees, and monkeys represent frugivores.

Driving processes

The main driving processes considered in the construction of the frugivory model are illustrated in Figure 2. These driving processes represent the core balancing forces that maintain a dynamic equilibrium in the system. More specifically, these processes balance out ‘positive’ processes that produce more agents, like germination, and production of seeds, with ‘negative’ processes that remove agents from the simulation, like starvation, tree competition for space, seed death, etc. In the sections below, more of the specific processes related to each agent will be briefly discussed. For complete details of the model’s procedures, refer to Appendix I.

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10 Figure 2. Main driving processes in the agent-based model of frugivory. * Reproduction of frugivores is optional in the model, and its activation is thus controlled by the user.

Space in the agent-based model: the NetLogo world

The NetLogo world, the computational space where agents interact, is a two-dimensional grid composed of squared patches. The grid behaves much like a Cartesian coordinate system, with x and y axes, and its centre on patch (0,0) (Wilensky, 1999; Bennett, 2015). Each patch is a 1 x 1 square, and the world is a square composed of a user-specified number of patches on each axis. For this model, I selected maximum x and y coordinates of 10 patches, which amounts to a total of 441 patches (see Figure 3). I assigned this model size to correspond to a plot of moist tropical forest that represents a one-hectare patch of terra firme forest in the Central Amazonia of Brazil. Each patch in the NetLogo world represents an area of approximately 5 m by 5 m. The simulation topology was selected so that wrapping was not enabled; that is, the world is said to have closed frontiers.

Death

•Frugivores: starvation •Trees: space, stochastic

processes, life strategy •Seeds: time deposited •Fruits: ingestion or seed

deposition from overripening

Birth

•Frugivores: reproduction* •Trees: seed germination •Seeds: ingested fruits

become seeds or overripe fruits become seeds

•Fruits: production by mature trees

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11 Figure 3. Model world (NetLogo world). Space in NetLogo functions like a Cartesian coordinate system, and patches have coordinates in the x and y axis (see image on the left), with the centre patch having coordinates (0,0). The full world is a box composed of 21 by 21 patches (see image on the right), each representing an area of forest of 5 m by 5 m.

Time in the agent-based model

NetLogo’s time counter runs with time steps called ‘ticks’, which represent one hour in the agent-based model. One tick is a full iteration of the model, which means that each of the model’s runtime processes runs once per tick. Since each tick represents one hour, all rates and procedures are scaled to this time unit, even if they are originally formulated in a different one, like months or years. Additionally, although all procedures run in each iteration of the model, they all have built-in specifications that constrain the agents that they can affect. Therefore, in every iteration, each procedure ‘asks’ its target agents if they have the right conditions (states) to perform it or be affected by it. If they do, the procedure will affect their states and, if they don’t, they will remain as they were in the previous iteration. The scheduling of the model’s procedures, the specific constraints of each sub-model, and more detailed information on the model’s time scales can be found in Appendix I. The following sections also summarise some of the model’s main procedures.

Modelling the tree community

The tree growth sub-model of the frugivory individual-based model was intentionally structured to reflect the relationship between carbon storage capacity and propagule size (fruit and seed size) in tropical forests. The sub-model’s specific construction was motivated by the results of studies that highlight that there is a tendency for large hardwood species to have large fruits and seeds (Bello, et al., 2015; Wright, et al., 2007; Diaz, et al., 2004; Thompson & Rabinowitz, 1989). The proposed conceptual framework of the model also responds to the fact that wood density, diameter at breast height, and tree height also appear to be positively related to carbon storage capacity across tree species in tropical forests. Therefore, after reviewing

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12 pertinent literature, I found that the main attributes needed to describe the link between propagule size and carbon storage capacity in the individual-based modelling framework were tree diameter, aboveground biomass, aboveground carbon storage, tree wood density, fruit size, and tree growth rate. In this section I will summarise the published relationships between these variables which I found to be the most useful in the making of the model. I also mention other important factors that were considered in the tree sub-model.

Aboveground biomass and stored carbon

In 2005, Chave and collaborators revised and compared several statistical models frequently used to explain the relationship between aboveground biomass and the product of wood density, trunk cross-sectional area, and total height, by using a dataset of around 2000 trees with diameters above 5 cm (Chave, et al., 2005). These models were tested for various types of forests, including dry, moist, and wet forests. According to the authors, their resulting revised regression models are suitable to reliably “predict aboveground tree biomass across a broad range of tropical forests” (Chave, et al., 2005). Given their versatility and their strong empirical foundation, these resulting models were deemed ideal candidates to estimate the aboveground biomass of trees in the individual-based model.

Although the authors’ results show several best predictive models, the model for moist forest stands that calculates biomass as a function of wood density and diameter, excluding height, is also the most compatible with the datasets that I selected to establish the model’s initial conditions (from Cavanaugh, et al. 2014 and Rankin-de-Merona, Hutchings, and Lovejoy, 1990; see Initial conditions and Appendix I for more details). Since the data for the initial conditions came from sites close to Manaus, Brazil, which is representative of a moist tropical rainforest, I selected the aboveground biomass estimation model for moist forests. For moist forest stands aboveground biomass (𝐴𝐺𝐵𝑒𝑠𝑡) of each tree is estimated according to the following expression:

𝐴𝐺𝐵𝑒𝑠𝑡= 𝜌 × 𝑒(−1.499 + 2.148 ln 𝐷 +0.207 (ln 𝐷)

2_{− 0.0281 (ln 𝐷)}3₎

Equation 1. Estimation of aboveground biomass as a function of tree density and diameter (Cavanaugh, et al., 2014; Chave, et al., 2005).

where 𝐷 is trunk diameter in cm, and 𝜌 is wood density in g/cm3_{(Cavanaugh, et al., 2014;}

Chave, et al., 2005). It is important to note that this model’s range of validity is limited, and spans trees with diameters from 5 to 156 cm, and values of 𝜌 × 𝐷2 between 50 and 1,000,000 (Chave, et al., 2005), but I used it for all diameter classes, since no other models were available for smaller trees. Carbon storage (𝐶𝑠𝑡𝑜𝑟𝑒𝑑) was calculated as follows for each individual tree (Cavanaugh, et al., 2014; Chave, et al., 2005):

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13 𝐶𝑠𝑡𝑜𝑟𝑒𝑑= 𝐴𝐺𝐵𝑒𝑠𝑡× 0.5

Equation 2. Estimation of aboveground stored carbon as a function of aboveground biomass (Cavanaugh, et al., 2014; Chave, et al., 2005).

Tree diameter, tree growth rate, and wood density

Scolforo and collaborators (2017) carried out a study in the Atlantic Forest of Brazil to develop an approach to estimate the diameter at breast height (DBH) growth rate in this environment, motivated by the existing knowledge gap in literature regarding estimation methods of this parameter for individual tree species (Scolforo, et al., 2017). The exponential model proposed by the authors measures the periodic annual diameter growth rate of a species, 𝑖𝑑, as a function of its stand density, measured in trees per hectare, as follows:

𝑖𝑑= (𝑎′+ 𝑐𝑇𝑃𝐻)𝑒𝑏𝐷

Equation 3. Estimation of diameter growth rate as a function of tree density (Scolforo, et al., 2017).

where 𝑎′, 𝑏, and 𝑐 are estimated parameters that vary from one species to another, and 𝑇𝑃𝐻 represents the number of trees of a species per hectare. Since this model was found to be suitable for describing the growth rate distribution of a tropical native forest while avoiding negative growth rate estimations, I selected it for the growth rate calculations. The authors estimated the model’s parameters for six different species with different growing behaviours and varying wood densities. Table 1 shows the estimated parameters of the fitted exponential model for the six studied species, as it appears in Scolforo, et al., 2017.

To select the model parameters to use in the agent-based model without the need to build a tree community composed strictly of the species studied by Scolforo, et al., 2017, I decided to classify the tree community according to two distinct life strategies related to growth rate: fast-growing trees and slow-fast-growing trees. These two life-history strategies are also related to wood density, which is can be a measure of functional behaviour that reflects the trade-offs between resource acquisition and survival through longevity; that is, it reflects whether a tree’s life strategy prioritises resource investment in growth speed (resource acquisition and less competition) or in stem robustness (greater chance of survival in time).

Trees that grow rapidly in height and stem size, therefore, have a shorter life span and light stems, whereas trees that have a greater life span and highly resistant, dense stems, grow slowly (Chao, et al., 2008). Following this reasoning, and since wood density is under phylogenetic control and can be used to reflect taxon-based properties (Chao, et al., 2008), I chose to select two of the models proposed by Scolforo, et al., 2017 to correspond to these two life strategies: the model for the species with the highest wood density, Xylopia

brasiliensis, for the slow-growth strategy, and the model for the species with the lowest wood

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14 model to trees classified as dense, and the fast-growth model to trees classified as light (see Agents and functional groups and Figure 1 for details). The mean wood densities with species or genus-specific standard deviations (Harja, Rahayu, & Pambudi, s.f.) for the six species studied by Scolforo and collaborators (2017) are shown in Table 1, and the selected model parameters are highlighted in bold (Xylopia brasiliensis and Inga vera).

Species 𝑎′ _𝑏 _𝑐 Wood Density (Species Mean) SD (Species) Xylopia brasiliensis Spreng. 0.0743 - 0.0504 - 0.0000082 0.7000 0.1457 (Genus) Sebastiania brasiliensis Spreng. 0.0367 - 0.0812 - 0.0000020 0.6735 0.0658

Inga vera Willd. 0.0377 - 0.0328 - 0.0000013 0.5750 0.0212

Triplaris gardneriana

Weddell 0.0995 - 0.0480 - 0.0000218 0.6300

0.0520 (Genus)

Amaioua guianensis Aubl. 0.0448 - 0.1414 - 0.0000066 0.6250 0.0636

Siparuna guianensis Aubl. 0.0509 - 0.1181 - 0.0000075 0.6618 0.0254

Table 1. Estimated parameter values for six tree species (Scolforo, et al., 2017) and their corresponding wood densities with their standard deviation (Harja, Rahayu, & Pambudi, s.f.). The species highlight in bold correspond to the species with the highest wood density (X. brasiliensis) and the lowest wood density (Inga vera). The models for these species (see Equation 3 for model details) were used in the agent-based model to parametrise the model for slow-growing and fast-growing trees, respectively. 𝑎′_,_{𝑏, and 𝑐 are estimated parameters that vary from one}

species to another, 𝑇𝑃𝐻 represents the number of trees of a species per hectare, and SD is the standard deviation

associated to the mean wood density of each species.

Fruit size

The interactions and relationships between fruit, seed, and frugivore sizes are diverse, complex in nature, and depend on the ecosystem and the species involved, among other factors. However, a well-documented general relationship exists between fruit size, seed size, and frugivore body-size. Jordano (2000) states, for instance, that size is the main source of functional variation in fruits in relation to the frugivores that eat them. Similarly, several other studies indicate that large seeds are exclusively dispersed by large mammals like apes and elephants (Chapman & Wrangham, 1992; Tutin, Williamson, Rogers, & Fernandez, 1991; Jordano, 2000), and that the sizes of fruits included in bird diets depends on their gape width (Wheelwright, Haber, Murray, & Guindon, 1984; Bello, et al., 2015; Levey, 1987; Jordano, 2000). These and other accounts, led me to propose a relatively simple framework that reflected and simplified this general tendency that I found in literature: large frugivores tend to eat large fruits, and large fruits tend to have large seeds.

Therefore, fruit size was included in the model as a binary qualitative variable with the functional trait values ‘large’ and ‘small’. Additionally, I also modelled frugivore size, and seed

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15 size as binary qualitative variables with the same categories, large and small, and I assigned large seeds to large fruits and small seeds to small fruits. Furthermore, I modelled the interactions between these agents to reflect the preference of large frugivores for large fruits, and the size constraints that generally prevent small frugivores from dispersing large fruits (see Modelling frugivory). Future, more detailed versions of the model, could make these variables quantitative and continuous, to explore richer, more complex forms of the relationships between fruit, seed, frugivore sizes.

Mortality

Tree mortality is one of the main driving processes in the agent-based model, since it determines the space available for seeds to germinate and it is crucial in structuring the tree community’s functional composition. To model this process as accurately as possible, I selected data from a mortality and recruitment study carried out by Rankin-de-Merona, Hutchings, and Lovejoy (1990), in which they report mortality rates for trees of varying diameters during a five-year period in Brazil’s central Amazonia. In this study, the authors followed five 1-ha plots of terra firme upland forest, and they counted the total number of trees in each, classified them into diameter classes, and reported both the number of dead trees and recruited trees (into the 10 cm DBH class) over the five-year period.

Although the authors report detailed data for each plot, I used the averages reported for the total inventory (see Table 2), divided by the number of hectares and the number of years to get the percentages of dead trees in each diameter class expressed as percentage of dead trees per hectare per year. To scale the rates to the model’s time scale (hours), I further converted the percentages to probability of death per hour. To calculate the mortality of trees with diameters smaller than 10 cm, which were not explicitly included in the study, I used the percentage of recruited trees reported by the same authors for the five-year period, as follows. A total of 3,125 trees were reported for the original inventory, and 138 were recruited after five years, so only about 4% of the total number of trees were recruited. Therefore, I took this to mean that around 96% of trees smaller than 10 cm died in those five years before reaching this diameter category (see Table 2). I scaled this percentage to match the model’s time scale, so that it represented probability of death per hour. For detailed information on the construction of the mortality sub-model, refer to Appendix I.

Size class Dead trees in class (%) < 10 95.58 10 40.91 15 24.43 20 15.91 25 7.39 30 3.41 35 3.98

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16 40 0.57 45 1.14 50 1.14 55 0 60 0 65 0 70 1.14 75 0 80 0 85 0 90 0 95 0 100 0 105 0 110 0

Table 2. Percentages of dead trees averaged for five 1-ha plots in the Central Amazonia of Brazil during a five-year period as reported by Rankin-de-Merona, Hutchings, and Lovejoy (1990). Trees under 10 cm in diameter were not measured in the study, so I calculated their death probability based on the number of trees that were recruited into the 10 cm size class over the time period in which the study was carried out.

Procedures: trees

For every tick (iteration) of the model, the sub-routines shown in Figure 4 are executed in that order for every tree in the simulation. First, the tree ages by an hour (a). Then, if the tree is determined to be old enough, it will change from a new tree to a mature tree that is able to reproduce; if the tree is already a mature tree, it will remain in this state (b). The following process (c) tracks whether it is time for the tree to reproduce and counts the time between reproductive seasons. If it is time for the tree to produce fruits or seeds, depending on its type (fruiting or nonfruiting, see Figure 1), it will reproduce (d). The next procedures, respectively, run the mortality model (e), calculate the tree’s growth rate (f), increase its diameter accordingly (g), calculate its aboveground biomass based on wood density and diameter (h), and, finally, calculate the tree’s stored carbon (i). For further details on the procedures and on their associated parameters, consult Appendix I.

Figure 4. Procedures for the tree sub-model. See main text and Appendix I for details.

a) age tree b) change from new tree to mature tree c) track reproductive season d) reproduce

e) kill trees _{growth rate}f) calculate g) increase _diameter

h) calculate aboveground

biomass

i) calculate carbon

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Modelling frugivory

Frugivory is defined as an animal-plant mutualism in which the consumption of fleshy fruits by animals is essential to the dispersal of angiosperm seeds (Jordano, 2000; Fleming, Breitwisch, & Whitesides, 1987). Therefore, I decided to model it to reflect the basic interactions between frugivores, seeds, fruits, and trees, as follows. Initially, fruiting trees produce young fruits which mature to become ripe fruits. If these fruits are not eaten, they decompose and leave their seeds behind. In the model, only fruits that are ripe can be eaten by frugivores. I included a constraint that dictates that small frugivores can only eat small fruits, while large frugivores prefer large fruits but can eat both. Frugivores that are foraging and have eaten ripe fruits of the right size, will drop their seeds periodically. The time period between each dropping event is determined by one of the model’s parameters.

Seeds, whether deposited by frugivores or as a result of fruit decomposition, will germinate to become a tree only if there is enough space around them to do so. To determine whether a seed can germinate or not, I included a state variable that is updated with every iteration of the model and that records the number of trees present around a seed in its current location (patch). Consequently, seeds can only germinate when this variable is lower than a fixed threshold. This constraint was included to mimic the effects of competition for space and light in the understory of a forest. If seeds take too long to germinate, they die. Figure 5 is a schematic diagram of the basic interactions of frugivory considered in the model. The figure serves as a reference point to support the following sections, which expand on these interactions and on the sub-models related to them and to each agent. For further details on the procedures and on their associated parameters, consult Appendix I.

Figure 5. Schematic diagram of the interactions of frugivory considered in the agent-based model. Arrows correspond to processes in the model and, as in previous figures, apples represent fruits, acorns represent seeds, pink trees represent fruiting trees, green trees represent nonfruiting trees, and monkeys represent frugivores.

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Procedures: fruits

Fruits in the model can be in one of three ‘development’ states: young, ripe, or overripe. Young fruits and overripe fruits cannot be consumed by frugivores, since I assume that immature fruits and fruits that are decomposing are not attractive to them. Once a fruit is overripe and is no longer appealing to frugivores, it will completely decompose to leave behind its seeds (or seed) in its place. The procedures governing fruit behaviour in the model are outlined in Figure 6. Briefly, fruits age in every time step (a) and, after a certain period has elapsed, they change from one state to the other (b and c). If they have been eaten by a frugivore while being ripe, they will become seeds immediately after being dropped (e), or, if they haven’t been eaten, they will first become overripe and then they will become seeds once the fruit has decomposed (d).

Figure 6. Procedures for the fruit sub-model. See main text and Appendix I for details.

Procedures: seeds

Once seeds are in the model, as a result of frugivore dropping, production by nonfruiting trees, or decomposition of overripe fruits, they will germinate only if the number of trees in the patch where they are located is smaller than a fixed threshold defined by one of the model’s parameters. Figure 7 summarises the procedures of the seed sub-model. The procedure set trees around me (a) updates the state variable that counts the trees in the patch where a seed is located to determine if it will germinate (d) or not. Moreover, seeds will only germinate if enough time has passed after they have been deposited. This waiting parameter simulates the time required for the seed to settle, germinate, and become a seedling. Seeds, like all other agents, also age with each time step, or tick (b). When a seed has been dropped for too long and it hasn’t germinated because it is surrounded by too many trees, it will die (c). Small seeds produced by both fruiting and nonfruiting trees have the possibility to self-disperse, or move around in the model, without the aid of frugivores (e). This procedure serves as a proxy for dispersal methods other than zoochory (abiotic).

a) age fruits b) change state from young to ripe c) change state from ripe to overripe d) go from overripe to seeds e) become seeds after being eaten and dropped

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19 Figure 7. Procedures for the seed sub-model. See main text and Appendix I for details.

Procedures: frugivores

The procedures for the frugivore sub-model are outlined in Figure 8. The default state for frugivores in the model is move (c). When their energy levels are above a certain threshold, frugivores will move randomly around the model world. Each time this procedure is executed, the frugivore’s energy decreases by a fixed amount. Once their energy is below a fixed threshold, they will start to forage, actively looking for food (d). Since both moving and foraging demand energy, frugivores must eat energy-rich fruits to replenish their reserves. When in this state, if they find a ripe fruit of the right size, they will eat it (b) and their energy will increase by an amount equal to the energy content of the fruit that they eat. Once a frugivore has eaten, it will drop the seeds it carries (f) after some time, which is tracked by the countdown procedure (e). Droppings are periodic and their frequency depends on a fixed parameter. If there aren’t enough fruits in the simulation, or if the frugivore doesn’t find them and its energy reserves run out, it will die of starvation (h). Frugivores reproduce (g) only if they have reached maturity and if their energy is sufficiently high. Reproduction is modelled as a probability, determined by a parameter, that serves as a proxy for fertility. The activation of the reproduction procedure is controlled by the user.

Figure 8. Procedures for the frugivore sub-model. See main text and Appendix I for details.

Initial conditions

For the individual-based model to reflect the relationships and processes related to frugivory and carbon storage in a tropical forest as accurately as possible, it was necessary to parametrise it using empirical data. These data also had to include real measurements of

a) set trees

around me b) age seed c) kill seed d) germinate

e) self-disperse

a) age

frugivores b) eat c) move d) forage

e) countdown of

dropping time f) drop fruits g) reproduce

h) die of starvation

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20 functional trait values that could be linked to aboveground carbon and fruit size through the regression models, allometric equations, and other mathematical relations used in the construction of the sub-models. Moreover, and to ensure coherence between the data, the studies from which they were extracted had to come from the same ecosystem, or at least from closely related environments.

After reviewing the literature that was available to me, I found that it was possible to use various studies related to the Central Amazonia of Brazil and to similar moist tropical forests to construct a coherent modelling framework embedded within a common ecosystem. Therefore, based on these findings, I decided to design the agent-based model as an idealised abstraction of a one-hectare plot of moist tropical forest (terra firme) in the Central Amazonia of Brazil to keep it as coherent and realistic as possible.

Some of the data used to parameterise the model were found in Cavanaugh, et al. (2014). This study examined the relationship between biodiversity and aboveground carbon storage in tropical forests by using data from a standardized tropical forest monitoring effort (TEAM Network). The study reports community weighted means (CWM) of wood density and diameter, mean aboveground carbon storage, and average stem density (trees per hectare) for undisturbed forests plots in several tropical forest sites. I decided to parametrise the model using data from the Manaus site (moist tropical forest in Brazil), to keep as much coherence as possible between the equations used in the sub-models and the data.

Table 3 lists the values from Cavanaugh, et al. (2014) and the values as they were used in the model. The measurements considered in the study are of all trees with diameters greater than 10 cm. The original data are expressed as means with coefficients of variation (CV) in parentheses, but the values that were used in the model were changed to standard deviations (CV x mean). Wood density was modelled as a normal distribution following Cavanaugh, et al. (2014) and Reyes, Brown, Chapman, & Lugo (1992). To avoid having trees with a wood density of zero, I used published minimum and maximum wood densities reported for Tropical America (Reyes, Brown, Chapman, & Lugo, 1992) as the limits of the normal distribution to estimate the wood densities of the initial tree population. See Appendix I for detail.

Data Cavanaugh, et al. 2014 Model

Country Brazil Central Amazonia (terra firme),

Brazil

Site Manaus (MAS)

Number of plots 6 1 (1 ha total)

Aboveground C storage (Mg C ha-1_{) 191 (0.16)} _{Used for calibration of the model} CWM wood density (g cm-3₎ _{0.67 (0.04)} Mean 0.67

SD 0.268

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21 Although the data from Cavanaugh, et al. (2014) includes basic information on the average value of stem diameter in a hectare of forest, it doesn’t explicitly refer to how this variable is distributed in the plant community. Including this information in the model was crucial, since it is necessary to know the proportion of trees in each diameter class to accurately estimate the aboveground carbon storage of the forest plot. For instance, when I initially assumed a normal distribution of diameters, the model overestimated the stored carbon by about one order of magnitude, as compared to that reported by Cavanaugh, et al. (2014).

I therefore used the inventory data published by Rankin-de-Merona, Hutchings, and Lovejoy (1990) for five hectares of tropical rainforest in Brazil’s Central Amazonia to model the diameter distribution of the tree community. Since the model represents one hectare of forest, I set the initial number of trees in each simulation to the average number of trees per hectare reported in this study, calculated as the total inventory divided by five. The stem diameter distribution was then appropriately scaled and calculated from the percentage of trees in the original inventory that belonged to each diameter class (see Figure 9). This calculation also considered the proportion of trees that were fruiting and nonfruiting, extracted from the data published by Osuri, et al. (2016). With this diameter distribution, the calculated stored carbon dropped to approximately 120 Mg C ha-1_{, resembling more closely that reported by}

Cavanaugh, et al. (2014).

It is noteworthy that this diameter structure, often referred to as a “J” distribution, is that typical of a mixed tropical forest, with more individuals in the smaller size classes than in the larger ones (Felfili, 1997). I assume that this distribution represents a mature forest that is in dynamic equilibrium, so other initial conditions are modelled to reflect this. For instance, the trees that begin the simulation are already mature and bear fruits and seeds. For detailed information on the proportions of fruiting and nonfruiting trees, and on the stem diameter distribution, refer to Appendix I.

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22 Figure 9. Diameter distribution used in the agent-based model. Distribution is based on data published in Rankin-de-Merona, Hutchings, and Lovejoy (1990). The data was scaled to correspond to trees in each diameter class per hectare. This figure indicates the total number of trees in each class (both fruiting and nonfruiting).

Detailed initial conditions, including stand density, initial number of trees, proportion of fruiting trees vs. nonfruiting trees, etc. are listed in Table 11 (Appendix I). The initial numbers of large and small frugivores, as well as the activation of the procedures that simulate heavy logging and frugivore reproduction, are selected by the user and are therefore not included in Table 11. Additional initial conditions used in computational experiments are described in the

In-silico experiments section. Figure 10 is an example of what the initial conditions of a standard

(control) simulation of the agent-based model look like in the NetLogo interface. Refer to Appendix I for further detail.

288 126 77 46 31 18 12 8 6 4 3 1 2 1 0 1 0 0 0 0 0 0 50 100 150 200 250 300 350 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100105110 Num be r of T ree s Diameter Class

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23 Figure 10. Example of the initial conditions of a normal scenario simulation of the agent-based model in NetLogo. Green trees represent nonfruiting trees, while pink trees represent fruiting trees. Small monkeys represent small frugivores, and large, dark-blue monkeys represent large frugivores. This simulation, for example, begins with the same number of small and large frugivores (two of each). The diameter distribution is an adapted version of that reported by Rankin-de-Merona, Hutchings, and Lovejoy (1990), and the average wood density and stand density correspond to those listed in Cavanaugh, et al., 2014. The initial estimate of tonnes of carbon per hectare (CPH) is calculated from the diameter distribution with the allometric equations used in the tree model, and it is reasonably close to the 191 tonnes of carbon per hectare calculated by Cavanaugh et al.

In-silico experiments

Defaunation experiments

The defaunation experiment was set up to study, at least preliminarily, how the extinction of frugivores affects carbon storage, the composition of the tree community, and the model’s dynamics. To evaluate the effects of different abundances of both large and small frugivores, I ran the model for several frugivore abundance combinations and then analysed the differences in the model’s general behaviour and in the resulting stored carbon per hectare. To model the defaunation scenarios and calibrate them as accurately as possible, I referred to literature on frugivore abundances in Brazilian terra firme forests. I found that the mean abundance of medium-sized and large mammals in a seasonally dry forest of Brazil is of 160 individuals per km2_{in the terra firme forest type (Mendes Pontes, 2004). I decided to}

recalculate this value to the experimental scale, one hectare, to use it to set up my experiments. Since the reported number of frugivores scales to 1.6 mammals per hectare, I rounded it to 2 and used it as a reference for the “normal”, or control conditions/scenario. Based on these normal conditions, I also set up three other frugivore abundance combinations that corresponded to three defaunation scenarios: complete defaunation, presence of only large frugivores, and presence of small frugivores. I used these four scenarios to study how variations in frugivore abundance and type affect carbon storage and overall model behaviour.

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24 The combinations and scenarios used for the defaunation experiments are summarised in Table 4.

All simulations were programmed to last ten years, provided that no frugivores died in the meantime; if a frugivore died, the simulation would automatically stop. For every combination of frugivore abundances (scenario) I carried out two independent runs of the model, for a total of eight runs. The model was programmed so that its complete set of outputs (results) was collected in a table file in which the values of the following variables were recorded for each time step: trees per hectare (TPH), carbon per hectare (CPH) in megagrams of carbon per hectare (Mg C/ha), number of fast-growing trees, number of slow-growing trees, mean wood density, mean tree diameter, number of fruiting trees with large fruits, number of fruiting trees with small fruits, and number of nonfruiting trees. The experiments were setup using the Behaviour Space tool in NetLogo.

Logging experiments

A procedure that simulates heavy logging was included in the model as an additional experimental condition to study defaunation under different scenarios. I included this user-activated procedure to study how different defaunation scenarios, when coupled with the selective loss of large, dense trees, affects carbon storage and general model behaviour. When active, the procedure targets trees that are larger than 15 cm in diameter and that have a wood density higher than the initial mean wood density of the tree community. For the procedure to determine whether a tree dies or not, it uses a probability of death based on a published logging rate for the Brazilian Amazonia (Gerwing, 2002), scaled to the model’s time unit (hours).

To perform the logging experiments, I activated the logging procedure and used the same general setup and frugivore abundance combinations as for the defaunation experiments. I recorded the same output variables, ran two repetitions of each scenario, and ran the simulations for ten years, provided that no frugivores died. The results of these scenarios were compared to the normal conditions simulated in the defaunation experiments. The combinations and scenarios used for the logging experiments are summarised in Table 4.

Experiment / Scenario Run numbers Large frugivores Small frugivores Years Defaunation Complete defaunation 1 0 0 10 2 0 0 10

Only large frugivores 3 2 0 10

4 2 0 10

Only small frugivores 5 0 2 10

6 0 2 10

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25 Normal conditions (for both

experiments) 8 2 2 10

Logging

Complete defaunation and logging 1 0 0 10

2 0 0 10

Only large frugivores and logging 3 2 0 10

4 2 0 10

Only small frugivores and logging 5 0 2 10

6 0 2 10

Only logging 7 2 2 10

8 2 2 10

Table 4. Frugivore abundances and general setup for the defaunation experiments.

Analysis of results

To have a better understanding of the model’s scope and of the experimental results, I examined the dynamic behaviour of all output variables for each scenario. Since I ran each scenario twice (two repetitions), I used the mean of both runs to make plots of each variable against time. Hence, I calculated the mean of each output variable in every time step in order to obtain a single, average value per time step for all scenarios. I then generated the plots of the means of all the output variables in time and compared the different scenarios and experiments.

All simulations for both the defaunation and logging experiments were programmed to run for ten years; however, I was aware that, since simulations were coded to automatically stop if frugivores died, there was a high probability that some of them would stop before reaching the termination time. Therefore, I made sure to filter and process the data so that the plots only contained information for the least runtime shared by all simulations of the same set of experiments (defaunation or logging). This allowed me to qualitatively assess how different parameters affect the model’s behaviour and to preliminarily infer how defaunation and logging could affect carbon storage in the Brazilian Amazonia.

Results

Effects of defaunation

After running the defaunation experiments, I found that at least one frugivore died in all simulations before the ten years of runtime were over. Therefore, to be able to compare the results of the eight simulations for the four scenarios, I only considered the data for the timeframe that was common to all of them; that is, the data that corresponded to the last common timestep shared by all runs, which was somewhere around 4.4 years (38079 steps). I then compared the results for this period for all simulations and analysed their behaviour. The results for the output variables in the last common step of all simulations are summarised

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26 below (Table 5). The dynamic behaviours of the means of the output variables are described in detail in the following subsections.

Run Small frugivores Large frugivores Years TPH CPH (Mg C/ha) Fast-growing trees % of fast-growing trees Slow-growing trees % of slow-growing trees Trees with large fruits % trees with large fruits Trees with small fruits % trees with small fruits Nonfruiting trees % nonfruiting Mean wood density Mean diameter 1 0 0 4.4 857 176.673 468 55% 389 45% 307 36% 366 43% 184 21% 0.667 16.728 2 0 0 4.4 862 176.098 408 47% 454 53% 329 38% 338 39% 195 23% 0.673 16.653 3 0 2 4.4 905 177.497 453 50% 452 50% 381 42% 356 39% 168 19% 0.670 16.191 4 0 2 4.4 918 177.391 477 52% 441 48% 371 40% 375 41% 172 19% 0.669 16.052 5 2 0 4.4 975 175.802 554 57% 421 43% 304 31% 499 51% 172 18% 0.667 15.273 6 2 0 4.4 933 175.566 544 58% 389 42% 290 31% 475 51% 168 18% 0.667 15.809 7 2 2 4.4 960 176.759 533 56% 427 44% 352 37% 451 47% 157 16% 0.669 15.493 8 2 2 4.4 992 176.976 541 55% 451 45% 359 36% 461 46% 172 17% 0.667 15.214 Table 5. Final values (for the last common step) of the output variables for all runs of the defaunation experiments. Each scenario was simulated twice (two repetitions) and the final values for both runs are shown in the table.

Stored carbon

For all simulations, the amount of carbon stored per hectare increased steadily and smoothly and reached similar final values after 4.4 years. As shown in Table 5, the final values of stored carbon per hectare in all simulations fall somewhere between 175 and 177 megagrams, and they appear to be quite similar throughout all simulations, suggesting that there are no significant qualitative differences in the behaviour of this variable when frugivores are absent in the model. Moreover, there appear to be no changes in the general dynamic behaviour of this variable when frugivore abundances change (Figure 11); that is, the speed with which stored carbon increases appears to be relatively constant in all scenarios.

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27 Figure 11. Means of stored carbon per hectare (CPH) in time for all scenarios of the defaunation experiments.

Number of trees per hectare

Although the amount of stored carbon appeared to be relatively constant for all simulations, the number of trees per hectare seems to have been affected by the different defaunation scenarios (see Figure 12). In all simulations, the number of trees per hectare increased rapidly at the beginning of the simulation and stabilised in time, exhibiting a saturation-like curve. For the complete defaunation scenario, in which there were no large or small frugivores present, the mean of the number of trees per hectare was the lowest overall. Additionally, the results for this scenario are the only ones that showed a lag-like period before the number of trees per hectare increased steadily. On the contrary, for the scenario with normal conditions, in which the number of both types of frugivores was the highest, the number of trees per hectare increased more rapidly and was notably higher than for the other scenarios. This is most likely the result of increased colonisation of space by germinating trees that results from more effective, frugivore-aided dispersal. When there are frugivores present, dispersal is more probable (and happens faster), and thus there are more trees germinating all over the plot; however, when there are no frugivores, dispersal is highly limited and it is only possible for small propagules, so the number of trees per hectare is lower overall. The scenario with only small frugivores showed the second overall highest mean of trees per hectare. This could be a result of several factors, including that small-fruited trees produce more fruits per fruiting event and that their fruits can self-disperse. These results suggest that not only the presence

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28 of frugivores, but also their abundances, have a direct and positive influence over the number of trees that grow in the modelled forest.

Figure 12. Means of trees per hectare in time for all scenarios of the defaunation experiments.

Tree growth speed

All scenarios in the tree growth speed plots (Figure 13) exhibit a saturation-like curve, in which the number of each type of tree increases rapidly in the beginning and then stabilises, reaching a relatively constant, maximum value. For all simulations the final number of fast-growing trees was higher than the number of slow-growing trees. However, for the scenario in which only large frugivores were present and for the complete defaunation scenario, the difference between fast- and slow-growing trees is less pronounced than in the other simulations. In the scenario with only small frugivores the number of fast-growing trees was notably higher than that of slow-growing trees. In the scenario representing normal conditions, in which both types of frugivores were present, there were more fast-growing trees overall but the difference between both types was not as marked as in the scenario where only small frugivores were present. Although the trends in these results are not as defined as those for trees per hectare and carbon per hectare, they suggest that frugivore size, frugivore abundance, and the distribution of wood density values (which are represented by growth speed) in the plant community are related.

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29 Figure 13. Means of fast-growing and slow-growing tree numbers in time for all scenarios of the defaunation experiments.

Tree type

In all scenarios, nonfruiting trees were always the least abundant (see Figure 14). The proportions of both types of fruiting trees (trees with small fruits and trees with large fruits) varied noticeably among the different scenarios. For the complete defaunation scenario, the numbers of trees with small and large fruits were not too different; in this scenario, the number of trees with small fruits was slightly higher than the number of trees with large fruits. Interestingly, in the scenario in which only large frugivores were present, trees with large fruits were slightly more abundant than trees with small fruits, although these followed closely. This suggests that when only large frugivores are present, large-fruited trees are favoured in terms of dispersal and colonisation.

For the scenario in which only small frugivores were present, the proportion of trees with small fruits was the highest of all scenarios (around 50% of trees had small fruits). This scenario, consequently, also showed the greatest difference in proportions of fruiting tree types. This suggests that when large-bodied frugivores are absent, trees with small propagules are disproportionately favoured, probably as a result of them having both the advantage of frugivore-mediated dispersal and of self-dispersal, contrary to large-fruited trees, which have no available means to disperse. Consequently, small-fruited trees outcompete large-fruited trees when only small frugivores are present. Finally, the scenario with normal conditions

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30 showed relatively high numbers of both types of fruiting trees and trees with small fruits were also more abundant, although not as dominant as in the scenario with only small frugivores. This suggests that large frugivores do influence the competitive ability of large-fruited trees. The results for these scenarios further suggest that frugivore abundance and size influence the functional composition of the tree community.

Figure 14. Means of numbers of trees of each type (nonfruiting, trees with large fruits, and trees with small fruits) in time for all scenarios of the defaunation experiments.

Mean diameter

The mean diameter of the tree community showed a similar general dynamic behaviour for all scenarios: first, the mean diameter dropped rapidly and, after briefly stabilising, continued to increase steadily in time (see Figure 15). The initial rapid drop in mean diameter occurs as a result of the recruitment of new, small trees once the simulation begins. Fruits that are overripe and fruits that have been eaten and transported by frugivores become seeds that then germinate to become young trees. This sudden influx of small trees causes the mean diameter to drop rapidly. Afterwards, however, the mean diameter stabilises because the forest’s carrying capacity is reached, and germination slows down due to competitive effects. Following this period, all trees continue to grow steadily, slowly increasing the mean diameter. The differences in mean diameter between simulations were like those described for trees per hectare, since these variables are closely related. For simulations with no frugivores (complete

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31 defaunation scenario), the changes in diameter were not as pronounced as in simulations with frugivores. This is because, as discussed in TPH section, simulations in which frugivores were present had the most trees per hectare, which means they must have had more new trees germinating than simulations with no frugivores. Therefore, the large influx of new trees had a more noticeable effect on the mean diameter in simulations with frugivores. As expected, the scenario with normal conditions had the most noticeable drop in diameter, suggesting that the abundance of frugivores has a direct effect on the behaviour of the mean diameter over time. This is, again, most likely a result of the influence of frugivores on dispersal and therefore on the number of trees per hectare. Mean diameter, like previous variables, also seems to be influenced by the abundance and by the sizes of frugivores present, since the curves for all scenarios were clearly differentiable.

Figure 15. Means of the mean diameter of trees in time for all scenarios of the defaunation experiments.

Other findings

Mean wood density appeared to be relatively constant in time for most simulations, except the complete defaunation scenario, in which it seemed to exhibit a decreasing trend. Although it seemed to fluctuate slightly over time in all scenarios (Figure 16), its final values remained relatively close to its starting value of 0.67 g/cm3_{. Even though the complete defaunation}

scenario showed the highest wood density of all studied scenarios, it exhibited a tendency to decrease over time and it also showed high variability among the two repetition runs. The other scenarios had more constant and closely related values for both runs. The behaviour of

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32 wood density in the different scenarios, like other output variables of the model, also shows the influence that both types of frugivores have on the functional composition of the tree community: when only large frugivores are present, mean wood density tends towards higher values; when only small frugivores are present, mean wood density tends towards lower values; and, when both types of frugivores are present, mean wood density takes intermediate values.

Figure 16. Means of the mean wood density of trees in time for all scenarios of the defaunation experiments.

Effects of logging

As with the defaunation experiments, I found that at least one frugivore died in all simulations of the logging experiments. Consequently, I only considered data for the time they all ran, which was also somewhere around 4.4 years (37749 steps). I then compared the results for this period for all simulations and analysed their behaviour. The results for the output variables in the last common step of all simulations are summarised below (Table 6). The following subsections describe the dynamic behaviours of the output variables in greater detail.

Run Small frugivores Large frugivores Years TPH CPH (Mg C/ha) Fast-growing trees % of fast-growing trees Slow-growing trees % of slow-growing trees Trees with large fruits % trees with large fruits Trees with small fruits % trees with small fruits Nonfruiting trees % nonfruiting Mean wood density Mean diameter 1 0 0 4.4 813 117.941 479 59% 334 41% 266 33% 377 46% 170 21% 0.666 13.902 2 0 0 4.4 846 117.716 475 56% 371 44% 286 34% 381 45% 179 21% 0.666 13.507 3 0 2 4.4 884 120.476 499 56% 385 44% 321 36% 382 43% 181 20% 0.668 13.414

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33 4 0 2 4.4 877 114.141 494 56% 383 44% 332 38% 373 43% 172 20% 0.667 13.031 5 2 0 4.4 863 104.619 486 56% 377 44% 260 30% 444 51% 159 18% 0.668 12.840 6 2 0 4.4 903 127.629 549 61% 354 39% 267 30% 490 54% 146 16% 0.665 13.199 7 2 2 4.4 938 119.274 511 54% 427 46% 310 33% 477 51% 151 16% 0.668 12.528 8 2 2 4.4 958 121.407 572 60% 386 40% 312 33% 513 54% 133 14% 0.666 12.414 Table 6. Final values (for the last common step) of the output variables for all runs of the logging experiments. Each scenario was simulated twice (two repetitions) and the final values for both runs are shown in the table.

Stored carbon

Unlike the runs for the defaunation experiments, those for the logging experiments showed no clearly defined, even trends for the dynamics of stored carbon per hectare (see Figure 17). Instead of increasing smoothly and constantly, stored carbon seems to fluctuate noticeably and, overall, appears to be negatively affected by logging in all scenarios. These runs suggest that logging introduces a lot of noise in this variable’s dynamic behaviour, and that, for most cases, the stored carbon doesn’t increase when heavy logging is activated in the model. For all simulations, the final value of stored carbon when logging was activated was always noticeably lower than that for normal conditions and for the scenarios of the defaunation experiments that had the same combination of frugivore abundances. It is noteworthy that the experiment in which only logging was activated had the highest stored carbon in the final step of all scenarios; this could suggest that the presence of frugivores can somewhat counteract the effects of logging on carbon storage.

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34 Figure 17. Means of stored carbon per hectare (CPH) in time for all scenarios of the logging experiments.

Number of trees per hectare

In the logging experiments, the variable that measures the number of trees per hectare behaved much like it did in the defaunation runs (see Figure 18). The curves in the logging experiments also exhibited a saturation-like behaviour, with a rapid increase at the beginning of the simulations followed by a stabilisation period. The complete defaunation and logging scenario had the least mean number of trees overall and exhibited a pronounced lag in the beginning, right before the number of trees per hectare increased rapidly. This lag seems to be longer than the one exhibited by the complete defaunation scenario of the defaunation experiments. This behaviour suggests, therefore, that complete logging and defaunation is, as expected, the worst scenario overall in terms of mean trees per hectare. Although their qualitative behaviours are similar, the final mean number of trees per hectare in all scenarios where logging was active was lower than the mean number of trees in the scenario with normal conditions. It is noteworthy, however, that the mean number of trees per hectare when only logging was active was higher than for the other logging scenarios and was closer to normal conditions; these results, along with those for stored carbon, suggest that the presence and abundance of frugivores could counteract the effects of logging to some extent.

Development of an individual-based model of frugivory to study the effects of defaunation on carbon storage in a tropical forest

Research Project I