Consequences of asymmetry between green and brown food webs on stability of aquatic and terrestrial ecosystems

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1 Food web structure and ecosystem functioning

Food web structure and dynamic are key factors of ecosystem functioning and the response of communities to environmental perturbations. Relevant researches are very dynamic in this field of ecology (Pimm 1982; Duffy 2002; Thebault & Loreau 2003; Rooney & McCann 2012; Thompson et al. 2012). These studies have led to the development of an extensive theoretical and empirical corpus that aims at determining the influence of food web structure on the stability of communities (Neutel et al. 2002), and the respective impact on ecosystem functioning of the control by resources (bottom-up) and by predation (top-down) (Hunter & Price 1992). I summarize here: 1) what specific food web structures are considered important to determine ecosystem functioning in current ecological research (Fig. 1); and 2) how human impacts can modify food web structure and what are the consequences on respective ecosystem functioning (Table 1).
Figure.1 Important food web structures determining ecosystem functioning in current ecological research. a) Food chains, , , represent primary producers, herbivores and carnivores respectively. b) Competition, , represent the resources and consumers respectively. c) Mutualism, two types of mutualism are presented. The first is the interaction between plant and pollinator ( , represent plants and pollinators respectively). The second is the interaction between primary producers and decomposers , , , represent primary producers, decomposers, nutrients and detritus respectively). d) Ominivory, , , represent primary producers, herbivores and omnivores respectively.
Human activities can strongly modify the structure of food chains and have severe consequences in impacted ecosystems. On one hand, harvesting of organisms and habitat fragmentation can cause large removals of top predators, resulting in herbivory out of control and dramatic reduction in the density of primary producers (Jackson 2001; Ripple et al. 2001; Terborgh 2001). On the other hand, farming, industrial and urban effluents can lead to enrichment in mineral nutrients and higher inputs of organic matter to ecosystems, which greatly disturbs the functioning of these ecosystems and can lead to explosive growth of herbivores (Jefferies 2004) or bacteria (Dodds & Cole 2007). Thus human impacts at the top and at the bottom of food chains drive cascades of consequences, which usually cause great losses of biodiversity and ecosystem functions.

 Competition

The role of interspecific competition in structuring communities has been long studied both theoretically and empirically (Holt et al. 1994; Worm et al. 2002). In exploitative competition two consumers compete for the same resource while apparent competition occurs among species consumed by a shared natural enemy (Fig.1-b). In both cases, species interact with each other in an indirect manner. Studying competition can help ecologists understand a large body of ecological patterns such as the coexistence and the dominance of species within communities (Tilman 1982), and the increase in ecosystem stability related to dampened oscillations between consumers and resources (McCann et al. 1998).
The responses of different species to global change can shift competitive balances to favor certain species (Tylianakis et al. 2008). For example, certain plant species can have a competitive advantage in environmental conditions with eutrophication or increased temperature and become dominant in the community (Tilman & Lehman 2001; Zavaleta et al. 2003). Invasive species can outcompete native species by enhancing the population of shared predators or through more effective exploitation on the resource (Snyder & Evans 2006). All these influences can drastically modify species distributions in the ecosystem and impact the main ecological processes such as primary productivity, nutrient cycles and stability.

 Mutualism

Mutualism is an interspecific interaction in which both partners benefit from the activity of each other (Fig.1-c). Mutualism is ubiquitous and exists in diverse forms in nature (Polis & Strong 1996). The interaction between plants and pollinators is one of the most well-known mutualistic interaction in which animals help plant reproduction through pollination and receive nectar as a reward (Memmott 1999). Another important mutualistic interaction is between primary producers and decomposers: most primary production becomes detritus thus providing the resource for decomposers and in return the decomposition process provides mineral nutrient which is essential for the growth of primary producers (Daufresne & Loreau 2001). These structures of mutualistic interactions are indispensable for contributing to the healthy functioning of ecosystems such as primary productivity (plant – pollinator interaction) and nutrient dynamics (primary producer – decomposer interaction, developed in following sections).
Both forms of mutualistic interactions and related ecosystem functioning can be negatively affected by anthropogenic changes. For example, global warming and habitat loss can reduce the spatial and seasonal overlap of plant flowering and pollinator activities (Fortuna & Bascompte 2006; Memmott et al. 2007). Eutrophication and enhanced atmospheric CO2 level can induce changes in stoichiometric composition of detritus and decomposers, which play an important role in stabilizing the ecosystem (chapter 2). Overall the loss or modification of such mutualistic interactions within food webs can result in severe degradation of the related ecosystem functions.

 Omnivory

Omnivory are consumers feeding on more than one trophic level (Pimm 1982), e.g., the omnivores consume resources from both plant and animal origins. Omnivory has been found ubiquitous in food webs and represents an important structural component in determining ecosystem functioning. The presence of omnivores can eliminate effects of trophic cascade as they can switch to feed on different resources (Pace et al. 1999). More specifically, omnivores feeding on detritus can have important effects on nutrient cycling and facilitate primary productivity to compensate negative cascading effects through herbivory (Thompson et al. 2007). Omnivory has been also included in discussions of food web structure and ecosystem stability. Classical food web theory has suggested destabilizing effects of omnivory (Pimm & Lawton 1978; Pimm 1982). However, more recent theory and experiments indicate that omnivory can be an important stabilizing structure (McCann & Hastings 1997; Holyoak & Sachdev 1998; Fussmann & Heber 2002) due to the “weak” link effects within food webs (McCann 2000; de Ruiter 2005).
While omnivory has important effects on regulating trophic cascades and promoting ecosystem stability, human impacts potentially reduce the positive effects of omnivory on ecosystem functioning. For example, reduced food web productivity due to reduced omnivory is reported in a decomposer-based food web (Kuijper et al. 2005). Ecosystems might require an increasing amount of omnivory to offset the destabilizing effects of spatial compression due to the reduced resource habitat scales compared with consumer foraging scale (McCann et al. 2005).
In summary, examples of species interactions listed above demonstrate that food web characteristics are important to determine ecosystem functioning. Due to human impacts, we can expect complex changes in food web structure, with potential major changes in ecosystem functioning (Jeppesen et al. 2010). Therefore studying the basic food web structure and related effects on ecosystem functioning is essential to understand and predict the consequences of such changes. This thesis is based on this principle to study the determining effects of specific food web structure on ecosystem functioning.

Modeling the food web structure

Understanding and modelling food web structure is an active area of theoretical ecology.
From mathematical perspectives, food webs are complex dynamic systems consisting of many biological species that interact in many different ways (i.e. trophic interaction, competition, mutualism etc. as listed in the previous section) and cause changes in time and space (McCann 2011). Using systems of differential equations is the main theoretical approach to describe the dynamics of interacting populations and the patterns of connections among them. These descriptions of food webs can be at different levels of complexity (i.e. from simple consumer-resource trophic interaction to large networks of different interactions) and there are numerous ways of analyzing the response of ecosystem functioning to the specific food web structure.
One of the fundamental building block of food web models is the consumer-resource trophic interaction (Fig. 2-a). In a consumer-resource relationship, the consumer depends for subsistence on the resource. Denoting the number of consumers at time by ( ) and the number of resources by ( ), the dynamics of the consumer-resource relationship can be described by equations:
where ( ) is the growth of the resources in the absence of the consumers, ( , ) is the functional response of the consumers feeding on the resources, is the consumption efficiency (i.e. the proportion of resource biomass assimilated by the consumers) and is the natural loss rate of the consumers. The growth of the resources can be either a linear function (i.e. ( ) = ) or including intra-species competition to have the logistic form (i.e. ( ) = (1 − ⁄ ), where is the carrying capacity). The functional response of the consumers ( , ) has also different forms. The first consumer-resource model was the Lotka-Volterra model that uses a linear functional response, ( , ) = , where is the attack rate. More realistic functional responses are used in later research such as the Holling Type II functional response ( , ) = 1+ ℎ , where ℎ is the handling time that represents the time used for consuming the resource.
The consumer-resource dynamics with realistic growth and functional responses can be generalised in population dynamics equations describing more complex food webs of interacting species. The generalized model is thus (assuming is the population size or population density of species ):
with the first term representing the growth of species feeding on other species, the second term is representing the predation by other species, and the last term is the natural loss of species . Applying the generalized consumer-resource dynamics in food web models, there are mainly two ways of looking at the dynamics of ecological systems.
The first is the concept of modules in ecology introduced by Robert Holt (1997). Here “modules” can been seen as sub-systems which are of intermediate complexity beyond consumer-resource interactions but below the diversity found in most ecosystems (Fig. 2-b). This way of modelling food webs assembles species into taxonomic entities or functional groups and generally consists of three to six interacting compartments (Holt & Hochberg 2001; Milo 2002). Theories are developed to understand how species interact and to study the mechanisms underlying the effects of food web structure by analysing the role of specific parameters (e.g. growth rate, attack rates etc.). For example, the study of consumer-resource interaction modules showed that weak attack rates can have stabilizing effects in ecosystems (McCann et al. 1998).
The second way of modelling food web structure is based on complex sets of interactions of many species with many links, which captures more realistic properties of real ecosystems (Pascual & Dunne 2006) (Fig.2-c). The network structure is either extracted from empirical studies or derived from some stochastic algorithm. For example, in the well-known niche model, species are characterized by their feeding centre and feeding range along a niche axis which determine a niche interval delimiting niche values of their prey (Williams & Martinez 2000). These network models are mainly used to investigate the effects of network structure on ecosystem stability (Montoya et al. 2006; Allesina & Pascual 2008; Thébault & Fontaine 2010).
Some important mechanism underlying network structure such as adaptive foraging and allometric structures are found to enhance the stability of ecosystems (Kondoh 2003; Brose et al. 2006).
Figure.2 Schematic presentation of different approaches for modeling food webs. a) The fundamental building block of food web models: the consumer-resource interactions. b) The “modules” in food web models. Modules are sub-systems which are of intermediate complexity beyond consumer-resource interactions but below the diversity found in most ecosystems. c) The network structure of food webs, which is based on complex sets of interactions of many species with many links. The circles in the figure represent different species or functional groups (i.e. compartments) and the arrows represent trophic links between species or compartments.
The two ways of modelling food web structure (modules and networks) clearly interact: the modules are the basic building blocks of complex networks (Milo 2002). Further, spatial structuring (McCann et al. 2005; Gravel et al. 2010b) and evolutionary processes (Loeuille & Loreau 2005) also have significant influences on food web structure and related ecosystem functioning. From the simplest consumer-resource interaction to the most complex ecological networks, modelling approaches help ecologists to explore and understand the relationship between food web structure and ecosystem functioning.
Many ecological properties can be easily measured in food web models. Analytic methods and simulations are widely used to decipher the dynamical outcomes of food web models based on differential equations (Brose et al. 2006; Attayde & Ripa 2008; Wollrab et al. 2012). The distribution of species and functional groups are revealed by the species biomass or the density of population in dynamic system models (Leroux & Loreau 2010). The coexistence of species under different conditions can also be predicted by such distribution (Daufresne & Loreau 2001). Estimations of primary and secondary productions are based on consumer and resource biomass and the functional responses among them (Zou et al. 2016). A measure of ecosystem stability, the coefficient of variation (variation/mean), examines the temporary variability of population dynamics in cyclic dynamics (Tilman 1999). These examples for measuring ecosystem functioning and stability are key methods in studying effects of food web structure and will be performed in this thesis.
The modeling approaches mentioned above so far discussed the importance of studying the dynamics of interacting populations to understand effects of food web structure on ecosystem functioning. Nevertheless, most of these studies ignore the overall functioning of the ecosystems: the energy and material flows. In particular, the nutrient material flows potentially introduce new interactions and have important consequences on ecosystem functioning. In the following sections I will summarize the importance of including nutrient cycling in food web studies and introduce the method used to integrate nutrient cycling into food web models in the thesis.

Nutrient cycling

While studies of population dynamics in communities focus on biotic interactions, the flows of energy and nutrient material in ecological systems are also important aspects to consider for understanding ecosystem functioning (DeAngelis 1980). These two aspects are interrelated: on the one hand, energy and nutrient materials can limit the species populations and influence the food web structures; on the other hand, interactions among species / functional groups may influence energy and material flows. Energy transfers are generally modeled as linear flows through trophic interactions (Fig. 3-a). Energy is seldom recycled within ecosystems due to its gradual dissipation through respiration. By contrast, nutrient materials can generate circular flows among all ecosystem components (Fig.3-b). Mineral nutrients are heavily recycled within ecosystems, which represents another important interaction among ecosystem components and may offer new challenges and questions compared with the population-community perspective. In many ecosystems, the internal recycling can account for a larger amount of nutrients than the inputs and the outputs to the ecosystem and has the potential to compensate nutrient limitation (Vitousek & Matson 2009). Therefore, nutrient cycling is one of the key processes in the overall ecosystem functioning.
To integrate nutrient cycling into food web studies, it is necessary to consider at least two additional components representing the limiting nutrient in their inorganic and organic forms: the mineral nutrient pool and the detritus pool respectively. Accordingly, nutrients that are unassimilated or lost from organisms (excretions, faeces, dead individuals or materials, etc.) return to the ecosystem via two main types of nutrient cycling processes. On the one hand, organisms release mineral nutrients in inorganic form via excretory processes (i.e. urine production), which is directly available for autotrophs and bacteria uptakes and termed as direct nutrient cycling (Vanni 2002). On the other hand, unassimilated organic matters (faeces), dead individuals and dead parts of higher plants return to the environment as detritus that need to be remineralized by decomposers before being available to autotrophs and bacteria (Moore et al. 2004). The process is named indirect nutrient cycling. Further, the availability of limiting nutrient is not only dependent on recycling within the local community but also on external nutrient inputs and outputs. Transportation of nutrients by physical forces (e.g. water, wind etc.) or by organisms at larger scales are also essential processes for nutrient dynamics. All above processes introduce new dynamical behaviors in food web models, which potentially lead to significant consequences on ecosystem functioning.
Figure.3 Contrasting patterns of energy flow and material cycling in ecosystems (adapted from (Loreau 2010)). a) Linear flows of energy through trophic interactions. b) Circular flows of materials among all ecosystem components.
Nutrient cycling and its potential effects on ecosystem functioning have been addressed in theoretical studies. In his work, DeAngelis (1980; 1989) discussed the effects of nutrient cycling on the resilience of the ecosystem (measured by the dominant eigenvalue of the Jacobian matrix at equilibrium) in models with increasing complexity. These models suggest that a high degree of nutrient cycling tends to increase the rate of biomass production but biomass is then restored less quickly after removal, making ecosystems less resilient to perturbations. Other studies have explored the impacts of nutrient cycling on trophic cascading effects (De Mazancourt et al. 1998; Leroux & Loreau 2010) and demonstrated that consumer-mediated nutrient cycling generally positively affected primary production due to indirect mutualism between ecosystem components. The meta-ecosystem theory connects a set of ecosystems by fluxes of organisms, dead organic matter and mineral nutrients, which reflects the nutrient dynamics in spatial context. The nutrient flux among ecosystems can affect the diversity and coexistence of organisms (Daufresne & Hedin 2005), the stability and the functioning of ecosystems (Loladze et al. 2000; Miller et al. 2004). However, modeling nutrient dynamics is still not very common in food web models compared to its importance on ecosystem functioning. In this thesis, I focus on the inclusion of nutrient dynamics in food web models, including both direct and indirect nutrient cycling among ecosystem components and spatial fluxes of nutrients in both inorganic and organic forms.
To do so, I use dynamic systems to describe nutrient fluxes in open ecosystems in which the limiting nutrient (in most ecosystems either nitrogen or phosphorus) is recycled between biotic and abiotic compartments. The mineral nutrient pool and detritus pool are denoted as and respectively. They are supplied by constant inputs and , and they lose nutrients from the ecosystem at constant rates and respectively. The nutrients that are lost by living compartments ( ) are recycled back to the ecosystem. There are two origins for these losses: one corresponds to natural loss such as excretion and death of individuals (occurs at rate ); the other is the fraction of nutrients that is not assimilated by consumers (1 − , ). We assume that only a fraction ( ) of the recycled nutrients goes to the mineral nutrient compartments ( ) that can be directly used by primary producers (direct nutrient cycling):
Here and are constant diffusion rates for nutrient and detritus respectively and and are indexes determining the asymmetry of nutrient and detritus fluxes between patches. Thus the differential equations describing the dynamics of and are:
Thus, in general, the dynamics of mineral nutrient and detritus consist of the following ingredients: inputs and outputs, nutrient fluxes due to direct and indirect nutrient cycling respectively, spatial fluxes between patches and the consumption by autotrophs and/or decomposers (Fig.4).
Figure. 4 Schematic fluxes of mineral nutrient and detritus in the ecosystems. Black arrows represent the consumption of nutrients and detritus by primary producers and decomposers. Red arrows represent inputs and outputs of nutrients and detritus. Blue arrows represent spatial fluxes of nutrients and detritus between patches. Green arrows represent nutrient fluxes due to direct (solid arrows) and indirect (dashed arrows) nutrient cycling respectively. , , are biotic components of the ecosystem which can represent primary producers, decomposer and herbivores respectively. Symbols and expressions are indicated in the text.
With the perspective of nutrient cycling, new components and new interactions are introduced to food web models. The interaction between autotrophs and decomposers is particularly interesting: on one hand, the production of both autotrophs and decomposers can be limited by the mineral nutrients; on the other hand, autotrophs produce organic matter which is the energy source of decomposers while decomposers in return mineralize mineral nutrients to support the production of autotrophs (Fig.5). Further, both autotrophs and decomposers support upper trophic levels within the ecosystem: there is a green food web based on the production of autotrophs (i.e. primary production) and a brown food web based on decomposition of organic matters (i.e. detritus). The complex interaction between autotrophs and decomposers reveals the complex interaction between the green and the brown food webs, which is a fundamental structure of ecosystems. This particular structure of food webs can have important consequences on ecosystem functioning. In the following section I summarize the interactions between these two food webs and how I plan to integrate these interactions into food web models to study their effects on ecosystem functioning.
Figure. 5 Indirect mutualism and resource competition in a primary producer-decomposer system with nutrient recycling (adapted from (Daufresne & Loreau 2001)). Solid and dashed arrows represent respectively the indirect mutualism (i.e. the primary producers provide detritus through death and excretion, which constitutes the energy resource for decomposers, and decomposers decompose the detritus and recycle the nutrient by mineralization) and the competition for mineral nutrients between primary producers and decomposers.

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Interactions between the green and brown food webs

Classical studies on trophic dynamics mediated by top consumers and resources consider exclusively the green food web based on primary production. However, in most ecosystems, the green food web is not the only pathway of energy and nutrient (Polis & Strong 1996; Cebrian 1999). The majority of primary production and the organic matters excreted by herbivores and carnivores go directly to detritus and support a diverse collection of consumers: the brown food web. In addition to its importance in ecosystem energy flows, the brown food web based on detritus play a significant role in nutrient cycling due to the decomposition process which regenerate nutrients back to the ecosystem (DeAngelis 1992; Moore et al. 2004). As mentioned in the previous section, primary producers in the green food web and decomposers in the brown food web have both competitive (i.e. growth based on mineral nutrients) and mutualistic (i.e. production of detritus by primary producers and remineralization of nutrients by decomposers) interactions (Fig.5). These interactions may extend to the whole food web and generate complex interactions between the green and the brown food webs.
At the food web scale, interactions between the green and the brown food webs often occur through three major ways:

1) Nutrient cycling

All organisms of both food webs lead to direct and indirect nutrient cycling that support the mineral nutrient and detritus pool respectively. This leads to the competitive and indirect mutualistic interactions between primary producers and decomposers mentioned above. It has been demonstrated that these complex interactions are dependent on the limitation types of decomposers and the stoichiometry mismatches between decomposers and their resources (Daufresne & Loreau 2001). According to ecological stoichiometry, the mismatch in elemental quality (i.e. nutrient to carbon ratios) between decomposers and their resources can determine decomposers nutrient uptakes. Increasing mismatch means that the decomposers need to take more nutrients, and the competition intensity between primary producers and decomposers then increases. Thus, through nutrient cycling, the green and the brown food webs are linked at the bottom of the food webs.

2) Generalist consumers

There are generalist predators that feed on prey from both the green and the brown food webs. For example, many aquatic consumers (e.g. filter-feeding organisms, planktivorous and piscivorous fish) consume prey on the basis of body size and can be trophic generalists which potentially link the autotroph-based pelagic webs and detritus-based benthic webs in freshwater ecosystems (Vander Zanden & Vadeboncoeur 2002; Vadeboncoeur et al. 2005; Shurin et al. 2006). In terrestrial ecosystems, the generalist predators (e.g. spiders, staphylinid and carabid beetles) are known to rely on food resources from both above-ground (i.e. feeding on plant herbivores) and below-ground (i.e. feeding on systems microbial detritivores) (Polis & Strong 1996; Wardle et al. 2004). Therefore, through generalist consumers, the green and the brown food webs are linked at the top of the food webs.

3) Spatial couplings

The green and brown food webs may occupy spatially separated habitats. For example, pelagic (based mainly on phytoplanktonic production, the green food web) and benthic (based mainly on detritus, the brown food web) habitats are spatially decoupled but there are many cross-habitat interactions between them (Jäger & Diehl 2014). Since nutrient cycling and generalist consumers link the green and the brown food webs at the bottom and at the top of food webs respectively, the spatial fluxes of nutrient and detritus and the mobility of consumers and predators lead to spatial couplings of the green and the brown food webs.
The effects of interactions between the green and the brown food webs on food web functioning have been largely documented in empirical studies. For example, the concept of ‘microbial loop’ demonstrate that predators in the brown food web can increase nutrient mineralization, which can indirectly affect primary production (Azam et al. 1983; Bonkowski 2004). It has also been shown that decomposer-mediated remineralization responds strongly to the quality and quantity of dead organic matter produced by the green food web (Wardle et al. 2003; Harrault et al. 2012). By contrast, interactions between the green and brown food webs have only been increasingly explored in recent theoretical studies. Attayde and Ripa (2008) have constructed a food web model comprising a green and a brown food chains coupled by nutrient cycling and a generalist carnivore. They demonstrated that both couplings interact to affect the mean abundance of the food web components along a gradient of nutrient enrichment. Generalist predators consuming prey from both food webs are reported to stabilize or destabilize the ecosystem under distinct conditions (Wolkovich et al. 2014). However, there is still a very large gap between empirical observations and theoretical studies on the interactions between the green and brown food webs and their important effects on ecosystem functioning.
A more complete framework integrating the interactions between the green and brown food webs is needed to study their effects on the ecosystem functioning. This is the goal of the thesis. The main interactions between both food webs and the related ecosystem functions studied in the thesis are briefly listed in Table 2. A more detailed plan of the thesis is given in the next section.
This thesis contains three modelling studies and one experimental study. Each of these studies is presented in one chapter and the chapters are linked by the principal idea: the interactions between the green and brown food webs are key to understand ecosystem functioning. I start by connecting the green and brown food chains by nutrient cycling in the first model (Chapter 2) and show how the top-down trophic cascading effects of one food chain can affect the production of the other food chain. The second model (Chapter 3) integrates additionally another important interaction: the generalist consumers feeding on prey from both food chains. Effects of the asymmetry in energy channel/turnover between the two food chains and nutrient cycling mediated competitive/mutualistic relationship between primary producers and decomposers on ecosystem stability are explored. The third model (Chapter 4) puts the interactions at bottom through nutrient cycling and at top through generalist consumers into a spatial context. It examines how the spatial fluxes of nutrient and detritus and spatial coupling by mobile consumers interact to affect the relative dominance of the green or the brown food webs. I also include an experimental study (Chapter 5) in which the theoretical predictions can be tested in the aquatic environment. In particular, the mesocosm experiment examines the top-down and bottom-up cascades under different scenarios of coupling between the green and brown food webs. Results in the Chapter 5 are still preliminary. Here I present an overview of the results from these four studies and a general discussion and perspectives of the thesis can be found in the last chapter (Chapter 6).
In this chapter the primary producer-based green chain and the decomposer-based brown chain are connected by nutrient cycling in a dynamical food web model. The model explores analytically the conditions that determine the direction of cascading effects from one food web to the other in different scenarios based on various assumptions. These assumptions include: 1) donor vs recipient control of decomposer production; 2) the limitation type of decomposers (i.e. carbon or nutrient limitation) and 3) different trophic lengths in both food chains. Numerical analysis are used to confirm the analytical predictions, with an additional analysis to compare linear vs type II functional responses. Results derived from different assumptions and under different functional responses provide a solid analysis on the robustness of the model predictions. Experiments published on cascading effects from one food web to the other are reinterpreted in relation to this work.

Table of contents :

Chapter 1 Introduction 
1.1 Food web structure and ecosystem functioning
1.2 Modeling the food web structure
1.3 Nutrient cycling
1.4 Interactions between the green and brown food webs
1.5 Structure of the thesis
Chapter 2 Interactions between the green and brown food web determine ecosystem functioning
Key words
Supporting Information
Appendix 1 Equilibrium results and related signs of partial derivatives for model 3-2
Appendix 2 Other models with different food chain lengths
Appendix 3 Simulations of models with type II functional responses
Chapter 3 Consequences of asymmetry between green and brown food webs on stability of aquatic and terrestrial ecosystems 
Chapter 4 Linking the green and brown food webs through spatial coupling and consequences on ecosystem functioning 
Chapter 5 Interactions between green and brown food webs in freshwater ecosystems: preliminary results of a mesocosm experiment
Ack now ledgments
Chapter 6 Discussion 
6.1 Importance of integrating interactions between the green and brown food webs into food web models
6.2 Perspectives


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