Importance of integrating interactions between the green and brown food webs into food web models

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Effects of the brown food chain on primary production

Primary production is directly proportional to the stock of mineral nutrients and primary producers (𝜑𝑃𝑃∗=𝑎𝑃𝑁𝑁∗𝑃∗). Since N* is independent of parameters from the brown food chain when the green food chain length is 3-level, the stock of primary producers (P*) is essential to understand the effects of the brown food chain on primary production.
First, direct nutrient cycling (1− 𝛿𝑖) by all compartments always increases primary production. Indeed, all δi terms contribute negatively to C*, which is positively correlated with P* (Table S1). Therefore primary production always decreases when δi increases (i.e. when a higher proportion of nutrient is recycled in organic form). The signs of partial derivatives (Appendix 1 Table S2) confirm this result, 𝜕𝜑𝑃𝑃∗𝜕𝛿𝑖⁄ is always negative.
Second, primary production is affected by both decomposers and their predators in the brown food chain. The signs of the effects of decomposer and predator parameters are condition-dependent except for the effects of decomposer nutrient uptake rate (Table S2).
When decomposers are N-limited, primary production always decreases with the rate of mineral nutrient consumption by decomposers (𝑎𝐵𝑁). As mentioned above (Table S1), N* does not change with 𝑎𝐵𝑁. Instead, increasing 𝑎𝐵𝑁 leads to a larger amount of nutrients being stored in the brown food chain (F* increases with 𝑎𝐵𝑁) and a smaller amount of nutrient being stored in the green chain including the primary producer compartment (C* and, thus, P* decrease when F* increases). Since primary production is directly proportional to producer biomass P*, primary production decreases as 𝑎𝐵𝑁 increases.
In most cases for other parameters of the brown food chains, the difference between δB and δF (relative proportion of direct/indirect nutrient cycling by decomposers and their predators) is the key factor determining the effect of the brown food web on the production of the green food web. When 𝛿𝐵−𝛿𝐹>0, i.e. when decomposers recycle a higher proportion of nutrients in organic form than their predator, the effects of nutrient release rate (dB) by decomposers on primary production are negative, otherwise the effects are positive. The effects of detritus consumption rates by decomposers (𝑎𝐵𝐷) on primary production are also partly determined by the sign of 𝛿𝐵−𝛿𝐹. They depend on the sign of (1−𝛿𝐵)+𝑒𝐵𝐷(𝛿𝐵−𝛿𝐹𝑞𝐵𝑞𝐷) when decomposers are C-limited and the sign of (1−𝛿𝐵)+𝑒𝐵𝐷(𝛿𝐵−𝛿𝐹) when decomposers are N-limited. Thus, if decomposers recycle a larger proportion of nutrients in organic form than their predators, larger decomposer consumption rate of detritus will generally result in larger primary production. Otherwise, the effects of this parameter might be negative on primary production.
Further, when decomposers are donor-controlled, the same condition 𝛿𝐵−𝛿𝐹 determines the effects of predators of decomposers on primary production. When 𝛿𝐵>𝛿𝐹, decomposers recycle a higher proportion of nutrients in organic form than their predators, and consumption of predators of decomposers increases primary production (𝜕𝜑𝑃𝑃∗𝜕𝑎𝐹𝐵⁄>0 and Fig. 2a, see also Fig. S2 in Appendix 3 for Type II functional responses). The primary production increases by 36.9% (29% when N-limited) when the consumption rate of predators of decomposers (𝑎𝐹𝐵) increases from 0.1 to 0.2 L (μg N) -1 day-1. Meanwhile, the rate of nutrient release from predators of decomposers affects negatively primary production (𝜕𝜑𝑃𝑃∗𝜕𝑑𝐹⁄<0, Fig. 2b). The primary production decreases by 22.8% (25.6% when N-limited) when the rate of nutrient release of predators (dF) increases from 0.5 to 1.0 day-1. The condition 𝛿𝐵<𝛿𝐹 leads to the opposite results (Fig. 2c,d, see also Fig. S2 in Appendix 3 for Type II functional responses). The primary production decreases by 59.7% (29.8% when N-limited) with increase in 𝑎𝐹𝐵 (i.e. negative effects of 𝑎𝐹𝐵on primary production) and increases by 58.7% (44.9% when N-limited) with increase in dF (i.e. positive effects of dF on primary production).

Effects of the green food chain on decomposer production

Traditional top-down regulations in the green food web follow a cascade – the non-adjacent levels have the same effects on primary production while the adjacent trophic levels have opposite effects (Leroux & Loreau 2008). We show that these cascading top-down effects of the green food web climb up the brown one and affect decomposer production. In all cases, the effects of carnivores and primary producers on decomposer production are always of the same sign while the effects of herbivores are opposite. Interestingly, when decomposers are N-limited, effects of the green food chain on decomposer production are condition-dependent (Table S2, conditions detailed below). In any case, decomposer production does not depend on the relative proportion of direct/indirect nutrient cycling (𝜕𝜑𝑃𝐵∗𝜕𝛿𝑖=0⁄ in all scenarios) because stocks of mineral nutrients and detritus at steady states are independent of δi. Effects of the green food chain on decomposer production are thus independent of the proportion of direct/indirect nutrient cycling too.
In case of C-limitation, the consumption rate of carnivores (𝑎𝐶𝐻) and the nutrient uptake rate of primary producers (𝑎𝑃𝑁) have positive effects on decomposer production while the consumption rate of herbivores (𝑎𝐻𝑃) has a negative effect (Table S2 and Fig. 3). Decomposer production increases by 30.8% (for both donor-controlled and Lotka-Volterra functions) when 𝑎𝐶𝐻 increases from 0.3 to 0.6 L (μg N) -1 day-1. It increases by 33.1% (for both donor-controlled and Lotka-Volterra functions) when 𝑎𝑃𝑁 increases from 0.3 to 0.6 L (μg N) -1 day-1. To the contrary, decomposer production decreases by 61.5% (61.6% for Lotka-Volterra function) when 𝑎𝐻𝑃 increases from 0.8 to 1.6 L (μg N) -1 day-1.
In case of N-limitation, the signs of these cascading effects is governed by the sign of 𝑒𝐵𝐷𝑎𝐵𝐷 /𝑙𝐷−𝑎𝐵𝑁/𝑙𝑁. The ratios 𝑎𝐵𝑁/𝑙𝑁 and 𝑒𝐵𝐷𝑎𝐵𝐷 /𝑙𝐷 represent the consumption rates of mineral nutrients and detritus by decomposers divided by the rate of nutrient loss from these compartments. A higher ratio implies that a higher proportion of nutrients and detritus is assimilated by decomposers rather than being lost from the ecosystem. The signs and magnitude of cascading effects of carnivores, herbivores and primary producers remain the same as in the C-limitated case if 𝑒𝐵𝐷𝑎𝐵𝐷 /𝑙𝐷>𝑎𝐵𝑁/𝑙𝑁 (Fig. 3a. b. c). If 𝑒𝐵𝐷𝑎𝐵𝐷 /𝑙𝐷<𝑎𝐵𝑁/𝑙𝑁, the directions of the cascading effects are opposite (Fig. 3d. e. f). The production of decomposers decreases by 7.9% (7.7% for Lotka-Volterra function) and by 8.4% (8.4% for Lotka-Volterra function) respectively with an increase in 𝑎𝐶𝐻 and 𝑎𝑃𝑁 while it increases by 15.5% (15.7% for Lotka-Volterra function) with an increase in 𝑎𝐻𝑃. The condition is independent of decomposer functional response. Thus, the cascading effects of the green food web on the production of decomposers strongly depend on the limitation of decomposers.

Cascading effects of the brown food chain on primary production

The predation on decomposers in the brown food web is thought to have a major influence on primary production in all ecosystems. Most empirical studies predict that predators of decomposers increase primary production by raising nutrient availability. In terrestrial ecosystems, the “microbial loop” hypothesis suggests that bacterial grazers, e.g. protozoa or nematodes, liberate nutrients locked up in bacterial biomass, thus increasing nutrient availability to primary producers (Krome et al. 2009; Irshad et al. 2011). In aquatic ecosystems, bacterivorous protozoa mostly act as remineralizers of the limiting nutrient (Caron et al. 1988) and induce growth of autotrophic plankton (Ferrier & Rassoulzadegan 1991). Models have rarely addressed direct positive effects of predators of decomposers on primary production but have focused on their beneficial effects on primary production in the context of algal-bacterial competition (Bratbak & Thingstad 1985; Thingstad & Lignell 1997; Thingstad 1998). Nevertheless, these models suggest that predators of decomposers allow coexistence of phytoplankton and bacteria on the same limiting mineral nutrient when bacteria are the superior competitors, and thus indirectly demonstrate that predators of decomposers can benefit primary production. Our model is the first to explain observed cases of positive effects of predators of decomposers on primary production through nutrient cycling. It also suggests that the effect of predators of decomposers on primary production can be negative depending on the relative ability of decomposers and their predators to recycle nutrients. To our knowledge, such issue has never been tested experimentally.
Previous food-web studies that included recycling processes modelled either direct (Leroux and Loreau 2010) or indirect (De Mazancourt et al. 1998) nutrient cycling in ecosystems. In real ecosystems (Vanni 2002), both direct and indirect nutrient cycling contribute to affect ecosystem functioning. For example, direct nutrient excretion by fish and zooplankton could meet respectively 5% and 26% of phosphorus demand of phytoplankton (Schindler et al. 1993). Indirect nutrient cycling through the remineralisation of detritus affects the productivity of lakes (Jansson et al. 2000). The integration of both direct and indirect nutrient cycling is one of the major novelties in our model. We show that the effects of predators of decomposers on primary production depend strongly on their relative proportion of direct/indirect nutrient cycling compared to those of decomposers. When predators of decomposers recycle directly a larger (smaller) proportion of their nutrient than decomposers, their consumption of decomposers increases (decreases) primary production. We propose a possible mechanism behind the positive effects of “microbial loop” on primary production by linking the proportion of direct nutrient cycling to stoichiometric mismatches between decomposers and their predators and between detritus and decomposers. Due to stoichiometric constraints (Vanni 2002), a species with a relatively low mineral nutrient content should excrete more nutrients than a species with a higher nutrient content. Therefore, if predators of decomposers have a higher carbon-to-nutrient ratio than their prey, they might recycle a higher proportion of inorganic nutrients than their prey, leading to positive effects on primary production (i.e. predators have a relatively low value of δF thus δB>δF). This condition is likely to be met since predators of decomposers such as flagellates prefer prey rich in nutrients (i.e. lower C:N) (Grover & Chrzanowski 2009). Besides, decomposers might recycle directly less mineral nutrients than predators of decomposers because of the higher C:N ratio in detritus than in decomposers (Caron et al. 1988; Thingstad & Lignell 1997). This should lead to a relatively high value of δB, and again to positive effects of predators of decomposers on primary production.

Does asymmetry always stabilize ecosystems?

Our results show that asymmetry is not always stabilizing in ecosystems and that asymmetry consequences strongly depend on the nature of interactions at the bottom of food webs and on whether we consider the coupling between two green or one green–one brown webs. The results derived from the G-G model demonstrate that the asymmetry in growth/attack rates between coupled green channels stabilizes the ecosystem. This is consistent with earlier modelling results showing that contrasted speeds of energy channels are essential to ecosystem stability (Rooney et al. 2006). However, results of the G-B model show that asymmetry does not necessarily increase stability and can instead be strongly destabilizing depending on stoichiometry-based interactions between primary producers and decomposers. These predictions contradict those of Rooney et al.’s (2006) model which did not integrate the coupling of green and brown food channels. However, a recent modelling study that considered the coupling of autotrophs and detritus by first-consumer level has also noted that asymmetry might have destabilizing effects on certain conditions (Wolkovich et al. 2014).
Previous studies on the stability consequences of asymmetry have focused on top-down effects from the generalist predator that couples two asymmetrical channels: the fast channel allows rapid recoveries of the predator from large perturbations while the slow channel dampens the strong responses of the fast channel (Rooney et al. 2006). Our results highlight that the bottom-up effects due to the complex relationship between autotrophs and decomposers is also influential for the effects of asymmetry on stability. In particular, effects of asymmetry on stability are strongly driven by the strength of competition between the producers of the two channels. When there is no competition between autotrophs and decomposers, asymmetry towards a slower green food channel is highly destabilizing whereas when competition is strong, asymmetry towards a faster green food channel tends to destabilize the ecosystem. The competition between autotrophs and decomposers is based on the consumer-driven nutrient recycling theory (CNR), that homeostatic organisms maintain their elemental composition by taking up mineral nutrients when their resource C:nutrient ratio is higher than their own C:nutrient ratio (Daufresne & Loreau 2001). The CNR theory has been recognized as key to understand ecosystem processes such as mineralization as well as interactions between green and brown food webs in both aquatic and terrestrial ecosystems (Chase 2000; Sardans et al. 2012; Daufresne & Loreau 2001; Cherif & Loreau 2007, 2013; Zou et al. 2016). Our results thus suggest that the stoichiometric compositions of detritus and decomposers are also key to understand the effects of asymmetry between energy channels on ecosystem stability. While we did not model different scenarios of competition between the coupled green channels, competition might also vary between primary producers as different autotrophs might be limited by different nutrients. Consequently, we might expect that asymmetry could also destabilize the dynamics of coupled green channels when producers weakly compete.
Nutrient cycling, a major component of the interaction between green and brown food channels, also affect ecosystem stability, in interaction with the effects of asymmetry between these food channels. While increased nutrient cycling tends to attenuate the destabilizing effects of asymmetry when competition between decomposers and primary producers is weak, it has a destabilizing effect when competition is strong especially when the strength of the two food channels are symmetric. Increased nutrient cycling also amplifies the destabilizing effect of symmetry between coupled green channels.

Differences in asymmetry degree and competition between basal trophic levels in aquatic and terrestrial ecosystems

Our model results suggest that the degree of asymmetry between green and brown food channels, as well as its direction (i.e. faster green or faster brown food channel), are fundamental to our understanding of ecosystem stability. So far, asymmetry between green and brown food channels within ecosystems has been rarely investigated (Rooney et al. 2008), and the few existing studies have not compared how this asymmetry varies among ecosystem types. Meta-analyses have focused on the comparison of the turnover of either green or brown food channels between aquatic and terrestrial ecosystems (Cebrian 1999, 2004; Cebrian & Lartigue 2004). They found that aquatic herbivores turn over slightly faster (i.e. 1.3 times on average) than terrestrial herbivore while aquatic detritus consumers turn over much faster (i.e. over 10 times faster) than their terrestrial counterparts. By further analyzing the data compiled by these meta-analyses, we suggest that turnover rates of green and brown channels are often asymmetric within an ecosystem, and that this asymmetry depends on ecosystem type. In aquatic ecosystems, the green channel seems to turnover faster than the brown channel, while it tends to be the opposite in terrestrial ecosystems. Future studies will need to further compare asymmetry degree between aquatic and terrestrial ecosystems to assess the robustness of this result. In particular, freshwater pelagic ecosystems were lacking from the dataset we analyzed. Several mechanisms might explain the difference in asymmetry degree between aquatic and terrestrial ecosystems. First, due to the negative relationship between body size and biomass turnover rate (Peters 1986), terrestrial autotrophs that are relatively large (e.g. vascular plants), tend to have relatively low turnover rates in comparison with aquatic autotrophs. The difference in body size ratios between herbivores and autotrophs and between decomposers and their consumers between aquatic and terrestrial ecosystems (Shurin et al. 2006) leads to difference in asymmetry degree, which may explain why terrestrial ecosystems tend to have a relatively faster brown channel. A second possibility is that terrestrial autotrophs may allocate more energy to defence against herbivory, resulting in slower growth and turnover than their aquatic counterparts (Strong 1992), which leads to relatively slower green food channels. Further studies exploring these mechanisms should help to test the robustness of our predictions on differences between ecosystem types.

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.
Summary
Key words
Introduction
Methods
Results
Discussion
Tables
Figures
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
Abstract
Introduction
Methods
Results
Discussion
Tables
Figures
Appendix
Chapter 4 Linking the green and brown food webs through spatial coupling and consequences on ecosystem functioning
Abstract
Introduction
Methods
Results
Discussion
Notes:
Tables
Figures
Chapter 5 Interactions between green and brown food webs in freshwater ecosystems: preliminary results of a mesocosm experiment
Introduction
Methods
Results
Discussion
Acknowledgments
Chapter 6 Discussion
6.1 Importance of integrating interactions between the green and brown food webs into food web models
6.2 Perspectives
References

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