Food web structure alters ecological communities top-heaviness with little effect on the biodiversity-functioning relationship

In a rapidly changing world, the composition, diversity and structure of ecological communities face many threats. Biodiversity-Ecosystem Functioning (BEF) and community food-chain analyses have focused on investigating the consequences of these changes on ecosystem processes and the resulting functions. These different and diverging conceptual frameworks have each produced important results and identified a set of important mechanisms, that shape ecosystem functions. But the disconnection between these frameworks, and the various simplifications of the study systems are not representative of the complexity of real-world communities. Here we use food webs as a more realistic depiction of communities, and use a bioenergetic model to simulate their biomass dynamics and quantify the resulting flows and stocks of biomass. We use tools from food web analysis to investigate how the predictions from BEF and food-chain analyses fit together, how they correlate to food-web structure and how it might help us understand the interplay between various drivers of ecosystem functioning. We show that food web structure is correlated to the community’s efficiency in storing the captured biomass, which may explain the distribution of biomass (top heaviness) across the different trophic compartments (producers, primary and secondary consumers). While we know that ecological network structure is important in shaping ecosystem dynamics, identifying structural attributes important in shaping ecosystem processes and synthesizing how it affects various underpinning mechanisms may help prioritize key conservation targets to protect not only biodiversity but also its structure and the resulting services.


31
Understanding the consequence of diversity on ecosystems process rates has become one of the ecologists 32 priorities since we realized that human activities threaten both species existence (MEA 2005)  analyze, model and ultimately gain understanding of the aggregated ecosystem processes they underlay, 59 from primary production to pressure of top carnivores (DeAngelis 1992), providing a way to estimate 60 ecosystem multi-functionality (de ned as the provisioning of multiple ecosystem functions; Barnes et al. 61 2018) and the potential to sustain various ecosystem services (Soliveres et al. 2016). By mapping trophic 62 interactions, food webs also map biomass routes through the communities, the dynamics of the transfer of 63 biomass through these routes can be modelled using adapted consumer-resource models such as Yodzis & 64 Innes (1992). In parallel, the structure of these routes can be analyzed through a set of measures, adapted 65 from graph theory, that carry a diversity of ecological information such as species degree of specialization, 66 distance to producers, etc. framework involving competition and consumption, but no consensus has yet been reached.

80
Most of these recent analyses, using food webs to investigate diversity e ects, although they integrate both 81 dimensions of diversity (vertical and horizontal), do not necessarily attempt to bridge the gap between 82 the conceptual frameworks that have emerged from the analysis of their e ects in isolation (namely BEF 83 and trophic chain theories). The analysis of trophic chains dynamics in particular has produced important 84 results for understanding the functioning of ecosystems (Ives et al. 2005 intra-guild predators) in a community, a variation in consumer richness will not have the same impact on 90 plant biomass (losing a predator leads to a reduction in plant richness, whereas a decrease in the richness of 91 omnivores leads to an increase in their biomass; Polis & Strong (1996)).

92
One important results from food chain theory, and more speci cally from analyzing the e ect of community-93 level trophic cascades (as opposed as species-level; Polis 1999), is the in uence on community shapes. By 94 shape we refer to what is generally called trophic structure, i.e., a quali cation of the distribution of biomass 95 or abundance along the di erent trophic levels of the community (cascade or pyramid, top or bottom heavy). 96 We use the term shape here to avoid confusion with the food-web network structure. Recent studies by 97  105 We believe that understanding the reciprocal feedback between biomass uxes -underpinning ecosystem 106 processes -food-web structure and community shape is an important key in the search for the mechanisms 107 driving diversity e ects on ecosystem functioning in complex communities. Investigating these relationship 108 may help us understand the interdependence between the di erent drivers of ecosystem functioning, and in 109 particular the way diversity and structure interact and drive ecosystem processes. We expect for example 110 that the BEF relationship will be di erent depending on community shape, re ecting di erent energetic 111 constraints on the dynamic transfers of biomass through trophic interactions. To test our hypothesis, we 112 used food webs to represent communities, and simulated their biomass dynamics using a consumer-resource 113 bioenergetic model adapted to food webs (Yodzis & Innes 1992; Williams et al. 2007). We investigated the 114 potential link between the emerging shape of the communities, their food-web structure and BEF relationship. 115 If our hypothesis proves to be valid, this would o er a possible explanation for the apparent idiosyncrasy of 116 the BEF relationship in food webs. It would also provide ideas about the possible mechanisms responsible for 117 the diversity-functioning relationship in complex ecological communities. described in the driving eq. 1 below: autotrophic production ( rst term of eq. 1), transfer of biomass through 124 consumption (second and third terms of eq. 1), and loss of biomass because of metabolism (fourth term of eq. 125 1) and imperfect assimilation ( ). The details of the model for plant growth ( ( )), functional response ( ji ) 126 and all parameter values are described in supplementary material (appendix 1, section S1).  In the nutrient intake model (Brose et al. 2005b(Brose et al. , 2005aBrose 2008), all producers share two nutrients 1 and 137 2 . Nutrients availability is determined by their respective rates of supply, turnover and consumption by 138 plants. Plants all have di erent half-saturation density for both nutrients, which results in a hierarchy of 139 competition between them, as a lower half-saturation means a higher intake e ciency. As plants do not 140 need all nutrients in the same quantities, we set nutrient content in plants ( 1 and 2 for respectively 1 and 141 2 ) to re ect this. We set 1 = 1 and 2 = 0.5, meaning that plants need a higher quantity of 1 than 2 . assimilation. The functional response and its parameters are described in supplementary material (appendix 150 1, section S1.1.2).

151
The biological rates controlling these processes -namely the growth, maximum consumption and metabolic 152 rates -are all dependant of two things: species metabolic class (vertebrate or invertebrate) and typical adult 153 body size. In other words, we have an allometric scaling of biological rates with body size, with di erent 154 allometric coe cient depending on the metabolic class.  for the biomass dynamics simulations. 183 We generated food webs with 10 levels of producers richness (from 2 to 20), and 7 levels of consumer richness 184 (from 5 to 35). For each of these 70 combinations of total species richness (7 to 55), we randomly generated 185 up to 100 di erent food webs with the ADBM model. For each food web, we randomly drew the producers 186 half-saturation density for the two shared nutrients, to generate a random hierarchy of competition among 187 the di erent food webs. This design produces food webs with di erent richness, structure and ability to 188 extract nutrients.

189
Because we wanted to set di erent typical consumer-resource body-mass ratio to explore the e ect of 190 allometric scaling, we did not use the original sampled body mass (used to generate food webs) in the 191 simulations to calculate biological rates but reassigned body masses based on a sampled consumer-resource 192 secondary consumers) to generate results at the food chain scale. As a precision we de ne omnivores as 215 species that can feed on both animals and producers.

216
To compare the biomass to intake relationships of communities with and without consumption, we also 217 simulated the biomass dynamics of communities with producers only. As we needed to see a variation in 218 intake, we simulated communities with varying richness (1 to 20) and supply rate (1 to 10). As intake is 219 always close to its maximum value in the absence of consumption, we used a linear regression to extrapolate 220 for a wider range of intake. Without consumption, the relationship between intake and stored biomass 221 should indeed be linear (metabolic losses scale linearly with species biomass).

222
Structure refers to the organization of trophic interactions between species within the food webs. Once 223 extinct species and the interactions to and from them were discarded, we measured the food web connectance, 224 we order a community compartments (P for producers, H for herbivores and C for secondary consumers) 238 according to their total biomass, if the result is P-H-C, the community has a BH pyramidal shape, P-C-H 239 gives a BH cascade shape, H-C-P and H-P-C both represent MH cascade shape, C-H-P is a TH pyramidal 240 shape (also called inverted pyramid of biomass) and C-P-H is a TH cascade-shaped community.  represents the food webs total intake, that which is equivalent in our model to primary production. We 276 expect that given energetic constraints (metabolism and imperfect assimilation), communities achieve higher 277 biomass, for the same intake, when there are no trophic interactions involved (e.g. a grassland with no 278 consumers). The majority of the food webs meets this expectation, displaying a regime below this reference 279 line. Yet, surprisingly, the producers-only baseline regime can be overshot in some cases (approx. 6.4 % of all 280 food webs). This can happen when food webs total intake is above a certain threshold, the value of this 281 intake threshold being dependent on the shape of the food webs. BH food webs ( g. 4, D and E) or MH 282 ( g. 4, C) have in average a lower biomass to intake regime than TH food webs ( g. 4, A and B), which 283 represent a lower ability to store the captured biomass. For example, for a total intake of 0.75, the theoretical 284 relationship for a grassland gives a biomass of approx. 5.5 ( g. 4), BH food webs have a biomass largely 285 below this value (< 2.5, g. 4, D and E) but TH food webs have a biomass between 2.5 and 7 ( g. 4 A and B), 286 higher than BH and in some case than the theoretical baseline. This does not seem to depend on food webs 287 shape (cascade or pyramid), but only on their top heaviness, although BH cascade-shaped food webs seem 288 not to be able to overshoot the baseline even at maximum intake, unlike their cascade-shaped counterpart. 289 Storage e ciency is also strongly correlated to food webs mean body-size consumer-resource ratio ( ), at 290 the same intake value, higher is correlated to higher biomass. functioning relationships independently of their shape ( g. 6 and g. 5). Total biomass increases with both 295 animal and plant richness with similar rates for all shapes ( g. 6), although unfortunately there is not enough 296 variation in food webs displaying TH pyramid or MH shapes to analyze their BEF relationship. Looking 297 at the ows within food webs, we see a similar result, with qualitatively analogous relationship for the 298 di erent shapes, although it appears that TH pyramid-shaped and MH food webs display a lower level of 299 intake ( g. 5). While we reach maximum productivity even for low richness for the BH food webs ( g. 5, 300 bottom row), producers appear more strongly controlled in the TH food webs ( g. 5, top row) -especially 301 cascade-shaped ( g. 5, left column) -and the MH cascades in which herbivores are less regulated ( g. 5, 302 C), resulting in low productivity. Consumption, on the other hand is higher, whatever the level of animal 303 richness in the TH food webs ( g. 5, top row). This higher consumption is driven mainly by higher secondary 304 consumption, in particular higher intra-guild consumption. In TH and BH cascade-shaped food webs, we see 305 that productivity and secondary consumption both increase with richness while primary consumption 306 decreases ( g. 5, A and D). The fact, however, that all richness-functioning relationships are qualitatively 307 similar seems to con rm the existence of a universal diversity e ect, albeit more or less strong depending on 308 shape, in food webs. light on the possible link between these di erent predictions, and thus on the concepts that frame them. of bottom heavy communities, presenting a relatively short trophic chain and a fairly low complexity, in the 329 sense that interactions seem to be only slightly entangled (they display a relatively weaker connectivity and 330 less omnivore/intraguild predation motifs, see g. 2 and 3). These communities have a high producer species 331 richness at their base, but a low consumer richness ( g. 6), thus displaying consumers feeding low in the 332 food chain and often generalists (which is translated by a high proportion of apparent competition motifs as 333 shown in g. 2). In other words, these communities are more horizontally than vertically diverse. Moving 334 along this gradient, we see higher and more complex communities at the other end (connectivity is larger and 335 they have a higher proportion of omnivore/intraguild predation motifs, see g. 2 and 3). Conversely, these 336 communities appear to be richer vertically than horizontally. In the middle, in an intermediate situation, 337 there are very few middle-heavy communities.

338
When we look at natural ecosystems, we realize that in the same way, they are dominated in most cases by 339  a particularly e cient functioning regime, which leads it to be able to store a large biomass in its apical 371 compartment, i.e., in top-heavy form. It is important to note, however, that although our approach yields communities with di erent shapes 374 (cascade-and pyramid-shaped), communities' shape does not appear to be related to particular food web 375 structures or to a particular functioning regime ( g. 4). For top-heavy communities, we are potentially 376 limited by the amount of data (only 20 food webs over the total 4589 display an inverted pyramidal shape). 377 The energy constraints are indeed such to maintain a high biomass of carnivores while the biomass of 378 producers is low that it is our understanding that very few communities in the context of our model have 379 been able to persist under these conditions. For bottom-heavy communities, however, we have almost as 380 many pyramid-shaped as we have cascade-shaped communities, and so we do not have this limitation. 381 And there seems to be very little di erence between the two, apart from the inability of the bottom-heavy 382 pyramids to overshoot the functioning regime of a purely competitive community. We think this is related to 383 the low relative biomass of carnivores. Indeed, in the cascade-shaped counterpart of the bottom-heavy 384 communities, we note that at high intakes, this baseline is slightly overshot, and that high intakes are 385 generally correlated with high animal diversity. This is what leads us to say that, in the context of our 386 analysis, top heaviness is a more important factor than shape in separating communities according to their 387 functioning regime. like we did here, the attributes of network structure that are important ecosystem processes, how species 409 contribute to di erent attributes, how di erent attributes interacts and how ecosystem processes feedback 410 on structure. This would ease the choice of conservation targets and make conservation more e cient. 411 We have emphasized the role of food web structure and its importance to understand ecosystem processes. 412 However, accurately sampling ecological networks such as food webs is not an easy task. of an interaction, to build mechanistic food-web models that produce realistic food webs, and more food-web 418 sampling are still needed. However, we show here that precise information may not necessarily be needed. In 419 fact, in the context of our work, species richness of trophic compartments and the animal to producer ratio 420 can be used to estimate the domain of variation of chain length, motifs distribution, and consumer-resource 421 body-mass ratio, which makes estimating the functioning regime of the community possible.

422
In conclusion, we show here that food web structure is important in understanding ecosystem functioning, 423 but is also the product of feedbacks between species richness and community functioning. If structure does 424 not appear to be in uencing qualitatively the diversity-functioning relationship, it still seems important 425 to other aspects of functioning such as the distribution of biomass along the food chain. This in turn 426 could result in di erent consequences when facing perturbations, as extinction risk increases with trophic 427 rank. Of course, before understanding the real-world implication, more work is needed. Our analysis lays 428 potentially interesting links, the validity and the generality of the relationships between food web structure, 429 top heaviness and functioning regime should be further tested, and the exact mechanisms underlying the 430 relationships identi ed. . We start by generating food webs with di erent levels of producer and consumer richness by sampling P producers and C consumers in a list of species (Benguela ecosystem as described in Yodzis, 1998). We retrieve the species body masses and metabolic classes. We pass the body masses to the Allometric Diet Breadth Model (ADBM, Petchey et al., 2008) to generate realistic food web interaction matrices. Simulation (bottom left). These matrices are passed to the Bioenergetic Food-Web model (Yodzis & Inès, 1992) to simulate their biomass dynamics. All species that have an average biomass below 10 −6 during the second half of the simulation are considered as extinct, all interactions from and to them are removed. Outputs (right side). Emerging food-web structures, total biomasses and uxes are calculated at the species level over the second half of the simulations and aggregated by trophic compartments (carnivores and omnivores in respectively dark and light orange, herbivores in black, producers in green). The whole system depends on the two basal nutrients (blue).

Figure 2
Distribution of some food web structural properties of interest. Here are represented the average food web height (maximum trophic level, A), consumer-resource body-size ratio (log10 scale, B), connectance (C), as well as the average frequency of 4 typical motifs in the food webs. These motifs correspond to typical trophic modules: omnivory (or intra-guild predation, D), linear food chain (E), apparent competition (F) and exploitative competition (G). Motifs are represented on top of these panels.

Figure 3
Typical food web structure and associated averaged biomass dynamics. Here are represented the average biomass dynamic for the three main compartments, for all bottom-heavy (A), middle-heavy (B) and top-heavy (C) food webs. For each compartment (plants in green, primary consumers in black and secondary consumers in light or dark orange, respectively for omnivores and carnivores), the total compartment biomass is averaged at each time step (solid line) and are represented with standard deviation (ribbon). A typical food web is plotted above the dynamics, following the same colour code. Nodes sizes represent the body mass of the di erent species (log10 scaled).

Figure 4
Bottom-heavy food webs have a lower intake-biomass regime on average but can exist at lower intake values and when consumers are on average smaller than their resources (log10(Z) < 0). This gure represents the relationship between food-web total intake and total biomass (each dots represent one food web) for di erent shapes, namely top-heavy (top, A and B), medium-heavy (middle row, C) and bottom-heavy (bottom, D and E) cascades (left, A, C and D) and pyramids (right, B and E). Dots are coloured according to the decimal logarithm of the average consumer-resource body-size ratio in the food web. The average shape is represented on the left of each plot for cascades and on the right for pyramids along with N, the number of food webs in each panel. The grey boxes represent the mean biomass of the three compartments (Plants P, Herbivores C1 and secondary consumers C2).

Figure 5
Animal richness -ux relationship in food webs with di erent shapes. This gures shows the e ect of total animal richness on food webs total intake for the di erent compartments (colour coded, see legend) and the di erent shapes, namely top-heavy (top, A and B), medium-heavy (middle row, C) and bottom-heavy (bottom, D and E) cascades (left, A, C and D) and pyramids (right, B and E). The solid line represents the average response and the shaded area represent the standard deviation around the mean. The average shape is represented on the left of each plot for cascades and on the right for pyramids along with N, the number of food webs in each panel. The grey boxes represent the mean biomass of the three compartments (Plants P, Herbivores C1 and secondary consumers C2).

Figure 6
Diversity -total biomass relationships in food webs with di erent shapes. This gures shows the e ect of producers and consumers richness on food webs total biomass for food webs of di erent shapes, namely top-heavy (top, A and B), medium-heavy (middle row, C) and bottom-heavy (bottom, D and E) cascades (left, A, C and D) and pyramids (right, B and E).