Pollinators in food webs: Mutualistic interactions increase diversity, stability, and function in multiplex networks

Ecosystems are composed of complex networks of many species interacting in different ways. While ecologists have long studied food webs of feeding interactions, recent studies increasingly focus on mutualistic networks such as those of plants who exchange food for reproductive services provided by animals such as pollinators. Here, we synthesize both types of consumer-resource interactions to better understand the controversial effects of mutualism on complex ecosystems. Contrary to classic theory, we find that the dynamics of pollination mutualisms can increase the diversity, stability, and several ecosystem functions of multiplex ecological networks. These effects strongly increase with floral reward productivity and are qualitatively robust to variation in the prevalence of mutualism and pollinators feeding upon vegetation and other species in addition to floral rewards. This work advances the ability of mechanistic network theory to synthesize different types of ecological interactions and illustrates how mutualism can enhance the diversity, stability, and function of complex ecosystems.


INTRODUCTION 38
As elegantly illustrated by Darwin's "tangled bank," 1 ecosystems are complex, 39 composed of many different types of interactions among many different species. 40 However, theory has classically predicted that complexity in terms of the number and "orgy of mutual benefaction" (pg. 95) 5 whose instability due to positive feedback loops 45 helps explain why mutualism is infrequent and unimportant in natural systems. 3 Yet, 46 mutualisms appear to be not only frequent but key to maintaining much of the 47 biodiversity that drives ecosystems 6,7 , especially agricultural ecosystems essential to 48 human wellbeing 8,9 . Here, we address such disparities between theory and observation 49 by developing and applying an integrated consumer-resource theory of feeding and 50 reproductive mechanisms. We use our multiplex network model based on this theory to 51 study how mutualism affects the dynamics, stability, and function of complex 52 ecosystems. 53 The integration pursued here benefits from long but largely separate traditions of 54 research on feeding and mutualistic interactions 8,10 . For example, feeding interactions 55 complexity of mutualism relative to antagonism in "merged" plant-pollinator and plant- representing interspecific interactions as randomly parameterized or density-93 independent effects 2,4,35,44 instead of density-dependent mechanisms whose effects may 94 dynamically vary quantitatively and even qualitatively. For example, whether a 95 "mutualistic" interaction results in net benefit to both partners often depends upon a 96 threshold past which more reproductive services or food will damage or fail to provide 97 benefits to satiated consumers of these resources 26,29,30,44 . Additionally, the random 98 network architectures 4,41 often misrepresent the empirically observed structure of 99 mutualistic interactions 45 . A broader problem is that narrowly focusing on stability 100 develops inefficient theory 46 that ignores how mutualisms alter the diversity, 101 population dynamics, and overall functioning of complex ecosystems. 102 To help resolve these contradictions and more broadly understand the ecology of 103 mutualistic interactions, here, we follow repeated calls for synthesizing different types 104 of interactions within networks 8,10,31-35 by developing and applying mechanistic 105 consumer-resource theory to "multiplex" ecological networks 34,36 . Our multiplex 106 networks integrate the structure and dynamics of feeding and reproductive mechanisms 107 from which a interspecific interactions and subsequent effects emerge including 108 predation, mutualism, and resource and apparent competition 29,44,47 . Realistically involving 16% to 65% of species in the networks. Initial herbivory in FW treatments 136 correspondingly increases from directly involving approximately a half to three quarters 137 7 of the species in the networks. We thus assess stability and function in networks of 138 increasing initial diversity, which corresponds to increasing mutualism in multiplex 139 networks or increasing herbivory in FW treatments. Within each multiplex network 140 treatment, we varied the reward productivity of plants with pollinators by a factor of 141 five between "Low" and "High" productivity. Species within our networks initialized in 142 this manner persist or go extinct during our simulations lasting 5000 timesteps (Fig. 2).

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Following transitory dynamics, our analyses of the final 1000 timesteps find that 144 mutualistic interactions increase diversity, stability, and ecosystem function of 145 multiplex networks and that these increases are greatly enhanced by High reward 146 productivity ( Fig. 3-4).

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Diversity. 149 Multiplex treatments with High reward productivity (High RO and High RP) had Low RO, and Low RP treatments (Fig. 3b). This difference is primarily due to the 158 consistently high persistence of pollinators (~60%) compared to the persistence of 159 added species in the FW treatments (Fig. 3f, 3g) and the increasing persistence of increases in persistence from ~5% to 50% with increasing mutualism (Fig. 3d). In 163 contrast, FW and Low rewards treatments had much lower persistence of carnivores (2-164 3%, Fig. 3d), omnivores (~15-30% Fig. 3e), and pollinators (~15-45%, Fig. 3f, 3g) that, 165 except for carnivores, decreased with increasing mutualism. In the High RO treatment, 166 herbivores achieved higher persistence (73%) than in RO FWs (61%), but in the other 167 multiplex treatments, herbivore persistence was lower (<32%) and declined 168 dramatically with increasing mutualism (Fig. 3h). Nonetheless, the low initial diversity 169 of carnivores (~3 species) and herbivores not added by the treatments (~5 species) 170 resulted in only minor changes to total diversity despite substantial differences in 171 persistence. Additionally, in all treatments, any decreases in persistence were not strong 172 enough to prevent overall increased final diversity (Fig. 3b) with increased initial 173 diversity and mutualism (Fig. 3a). biomass was up to twice as high while productivity and consumption were up to an 190 order of magnitude higher in multiplex than in FW treatments. In all treatments, total 191 consumption ( Fig. 4d) very closely matched total production and was distributed 192 according to the biomass of animals (Fig. 4d).

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The higher biomass of multiplex compared to FW treatments (Fig. 4b) was 194 primarily due to increases in animal abundance while productivity differences (Fig. 4c) 195 were primarily due to strong increases in rewards combined with smaller increases in 196 animals. These differences emerge primarily due to the interactive dynamics of rewards 197 whose growth potential, contrary to all other stocks of biomass, depends not on its own  Stability. 218 We evaluated the stability of our networks by analyzing coefficients of variation (two-tailed P < 0.0001), while total community biomass decreased by ~10% in High 255 rewards treatments and ~6% in Low RP treatments (two-tailed P < 0.0001), but was 256 unchanged in Low reward RO treatments (P = 0.49, Table 1). The magnitude of these 257 reductions became larger as mutualism and diversity increased, with the minor 258 exception of total biomass in Low RO treatments. Compared to the original simulations, 259 total biomass in Low RO controls increased with initial increases of mutualism and 260 diversity but then decreased precipitously with further increases, leading to no 261 substantial change overall. More dramatically, large mean squared deviations in 262 abundances of species between the control and original simulations indicate large 263 differences between which species were abundant (Table 1)  Additionally, these differences are exacerbated at higher levels of mutualism and 273 diversity. See Methods S1 for sensitivity analyses that further corroborate the roles of 274 mutualism and rewards as outlined above.

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In this study, we investigated whether and how mutualisms between plants and Rewards Plus (RP) treatment (Fig 3d). High RO and RP networks with the most 291 mutualistic interactions exhibit the highest productivity (Fig. 3c). Multiplex networks 292 (RO and RP) with the most mutualistic interactions have higher abundance (Fig. 3b), 293 productivity (Fig. 3c), and guild-level stability (Fig. 3d) than their corresponding FW 294 networks except for productivity in Low RO networks.   (Table 1) biomass, and productivity on average of all consumer guilds over that in low rewards 347 networks ( Fig. 3d-h, Fig. 4b-c) excepting the decrease in herbivore persistence in RP 348 networks (Fig 3h). This suggests that, in natural systems, we may expect the weakest 349 increases in persistence, biomass, and productivity due to increased mutualism to occur  Key limitations of our work concern the match between the network architecture involving coral, mycorrhizal fungi, frugivores, and other seed eaters that disperse seeds, 384 all of which involve the exchange of food for increased growth of primary producers. 385 We have advanced theory on multiplex networks in order to explore the effects Network architecture. 404 We created multiplex networks (Fig. 1) by creating realistic food webs using the 405 stochastic "niche model" (Fig. 1a) parameterized with 50 species (Sf = 50) and 10% 406 directed connectance (Cf = Lf / Sf 2 = 0.1 where Lf is the number of feeding links. 14 The 407 niche model assigns each species i three traits: (1) a niche value (ni) drawn randomly 408 from a uniform distribution between 0 and 1, (2) a feeding range (ri) where ri = xni and x 409 is drawn from randomly from a beta distribution with expected value 2Cf, and (3) a 410 feeding centre (ci) drawn randomly from a uniform distribution between ri/2 and min(ni, as determined by the plant-pollinator network (Fig. 1c). This leaves 20 -P plant species 426 without pollinators. 427 We linked pollinators to consumers in the food web in Rewards Only (RO) 428 treatments by setting each pollinator's ni to +/-5% of the ni of a randomly selected 429 strict herbivore (TL = 2) from the food web (Fig. 1d). Pollinators' ri and ci were set to increases from 56 to 88 in RO multiplex networks and corresponding FWs ( Figure S3).

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In the Rewards Plus (RP) treatments (Fig. 1e), we set each pollinator's ni, ri and ci to +/-436 5% of the corresponding ni, ri and ci of a randomly selected herbivore or omnivore that (1) 456 where xi is the allometrically-scaled mass-specific metabolic rate of species i and eji is where wij is i's relative preference for j, h is the Hill coefficient, 68 and B0ij is the "half- (1-1) (1-2) 501 22 Parameterization.

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Vital rates for consumers follow previously described allometric scaling for 503 invertebrates 63 . Specifically, we set plant species' "body mass" to a reference value (mi 504 = 1) 16 Table   527 S4 for a summary of model parameters and values.

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Simulations. 529 We simulated each of our N = 24,276 networks subjected to each of the two  (Tables S1-S3).

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Outputs. 541 We quantified ecosystem stability and function using species persistence, 542 biomass, productivity, and variability at or near the end of the simulations. We persistence as the fraction of the initial species that survived to the end of the simulation 557 (i.e. whose biomass stayed above the extinction threshold). 558 We calculated all outputs at the end of the simulations except for biomass 559 variability, which we calculated over the last 1000 timesteps. Species persistence is the 560 fraction of the initial species whose biomass stayed above the extinction threshold 561 throughout the simulation. Final biomass is the total biomass for the whole community 562 and/or each guild of species. Plant productivity is the summed rates of species' biomass 563 increases due to growth minus losses due to rewards production. Rewards productivity 564 is the rate at which all rewards were produced by all plants with pollinators.

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Consumption is the summed rates of biomass lost by resources due to feeding by 566 animals. Animal productivity is assimilation minus losses due to metabolic in our treatments, so their guild persistence is not shown (but see Figure S1).