How Structured Is the Entangled Bank? The Surprisingly Simple Organization of Multiplex Ecological Networks Leads to Increased Persistence and Resilience
[['In his description of the “entangled bank” of species , Darwin illustrated the principle that species must manage complex interdependencies to successfully coexist in natural communities [1–7] .', 'In this context , evolutionary constraints set a landscape of trade-offs over which species must solve their basic needs within the context of other species ( e . g . , competition for refuges among herbivores forced by the common need to avoid predators ) and stringent environmental conditions .', 'To some extent , each species has found unique solutions—in how they manage interactions with other species—that have shaped their distinctive niches .', 'However , beyond species identity , common sets of trade-offs may lead to similarities in the way species are involved in different interaction types .', 'In other words , the apparently endless solutions discovered by species to simultaneously satisfy multiple requirements and deal with multiple stresses might actually be much more limited and structured than we anticipated .', 'Yet we do not know what the full “entangled bank” of species looks like or if there are structural patterns at the community level that reflect common solutions in the way species manage being involved in different interaction types .', 'Indeed , the analysis tools from network science are only recently addressing the “multiplex” nature of most natural networks , i . e . , the fact that they include different interaction types between a given set of species ( e . g . , [8–11] ) .', 'As the first datasets including several interaction types between a given set of species are now emerging in ecology [5 , 12–16] , we have a unique opportunity to disentangle the bank of species interactions .', 'Until now , layers in such ecological networks have been analyzed separately from each other; i . e . , the structure of trophic webs has been analyzed independently of the structure of competition or mutualistic webs ( [13–15 , 17–19] , but see [5] ) .', 'However , the way network layers are intertwined with each other matters for community dynamics and resilience [1 , 2 , 20] .', 'Thus , it is critical to move beyond unidimensional analyses of ecological networks .', 'In this paper , we explore a comprehensive ecological network in which the species of a local community are linked by trophic and widely diverse positive and negative non-trophic interactions [14 , 21] .', 'The network , hereafter referred to as the Chilean web , includes three layers of interactions among 106 co-occurring species in the marine rocky intertidal community of the central coast of Chile: a trophic layer ( i . e . , a food web; 1 , 362 trophic links ) , a negative non-trophic layer ( e . g . , interference , competition for space; 3 , 089 links ) , and a positive non-trophic layer ( e . g . , habitat/refuge provisioning by sessile species that create structure for others; 172 links ) , making it a three-dimensional multiplex network [9 , 11] .', 'We first quantified the three-dimensional structure of this multiplex network using a probabilistic clustering method .', 'We then used dynamical modeling to investigate how the identified structure modulates the multi-species dynamics and the resilience of the ecological community to perturbations .', 'Overall , our results suggest that the enormous ecological complexity of this community can be simplified into surprisingly clear patterns of organization that are taxonomically coherent , can be broadly predicted from simple species traits , and are functionally important for dynamics and resilience .', 'These blocks might represent ecological and evolutionary constraints acting on the multiple requirements and impacts that allow species to persist in complex systems .', 'Our results , therefore , pave the way for a new generation of research untangling complex networks with multiple link types .'], ['Looking at the way pairs of species are three-dimensionally connected in the Chilean web shows that 2 , 891 of these pairwise links are interaction-specific ( Table 1; S1 Fig ) .', 'In other words , pairs of species tend to engage in only one type of interaction: trophic , positive non-trophic , or negative non-trophic interactions .', 'We compared these occurrences to those observed in random multiplex networks with the same expected degree sequence as in the Chilean web ( see Materials and Methods ) .', 'Note that these random networks are very constrained and are , as a consequence , very similar to the Chilean web ( S9 and S10 Figs ) .', 'We found that the interaction-specific links ( i . e . , the cases in which a pair of species is linked by only one interaction type ) are significantly more frequent in the Chilean web than expected in the random counterparts ( p-value < 10−4; Table 1 ) .', 'In contrast , 125 pairs involve two interaction types simultaneously , which is far less than expected ( p-value < 10−4; Table 1 ) .', 'Notably , six pairs of species are linked at the same time by the three interaction types in this interaction web , which is more than expected ( p-value < 10−2; Table 1 ) .', 'These patterns suggest a fine-scale , species-level constraint on how pairs of species interact in webs with several interaction types; i . e . , multiplex pairwise interactions are remarkably rare .', 'It does not mean that species are not involved in multiple interaction types; they usually are , but with different partners .', 'This lack of multiplex pairwise interactions may reflect evolutionary constraints in developing adaptations simultaneously for different interaction types with the same species .', 'For example , in the Chilean web , it is relatively rare for a species to facilitate its prey ( there are only two pairs of species simultaneously linked by a trophic and a facilitation link ) .', 'One exception is the scurrinid limpet Scurria variabilis , which lives on top of the shell of another limpet , the keyhole limpet Fissurela limbata , which , in turn , can eat the juveniles of S . variabilis [22] .', 'The positive effect on S . variabilis is quite strong , since they can spend their entire benthic life grazing on the Fissurella shells [22 , 23] .', 'However , it is likely that the trophic link is weak , because the species are primarily herbivores [24–26] , which would reinforce the notion that such combination of interaction types is rare .', 'There are , however , more examples in the Chilean web of species that compete with their prey or with their predator ( e . g . , anemones eat mussels and compete for space with them ) , of species facilitating their competitor ( e . g . , algae facilitate mussel recruitment but compete for space once mussels are established ) [27] , and , interestingly , of prey facilitating their own predators ( e . g . , mussels facilitate settlement of their predatory crabs ) [4] .', 'While these types of examples tend to dominate our intuitive perception of insurmountable ecological complexity , the data suggests that they are the exception , not the rule .', 'When we take into account all three types of interactions , as well as the identity of the participants , do groups of species have similar interaction profiles ?', 'To address that question , we used a probabilistic algorithm to detect groups of species ( hereafter referred to as “multiplex clusters” ) that resemble each other in the way they interact with others in their combined trophic and non-trophic interactions ( i . e . , the way they interact in three dimensions ) .', 'Our work hereby builds on previous efforts aimed at detecting compartments [28 , 29] or structural patterns [30] in food webs but extends those approaches to networks with several interaction types .', 'In particular , previous studies have used similar approaches to characterize the trophic niche of species by identifying “trophic species” , i . e . , groups of species that are similar in terms of their predators and prey .', 'Here , our approach applied to the Chilean web allows , for the first time , to our knowledge , the visualization of the multidimensional ecological niche of species [31] .', 'When applied to the Chilean web , and associated with a model selection procedure , the probabilistic algorithm identified 14 multiplex clusters , i . e . , much less than the number of species ( Figs 1 and S2 ) .', 'Those clusters differ from each other in the types of links they are involved in , the pattern of incoming and outgoing links ( Fig 2 ) , and the identity of the species they interact with ( S4 and S5 Figs ) .', 'We note that the definition of the clusters requires taking into account the three layers of interactions simultaneously , because none of the layers contains by itself enough information to recover these multiplex clusters ( S6 Fig , S1 Table and S1 Text ) .', 'Clusters 2 , 5 , and 8 are the cornerstone of that organization , both because of the high frequency of interactions engaged in with others and because of the variety of their interaction partners ( Figs 1 and 2 ) .', 'Cluster 5 is an overall hub of interactions , with both a high frequency and a wide variety of interactions with others ( Figs 1 and 2 ) .', 'Clusters 6 and 10 are two groups of species involved in similar interaction types and partners but that do not have a single interaction with each other ( S4 and S5 Figs ) ; indeed , the two groups of species are spatially segregated across the tidal gradient , with one group typically found in the lower shore ( cluster 6 ) and the other found at the uppermost level ( cluster 10 ) .', 'Most of the remaining clusters contain more species ( 7 to 23 species ) that are , from a connectivity point of view , redundant and exchangeable .', 'These clusters differ from one another by the identity of the species they interact with ( e . g . , clusters 9 and 7 are more generalist consumers than cluster 14 ) , but also by the way they interact with the species of clusters 2 , 5 , and 8 ( e . g . , cluster 11 is facilitated while 12 competes with cluster 5; S4 and S5 Figs ) .', 'In particular , cluster 4 comprises peripheral species that share a low interacting frequency with the other clusters .', 'The cluster number and their species composition was largely conserved after removal of up to 30% of the species in the Chilean web ( S3 Fig and S1 Text ) .', 'This shows that the probabilistic algorithm is robust against perturbations due to species removal but also that the retrieved organization is significant .', 'This is , however , not unexpected since , in essence , the multiplex clusters gather species that share similar interaction patterns and are therefore largely substitutable in terms of their multiplex connectivity .', 'Do the specific combinations of trophic and non-trophic links characterizing the clusters have functional consequences ?', 'We examined the relationship between the multiplex connectivity pattern identified in the Chilean web and the dynamic behavior of this network .', 'To this end , we used a bio-energetic consumer-resource model ( as in [32] ) in which we incorporated the broad categories of non-trophic interactions found in the Chilean web .', 'Because of species redundancy in the interaction patterns within a cluster , in this initial investigation , we used the clusters as the simulation units of the model .', 'Later refinements should relax this assumption and look into the coherence of species dynamics within clusters .', 'We compared the dynamics of', '( i ) the webs of the 14 clusters identified in the Chilean web to', '( ii ) equivalent random webs in which all non-trophic links were randomized throughout the web ( see Materials and Methods ) .', 'Simulation results suggest that the way non-trophic interactions are mapped onto the trophic ones in the Chilean web tends to increase species persistence and the total biomass realized ( Fig 3 left ) , as compared to a random allocation of non-trophic interactions .', 'This occurs for a broad range of trophic and non-trophic parameter values ( S8 Fig and S1 Text ) .', 'Moreover , the mapping of the non-trophic interactions in the Chilean web tends to decrease secondary extinctions ( Fig 3 right ) .', 'The different clusters had very different effects on web dynamics .', 'For instance , biomass loss was observed after the removal of the cornerstone clusters ( clusters 2 , 5 , and 8 ) and at a higher level than expected ( cluster 5 , p-value = 0 . 056; clusters 2+8 jointly , p-value = 0 . 06; see S7 Fig ) .', 'If we go one step further and disregard the identity of the species , can we identify deeper cores of multiplex organization ?', 'By analyzing the interaction parameters estimated in the probabilistic model for the different clusters , we were able to identify groups of clusters whose species are involved ( or not involved ) in similar combinations of interactions , i . e . , “multiplex functional groups” ( Figs 4A and S11 ) .', 'The Chilean web thereby further collapses into a set of only five multiplex functional groups ( Figs 4A and S11 ) .', 'Those multiplex functional groups can broadly be characterized as groups dominated by consumers ( 1 , 4 , 7 , 9 , 14 ) , one composed mostly of competitors ( 3 , 11 , 12 ) , another dominated by facilitators/competitors ( 6 , 10 , 13 ) , a more heterogeneous group composed of consumers/competitors ( 2 , 8 ) , and , finally , one overall hub of species interacting with many other species in many different ways ( 5 ) .', 'We find that the species composition of the functional groups is coherent with broad taxonomic classifications , considered as a coarse proxy for phylogenetic relatedness ( Fig 4C ) .', 'Each functional group has indeed a tendency to gather closely related species ( p-value < 10−4 ) .', 'But exceptions exist .', 'For instance , the group of facilitators/competitors ( made of clusters 6 , 10 , 13 ) is composed of very different species corresponding to different phyla ( mainly algae and barnacles; p-value > 0 . 1 ) , but they share the fact that they are sessile species that create biotic structure for others .', 'Interestingly , the multiplex functional groups are not only characterized by similar multidimensional interaction pattern ( by definition; Figs 4A and S11 ) , but they are also very well predicted by simple species attributes ( Figs 4B and S12 ) , in particular trophic level category ( autotroph , herbivore , intermediate , top ) , mobility ( mobile versus sessile ) , and shore height ( ordinal ) .', 'The analysis first splits the data among autotroph species ( mainly the competitors’ group and a few of the facilitators/competitors’ group ) and the rest of the species .', 'The second split separates mobile ( the consumers’ group ) from sessile species , which are then divided between carnivores ( the consumers/competitors’ group ) and herbivores , themselves split among species from lower ( the multiplex hub and a few consumers ) and those from higher shore ( the facilitators/competitors’ group ) .', 'Higher on the shore is more environmentally stressful because of increased exposure to air and desiccation [33 , 34] .', 'It might , therefore , be more likely for sessile species at mid-high shore to facilitate mobile species that need shelter from environmental stress [35 , 36] , while species lower on the shore are perhaps more likely to provide refuge from predation .', 'Shore height could thereby mediate the frequency of facilitation of mobile by sessile species in this dataset .', 'In sum , the five multiplex functional groups gather species that engage in roughly similar ecological interactions ( Fig 4 ) : ( 1 ) A group of mobile consumers ( clusters 1 , 4 , 7 , 9 , 14 ) , mostly carnivores , composed of crabs , sea snails , chitons , starfishes , and birds , most of which consume prey species and often find themselves in competition with others .', '( 2 ) A small group of sessile , inedible consumers ( anemones; clusters 2 and 8 ) that eat dead or detached animals or their fragments are the source and target of many competitive links with other sessile species and are key players in the resilience of the community .', 'Their classification into a separate group likely reflects their peculiar life habits ( sessile scavengers ) .', '( 3 ) An overall hub of sessile , edible consumers that also facilitate others and are key in the resilience of the community ( cluster 5 ) .', 'This group contains two common mussel species that differentiate themselves from the other groups by their involvement in all interaction types and particularly in positive interactions ( both incoming and outgoing; Figs 2 , S4 and S5 ) , supporting many ecological studies that highlight their role as foundational or engineering species [4 , 37 , 38] .', 'They indeed provide habitat and substrate for many other invertebrate species seeking shelter .', '( 4 ) A group of sessile primary producers ( algae; clusters 3 , 11 , 12 ) that compete for space and usually find themselves in competitive loops while being frequently consumed .', '( 5 ) Finally , a group of sessile species ( clusters 6 , 10 , 13 ) that is a mix of algae and barnacles that compete for space with other sessile species while facilitating mobile consumers by creating biotic structure that provides refuges and habitat for other species ( for instance , the kelp Lessonia nigrescens facilitates recruitment and provides critical shelter or habitat to diverse species ) .'], ['The wave-exposed Chilean marine intertidal ecosystem of 106 species includes over 4 , 600 interactions that span predation , competition , and facilitation .', 'Despite the wide range of possible combinations of interactions among species , our data suggests that the combinations of interactions that are actually realized in this intertidal community are constrained to be far fewer than those “possible . ”', 'Our analysis of the Chilean web further reveals a clear organization of species into a small subset of multiplex clusters , which themselves collapse into multiplex functional groups .', 'The identification of this organization into clusters and , therefore , into functional groups requires taking into account the three layers of interactions and would not be possible with a monolayer , unidimensional niche approach of this ecological network .', 'The functional groups identified are taxonomically coherent , with each group gathering closely related species , suggesting some level of conservatism of the three-dimensional interaction niche space .', 'The functional groups are also well-predicted by simple traits , such as trophic level , mobility , and shore height .', 'Previous work on different single-interaction-type networks ( food webs , bipartite mutualistic , and bipartite antagonistic ) showed that only a limited number of traits is required to explain all species interactions in a given ecological network , meaning that ecological networks are structured by a few dimensions ( or trait-axes ) [31] .', 'Our analysis of the Chilean web suggests that this result may hold when considering multiplex ecological networks .', 'Together , the small sets of interaction types in which species engage with each other and the astonishingly limited set of multiplex functional groups seems to reflect predictable evolutionary and ecological constraints operating in this entangled bank of species .', 'This opens up a pathway toward simplifying ecosystem complexity into basic building blocks .', 'Previous theoretical studies have suggested that the incorporation of non-trophic interactions in food webs can have important consequences for species diversity [1 , 5 , 7] , overall productivity [1] , frequency of functional extinctions [39] , stability [6 , 20 , 40–42] , and the complexity–stability relationship [6 , 40 , 43] .', 'May’s pioneering work in the early 1970s already included several interaction types [44] .', 'Combining trophic and competitive interactions and using community matrices derived from real food webs , Yodzis [42] showed that a certain level of intraspecific interference contributed to the local stability of ecological communities , whereas interspecific competition tended to be destabilizing .', 'In recent extensions of May’s work , Allesina and Tang [40] showed that matrices including mixtures of competition and mutualism were less likely to be locally stable than predator–prey matrices .', 'Using a similar approach , Mougi and Kondoh [6] found that introducing a small proportion of mutualistic links could destabilize an otherwise stable food web , but that stability reached a peak at a moderate mixture of both interaction types ( but see [45] ) .', 'Studies on bipartite networks have suggested that the way different bipartite networks ( e . g . , mutualistic and antagonistic networks ) are connected to each other could affect their stability [5] .', 'Our study extends these results to show that the specific three-dimensional signature of the clusters and , in particular , the non-randomness of non-trophic interactions , can promote higher species persistence , higher total biomass , and higher robustness to extinctions than random networks in which the multidimensional connectivity pattern is lost .', 'A long history of theoretical and empirical work on food webs highlighted the importance not only of the structure of food webs ( i . e . , the repartition of the links in the web ) [42 , 46–48] but also of the specific pattern of interaction strength for the stability of ecological communities [18 , 19 , 49] .', 'Here , with the exception of a few common links , we lack information about interaction strengths for the entire Chilean web and especially about the strength of the non-trophic links .', 'Getting information about those interaction strengths , their structure , the way they should be modeled , and their functional relevance remains an important empirical but also theoretical challenge .', 'To what extent the connectivity patterns identified in the Chilean web are unique to this intertidal community or general to all marine organisms or even to all ecosystems must be evaluated by comparison to those other ecosystems as more data on multiplex ecological networks becomes available [13 , 14 , 50] .', 'The five functional groups identified could very well correspond to sets of strategies largely generalizable to other ecosystems .', 'For example , a cluster of mobile consumers ( top predators ) might generally emerge .', 'In the same vein , a group of sessile edible species competing for space is probably identifiable in many ecosystems .', 'In terrestrial ecosystems , such a group would mostly be composed of basal primary producers , whereas in marine systems it could include sessile animals and exclude some primary producers that are not sessile ( e . g . , phytoplankton ) .', 'Groups of sessile species that create biotic structure and habitat for others—notably , mobile consumers—while also competing for space are likely to be common across many ecosystems .', 'Finally , identifying “multiplex hubs” in other ecosystems—such as mussels in the Chilean web , which create structure while also being an important food source—may help target a small subset of species that play a disproportionately important role for the community resilience .', 'Conversely , some groups may be unique to marine benthic systems , such as the group of sessile , inedible scavengers formed here by anemones .', 'It is noteworthy that a number of key groups of species are absent from the current version of the dataset ( Materials and Methods ) .', 'In particular , parasites are not included in the web .', 'Studies have shown that food webs that also take parasites into account have increased connectivity and longer food chains , and the parasite–host links dominate numerically over predator–prey links [12] .', 'Detritus ( and thereby decomposers ) are known to play an important role for the dynamics and structure of many communities and may also affect their stability [49 , 51 , 52] .', 'It is unclear , however , what the significance is of local nutrient recycling in benthic marine and stream communities .', 'In any case , adding missing species into the Chilean web could , depending on the connectivity of the newly introduced species , lead to either the emergence of new functional groups or the splitting of some of the current functional groups into additional groups [15] .', 'The spatial and temporal variations of the patterns identified in the Chilean web remain to be investigated .', 'This variability in space and time has been suggested to be essential to the stability and function of ecosystems [53] .', 'The role of space may be particularly relevant in intertidal communities where mobile species ( mainly consumers ) could connect distant communities along the shore , with possible important consequences for the stability of these communities [48 , 53] .', 'In addition , the incorporation of several interaction types in spatial ecology frameworks has been shown to have important consequences for community dynamics .', 'For instance , Lurgi et al . [41] showed , using a spatially explicit individual-based model , that an increasing proportion of mutualistic links in a food web positively affected the dynamic stability of model communities .', 'How the topological structure of multiplex ecological networks modulates the multi-species dynamics and the resilience of ecosystems to perturbations , such as climate change , must be further investigated through other datasets [15] , further dynamical modelling [1 , 5 , 20 , 41 , 45] , and other approaches incorporating link weighting [3] .', 'Until then , our results will help us guide future empirical studies and move toward a more general theory of how to leverage the full diversity of species interactions for understanding and predicting the dynamics and resilience of complex ecological systems .'], ['The dataset [14] includes all the species that were found to co-occur during community structure surveys carried out at several rocky intertidal sites with similar wave exposure spread along 700 km of the central Chilean coast ( [27] , see [54 , 55] for sampling details and species list ) .', 'Construction of the network was based on expert knowledge [14] .', 'An interaction was included in the network if one species plausibly had a direct measurable effect on the growth , survival , or feeding rates of another species over an ecologically relevant time period ( 1–2 y ) [14] .', 'The dataset does not include parasites , endo-symbionts , or decomposers , because such data was unavailable for that community .', 'The network was split into three separate matrices for trophic , positive non-trophic , and negative non-trophic interactions ( in each matrix , interactions are coded as 0 or 1 ) [14] .', 'As a live and continuously improving network , some changes have been made to the network since first published [14] .', 'These are mostly taxonomic changes and the inclusion of porcellanid crabs as part of the wave-exposed network .', 'Furthermore , the biofilm taxa and plankton ( zooplankton and phytoplankton ) were each considered as a single node in the Chilean web due to lack of information .', 'The main assumptions made to build this network as well as possible related bias are discussed in Appendix A of [14] .', 'In particular , we acknowledge that there may be “a bias in favor of negative non-trophic interactions at lower trophic levels , ” because “measuring the relative importance of interference competition among rare species under natural conditions is particularly challenging” [14] .', '“When local experimental information was lacking for a pair of sessile species , we probably had a greater tendency in assigning ( i . e . , benefit of doubt ) the interaction to competition for space than when dealing with pairs of mobile species at higher trophic levels . This would create a bias in favor of negative non-trophic interactions at lower trophic levels . However , the sheer number of species at bottom versus high trophic levels would make it difficult to alter the general pattern” [14] .', 'Data deposited in the Dryad repository: http://dx . doi . org/10 . 5061/dryad . b4vg0 [21] .', 'The pairwise multiplex interactions observed in the Chilean web were compared to those observed in random multiplex networks simulated layer by layer .', 'For each layer , we imposed that the expected in- and out-degree sequences were equal to the degree sequences in the original layer of the Chilean web .', 'To do so , we used the procedure explained in the “random network” paragraph hereafter .', 'We calculated the statistical significance of any observed number of links by computing the empirical distribution of the number of links in the 104 random multiplex networks .', 'How can we tell what a multiplex network looks like ?', 'How can we summarize its structure ?', 'To answer these questions , classical approaches consist of pooling nodes that have similar connectivity patterns into clusters to extract the high-level structure of a complex network .', 'Most of these approaches rely on finding modules or communities ( clusters of nodes that are more connected inside than outside their cluster [56] ) .', 'But , in ecological networks , could there be relevant structural patterns that we do not find because we have not thought to search beyond the modular structure ?', 'To circumvent this problem , we used a probabilistic clustering approach based on Stochastic block models [57–59] .', 'Here , the cluster identification does not rely on any a priori hypothesis about the connectivity patterns to be found but aims precisely at identifying significant hidden connectivity patterns ( e . g . , modularity , centrality , hierarchy ) or combinations of these patterns .', 'Stochastic block models have been widely used for networks with one layer ( see [30 , 60] for ecological networks ) , but not for multiplex networks as proposed in this paper .', 'We followed the notations and the estimation procedure previously described in [60 , 61] and extended the model to multiplex networks with 3D-interactions using an appropriate probability distribution .', 'The use of a probability distribution allows us to account for the randomness and the variability of the network and ensures a significant robustness to potential errors ( spurious or missing links , for instance ) .', 'We consider n = 106 interacting species , with Yij standing for the observed measure of these 3D interactions and Y = ( Yij ) .', 'Yij is a 3-dimensional vector such that Yij = ( Yij1 , Yij2 , Yij3 ) , where Yij1 = 1 if there is a trophic interaction from i to j and 0 otherwise , Yij2 for a positive interaction , and Yij3 for a negative interaction .', 'We now introduce the vectors ( Z1 , … , Zn ) , where for each species i Ziq are the component of vector Zi such that Ziq = 1 if i belongs to cluster q and 0 otherwise .', 'We assume that there are Q clusters with proportions a = ( a1 , … , aQ ) and that the number of clusters Q is fixed ( Q will be estimated afterward; see below ) .', 'In a Stochastic block model , the distribution of Y is specified conditionally to the cluster membership:', 'Zi~Multinomial ( 1 , a ) , Zj~Multinomial ( 1 , a )', '( 1 )', 'Yij|ZiqZjl=1~f ( . , θql ) ,', '( 2 )', 'where the distribution f ( . , θql ) is an appropriate distribution for the Yij of parameters θql .', 'The novelty here is to use a 3D-Bernoulli distribution [62] that models the intermingling connectivity in the three layers—trophic , positive non-trophic , and negative non-trophic interactions .', 'The objective is to estimate the model parameters and to recover the clusters using a variational expectation–maximization ( EM ) algorithm [60 , 63] .', 'It is well known that an EM algorithm’s efficiency is governed by the quality of the initialization point .', 'We propose to use the clustering partition obtained with the following heuristical procedure .', 'We first perform a k-means clustering on the distance matrix obtained by calculating the Rogers and Tanimoto distance ( R package ade4 ) between all the 3D interaction vectors Vi = ( Yi . , Y . i ) associated to each species i .', 'Second , we randomly perturb the k-means clusters by switching between 5 and 15 species membership .', 'We repeat the procedure 1 , 000 times and select the estimation results for which the model likelihood is maximum .', 'Lastly , the number of groups Q is chosen using a model selection strategy based on the integrated classification likelihood ( ICL ) ( see S2 Fig ) [61] .', 'The algorithm eventually provid
['Introduction', 'Results', 'Discussion', 'Materials and Methods']
['Species are linked to each other by a myriad of positive and negative interactions .', 'This complex spectrum of interactions constitutes a network of links that mediates ecological communities’ response to perturbations , such as exploitation and climate change .', 'In the last decades , there have been great advances in the study of intricate ecological networks .', 'We have , nonetheless , lacked both the data and the tools to more rigorously understand the patterning of multiple interaction types between species ( i . e . , “multiplex networks” ) , as well as their consequences for community dynamics .', 'Using network statistical modeling applied to a comprehensive ecological network , which includes trophic and diverse non-trophic links , we provide a first glimpse at what the full “entangled bank” of species looks like .', 'The community exhibits clear multidimensional structure , which is taxonomically coherent and broadly predictable from species traits .', 'Moreover , dynamic simulations suggest that this non-random patterning of how diverse non-trophic interactions map onto the food web could allow for higher species persistence and higher total biomass than expected by chance and tends to promote a higher robustness to extinctions .']
['Within an ecosystem , species interact with each other in many different ways , including predation , competition , and facilitation , and this can be modelled as a network of multiple interaction types .', 'The variety of interaction types that link species to each other has long been recognized but has rarely been synthesized for entire multi-species ecosystems .', 'Here , we leverage a unique marine ecological network that integrates thousands of trophic and non-trophic interactions .', 'We show that , despite its multidimensional complexity , this ecological network collapses into a small set of “functional groups , ” i . e . , groups of species that resemble each other in the way they interact with others in their combined trophic and non-trophic interactions .', 'These groups are taxonomically coherent and predictable by species attributes .', 'Moreover , dynamic simulations suggest that the way the different interaction types relate to each other allows for higher species persistence and higher total biomass than is expected by chance alone , and that this tends to promote a higher robustness to extinctions .', 'Our results will help to guide future empirical studies and to develop a more general theory of the dynamics of complex ecological systems .']
['community ecology', 'conservation biology', 'conservation science', 'ecology and environmental sciences', 'species extinction', 'ecology', 'species delimitation', 'food web structure', 'predation', 'trophic interactions', 'speciation', 'biology and life sciences', 'theoretical ecology', 'species interactions', 'evolutionary biology', 'evolutionary processes']
An ecological network synthesizing all known interactions between species exhibits a clear pattern of organization that reflects evolutionary and ecological constraints operating in this entangled bank of species.