Complex Ecological Networks

Mathilde Besson*

1,2m athilde.besson@ um ontreal.ca

Eva Delmas*

1,2eva.delm as@ um ontreal.ca

Timothée Poisot

1,2tim othee.poisot@ um ontreal.ca

Dominique Gravel

2,3dom inique.gravel@ usherbrooke.ca

1 - U niversité de M ontréal, D épartem ent de Sciences B iologiques2 - Q uébec C entre for B iodiversity Sciences3 - U niversité de Sherbrooke, D épartem ent de B iologie

* These authors contributed equally to the w ork

Abstract: Ecological netw orks provide a useful abstraction of ecological system s, representing them as graphs, com posed of nodes (species) and edges (interactions). This form alism allow s to use a w hole set of m easures, extended from graph theory, to study ecological system s. In this chapter, w e review som e of the m ost prom inent findings and areas of research from the last decade. W e start by review ing how it w as used to uncover invariance in the organization of ecological system s. Then w e show the im portance of structure w hen studying system s dynam ics and how this coupled approach sheds new light on em erging properties of ecological system s. Through this chapter w e w ant to highlight the im portant contribution of netw orks in clarifying ecosystem properties and functioning, but also the potential to develop new approaches, for exam ple to com pare ecosystem s and to relate species traits to com m unity structure.

Keywords: A ssem bly, C oexistence, C om m unities, G raph theory, N etw ork structure, C om m unity dynam ics, Species interactions, Stability

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Glossary

Adjacency matrix: M atrix representing species interactions. If tw o species i and j interact, the intersection of the m atrix at i , j w ill be 1, and 0 if not. Assembly rules: Ecological processes leading to a specific species' com position of a com m unity,e.g. com petition, predator-prey interactions, arrival history, etc.Degree: The degree of a node is its num ber of links (e.g. interactions per species). A t higher level, the degree distribution represents the cum ulative distribution of links per node w ithin the netw ork or a subnet of the netw ork.Ecological interactions: Every type of contact betw een tw o species that alters the fitness of one or both species. Interactions can be directed or undirected, w eighted or unw eighted. They usuallyfall into one on these 5 m ain classes: com petition, predation, parasitism , m utualism and com m ensalism . Ecosystem functioning: B iotic and abiotic processes that sustain ecosystem s, including flues of energy and nutrients betw een the com ponents of ecological system s and the resulting stocks, e.g. biogeochem ical cycles.Graph theory: M athem atical fram ew ork used to represent the relationship betw een the objects of a netw ork.Network structure: G eneral shape of a netw ork em erging from the organization of the interactions betw een its com ponents. It is com m only described in ecology using connectance, link distribution, topological indices (such as nestedness, m odularity, centrality), etc.Nodes/Links, Vertices/Edges: Follow ing graph theory, species are represented as nodes (or vertices), and interactions betw een them are represented by links (or edges).Phylogenetic signal: Tendency of phylogenetically close species to have sim ilar traits (and as a consequence, sim ilar interactions).Unipartite / Bipartite network: The graphical representation of the entire adjacency m atrix offers an unipartite netw ork representation (see Figure 1), w here the hierarchy betw een nodes and their position into the netw ork is not alw ays visible. O n contrary, a bipartite or k-partite netw ork is a hierarchical representation of the netw ork (Figure 2), w here nodes are separated depending on their position or function into the netw ork (e.g. pollinator-plant as bipartite netw ork).

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Introduction

Interactions betw een the com ponents of any ecological system s are organized non-random ly. Thespecies that form a com m unity for exam ple do not interact at random . The resulting organization of interactions betw een species drives som e properties of the com m unity such as stability, productivity, and the ability to resist extinctions, all of w hich eventually feedback on the organization of the system . The constant interplay betw een the organization of interactions and system dynam ics constrains its structure. Studying the structure of ecological system s provides insights on the fundam ental rules and processes that govern ecosystem form ation, m aintenance and functioning.The organization of interactions in a com m unity is best represented as a netw ork. Graph theory is a field of m athem atics developed to analyze the structure of such system s. Every com m unity can be abstracted by a graph, w hich is a representation of the system com ponents and their arrangem ent (Figure 1a). These com ponents are called nodes and are linked together by edges. In an ecological system , nodes can be individuals, populations, com m unities or landscape patches and edges can represent trophic interactions, energetic flues and m ore generally every kind of interactions. B oth nodes and edges can carry additional inform ation such as w eight (e.g. species abundance, intensity of the gene flow betw een tw o populations, etc.), location in space and tim e, and labels (e.g. species identity). Specific inform ation can be attached to edges, m odifying the characteristics of the graph, e.g. the environm ental dependence of an interaction. G raphs can be directed (i.e. interaction goes from A to B ) or undirected, weighted (i.e. different strength of interaction am ong the netw ork) or unweighted (Figures 1 and 2). This inform ation is sum m arized in the adjacency matrix, typically nam ed A (Figure 1b). The adjacency m atrix Acan be used to answ er various ecological questions. U sing it directly allow s to follow direct interactions and the netw ork structure, and using the inverse of A can be useful to obtain indirect interactions, and even m ore (M ontoya et al. 2009). In this chapter, for sim plicity, w e w ill focus m ostly on Species Interaction Networks (SIN ). Ecological system s such as landscape, genetic or nutrient netw orks are not represented here, but they can be studying using the sam e fram ew ork as defined further. D escribing and understanding the structure of SIN is an active, and grow ing, field of ecological research. W e provide here an overview of som e of the m ost prom inent findings and areas of research from the last decade. Starting from a discussion of som e invariant properties of the structure of species interaction netw orks, w e w ill then discuss how this structure affects com m unity dynam ics and properties. W e w ill follow by a discussion of the w ays ecological netw orks can be studied under fam iliar concepts from ecological theory, and finally how this approach scales up to larger tem poral and spatial scales.

Invariants in ecological networks

O ne striking particularity of ecological netw orks is their consistency: even though they depict interactions betw een different organism s across all sorts of ecosystem s, they all tend to look the sam e (Jordano et al. 2003). R em arkably, even w hen interactions am ong species them selves vary, the overall netw ork structure tends to rem ain unchanged (K em p et al. 2017). M ost ecological

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netw orks have a very specific and sim ilar degree distribution (W illiam s 2011) (Figure 1d), w hereby m ost species have a sm all num ber of interactions, and a sm all proportions of species have a large num ber of interactions. In food w ebs, w hich represent interactions betw een prey andtheir predators, there is a w ell-described relationship betw een the num ber of species and the num ber of interactions. The num ber of interactions ( L ) increases proportionally to the num ber of species (S ) raised to som e exponent, or L∝S

k

. M artinez (1992) suggested that this exponentis approxim ately equal to 2, i.e. the num ber of interactions is proportional to the squared num ber of species. B rose et al. (2004) show ed that this relationship holds even across space; it is possibleto estim ate how m any interactions a species w ill establish across its entire range. In other instances, netw orks m ay differ on som e aspects of their structure, despite obeying to a shared underlying principle. For exam ple, Fortuna et al. (2010) show ed that in netw orks w ith a low connectance (Figure 1c), nestedness (the degree to w hich the diet of specialists and generalists overlaps – Figure 2) and m odularity (the tendency of species to form densely aggregated clusters– Figure 2) are positively correlated. In netw orks w ith higher connectance, this becom es the opposite: netw orks w ith a large num ber of interactions are either nested (and not m odular) or m odular (and not nested). In the recent years, it em erged that m any aspects of netw ork structure covary w ith connectance (Poisot and G ravel 2014; C hagnon 2015), suggesting that sim ply know ing how m any species there are, and how m any interactions they establish, is already very inform ative about the netw ork structure.A nother rem arkable generality of netw ork structure is the distribution of particular interconnection betw een three-species subsets. M ilo (2002) found that netw orks (not just ecological but other types of netw orks such as neuronal or electronical netw orks as w ell) can be characterized by the over or under representation of som e of these three-species subsets, w hich they called m otifs (Figure 1e). M otifs can be m ore broadly defined as specific arrangem ents of interconnection betw een three (or m ore) nodes. The frequency at w hich they occur in a netw ork can be com puted and com pared to random ized netw orks in order to reveal significant aspects of the structure. Three-species m otifs represent the sim plest building blocks of netw orks, and m ore im portantly typical interaction m odules found in com m unities. A s such, they offer the possibilityto integrate and test theories developed w ith sim ple m odules in larger, m ore realistic netw orks (e.g. om nivory, M cC ann et al. 1998, H olt 1997). Food w ebs, for exam ple, are characterized by an over representation of linear food chains and om nivory and an under representation of apparent and exploitative com petition (Figure 1a,e) (B ascom pte and M elián 2005a; C am acho et

al. 2007). Stouffer and B ascom pte (2010) found that realistic m otif distribution prom otes stability in food w ebs, w ith over-represented m otifs being m ore stable in isolation and correlated w ith higher stability in large realistic com m unities, and conversely. M otifs can also be used to characterize species role in netw orks. From the 13 different three-species m otifs em erge 30 unique positions for species to occupy in these m otifs, representing how the species is em bedded in its com m unity. The different positions a species w ill occupy, and the frequency w ith w hich it w ill occupy these different positions in netw orks are called species m otif role (Stouffer et al. 2012). These roles have been show n to be evolutionary conserved in food w ebs (Stouffer et al. 2012) and to have less variability in tim e than expected in host-parasitoids bipartite netw orks (B aker et al. 2015).A nother invariant netw ork property relates to evolutionary history. Phylogeny is a key determ inant of ecological netw ork structure, being related to species position and interactions

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into the com m unity. Phylogenetically close species tend to inherit traits from their com m on ancestors (e.g. body size, habitat, defensive strategy, m etabolic type, phenology), increasing theirpropensity to interact w ith the sam e group of species or w ith sim ilar species, a phenom enon called phylogenetic signal. This conservatism of interactions has been found to hold across different types of interactions such as antagonistic or m utualistic interactions (Fontaine and Thébault 2015). H ow ever, depending in the species role (e.g. host or parasite, pollinator or plant)the link organization w ill be different, leading to an asym m etrical structure for pairw ise interactions. For instance, closely related hosts tend to share parasites, w hile closely related parasites, because of com petition for resources, tend to have different hosts (K rasnov et al. 2012). The conservatism of interactions is consequently unequal all over the netw ork. Follow ing the logic that closely related species interact w ith the sam e group of species, R ezende et al. (2009) show ed that phylogenetic structure of ecological netw orks explains alm ost entirely the form ation and com position of m odules and the connections betw een them . The species connecting m odules together are indeed usually phylogenetically close. C attin et al. (2004) also found, using a niche-hierarchic m odel, that diet is constrained by the phylogenetic origin of consum ers. The nested structure of trophic netw orks is then influenced by the phylogenetic signal of interacting species and their traits com patibility. In contrast, the nested structure of m utualistic netw orks w ould be a consequence of trait com plem entary betw een species (R ezende et al. 2007). For now , m echanism s underlying the nestedness-phylogeny relationship rem ain to be further investigated. M oreover, because of species plasticity, phylogeny alone does not fully explain the structure and evolution of ecological netw orks.

From structure to properties

The relationship betw een ecological netw ork structure and stability is a long-lasting object of research in com m unity ecology. M acA rthur (1955) and Elton (1958) first proposed that diverse com m unities should have a m ore stable dynam ic than sim ple ones because disturbances are m oreeasily spread through highly connected nodes. M ay (1972) countered this hypothesis using a m athem atical m odel based on random ecological netw orks and proposed there should be a lim it to ecosystem com plexity. This counter-intuitive proposition sparkled live debates still lasting today (M cC ann 2000; see A llesina and Tang 2015). Tw o different approaches to the problem follow ed: one focused on dynam ical stability and the other on the resistance of com m unities to species lost. D espite their dissim ilarities, these approaches are not totally independent (D onohue et al. 2013) and revealed that species diversity has no direct influence on com m unity stability. H ow ever, the structure of ecological netw ork such as the distribution of interaction strength and netw ork topology seem s to play a crucial role (Yodzis 1981).

A s m entioned above, the degree distribution of ecological netw orks often follow s a pow er-law distribution (M ontoya and Solé 2002), indicating that few species are highly connected to the rest of the com m unity and a large num ber of species are w eakly connected to others. This organization com bined w ith the m yriad of w eak interactions found across ecological netw orks buffers species variations and stabilizes the dynam ics of the entire com m unity (B ascom pte et al. 2005b; Jacquet et al. 2016). O ther aspects of com m unity structure, such as the predator-prey body-m ass ratio (Em m erson and R affaelli 2004; B rose et al. 2006a) and netw ork architecture (M ontoya et al. 2006; Thébault and Fontaine 2010), determ ine the distribution and strength of

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interactions and together drive the stability of ecological netw orks (Jacquet et al. 2016).Perturbations in ecological com m unities such as landscape fragm entation, habitat loss, or speciesinvasion, are the prim ary drivers of species loss. Extinctions m ay happen directly, for instance if a particular habitat is elim inated, or indirectly follow ing a first species loss (a phenom enon referred as secondary extinction or cascades). Such extinctions are used to m easure the robustness of ecological com m unities. Sim ulation experim ents revealed that the likelihood of secondary extinctions increases w ith com m unity size (Lundberg et al. 2008), decreases w ith netw ork connectance (D unne et al. 2002) and prim arily affects the m ost isolated species in the netw ork. The loss of a highly connected species, also called a hub, induces a higher rate of secondary extinctions than the loss of a random and w eakly connected species (Solé and M ontoya 2001). Sim ilarly, species responsible for im portant energy-flow in the netw ork (carbon,nitrogen or biom ass) can trigger secondary extinctions (A llesina and B odini 2004).The netw ork architecture also affects the com m unity response to perturbations. In agreem ent w ith M acA rthur's intuition, it w as found that species w ith low degree also m ore strongly propagate perturbations follow ing perm anent changes in the environm ent because of their tight connections (M ontoya et al. 2009). A lternatively, the m ost connected species diffuse such perturbations through the netw ork and even though they affect a higher num ber of species, their average effect on other ones is m uch sm aller. O verall netw ork properties also affect the response to perturbation. Thanks to their structural properties (high nestedness and connectance, Jordano et al. 2003), m utualistic netw orks persist longer than random ly structured netw orks (M em m ott et

al. 2004; Fortuna and B ascom pte 2006). O n the other hand, presence of m odules in the com m unity structure lim its propagation of perturbations across the rest of the netw ork and, as such, secondary extinctions (Stouffer and B ascom pte 2010).Eluding the consequences of biodiversity lost for ecosystem functioning is also an im portant field w here the netw ork approach has been useful. The hypothesis that an increase in species diversity results in an increased productivity dates back to D arw in (1859) and a form al theory forw hat is now called the biodiversity-ecosystem functioning (B EF) relationship w as proposed in the m id 90s. In a trophic group (i.e. a group of species that all belong to the sam e trophic level, e.g. producers or herbivores), increasing diversity im proves resource use efficiency and translates into larger productivity (Loreau 2010) (e.g. nutrients for producers, or producers for herbivores). Yet, w hen the trophic group under focus is coupled to other(s), the action of diversity on functioning is m ore variable (D uffy et al. 2007). This m akes the B EF relationship unpredictable in real-w orld com m unities (H arvey et al. 2013), com posed of several trophic groups that are virtually never differentiable – as intraguild predation and om nivory blur the frontier betw een levels. The m ultiplicity of the factors influencing the B EF relationship calls for a m ore general fram ew ork that allow s the integration of the theories developed for trophic groups and for sim ple m odules or sub-system s (G ravel et al. 2016). B y m apping transfer of biom ass and energy and/or constraints on organism through the different com partm ents that com pose a natural com m unity, ecological netw orks – and food w ebs in particular – offer the possibility to perform this integration. A nalyses perform ed on sim ulated food-w ebs w ith fixed species richness have show n that interactions, and m ore specifically their structure, have a significant influence on productivity (Thebault and Loreau 2003; Thébault et al. 2007; Poisot et

al. 2013). The structure of interactions is indeed a reflection of com m unity properties, essential

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to ecosystem functioning. It seem s then essential to integrate it in B EF studies.

Mechanisms underlying pairwise interactions

Ecological interactions betw een species should be view ed as the result of low level processes involving pairs of individuals. A pollinator is able to effectively reach the nectar in a plant because their respective traits m atch, they have com patible phenologies, and they occur in the sam e environm ent. A virus can infect its host because it is able to attach to the cell surface, effectively penetrate it, and hijack the cellular m achinery to its benefit. Interactions that are not allow ed because trait values do not m atch have been called "forbidden links" (O lesen et al. 2011). This prom pted a search for "linkage rules" (B artom eus 2013) in ecological netw orks, i.e. the relationships that m ust exist betw een traits of tw o organism s in order for an interaction betw een them to exist. These can be identified from existing data on traits and interactions (B artom eus et al. 2016), and then used to generate realistic ecological netw orks (C rea et al. 2015). G onzález-Varo and Traveset (2016) pointed out that interactions are happening betw een individuals, and as a consequence, it requires to consider not only how the traits are distributed atthe individual scale, but also how different behaviors m ay allow organism s to overcom e som e of the forbidden interactions.A lthough traits are an im portant part of w hat m akes interactions happen, they are only relevant insofar as the organism s are able to encounter one another. The im portance of neutral dynam ics (i.e. how abundances of different species can determ ine the probability that they can interact, based on how often they w ould get in contact by chance) is, som ew hat counter-intuitively, great. C anard et al. (2012) revealed that realistic food w ebs can be predicted w ith only know ledge of abundances. In a host-parasite system , local abundances has also been identified as a key predictor of species interactions (C anard et al. 2014). M ore broadly, because interactions em erge from all of these ecological m echanism s, there is a need to develop a deeper understanding of their variability (Poisot et al. 2015). B eyond the fundam ental advance that this represents, this w ould allow to m odel interactions based on external inform ation instead of docum enting all of them (M orales-C astilla et al. 2015).The realization of an interaction betw een individuals has, by definition, an effect on population dynam ics. B ut it is also archetypical of com plex system dynam ics, w here low level processes propagate up to higher level of organization and im pact em erging properties of the com m unity. Ifw e consider for instance a population A , its dynam ic is not the sam e w hen it m ultiplies in isolation – w here it can grow exponentially if resources are unlim ited (M althus 1798) or logistically otherw ise (Verhulst 1938) – or w hen it is em bedded in a real-w orld com m unity, com posed of several species interacting w ith one another through different processes. That population can lose individuals to predation, have parasitism increase its death rate and at the sam e tim e see its establishm ent eased through facilitation. It then becom es necessary to account for the entire set of interactions to understand population, com m unity and ecosystem dynam ics. B ut the effect of interactions on dynam ics is not alw ays straightforw ard to elude, both in term s ofdirectionality and intensity, as there is different types of interactions and m ultiple factors influencing their occurrence and strength.Ecological netw orks are also spatially and tem porally variable (Trøjelsgaard and O lesen 2016). There are tw o drivers to this variability: changes in species com position, and changes in the w ay

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these species interact (Poisot et al. 2012). C hanges in species alone are able to generate variation in netw ork properties (H avens 1992). Spatial variation in netw ork structure can also reflect deep-tim e constraints; for exam ple, D alsgaard et al. (2013) revealed that historical clim ate change trends have a signature on the nestedness and m odularity of pollination netw orks. Even w hen thesam e species are present, interactions betw een them can vary. C arstensen et al. (2014) and Trøjelsgaard et al. (2015) investigated this phenom enon in m utualistic netw orks. Interaction turnover results from variations in partner fidelity (som e species pairs are extrem ely closely associated), but also from variations in the local environm ent in w hich the species interact. Interestingly, netw orks overw helm ingly tend to conserve their structure even w hen interactions w ithin them change. D íaz-C astelazo et al. (2010) surveyed a pollination netw ork over 10 years, and found im portant species turnover during this period. N evertheless, the netw ork retained its structure because species w here replaced by their functional equivalent; a generalist pollinator often succeeded to another generalist pollinator. C onversely, species tend to retain their role in different com m unities: B aker et al. (2015) show ed that species keep occupying the sam e positionin the netw ork across space, regardless of the species they interact w ith at every location.

From the regional species pool to local structured communities

D escribing the variation in ecological netw ork structure at large spatial scales m ay represent an additional layer of inform ation com pared to sim ple species lists. A s such, ecological netw orks are a pow erful tool to shed new light on the processes underlying species distribution (C azelles et al. 2016) and variation in som e ecosystem functions (e.g. trophic regulation). U ntil recently, the prevailing idea w as that at large spatial scales, the role of biotic interactions on distribution isvery sm all com pared to that of abiotic conditions, and as such is im portant only locally (Pearson and D aw son 2003; B oulangeat et al. 2012). Em pirical observations of species-environm ent relationship are used to approxim ate species physiological tolerance to environm ental conditions and potentially predict their range under different scenarios of clim ate change (e.g. A raújo et al. 2006). W hile these species distribution m odels provide a useful approxim ation of their potential range shift (Pearson et al. 2002), there is m ounting evidence that biotic interactions – both positive and negative – play a critical role in shaping com m unities not only at local scales (B oulangeat et al. 2012), but also at m acro-ecological scales (D avis et al. 1998; A raújo and Luoto 2007; H eikkinen et al. 2007; G otelli et al. 2010; A raújo et al. 2011).It w as proposed that the role of interactions in shaping species distribution could be approxim ated from know ledge of species co-occurrence (A raújo et al. 2011). This very active field of research has been recently pushed by the developm ent of joint species distribution m odels (JSD M ), w hich account sim ultaneously for the effect of the environm ent and co-distribution (Pollock et al. 2014). B ut there are lim itations to this approach. For instance, it does not allow to distinguish betw een co-occurrence caused by biotic interactions and correlated responses to unm easured environm ental variables (Pollock et al. 2014). C onversely, the lack of association betw een species is no evidence of absence of interaction (C azelles et al. 2016). Further w ork is therefore needed to m ove from correlative species distribution m odels (SD M ) tow ard m ore theoretically sound m odels. In particular, developing m ethods allow ing to include prior inform ation about the underlying ecological netw ork w hen estim ating (J)SD M could shed

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light on the fundam ental processes underlying species distribution and thus m aking m ore accurate predictions (C azelles et al. 2016). A dditionally, Poisot et al. (2017) recently show ed thatbiotic interactions respond to environm ental conditions on their ow n, independently of species.Ecological netw orks also offer an ideal fram ew ork to study the conditions for the m aintenance ofbiodiversity in com m unities. The com petitive exclusion principle states that the num ber of coexisting species should be equal or sm aller than the num ber of resources. This stands in contradiction w ith the existence of ecological com m unities containing species that overlap in som e extent in their resources or consum ers. Phytoplanktonic com m unities are often considered to illustrate this paradox (H utchinson 1961), as they exhibit a high biodiversity w hile species are com peting for a lim ited num ber of shared resources (e.g. light, nitrate). Species coexistence m echanism s (C hesson 2000) are based on species traits that either decrease fitness differences (equalizing m echanism s) and/or increase niche differentiation betw een species (stabilizing m echanism s).The coexistence theory and the representation of ecological com m unities as netw orks of interactions has brought new perspective on species coexistence. M artinez et al. (2006) for instance show ed that the global non-random structure of the food w ebs im prove com m unity persistence (i.e. species coexistence). The distribution of m otifs in food w ebs (Stouffer and B ascom pte 2010, see section Invariants in ecological networks) as w ell as species' role w ithin m otifs (Stouffer et al. 2012) are related to com m unity persistence. In m utualistic netw orks for instance, the nested structure m inim izes interspecific com petition and increase the num ber of coexisting species (B astolla et al. 2009; Sugihara and Ye 2009). Interactions structure also tend to im pact species coexistence into com m unities, as highlighted by B ascom pte et al. (2006), the fact that one species A depends strongly on another species B as resource for food or pollination, and the other species, B , only w eakly depends on A , also called asym m etry of dependences, increases coexistence of species. A s an other exam ple, using food w eb structure B rose et al. (2006b) show ed that the allom etric scaling of m etabolic rates of species im prove com m unity persistence. A ll these types of approach, w hether they are based on m otifs, species' role or allom etric scaling, have highlighted the im portance of netw ork structure in species coexistence.Ecologists have also questioned the w ay com m unities are form ed and the hypothetical set of rules em bedding their assem bly. The netw ork approach allow s to explore in details the different processes influencing ecological com m unities assem bly. C apitán et al. (2009), for instance, characterized the sequence of species arrival in a com m unity w ith an assem bly graph. It allow s to follow step by step every possible path in com m unity assem bly from 0 to x species am ong several trophic levels, and to highlight underlying m echanism s. Verdú and Valiente B anuet ‐

(2008), for instance, found that nested com m unity provides generalists species w hich facilitate the presence of other species into the netw ork. A t the sam e tim e, O lesen et al. (2008) observed that new ly arriving species tend to interact m ore easily w ith already w ell-connected or generalist species. Such results could let us think about the D rake's controversial idea that species arrival history w ould be an im portant factor driving com m unity assem bly (D rake 1991). This proposition w as supported by netw ork analyses, such as in C am pbell et al. (2011) for m utualisticnetw orks, but still rem ains object of debate.The addition of ecological netw orks into m odels of diversity dynam ics fostered the developm ent

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of theory of com m unity assem bly at both, fine and large spatial scales. N iche and neutral theoriesdom inated m ost of com m unity assem bly research since the publication of H ubbell’s book in 2001. A w ide range of m odels have been used, m ost of them w ith very abstract and phenom enological representations of the niche. B ut only recently, w ith the addition of trophic constraints (G ravel et al. 2011) and other types of interactions (C azelles et al. 2016) to M acA rthur and W ilson’s (1967) m odel of island biogeography, that all types of interactions w ereconsidered in the process of com m unity assem bly. The m odel w as first extended by assum ing that predator could only colonize com m unities w ith prey already present, and go extinct w ith their last prey. This m odification w as sufficient to explain the observation of a sequential construction of food w ebs after the defaunation treatm ent of the fam ous experim ent by Sim berloff and W ilson (1969, Petchey et al. 2008). The m odel w as further use to illustrate a reciprocal feedback betw een colonization-extinction dynam ics and local food w eb dynam ics, w here properties of the regional food w eb constrain the developm ent of the local m otif structure, and alternatively local dynam ics influence the assem bly process (M assol et al. 2017). This m odeling approach allow s a general representation of the niche in studies of assem bly dynam ics (Jacquet et al. 2017) and propose a unifying fram ew ork to explain the construction of local com m unities from a sam ple of the regional species pool.

Conclusion

G raph theory delivered im portant scientific discoveries, such as im proved understanding of breakdow n of electricity distribution system s or the propagation of infections in social netw orks. It is also a pow erful tool to investigate key questions in ecology. G raph theory provides a rem arkably sim ple w ay to characterize the com plexity of ecological netw orks. Indices such as connectance, degree distribution or netw ork topology serve as basic m easurem ents to describe their structure. Such indices facilitate com parison betw een different system s and revealing com m onalities and variations. N ow adays, the relatively im portant num ber of netw ork studies leads to a m yriads of w ays to sam ple, analyze and interpret them (see D elm as et al. 2017).Studying ecological netw orks have how ever a larger purpose than just their description and classification. B asic m easurem ents are correlated to several environm ental conditions and netw ork analysis appears to be helpful in different ecological fields. A s w e seen through this chapter, it can be used to study dynam ics of ecological system s and their responses to changes, according to their stability over tim e or the B EF relationships in the system . It also highlights theunderstanding of m echanism s underlying ecological properties such as com m unity assem bly, coexistence and species distribution. N etw ork studies w ere a key to reveal relationships betw een different properties of ecological netw ork such as trait and structure.

10

Further Readings

B artom eus, I., G ravel, D . and Tylianakis, J. M . et al. (2016) ‘A com m on fram ew ork for identifying linkage rules across different types of interactions’, Functional Ecology, 30(12), pp. 1894–1903. A vailable at: http://onlinelibrary.w iley.com /doi/10.1111/1365-2435.12666/full.B ascom pte, J. (2007) ‘N etw orks in ecology’, B asic and A pplied Ecology, 8(6), pp. 485–490. doi:10.1016/j.baae.2007.06.003.D unne, J. A ., W illiam s, R . J. and M artinez, N . D . (2002) ‘Food-w eb structure and netw ork theory: The role of connectance and size’, Proceedings of the N ational A cadem y of Sciences, 99(20), pp. 12917–12922. doi:10.1073/pnas.192407699.Evans, D . M ., K itson, J. J. N . and Lunt, D . H . et al. (2016) ‘M erging D N A m etabarcoding and ecological netw ork analysis to understand and build resilient terrestrial ecosystem s’, Functional Ecology. Edited by T. Poisot, 30(12), pp. 1904–1916. doi: 10.1111/1365-2435.12659.Jordano, P. (2016) ‘Sam pling netw orks of ecological interactions’, Functional Ecology. Edited byD . Stouffer, 30(12), pp. 1883–1893. doi: 10.1111/1365-2435.12763.Jordano, P., B ascom pte, J. and O lesen, J. M . (2003) ‘Invariant properties in coevolutionary netw orks of plant–anim al interactions’, Ecology Letters, 6(1), pp. 69–81. doi: 10.1046/j.1461-0248.2003.00403.x.K éfi, S., B erlow , E. L. and W ieters, E. A . et al. (2012) ‘M ore than a m eal... integrating non-feeding interactions into food w ebs: M ore than a m eal ...’, Ecology Letters, 15(4), pp. 291–300. doi: 10.1111/j.1461-0248.2011.01732.x.M artinez, N . D . (1992) ‘C onstant C onnectance in C om m unity Food W ebs’, The A m erican N aturalist, 139(6), pp. 1208–1218. A vailable at: http://w w w .jstor.org/stable/2462337.M ontoya, J. M ., Pim m , S. L. and Solé, R . V. (2006) ‘Ecological netw orks and their fragility’, N ature, 442(7100), pp. 259–264. doi: 10.1038/nature04927.O lesen, J. M ., B ascom pte, J. and D upont, Y. L. et al. (2011) ‘M issing and forbidden links in m utualistic netw orks’, Proceedings of the Royal Society of London B: Biological Sciences, 278(1706), pp. 725–732. doi: 10.1098/rspb.2010.1371.Peralta, G . (2016) ‘M erging evolutionary history into species interaction netw orks’, Functional Ecology. Edited by S. K efi, 30(12), pp. 1917–1925. doi:10.1111/1365-2435.12669.Pilosof, S., Porter, M . A ., Pascual, M . and K éfi, S. (2017) ‘The m ultilayer nature of ecological netw orks’, N ature Ecology & Evolution, 1(4), p. 0101. doi:10.1038/s41559-017-0101.Trøjelsgaard, K . and O lesen, J. M . (2016) ‘Ecological netw orks in m otion: m icro and m acroscopic variability across scales’, Functional Ecology, 30(12), pp. 1926–1935. doi: 10.1111/1365-2435.12710.

11

References

A llesina, S. and B odini, A . (2004) ‘W ho dom inates w hom in the ecosystem ? Energy flow bottlenecks and cascading extinctions’, Journal of Theoretical Biology, 230(3), pp. 351–358. doi:10.1016/j.jtbi.2004.05.009.A llesina, S. and Tang, S. (2015) ‘The stability–com plexity relationship at age 40: a random m atrix perspective’, Population Ecology, 57(1), pp. 63–75. doi: 10.1007/s10144-014-0471-0.A raújo, M . B . and Luoto, M . (2007) ‘The im portance of biotic interactions for m odelling species distributions under clim ate change’, Global Ecology and Biogeography, 16(6), pp. 743–753. doi:10.1111/j.1466-8238.2007.00359.x.A raújo, M . B ., R ozenfeld, A ., R ahbek, C . and M arquet, P. A . (2011) ‘U sing species co-occurrence netw orks to assess the im pacts of clim ate change’, Ecography, 34(6), pp. 897–908. doi: 10.1111/j.1600-0587.2011.06919.x.A raújo, M . B ., Thuiller, W . and Pearson, R . G . (2006) ‘C lim ate w arm ing and the decline of am phibians and reptiles in Europe’, Journal of Biogeography, 33(10), pp. 1712–1728. doi: 10.1111/j.1365-2699.2006.01482.x.B aker, N . J., K aartinen, R ., R oslin, T. and Stouffer, D . B . (2015) ‘Species’ roles in food w ebs show fidelity across a highly variable oak forest’, Ecography, 38(2), pp. 130–139. doi: 10.1111/ecog.00913.B artom eus, I. (2013) ‘U nderstanding linkage rules in plant-pollinator netw orks by using hierarchical m odels that incorporate pollinator detectability and plant traits’, PloS one, 8(7), p. e69200. A vailable at: http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0069200B artom eus, I., G ravel, D . and Tylianakis, J. M . et al. (2016) ‘A com m on fram ew ork for identifying linkage rules across different types of interactions’, Functional Ecology, 30(12), pp. 1894–1903. A vailable at: http://onlinelibrary.w iley.com /doi/10.1111/1365-2435.12666/fullB ascom pte, J. and M elián, C . J. (2005a) ‘Sim ple trophic m odules for com plex food w ebs’, Ecology, 86(11), pp. 2868–2873. doi: 10.1890/05-0101.B ascom pte, J., Jordano, P. and O lesen, J. M . (2006) ‘A sym m etric C oevolutionary N etw orks Facilitate B iodiversity M aintenance’, Science, 312(5772), pp. 431–433. doi: 10.1126/science.1123412.B ascom pte, J., M elián, C . J. and Sala, E. (2005b) ‘Interaction strength com binations and the overfishing of a m arine food w eb’, Proceedings of the National Academy of Sciences of the

United States of America, 102(15), pp. 5443–5447. doi: 10.1073/pnas.0501562102.B astolla, U ., Fortuna, M . A . and Pascual-G arcía, A . et al. (2009) ‘The architecture of m utualistic netw orks m inim izes com petition and increases biodiversity’, Nature, 458(7241), pp. 1018–1020. doi: 10.1038/nature07950.B oulangeat, I., G ravel, D . and Thuiller, W . (2012) ‘A ccounting for dispersal and biotic interactions to disentangle the drivers of species distributions and their abundances’, Ecology

Letters, 15(6), pp. 584–593. doi: 10.1111/j.1461-0248.2012.01772.x.B rose, U ., Jonsson, T. and B erlow , E. L. et al. (2006a) ‘C onsum er–R esource B ody-Size

12

R elationships in N atural Food W ebs’, Ecology, 87(10), pp. 2411–2417. doi: 10.1890/0012-9658(2006)87[2411:C B R IN F]2.0.C O ;2.B rose, U ., O stling, A ., H arrison, K . and M artinez, N . D . (2004) ‘U nified spatial scaling of species and their trophic interactions’, Nature, 428(6979), pp. 167–171. doi: 10.1038/nature02297.B rose, U ., W illiam s, R . J. and M artinez, N . D . (2006b) ‘A llom etric scaling enhances stability in com plex food w ebs’, Ecology Letters, 9(11), pp. 1228–1236. doi: 10.1111/j.1461-0248.2006.00978.x.C am acho, J., Stouffer, D . and A m aral, L. (2007) ‘Q uantitative analysis of the local structure of food w ebs’, Journal of Theoretical Biology, 246(2), pp. 260–268. doi: 10.1016/j.jtbi.2006.12.036.C am pbell, C ., Yang, S., A lbert, R . and Shea, K . (2011) ‘A netw ork m odel for plant–pollinator com m unity assem bly’, Proceedings of the National Academy of Sciences, 108(1), pp. 197–202. doi: 10.1073/pnas.1008204108.C anard, E. F., M ouquet, N . and M ouillot, D . et al. (2014) ‘Em pirical evaluation of neutral interactions in host-parasite netw orks’, The American Naturalist 183(4), pp. 468–479. doi: 10.1086/675363.C anard, E., M ouquet, N . and M arescot, L. et al. (2012) ‘Em ergence of Structural Patterns in N eutral Trophic N etw orks’, PLOS ONE, 7(8), p. e38295. doi: 10.1371/journal.pone.0038295.C apitán, J. A ., C uesta, J. A . and B ascom pte, J. (2009) ‘Statistical M echanics of Ecosystem A ssem bly’, Physical Review Letters, 103(16), p. 168101. doi: 10.1103/PhysR evLett.103.168101.C arstensen, D . W ., Sabatino, M ., Trøjelsgaard, K . and M orellato, L. P. C . (2014) ‘B eta D iversity of Plant-Pollinator N etw orks and the Spatial Turnover of Pairw ise Interactions’, PLoS ONE, 9(11), p. e112903. doi: 10.1371/journal.pone.0112903.C attin, M .-F., B ersier, L.-F. and B anaWek-R ichter, C . et al. (2004) ‘Phylogenetic constraints and adaptation explain food-w eb structure’, Nature, 427(6977), pp. 835–839. doi: 10.1038/nature02327.C azelles, K ., A raújo, M . B ., M ouquet, N . and G ravel, D . (2016) ‘A theory for species co-occurrence in interaction netw orks’, Theoretical Ecology, 9(1), pp. 39–48. doi: 10.1007/s12080-015-0281-9.C hagnon, P.-L. (2015) ‘C haracterizing topology of ecological netw orks along gradients: the lim its of m etrics’ standardization’, Ecological Complexity, 22, pp. 36–39. A vailable at: http://w w w .sciencedirect.com /science/article/pii/S1476945X 15000070C hesson, P. (2000) ‘M echanism s of M aintenance of Species D iversity’, Annual Review of

Ecology and Systematics, 31(1), pp. 343–366. doi: 10.1146/annurev.ecolsys.31.1.343.C ohen, J. E. (1989) ‘Food w ebs and com m unity structure’, Perspectives in ecological theory, pp.181–202.C rea, C ., A li, R . A . and R ader, R . (2015) ‘A new m odel for ecological netw orks using species-level traits’, Methods in Ecology and Evolution. A vailable at: http://onlinelibrary.w iley.com /doi/10.1111/2041-210X .12471/pdf

13

D alsgaard, B ., Trøjelsgaard, K . and M artín G onzález, A . M . et al. (2013) ‘H istorical clim ate-change influences m odularity and nestedness of pollination netw orks’, Ecography, 36(12), pp. 1331–1340. doi: 10.1111/j.1600-0587.2013.00201.x.D arw in, C . (1859) On the Origin of Species by Means of Natural Selection, or Preservation of

Favoured Races in the Struggle for Life. John M urray, London.D avis, A . J., Law ton, J. H ., Shorrocks, B . and Jenkinson, L. S. (1998) ‘Individualistic species responses invalidate sim ple physiological m odels of com m unity dynam ics under global environm ental change’, Journal of Animal Ecology, 67(4), pp. 600–612. doi: 10.1046/j.1365-2656.1998.00223.x.D elm as, E., B esson, M . and B rice, M .-H . et al. (2017) ‘A nalyzing ecological netw orks of speciesinteractions’, pp. –. doi: 10.1101/112540.D íaz-C astelazo, C ., G uim arães, P. R . and Jordano, P. et al. (2010) ‘C hanges of a m utualistic netw ork over tim e: reanalysis over a 10-year period’, Ecology, 91(3), pp. 793–801. A vailable at: http://w w w .jstor.org/stable/25661111D rake, J. A . (1991) ‘C om m unity-A ssem bly M echanics and the Structure of an Experim ental Species Ensem ble’, The American Naturalist, 137(1), pp. 1–26. doi: 10.1086/285143.D uffy, J. E., C ardinale, B . J. and France, K . E. et al. (2007) ‘The functional role of biodiversity in ecosystem s: incorporating trophic com plexity’, Ecology Letters, 10(6), pp. 522–538. doi: 10.1111/j.1461-0248.2007.01037.x.D unne, J. A ., W illiam s, R . J. and M artinez, N . D . (2002) ‘N etw ork structure and biodiversity lossin food w ebs: robustness increases w ith connectance’, Ecology Letters, 5(4), pp. 558–567. doi: 10.1046/j.1461-0248.2002.00354.x.D onohue, I., Petchey, O . L., M ontoya J. M . et al. (2013) ‘O n the dim ensionality of ecological stability’, Ecology Letters, 16(4), pp. 421–429. doi: 10.1111/ele.12086.Elton, C . C . (1958) ‘The R easons for C onservation’, in The Ecology of Invasions by Animals and

Plants. Springer N etherlands, pp. 143–153. doi: 10.1007/978-94-009-5851-7_8.Em m erson, M . C . and R affaelli, D . (2004) ‘Predator–prey body size, interaction strength and the stability of a real food w eb’, Journal of Animal Ecology, 73(3), pp. 399–409. doi: 10.1111/j.0021-8790.2004.00818.x.Fontaine, C . and Thébault, E. (2015) ‘C om paring the conservatism of ecological interactions in plant–pollinator and plant–herbivore netw orks’, Population Ecology, 57(1), pp. 29–36. doi: 10.1007/s10144-014-0473-y.Fortuna, M . A . and B ascom pte, J. (2006) ‘H abitat loss and the structure of plant-anim al m utualistic netw orks: M utualistic netw orks and habitat loss’, Ecology Letters, 9(3), pp. 281–286.doi: 10.1111/j.1461-0248.2005.00868.x.Fortuna, M . A ., Stouffer, D . B . and O lesen, J. M . et al. (2010) ‘N estedness versus m odularity in ecological netw orks: tw o sides of the sam e coin?’, Journal of Animal Ecology, 79(4), pp. 811–817. doi: 10.1111/j.1365-2656.2010.01688.x.G onzález-Varo, J. P. and Traveset, A . (2016) ‘The Labile Lim its of Forbidden Interactions’, Trends in Ecology & Evolution, 31(9), pp. 700–710. doi: 10.1016/j.tree.2016.06.009.

14

G otelli, N . J., G raves, G . R . and R ahbek, C . (2010) ‘M acroecological signals of species interactions in the D anish avifauna’, Proceedings of the National Academy of Sciences, 107(11), pp. 5030–5035. doi: 10.1073/pnas.0914089107.G ravel, D ., A lbouy, C . and Thuiller, W . (2016) ‘The m eaning of functional trait com position of food w ebs for ecosystem functioning’, Philosophical Transactions of the Royal Society B:

Biological Sciences, 371(1694), p. 20150268. doi: 10.1098/rstb.2015.0268.G ravel, D ., C anham , C . D ., B eaudet, M . and M essier, C . (2006) ‘R econciling niche and neutrality: the continuum hypothesis’, Ecology Letters, 9(4), pp. 399–409. doi: 10.1111/j.1461-0248.2006.00884.x.G ravel, D ., M assol, F. and C anard, E. et al. (2011) ‘Trophic theory of island biogeography: Trophic theory of island biogeography’, Ecology Letters, 14(10), pp. 1010–1016. doi: 10.1111/j.1461-0248.2011.01667.x.G ravel, D ., Poisot, T., A lbouy, C ., Velez, L. and M ouillot, D . (2013) ‘Inferring food w eb structure from predator–prey body size relationships’, Methods in Ecology and Evolution, 4(11), pp. 1083–1090. doi:10.1111/2041-210X .12103.H arvey, E., Séguin, A . and N ozais, C . et al. (2013) ‘Identity effects dom inate the im pacts of m ultiple species extinctions on the functioning of com plex food w ebs’, Ecology, 94(1), pp. 169–179. doi: 10.1890/12-0414.1.H avens, K . (1992) ‘Scale and structure in natural food w ebs’, Science (New York, N.Y.), 257(5073), pp. 1107–1109. doi: 10.1126/science.257.5073.1107.H eikkinen, R . K ., Luoto, M . and V irkkala, R . et al. (2007) ‘B iotic interactions im prove prediction of boreal bird distributions at m acro-scales’, Global Ecology and Biogeography, 16(6), pp. 754–763. doi: 10.1111/j.1466-8238.2007.00345.x.H olt, R . D . (1997) ‘C om m unity m odules’, A.C. Gange, V.K. Brown (Eds.), Multitrophic

interactions in Terrestrial Ecosystems, 6th Symposium of the British Ecological Society,

Blackwell Science, pp. 333–350.H ubbell, S. P. (2001) The Unified Neutral Theory of Biodiversity and Biogeography (MPB-32). Princeton; O xford: Princeton U niversity Press. A vailable at: http://w w w .jstor.org/stable/j.ctt7rj8w .H utchinson, G . E. (1961) ‘The Paradox of the Plankton’, The American Naturalist, 95(882), pp. 137–145. doi: 10.1086/282171.Jacquet, C ., M oritz, C . and M orissette, L. et al. (2016) ‘N o com plexity–stability relationship in em pirical ecosystem s’, Nature Communications, 7, p. 12573. doi: 10.1038/ncom m s12573.Jacquet, C ., M ouillot, D ., K ulbicki, M ., G ravel, D . (2017) ‘Extensions of Island B iogeography Theory predict the scaling of functional trait com position w ith habitat area and isolation’, Ecology Letters. Edited by D . Storch, 20(2), pp. 135–146. doi: 10.1111/ele.12716.Jordano, P., B ascom pte, J. and O lesen, J. M . (2003) ‘Invariant properties in coevolutionary netw orks of plant–anim al interactions’, Ecology Letters, 6(1), pp. 69–81. doi: 10.1046/j.1461-0248.2003.00403.x.K em p, J. E., Evans, D . M ., A ugustyn, W . J. and Ellis, A . G . (2017) ‘Invariant antagonistic

15

netw ork structure despite high spatial and tem poral turnover of interactions’, Ecography, pp. n/a–n/a. doi: 10.1111/ecog.02150.K raft, N ., C ornw ell, W ., W ebb, C . and A ckerly, D . (2007) ‘Trait Evolution, C om m unity A ssem bly, and the Phylogenetic Structure of Ecological C om m unities.’, The American

Naturalist, 170(2), pp. 271–283. doi: 10.1086/519400.K rasnov, B . R ., Fortuna, M . A . and M ouillot, D . et al. (2012) ‘Phylogenetic Signal in M odule C om position and Species C onnectivity in C om partm entalized H ost-Parasite N etw orks’, The

American Naturalist, 179(4), pp. 501–511. doi: 10.1086/664612.Leibold, M . A ., C hase, J. M . and Ernest, S. K . M . (2017) ‘C om m unity assem bly and the functioning of ecosystem s: how m etacom m unity processes alter ecosystem s attributes’, Ecology, 98(4), pp. 909–919. doi: 10.1002/ecy.1697.Loreau, M . (2010) ‘Linking biodiversity and ecosystem s: tow ards a unifying ecological theory’, Philosophical Transactions of the Royal Society B: Biological Sciences, 365(1537), pp. 49–60. doi: 10.1098/rstb.2009.0155.Lundberg, P., R anta, E. and K aitala, V. (2008) ‘Species loss leads to com m unity closure’, Ecology Letters, 3(6), pp. 465–468. doi: 10.1111/j.1461-0248.2000.00170.x.M acA rthur, R . (1955) ‘Fluctuations of A nim al Populations and a M easure of C om m unity Stability’, Ecology, 36(3), p. 533. doi: 10.2307/1929601.M acA rthur, R . H . and W ilson, E. O . (1967) The theory of island biogeography. Princeton: Princeton U niversity Press.M aherali, H . and K lironom os, J. N . (2007) ‘Influence of Phylogeny on Fungal C om m unity A ssem bly and Ecosystem Functioning’, Science, 316(5832), pp. 1746–1748. doi: 10.1126/science.1143082.M althus, T. R . (1798) ‘A n Essay on the Principle of Population, as it A ffects the Future Im provem ent of Society: W ith R em arks on the Speculations of M r. G odw in, M r. C ondorcet, and O ther W riters.’M artinez, N . D . (1992) ‘C onstant C onnectance in C om m unity Food W ebs’, The American

Naturalist, 139(6), pp. 1208–1218. A vailable at: http://w w w .jstor.org/stable/2462337M artinez, N . D ., W illiam s, R . J. and D unne, J. A . (2006) ‘D iversity, com plexity, and persistence in large m odel ecosystem s’, Ecological networks: linking structure to dynamics in food webs, pp.163–185.M assol, F., D ubart, M ., C alcagno, V. et al. (2017) ‘Island B iogeography of Food W ebs’, in Advances in Ecological Research. Elsevier, pp. 183–262. doi: 10.1016/bs.aecr.2016.10.004.M ay, R . M . (1972) ‘W ill a Large C om plex System be Stable?’, Nature, 238(5364), pp. 413–414. doi: 10.1038/238413a0.M cC ann, K . S. (2000) ‘The diversity–stability debate’, Nature, 405(6783), pp. 228–233. doi: 10.1038/35012234.M cC ann, K ., H astings, A . and H uxel, G . R . (1998) ‘W eak trophic interactions and the balance of nature’, Nature, 395(6704), pp. 794–798. doi: 10.1038/27427.

16

M em m ott, J., W aser, N . M . and Price, M . V. (2004) ‘Tolerance of pollination netw orks to species extinctions’, Proceedings of the Royal Society B: Biological Sciences, 271(1557), pp. 2605–2611. doi: 10.1098/rspb.2004.2909.M ilo, R . (2002) ‘N etw ork M otifs: Sim ple B uilding B locks of C om plex N etw orks’, Science, 298(5594), pp. 824–827. doi: 10.1126/science.298.5594.824.M ontoya, J. M . and Solé, R . V. (2002) ‘Sm all W orld Patterns in Food W ebs’, Journal of

Theoretical Biology, 214(3), pp. 405–412. doi: 10.1006/jtbi.2001.2460.M ontoya, J. M . and Solé, R . V. (2003) ‘Topological properties of food w ebs: from real data to com m unity assem bly m odels’, Oikos, 102(3), pp. 614–622. doi: 10.1034/j.1600-0706.2003.12031.x.M ontoya, J. M ., Pim m , S. L. and Solé, R . V. (2006) ‘Ecological netw orks and their fragility’, Nature, 442(7100), pp. 259–264. doi: 10.1038/nature04927.M ontoya, J., W oodw ard, G ., Em m erson, M . C . and Solé, R . V. (2009) ‘Press perturbations and indirect effects in real food w ebs’, Ecology, 90(9), pp. 2426–2433. doi: 10.1890/08-0657.1.M orales-C astilla, I., M atias, M . G ., G ravel, D . and A raújo, M . B . (2015) ‘Inferring biotic interactions from proxies’, Trends in Ecology & Evolution, 30(6), pp. 347–356. doi: 10.1016/j.tree.2015.03.014.O lesen, J. M ., B ascom pte, J. and D upont, Y. L. et al. (2011) ‘M issing and forbidden links in m utualistic netw orks’, Proceedings of the Royal Society of London B: Biological Sciences, 278(1706), pp. 725–732. doi: 10.1098/rspb.2010.1371.O lesen, J. M ., B ascom pte, J., Elberling, H . and Jordano, P. (2008) ‘TEM PO R A L D Y N A M IC S IN A PO LLIN ATIO N N ETW O R K ’, Ecology, 89(6), pp. 1573–1582. doi: 10.1890/07-0451.1.Pearson, R . G . and D aw son, T. P. (2003) ‘Predicting the im pacts of clim ate change on the distribution of species: are bioclim ate envelope m odels useful?’, Global Ecology and

Biogeography, 12(5), pp. 361–371. doi: 10.1046/j.1466-822X .2003.00042.x.Pearson, R . G ., D aw son, T. P., B erry, P. M . and H arrison, P. A . (2002) ‘SPEC IES: A Spatial Evaluation of C lim ate Im pact on the Envelope of Species’, Ecological Modelling, 154(3), pp. 289–300. doi: 10.1016/S0304-3800(02)00056-X .Petchey, O ., Eklöf, A ., B orrvall, C . and Ebenm an, B . (2008) ‘Trophically U nique Species A re V ulnerable to C ascading Extinction’, The American Naturalist, 171(5), pp. 568–579. doi: 10.1086/587068.Poisot, T. and G ravel, D . (2014) ‘W hen is an ecological netw ork com plex? C onnectance drives degree distribution and em erging netw ork properties’, PeerJ, 2, p. e251. doi: 10.7717/peerj.251.Poisot, T., C anard, E. and M ouillot, D . et al. (2012) ‘The dissim ilarity of species interaction netw orks’, Ecology Letters, 15(12), pp. 1353–1361. doi: 10.1111/ele.12002.Poisot, T., G uéveneux-Julien, C . and Fortin, M .-J. et al. (2017) ‘H osts, parasites and their interactions respond to different clim atic variables: PO ISO T et al.’, Global Ecology and

Biogeography, 26(8), pp. 942–951. doi: 10.1111/geb.12602.Poisot, T., M ouquet, N . and G ravel, D . (2013) ‘Trophic com plem entarity drives the biodiversity-ecosystem functioning relationship in food w ebs’, Ecology Letters, 16(7), pp. 853–861. doi:

17

10.1111/ele.12118.Poisot, T., Stouffer, D . B . and G ravel, D . (2015) ‘B eyond species: w hy ecological interaction netw orks vary through space and tim e’, Oikos, 124(3), pp. 243–251. doi: 10.1111/oik.01719.Pollock, L. J., Tingley, R . and M orris, W . K . et al. (2014) ‘U nderstanding co-occurrence by m odelling species sim ultaneously w ith a Joint Species D istribution M odel (JSD M )’, Methods in

Ecology and Evolution, 5(5), pp. 397–406. doi: 10.1111/2041-210X .12180.R ezende, E. L., A lbert, E. M ., Fortuna, M . A . and B ascom pte, J. (2009) ‘C om partm ents in a m arine food w eb associated w ith phylogeny, body m ass, and habitat structure’, Ecology Letters, 12(8), pp. 779–788. doi: 10.1111/j.1461-0248.2009.01327.x.R ezende, E. L., Jordano, P. and B ascom pte, J. (2007) ‘Effects of phenotypic com plem entarity and phylogeny on the nested structure of m utualistic netw orks’, Oikos, 116(11), pp. 1919–1929. doi: 10.1111/j.0030-1299.2007.16029.x.Sim berloff, D . S. and W ilson, E. O . (1969) ‘Experim ental Zoogeography of Islands: The C olonization of Em pty Islands’, Ecology, 50(2), pp. 278–296. doi: 10.2307/1934856.Solé, R . V. and M ontoya, M . (2001) ‘C om plexity and fragility in ecological netw orks’, Proceedings of the Royal Society of London B: Biological Sciences, 268(1480), pp. 2039–2045. doi: 10.1098/rspb.2001.1767.Souza, A . F., B ezerra, A . D . and Longhi, S. J. (2016) ‘Q uasi-neutral com m unity assem bly: Evidence from niche overlap, phylogenetic, and trait distribution analyses of a subtropical forest in South A m erica’, Perspectives in Plant Ecology, Evolution and Systematics, 23, pp. 1–10. doi: 10.1016/j.ppees.2016.09.006.Stouffer, D . B . and B ascom pte, J. (2010) ‘U nderstanding food-w eb persistence from local to global scales’, Ecology Letters, 13(2), pp. 154–161. doi: 10.1111/j.1461-0248.2009.01407.x.Stouffer, D . B ., Sales-Pardo, M ., Sirer, M . I. and B ascom pte, J. (2012) ‘Evolutionary C onservation of Species’ R oles in Food W ebs’, Science, 335(6075), pp. 1489–1492. doi: 10.1126/science.1216556.Sugihara, G . and Ye, H . (2009) ‘C om plex system s: C ooperative netw ork dynam ics’, Nature, 458(7241), pp. 979–980. doi: 10.1038/458979a.Thebault, E. and Loreau, M . (2003) ‘Food-w eb constraints on biodiversity-ecosystem functioning relationships’, Proceedings of the National Academy of Sciences, 100(25), pp. 14949–14954. doi: 10.1073/pnas.2434847100.Thébault, E. and Fontaine, C . (2010) ‘Stability of Ecological C om m unities and the A rchitecture of M utualistic and Trophic N etw orks’, Science, 329(5993), pp. 853–856. doi: 10.1126/science.1188321.Thébault, E., H uber, V. and Loreau, M . (2007) ‘C ascading extinctions and ecosystem functioning: contrasting effects of diversity depending on food w eb structure’, Oikos, 116(1), pp.163–173. doi: 10.1111/j.2006.0030-1299.15007.x.Tilm an, D . (2004) ‘N iche tradeoffs, neutrality, and com m unity structure: A stochastic theory of resource com petition, invasion, and com m unity assem bly’, Proceedings of the National

Academy of Sciences of the United States of America, 101(30), pp. 10854–10861. doi:

18

10.1073/pnas.0403458101.Trøjelsgaard, K . and O lesen, J. M . (2016) ‘Ecological netw orks in m otion: m icro- and m acroscopic variability across scales’, Functional Ecology, 30(12), pp. 1926–1935. doi: 10.1111/1365-2435.12710.Trøjelsgaard, K ., Jordano, P., C arstensen, D . W . and O lesen, J. M . (2015) ‘G eographical variationin m utualistic netw orks: sim ilarity, turnover and partner fidelity’, Proceedings of the Royal

Society B: Biological Sciences, 282(1802), pp. 20142925–20142925. doi: 10.1098/rspb.2014.2925.Verdú, M . and Valiente B anuet, A . (2008) ‘The N ested A ssem bly of Plant Facilitation N etw orks ‐

Prevents Species Extinctions’, The American Naturalist, 172(6), pp. 751–760. doi: 10.1086/593003.Verhulst, P. (1938) ‘N otice sur la loi que la population suit dans son accroissem ent’, Curr. Math.

Phys, 10.W illiam s, R . J. (2011) ‘B iology, M ethodology or C hance? The D egree D istributions of B ipartite Ecological N etw orks’, PLoS One. Edited by J. Langow ski, 6(3), p. e17645. doi: 10.1371/journal.pone.0017645.W illiam s, R . J. and M artinez, N . D . (2000) ‘Sim ple rules yield com plex food w ebs’, Nature, 404(6774), pp. 180–183. doi: 10.1038/35004572.W illiam s, R . J., B rose, U . and M artinez, N . D . (2007) ‘H om age to Yodzis and Innes 1992: scaling up feeding-based population dynam ics to com plex ecological netw orks’, in From

energetics to ecosystems: the dynamics and structure of ecological systems. Springer, pp. 37–51. A vailable at: http://link.springer.com /content/pdf/10.1007/978-1-4020-5337-5_2.pdf Yodzis, P. (1981) ‘The stability of real ecosystem s’, Nature, 289(5799), pp. 674–676. doi: 10.1038/289674a0.

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Figures

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Figure: Graphical representation of an ecological network (a), where species are represented by

circles and their directed interactions by arrows. The representation is formalized in the

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adjacency matrix (b). In an unipartite representation as this one, each species is represented

both as a column and a row. 1 indicates an interaction between two species (e.g. the green

square in (b)), and 0 indicates the absence of interaction. This matrix facilitates computation of

characteristics such as the connectance (c) and the degree distribution (d). (c) represents the

level of connection into the network and is calculated as showed in the figure. (d) represents the

distribution of interaction per species. The circles size is relative to the amount of interactions a

species have (d1). This distribution is non-random and generally follows a power-law

distribution (d2). The network can be split into subnets composed of 3 species, called motif (e).

Among the 13 different possible motifs, we only represented the most commonly found in natural

communities.

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Figure 2: Network topology, example of a fictional plant-pollinator network. (a) shows a

perfectly nested network, where specialists pollinators are visiting plants embedded into the diet

of more generalist pollinators. (b) shows a perfectly modular network, where sub-groups of

species interact more strongly with each over than with the rest of the network. (c) shows a

random network. Two representations are possibles. Top: Bipartite representation using nodes

and edges ; Bottom: Ordered interaction matrix. Here, we used striped yellow squares instead of

1 for presence of interaction and empty squares in absence of interaction.

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