Structure and dynamics of pollination networks: the role of alienplants

Fernanda S. Valdovinos, Rodrigo Ramos-Jiliberto, Jose D. Flores, Claudia Espinoza andGioconda Lopez

F. S. Valdovinos (fevaldovinos@gmail.com), R. Ramos-Jiliberto, C. Espinoza and G. Lopez, Depto de Ciencias Ecologicas, Facultad de Ciencias,Univ. de Chile, Las Palmeras 3425 Nunoa, Santiago, Chile. � J. D. Flores, Dept of Mathematics, The Univ. of South Dakota, 414 E. ClarkStreet, Vermillion, SD 57069, USA.

Research on ecological communities, and plant�pollinator mutualistic networks in particular, has increasingly benefitedfrom the theory and tools of complexity science. Nevertheless, up to now there have been few attempts to investigate theinterplay between the structure of real pollination networks and their dynamics. This study is one of the firstcontributions to explore this issue. Biological invasions, of major concern for conservation, are also poorly understoodfrom the perspective of complex ecological networks. In this paper we assess the role that established alien species playwithin a host community by analyzing the temporal changes in structural network properties driven by the removal ofnon-native plants. Three topological measures have been used to represent the most relevant structural properties for thestability of ecological networks: degree distribution, nestedness, and modularity. Therefore, we investigate for a detailedpollination network, 1) how its dynamics, represented as changes in species abundances, affect the evolution of itsstructure, 2) how topology relates to dynamics focusing on long-term species persistence; and 3) how both structure anddynamics are affected by the removal of alien plant species. Network dynamics were simulated by means of a stochasticmetacommunity model. Our results showed that established alien plants are important for the persistence of thepollination network and for the maintenance of its structure. Removal of alien plants decreased the likelihood of speciespersistence. On the other hand, both the full network and the subset native network tended to lose their structure throughtime. Nevertheless, the structure of the full network was better preserved than the structure of the network without alienplants. Temporal topological shifts were evident in terms of degree distribution, nestedness, and modularity. However theeffects of removing alien plants were more pronounced for degree distribution and modularity of the network. Therefore,elimination of alien plants affected the evolution of the architecture of the interaction web, which was closely related tothe higher species loss found in the network where alien plants were removed.

The introduction of alien species into native ecosystems,together with habitat deterioration and climatic change,constitute the major anthropogenic threats for the persis-tence and integrity of pollination systems (Memmott andWaser 2002). The effects of alien plant invasions on nativepollination systems may be competitive, neutral, or facil-itative (Bjerknes et al. 2007, Sargent and Ackerly 2008).Alien plants may compete with native ones either throughreducing visitation rates of pollinators or through increasingheterospecific pollen transfer on native flowers (Chittka andSchurkens 2001). However, an alien’s effects may be neutralif native plants are not pollen limited, or if they compensatefor the loss of pollinators (Totland et al. 2006). At thelandscape level, whenever alien plants represent valuablefood resources for many pollinators, their effect on nativebiota could be more facilitative than competitive by meansof increasing pollinator densities (Bjerknes et al. 2007).

Recently, the study of anthropogenic impacts onpollination systems has switched from a ‘single species’

approach, which focuses on one or a few plant�animalspecies interactions, to the ‘pollination web’ approach,which focuses on entire communities (Memmott and Waser2002, Olesen et al. 2002, Morales and Aizen 2006,Memmot et al. 2007, Aizen et al. 2008). Here we use thepollination web approach to evaluate the roles played byestablished alien plants in the preservation of the structureand the persistence of the member species in a real plant�pollinator network.

The dynamics of pollination networks, here representedas changes in species abundances, may be affected by theavailability of mutualistic partners and by the pattern ofinteractions between plants and animals. That is, thedynamics within the network depends on its topology.Conversely, the evolution of the topology of a network isinfluenced by the dynamics of its member species, giventhat species and interactions are removed when populationsgo extinct following severe decreases in their abundances.Such systems of interconnected parts in which there is a

Oikos 118: 1190�1200, 2009

doi: 10.1111/j.1600-0706.2009.17364.x,# 2009 The Authors. Journal compilation # 2009 Oikos

Subject Editor: Jordi Bascompte. Accepted 6 February 2009

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causal and bidirectional relationship between their structureand dynamics have been referred to as adaptive networks(Gross and Blasius 2008).

Until now, pollination web studies have not explicitlyadopted the adaptive network approach. Studies of anthro-pogenic impacts on pollination webs (Memmott and Waser2002, Morales and Aizen 2002, 2006) and analyses ofnetwork robustness to species removal (Memmott et al.2004) are based on a purely network topology perspectivethat ignores the dynamics of constituent species anddisregards the evolution of the topology. On the otherhand, Olesen et al. (2008) investigate the mechanismsunderlying the topology of a pollination web by followingdaily pollination dynamics over successive flowering sea-sons. These previous approaches provide the backdrop forthis project which focuses on the bidirectional causalitybetween topology and dynamics in pollination network andhow this interplay could be affected by forcing variablessuch as biological invasions or habitat loss.

A theoretical way of incorporating dynamics intocomplex mutualistic networks was introduced by Fortunaand Bascompte (2006), who presented a stochastic meta-community model in which the pattern of species interac-tions follows exactly that of an empirical pollinationnetwork. In this paper we make use of their model, whichmerges the tradition of dynamical systems research withthat of complex networks based on graph theory, to revealhow the removal of an established set of alien plants couldaffect the interplay between topology and dynamics in awell-resolved pollination network. Specifically, for both thefull network and the sub-network without alien plants weexplore: 1) how network dynamics, represented as changesin species abundances, affects the evolution of networktopology through changes in several structural properties(degree distribution, nestedness, and modularity); and 2)how topology relates to dynamics, with a focus on long-term species persistence.

Material and methods

Database and adjacency matrices

Our analyses were made on a plant�pollinator communityof the subandean zone of central Chile, at 338S latitude and1800 m a.s.l. This zone correspond to a Mediterranean-typeclimate with precipitation concentrated in the wintermonths, followed by progressive drying in the summerand autumn (Arroyo et al. 1981). The vegetation is mainlycomposed by herbs and shrubs, and around 83% arebiotically pollinated. Important characteristics of the An-dean zone in central Chile, in contrast to many othertemperate mountain areas, are the richness of the bee faunaand the high occurrence of bee-pollinated plants (Arroyo etal. 1982). Effective visits of insects on flowers were recordedduring the flowering season from November 2006 untilMarch 2007. Effective visitors were defined as insects thatmake contact with reproductive structures of flowers, with acessation of flying.We used two sampling procedures: (1)recording the number of effective visits per insect species oneach of the plant species, by means of repeated 15-minobservation periods, and (2) recording the occurrence of

effective visits by each insect species on each plant, throughslow walks along random transects. Plants and insects wereidentified to species or morphospecies with the help oftaxonomists. The pollination network was composed of 77plant species and 110 insect species with a total of 362pollination interactions. Among the plant species, 14 werealien plants.

From collected data, we constructed two differentadjacency matrices corresponding to: 1) the completeobserved network (hereafter the ‘full network’), and 2) theobserved full network without alien plants species and theirinteractions (hereafter the ‘native network’). Elements of theadjacency matrices mij were ones or zeros, representingrespectively observed and unobserved effective visits ofinsect j on plant i. A comparison of the two matricesallowed us to characterize the role of alien plants within theobserved community in terms of their contribution tospecies persistence, network structure, and evolution ofnetwork topology. We do not know what the networkstructure was before alien species entered the community.Here we explore the role of the established alien speciesthrough simulating the fate of the system after the completeremoval of aliens, assuming that if these species disappearthe network cannot reorganize by establishing new links orredistributing existing links.

Network dynamics and persistence

In order to study the dynamics of the network we used themetacommunity model presented by Fortuna and Bas-compte (2006). Their model considers mutualists inhabit-ing a landscape consisting of an infinite number ofidentical, well-mixed patches. The interaction is obligatefor the animals, while plants are able to survive in theabsence of animals but cannot reproduce without them.Fortuna and Bascompte (2006) introduced a set ofdifferential equations describing the fraction of the totalavailable patches occupied by plant i, pi, and animal j, aj.The general model is represented by:

dpidt

�

X

n

j�1

�

cijpiaj

Vj

�

(1�d�pi)�eipi

daj

dt�cjaj(Vj�aj)�ejaj

where cij is the per capita colonization rate of plant i whenpollinated or dispersed by animal j, and cj is the per capitacolonization rate of animal j (which may only colonizepatches occupied by the plants it interacts with). Per capitaextinction rates for plant i and animal j are givenrespectively by ei and ej. It is assumed that the extinctionof plants from a patch causes the secondary extinction ofanimals exclusively dependent on that plant. Parameter drepresents the fraction of patches permanently lost throughhabitat destruction, and vj is the union of the patchesoccupied by n plant species interacting with the same janimal species (i.e. the total available patches for the jthanimal, see Fortuna and Bascompte 2006 for modeldetails).

Following Fortuna and Bascompte (2006), we randomlysampled the value of e/c from a uniform distribution

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centered in chosen values of kp�ei/ci for plants and ka�ej/cjfor animals, with an interval size of 0.1. We used k�0.25,k�0.5, and k�0.75, with k�kp�ka. Initial conditions foreach species in the network were also randomly sampledfrom a uniform distribution on the unit interval. A specieswas considered extinct when its fraction of occupied patchesfell below a threshold value of 0.001. We performedsimulations at three levels of habitat loss: d�0.25, d�0.5and d�0.75. The metacommunity model was implementedwith MATLAB codes. Each adjacency matrix was run for2000 iterations, a time at which the fraction of occupiedpatches remained constant for all species.

For each combination of parameter values, 1000 modelrealizations were run for each adjacency matrix. To evaluateif the differences in persistence between the full and nativenetworks could be attributed to the removal of the alienspecies and not to reduction in matrix size, in eachrealization we selected and removed a random sample of14 plant species. We thus created an empirical distributionfor what to expect of the dynamics of networks with thesame species richness as the native networks. We refer tothese null matrices as ‘random-species networks’.

Network topology and its evolution

Topological properties feature specific patterns of organiza-tion of the components (i.e. species) within the network andare used to characterize the architecture of interactions.Such properties provide a static description of the networkconnectivity, i.e. the degree to which species are connectedto one another through the network. Throughout thesequence of changes in species persistence resulting fromruns of the dynamic model, three main topological proper-ties were monitored: degree distribution, nestedness, andmodularity. These network metrics allow characterizing theorganization of the constituent species in terms of theirinteractions and according to their degree of specialization.The specific structure of a pollination network, representedthrough these topological metrics, informs us about theability of the community to respond to different kinds ofenvironmental perturbations.

The degree of a species consists of the number of itsinteracting species. The function which describes thehistogram of all species degrees in a network is called adegree distribution. In mutualistic networks, as in other realnetworks, degree distributions are very heterogeneous(Jordano et al. 2003), with many specialist species andfew super-generalist species. We calculated the cumulativedegree distribution P(k) (Newman 2003) of animals andplants for each network. This distribution shows thefraction of plant (or animal) species in the network thatinteract with k or more animals (or plants). For eachobserved distribution we fitted three alternative models:exponential (P(k)�e�ak), power law (P(k)�e�g) andtruncated power law (P(k)�k�ge�k/k

c) where a and gare fitted constants and kc is the truncation value thatdefines the exponential cut-off. The truncated power law isthe most general of these three models. If g is zero, thetruncated power law model will be equivalent to theexponential model, and if kc is higher than the maximumobserved degree, the truncated power law will approach the

power law model in the positive quadrant. Akaike’sapproach was used to select the best model describing theobserved degree distribution (Burnham and Anderson2004). To avoid overparameterization, we used the cor-rected AIC (AICc), which converges to AIC as the samplesize gets large. The individual AICc values were rescaled toDi�AICci�AICcmin, where AICcmin is the minimumamong the AICci values calculated for the different models.This transformation forces the best model to have Di�0,with the rest having positive values. Models with Di52 areconsidered to have substantial support (Burnham andAnderson 2004). When more than one model had Di52,the highest percentage of explained variance was used todiscriminate between the models supported by AICc. Inorder to compare the degree distribution among the studiednetworks, we standardized the value of the exponent g ofthe fitted truncated power-law model by means of standardnormal deviates (z-scores) from the mean of 1000 randommatrices generated by the null model II of Bascompte et al.(2003). This null model assumes that each plant�animalpair interacts with a probability proportional to theobserved number of interactions of both species (Bascompteet al. 2003, Guimaraes and Guimaraes 2006). This nullmodel lacks nestedness but preserves the heterogeneity ofthe adjacency matrix. This procedure allows us to eliminatethe effect of changing matrix size and connectance (i.e. thefraction of all possible links that are realized in the network)on the assessment of this topological property.

A nested network implies that the more specialist speciestend to interact with species that are proper subsets of thosespecies interacting with the more generalist ones (Bascompteet al. 2003). We measured the degree of nestedness throughthe matrix temperature T, with values ranging from 0 forperfectly nested networks to 100 for completely non-nestednetworks (Atmar and Patterson 1993). In order to evaluatethe statistical significance of observed nestedness and tocompare the degree of nestedness among the studiednetworks, we standardized the index T by means of standardnormal deviates (z-scores) of each matrix with respect to thedistribution of T obtained from 1000 matrices generatedfrom null model II of Bascompte et al. (2003). This allowselimination of the effect of changing matrix size andconnectance on the nestedness measure. Calculation ofmatrix temperatures were performed with the softwareANINHADO (Guimaraes and Guimaraes 2006).

A network is said to be modular when its member speciesare organized into compartments (modules) in which plantand animal species have more interactions among them thanwith species that belong to other modules. Modules mayreflect the specificity of interactions, convergence towardpollination syndromes, and phylogenetic clustering ofclosely related species (Olesen et al. 2007). Therefore anetwork exhibiting many little modules represents a com-munity composed of several groups of a few coevolvingspecies. The extinction of a species in such a network willmostly affect species within its module. On the other hand,the deleterious effect of species extinction could spreadwidely over a network structured into a few large modules.The degree of network compartmentalization into moduleswas measured through the modularity index M of Guimeraand Amaral (2005a, 2005b). This algorithm identifiesmodular structure that leads to many within-module links

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and as few as possible between-module links. From thatstructure, we obtained the number and size of modules, aswell as the fraction of network interactions that occurr bothwithin-modules and among-modules. Statistical significanceof modularity was assessed through estimating M on 100random networks with the same degree distribution as thefull network (Guimera et al. 2004). From the obtainedempirical distribution of M we expressed network mod-ularity as z-scores to control for matrix size and connectance.Two additional indices were used in the modularity analysisto associate a role to each of the interacting species (Guimeraand Amaral 2005a, 2005b). Within-module standardized

connectivity of species i, zi, is given by zi�kis � kssks

where kis

is number of interactions of i with other species in its own

module s. Parameters ks and sks are the average and standarddeviation of within-module k of all species in s. Among-

module connectivity of species i, ci, is given by ci�

1�aNM

t�1

kitki

!2

where kit is number of interactions of i with

species in module t, and ki is the number of interactions (i.e.degree) of species i. Roles for each species were assignedfollowing Olesen et al. (2007): (1) network hubs, z�2.5and c�0.62; (2) module hubs, z�2.5 and c50.62; (3)peripherals, z52.5 and c50.62; and (4) connectors, z52.5 and c�0.62. Network hubs are species that act as a‘glue’ within an ecological network since they monopolizemost of species interactions. Therefore, these species are veryimportant for preserving the network structure (Olesen et al.2007). A module hub is a species that interacts mostly withspecies within its module and has few interactions outside ofit. Peripheral species have very few interactions with otherspecies. Connector species interact more with species outsidetheir module than with species in their own module (Olesenet al. 2007).

To evaluate the evolution of the topology of both the fulland native network, we identified the adjacency matrices attime 100, 200, 400, 800 and 2000 from each of 100realizations of the model. For the 1000 matrices so obtainedplus the two initial matrices, we analyzed the threetopological properties described previously. For each timestep, we computed the mean and 95% CI of the z-scores of

the (size-controlled) topological measures, in order to testfor differences between networks as well as across time.

Results

Network dynamics and species persistence

The fraction of alien species increased through time (Table1), revealing that the persistence of alien plants was higherthan the persistence of the native species. These differencesin species persistence also imply that the fraction of alienlinks increased with time (Table 1). Furthermore, globalextinction (the number of networks in which�90% initialspecies went extinct) occurred more frequently in the nativenetwork than in the full network (Table 1). To assess therole of alien plants in shaping the observed differencesbetween the full and native networks we contrasted thedynamic outcomes with that obtained from a set ofrandom-species networks.

The fraction of species that went extinct in the nativenetwork was significantly higher than in the full networkand in the random-species networks (Kruskal�Wallis test,multiple comparisons of mean ranks, pB0.05, Fig. 1).Exceptions to this trend were found where extinctions wererather high as a consequence of a large value of theparameter k. Therefore, for low and moderate ratios ofthe extinction/colonization rate, the removal of alien plantsdecreased species persistence. For an extinction/colonizationvalue of k�0.75 combined with habitat loss rates ofd�0.25 and 0.5, the fraction of extinct species was so largethat the effect of initial deletions of nodes was unimportant.The largest differences in persistence between the full andthe native network were found at d�0.5 and k�0.5.

Network topology and its evolution

Alien plant species were visited by more pollinator speciesand are therefore more generalist than their native counter-parts (Mann�Whitney test, pB0.05). However, none ofthe aliens was the most connected species in the network.The range of generalism for the native flora is 1�31pollinators and for alien flora is 1�10 pollinators. There-fore, most alien plants fall in the upper middle positionwithin the range of generalism exhibited by all plants in thenetwork. Similarly, most alien plants fell in the upper

Table 1. Basic properties (average of 100 realizations995% CI) of the full and native pollination networks through time. Parameters valueswere k�0.5 and d�0.5. Global extinction refers to the number of networks in which �90% of initial species went extinct.

Time 0 100 200 400 800 2000

Full networkPlants 77 54.590.8 47.791.1 42.491.4 38.891.7 35.792.1Animals 110 66.491.7 51.991.6 43.791.4 38.891.3 34.891.6Fraction of alien species 0.182 0.21890.003 0.23690.005 0.25890.007 0.27890.010 0.29390.012Fraction of alien links 0.229 0.23690.002 0.24590.003 0.25790.004 0.27090.006 0.27890.007Connectance 0.043 0.08090.002 0.10590.003 0.13090.005 0.15090.007 0.17090.009Global extinction 0 0 0 0 2

Native networkPlants 63 40.090.9 30.091.3 22.391.7 15.792.0 10.092.0Animals 97 56.191.4 43.491.6 32.592.4 23.992.8 15.193.0Connectance 0.046 0.09290.003 0.13490.007 0.18790.014 0.22790.030 0.22690.034Global extinction 0 0 8 23 52

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middle position of the nested matrix. Thus, although aliensshould not be considered the core of the pollinationnetwork, they monopolize an important fraction of mu-tualistic interactions.

Next we tested how the removal of alien plants comparesto equivalent levels of random plant removal. Table 2 showsthat the effects of the experimental removal of aliens did notdiffer from those of random removals, in terms of secondaryextinctions, number of interactions, or connectance. This isa key result because it demonstrates that the cause ofdifferences in persistence between the full and nativenetworks does not rest on trivial topological divergences.This suggests that the differences in dynamic outcomesbetween the tested networks lie on more complex topolo-gical properties associated with alien species. The examina-tion of degree distribution, nestedness and modularity ofboth the full and native networks may help to disentanglethe causes of their differences in persistence.

The exponential model best described the plants’ degreedistributions for both networks prior to running thedynamic model. Initial degree distributions of animals for

both networks were best described by a truncated powerlaw. The evolution of the degree distributions of animals inthe networks was similar: they changed from a truncatedpower law to a power law distribution. However, the fulland native networks differed in the evolution of plants’degree distributions. For both networks, degree distribu-tions of plants initially changed from exponential totruncated power law. However, plants in the full networkretained a truncated power law distribution until the end ofsimulations, while plants in the native network shifted to apower law distribution. The evolution of the degreedistributions for plants in the two networks is graphicallyshown in Appendix 1. In order to describe the evolution ofdegree distribution in the full and native networks, we fitteda truncated power law model to the observed cumulativedegree distributions at each time step. The value of thedegree distribution exponent of the fitted model increasedasymptotically with time (results not shown), but itsdeviations from the null models (z-scores) decreased withtime for both plants and animals (Fig. 2). In the long term,the degree distributions of both networks became similar tothat of random networks of equal size and similarconnectance, although this structural decay was faster andmore pronounced in the native network. Therefore, thestructure of degree distribution was more conserved in thefull network than in the native network, after controllingfor network size and connectance.

Both the full network and the native network weresignificantly nested before running the dynamic model.However, controlling for size and connectance, both net-works lost their nested structure over the course of the

Figure 1. Fraction of extinct species averaged over 1000 model realizations for the full network (A), the native network (B), and therandom-species networks (C). Different parameter values were used to represent habitat loss (d) and extinction/colonization ratio (k).Open and closed circles represent plants and animals respectively. Error bars are 95% CI. Equal letters indicate non-significant differences(Kruskal�Wallis, multiple comparisons of mean ranks, pB0.05).

Table 2. Comparison between basic topological features of thenative network and random-species networks. For random-speciesnetworks, mean of 1000 runs and 95% CI are given.

Nativenetwork

Random-speciesnetworks

p-value

Number of animals 97.0 99.5790.28 0.572Number of links 279.0 295.6391.01 0.306Connectance 0.046 0.04790.0001 0.449

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model simulations. Thus, although the native network lostits nested structure sooner than the full network, thepresence of alien plants does not appear to be a determiningfactor for the conservation of the nested structure (Fig. 3).

In their initial states, both the full and native networkswere significantly modular and exhibited the same numberof modules, but had different module sizes (Table 3). At theoutset of the dynamic simulations, the number of modulesremained homogeneous between the two networks untiltime 200 (Table 3). After that point, the native network hadsignificantly fewer modules than the full network. Thisdivergence in the number of modules occurred simulta-neously with the lost of modularity of the native network.Although the modularity of both networks decayed through

time, only the full network retained its modular structure inthe long term (Fig. 3) Species identified as network hubs ormodule hubs constituted a minor fraction of the nodes ofboth networks, as compared to peripheral and connectorspecies (Fig. 4). The fractions of hubs and peripherals (i.e.the number of nodes belonging to each role over the totalnumber of nodes) decreased through time in both networkswhile the fraction of connectors increased. The processesbehind these role shifts are summarized in Table 4. Thedecrease in the relative abundance of peripheral nodes isdriven by their extinction, while hub species decreasedbecause their role shifted to peripheral or connector species.Connectors increased their representation in the networksdue to their low extinctions together with the conversion ofsome hubs into connectors. Across the entire time intervalused in the simulations, the network in which alien plantswere removed presented more extinctions in all roles ascompared to the full network and the full networkpresented more role shifts than the native network. Only

Figure 2. Temporal shifts of cumulative degree distributions forplants and animals in the full network (closed symbols) and thenative network (open symbols). Triangles, squares and circlesrepresent networks in which the best fitted model was exponential,truncated power law, and power law respectively. The values onthe ordinate are z-scores of the exponents of the fitted truncatedpower law model. Average of 100 model realizations and 95% CIare shown, with parameters d�0.5 and k�0.5. Values above thehorizontal reference line are significantly different (p B0.05, one-tailed test) from those of null networks of equal size and similarconnectance.

Table 3. Basic description (average of 100 realizations995% CI) of the modular structure of the full and native pollination networksthroughout time.

Time 0 100 200 400 800 2000

Full networkNumber of modules 12.0 7.390.2 6.690.2 6.190.2 5.890.1 5.690.1Modules’ median size 18.5 16.790.4 15.490.5 14.290.4 13.490.4 12.790.4

Native networkNumber of modules 12.0 7.390.2 6.390.2 5.490.2 4.590.4 5.090.3Modules’ median size 15.0 13.390.4 11.790.4 10.390.6 8.690.8 10.490.9

Figure 3. Standard normal deviates (z-scores) of temperature(upper plot) and modularity (lower plot) indices through time,with parameters d�0.5 and k�0.5. Average of 100 modelrealizations and 95% CI are shown for the full network (closedcircles) and the native network (open circles). Values below (fortemperature) and above (for modularity) the horizontal referenceline are significantly different (pB0.05, one-tailed test) from thoseof null networks of equal size and similar connectance.

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the relative number of module hubs remained similarbetween the two networks over time.

Through time, species richness decreased while connec-tance increased. The negative relationship between speciesrichness and connectance displays similar slopes in bothnetworks (p�0.107, GLM test for homogeneity of slopes)but a lower elevation for the native community (pB0.05,ANCOVA, Fig. 5). This means that, controlling fornetwork size, the removal of alien plants decreasedconnectance. Note also from Fig. 5 that only the nativenetwork exhibits richnessB34 species, indicating that thepersistence of the community members is sensitive to alienremoval.

Discussion

The few available studies that evaluated the networkconsequences of alien species in plant�pollinator websconcluded that invasive species become well integratedinto the existing network (Memmott and Waser 2002,Olesen et al. 2002, Morales and Aizen 2002, 2006, Aizenet al. 2008). These studies focused on how the patterns of

connections between plants and pollinators differ betweennative and alien complexes. However, these studies did notevaluate the dynamic implications of the alien specieswithin the network. In this project we assessed how thesimulated experimental removal of established alien plantsis likely to modify the long-term dynamics of the network,and at the same time we tracked the evolution of networktopology behind the projected dynamics.

Our results on long-term network dynamics suggest thatalien plants are important for the persistence of the studiedpollination network. The removal of alien plants decreasedthe likelihood of species persistence over a large fraction ofthe sampled parameter space. Our results corroborateprevious work which suggests that alien species, onceestablished, do not form an isolated set of species andinteraction, but are intimately integrated into the hostnetwork (Memmott and Waser 2002, Olesen et al. 2002,Morales and Aizen 2002, 2006, Aizen et al. 2008).Therefore, their eventual removal from the communitycould cause profound effects. Furthermore, we found thatthose effects were more severe than expected from theremoval of any other set of plants. Since our methods didnot consider idiosyncratic properties of species other than

Figure 4. Temporal shifts of the fraction of nodes belonging to the classes of network hubs, module hubs, peripherals, and connectors.Average of 100 model realizations and 95% CI are shown for the full network (closed circles) and the native network (open circles).Parameter values were d�0.5 and k�0.5.

Table 4. Dynamic processes behind temporal shifts of species’ modularity roles (average of 100 realizations995% CI) in the full and nativepollination networks with parameter values of k�0.5 and d�0.5.

Time 0�100 100�200 200�400 400�800 800�2000

Full networkExtinctions of peripheral nodes 65.6092.21 21.0290.86 13.3290.72 8.1990.65 6.1490.63Extinctions of hub or connector nodes 0.5390.15 0.2590.11 0.2490.11 0.2590.10 0.1890.08Nodes converting to peripherals 16.9090.70 8.5590.72 8.1190.73 7.0190.76 6.2790.72Nodes converting to hubs or connectors 6.0590.43 6.9890.68 5.9390.69 5.7390.65 5.5390.60

Native networkExtinctions of peripheral nodes 63.4992.11 22.2790.99 16.5791.38 14.6491.75 16.5893.13Extinctions of hub or connector nodes 0.3990.11 0.5590.19 1.3990.52 1.7690.73 3.6390.92Nodes converting to peripherals 11.8790.45 6.9790.59 5.8190.63 4.6990.77 4.2590.82Nodes converting to hubs or connectors 4.8990.39 5.1290.50 3.6090.52 3.4790.67 3.9490.76

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their connectivity, we searched for possible mechanismsbehind the projected dynamic, given the influence that alienspecies exerted on the topology of the observed fullnetwork. Although both the full and native networkstended to lose their initial structure over time, the structureof the full network was better preserved than the structureof the native one. Removing the alien plants allowed betterunderstanding of their connectivity properties that mightexplain their topological role in the network. Theirexclusion from the community produced a gap in thecentral region of the degree distribution of the network. Asa consequence, the structure of the native network becamemore sensitive to extinctions driven by dynamics. Althoughthe initial topology of the native network did not differfrom that of the full network, extinctions that took placeafter the initiation of dynamics resulted in the increasingdivergence of the topology of the two networks over time.

Regarding degree distribution, the native network lost itsstructure more dramatically than the full network, becom-ing indistinguishable from a random network after arelatively short time. Degree distributions of full, native,and random networks increased in steepness across time,revealing that increasing representation of specialists. Thiscan be explained by the primary extinction of specialistsgenerated by the dynamics (Fortuna and Bascompte 2006),which leads to decreasing connectivity of generalists, and issupported by demographic processes underlying temporalshifts in the distribution of species across the four primarymodularity roles. Dynamics promoted the extinction ofperipheral nodes, leading to decreased connectivity of thehubs and their shift to peripheral or connector roles. For theoverall degree distributions, dynamics mainly resulted in aswitch from a truncated power law to a power law degreedistribution, with the exception of plants in the full networkwhich conserved the truncated power law distribution.Networks with truncated power law distributions are lessfragile to the loss of the most-connected nodes thannetworks with power law distributions, while both kinds

of networks have shown to be robust to random deletion ofnodes (Albert et al. 2000, Jordano et al. 2003). Therefore,the pollination network studied may be comparatively morefragile to perturbations affecting the most-connected speciesif alien plants are removed.

Two results deserve special attention in relation tochanges in nestedness over time. First, pollination networkslost their nested structure with time, as a consequence ofspecies extinctions. Second, although both networks wereinitially strongly nested as compared to corresponding nullmodels, the native network exhibited a lesser degree ofnestedness as compared to the full network. This asymmetrycould induce slight differences in initial conditions betweenboth networks that could explain the subsequent differencesin dynamic outcomes. We also found, in agreement withprevious work (Bascompte et al. 2003, Memmott et al.2004, Fortuna and Bascompte 2006), that both native andfull networks exhibited a higher long-term species persis-tence that a null network lacking nestedness (results notshown). This suggests that the loss of nested structurethrough time is both a consequence of previous extinctionsand a driver of subsequent species loss.

Modularity was also conserved in the full network butnot in the native one. A relationship between modularityand species richness could help to explain this trend. Olesenand coworkers (2007) tested modularity in 51 pollinationsystems and found that networks with more than 150species were always modular, but networks with less than 50species did not exhibit significant modularity. Conse-quently, differences in modularity between the two net-works analyzed here could be explained by the higher rate ofspecies extinction � and consequently decreased richness �in the native network. According to Olesen et al. (2007),possible reasons for the lack of modularity in smallernetworks are: 1) a lack of module-detecting power of thealgorithm at small network sizes, and 2) the increase ofconnectance in pollination networks with network sizedecreases, which leads to an increase in the links betweengeneralist species, which may reduce the level of modularity.This reasoning remains valid in our study since we used thesame algorithm, and we also verified an inverse relationshipbetween network size and connectance (Fig. 5). On theother hand, disturbances are expected to spread more slowlythrough a modular structure than through a non-modularone (Olesen et al. 2007). Furthermore, modularity is able toconfer stability by dampening deviations from equilibriumin the transients of nonlinear systems (Ruiz-Moreno et al.2006). Conversely, the network consequences of deleting aspecies depends on its modularity role, e.g. an extinction ofa module hub may cause its module to fragment with minorimpact on other modules (Prado and Lewinsohn 2004),whereas the extinction of connector species may cause theentire network to fragment into isolated units, probablywith a negligible impact on the internal structure of eachmodule (Olesen et al. 2007). Regarding connectivity rolesderived from our modularity analysis, 16% of species in theinitial native network were structurally important (i.e. theywere assigned to the roles of hubs or connectors), in contrastto 21% in the full network. This difference was approxi-mately conserved with the addition of dynamics. Olesen

Figure 5. Relationship between network connectance and speciesrichness for the analyzed networks. At each of the times 100, 200,400, 800 and 2000, one hundred matrices were obtained fromboth the full and the native network. At time 0 there is a singleinitial matrix for each of the two networks. Black points represent501 full networks and gray points represent 501 native networks.

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et al. (2007) found that on average 15% of species werestructurally important in mutualistic networks, with theirloss potentially leading to extinction cascades. Therefore,the highest proportion of structurally important species inthe full pollination network relative to the native networkagrees with the observed differences in their persistence.

In the pollination network studied here, alien plantsenhanced connectance for all levels of species richness.Dunne et al. (2002) studied the effect of connectance on therobustness of real food networks to the removal of species,and their results suggested that higher connectance confersrobustness. This suggests that in our study system, alienplants may increase the robustness of the pollinationnetwork by increasing its connectance. Memmott andWaser (2002) explored the contribution of alien plants tothe connectance of a well resolved pollination network fromthe central USA. They found that the connectance of thesub-network of alien plants was lower than the connectanceof sub-networks of equal size with only native plants.Nevertheless they did not test the contribution of aliens tothe connectance of the whole network. In our studynetwork, the sub-network of alien plants also showed alower connectance than native networks of equal size, butwe showed that the effect of removing the set of alien plantswas to increase overall network connectance. However, incontrast to our system, the alien plants studied byMemmott and Waser (2002) were more specialist thantheir native counterparts. Therefore we hypothesize that theremoval of alien plants from such a community would beless deleterious than in the community we studied.

In this research we were not able to fully address theeffects of biological invasions on native pollination com-munities. To investigate this effect properly it is necessary toknow the interaction network before the arrival of theinvasive species, after their establishment and ideally afterthe invasive species have been removed experimentally inthe field. Our aim in this project was to evaluate how thesimulated removal of an established set of alien plants islikely to affect the temporal evolution of a pollinationnetwork in terms of changes in topology and the con-sequences of such removals at the level of species persis-tence. In this way we approached the question about thelikely roles played by the established alien flora through theinterplay between structure and dynamics of pollinationnetworks. As in any theoretical study, ours suffers fromlimitations imposed by implicit and explicit model assump-tions. We explored the role of alien plant species byassuming that if these species disappear, the network wouldnot be able to reorganize by creating new interactions ordistributing some of the existing ones. The model used hereassumes that the mutualistic interactions markedly affectthe abundances of species, and does not consider explicitspatial structure or climatic forcing. Therefore our resultsmust be interpreted with caution, considering that themodel does not take into account several importantcomponents of natural biological complexity. Nevertheless,these limitations also open new avenues for further research,in which our results could be used as a template to becompared with the outcomes of more realistic andsophisticated models. The main message arising from our

analyses is that the removal of alien plant species from acommunity could erode the structure of the pollinationnetwork leading to an increase in species extinctions.Therefore, management plans for eradication of alienspecies should consider investigating the long-term com-munity consequences, with particular attention paid to thecomplex network structure and dynamics of the communityand its constituent native and alien species.

Acknowledgements � The dataset was obtained during the first yearof execution of the project CONICYT-PBCT ACT34/2006. Theauthors thank Miguel A. Fortuna for providing useful details onthe modeling procedures, Waldo Morales-Alvarez for computingassistance, and Jorge Soto-Andrade for a critical reading of the firstversion of the manuscript. We specially thank Jennifer A. Dunne,Jens M. Olesen and Jordi Bascompte for their careful commentsthat considerably improved the content and presentation of thispaper.

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Appendix 1

Temporal shift of the cumulative degree distribution of plants for a single model realization with parameters d�0.5 andk�0.5. Solid circles represent the observed distribution. Dotted, solid, and dashed lines represent fitted power law,truncated power law, and exponential functions respectively. Plants in the full network (A) present an initial degreedistribution that was best fitted by the exponential function. From iteration 100, a truncated power law model best fittedthe distribution. In the native network (B), degree distribution began as a truncated power law, but from time iteration 400it changed into a power law.

Figure A1.

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