Dendritic Connectivity Controls Biodiversity Patterns in Experimental Metacommunities

This document is the accepted manuscript version of the following article: Carrara, F., Altermatt, F., Rodriguez-Iturbe, I., & Rinaldo, A. (2012). Dendritic connectivity controls biodiversity patterns in experimental metacommunities. Proceedings of the National Academy of Sciences of the United States of America PNAS, 109(15), 5761-5766. https://doi.org/10.1073/pnas.1119651109 Dendritic connectivity controls biodiversity patterns in experimental metacommunities

Francesco Carrara ∗ †,Florian Altermatt ‡† ,Ignacio Rodriguez-Iturbe § and Andrea Rinaldo ∗ ¶

∗Laboratory of Ecohydrology ECHO/IEE/ENAC, Ecole´ Polytechnique FédéraleLausanne, 1015 Lausanne, Switzerland,‡Department of Aquatic Ecology, Eawag, 8600 Dübendorf, Switzerland,§Department of Civil and Environmental Engineering, Princeton University, Princeton, NJ 08544, USA,¶Dipartimento IMAGE, Universitàdi Padova, 35131 Padova, Italy, and †These authors contributed equally to this work.

Submitted to Proceedings of the National Academy of Sciences of the United States of America

Biological communities often occur in spatially structured habitats vation. Directional dispersal refers to the pathway constrained where connectivity directly affects dispersal and metacommunity by the habitat connectivity and does not imply downstream- processes. Recent theoretical work suggests that dispersal con- biased dispersal kernels, that is, in all treatments dispersal strained by the connectivity of specific habitat structures, such as kernels were identical and symmetric. Disturbance consisted dendrites like river networks, can explain observed features of bio- of medium replacement and reflects the spatial environmen- diversity, but direct evidence is still lacking. We experimentally show that connectivity per se shapes diversity patterns in microcosm tal heterogeneity inherent to many natural systems (Materials metacommunities at different levels. Local dispersal in isotropic and Methods). lattice landscapes homogenizes local species richness and leads to The microcosm communities were composed of nine proto- pronounced spatial persistence. On the contrary, dispersal along zoan and one rotifer species, which are naturally co-occurring dendritic landscapes leads to higher variability in local diversity and in freshwater habitats, with bacteria as common food resource among-community composition. Although headwaters exhibit rela- [21]. These species cover a wide range of body sizes (Fig. 1B), tively lower species richness, they are crucial for the maintenance of intrinsic growth rates and other important biological traits regional biodiversity. Our results establish that spatially constrained [23] (see Table S1). Thus, the microcosm communities cover dendritic connectivity is a key factor for community composition and substantial biological complexity in terms of more structured population persistence. trophic levels and species interactions that can not be en- tirely captured by any model [24] (see Materials and Methods microbial metacommunities ∣ directional dispersal ∣ dendritic ecosystems ∣ and SI ). Previous microbial experiments found that spatio- community ecology temporal heterogeneity among local communities induced by disturbance [25] and dispersal [26, 27, 28] events have a strong major aim of community ecology is to identify processes influence on species coexistence and biodiversity. In previous Athat define large-scale biodiversity patterns [1, 2, 3, 4, 5, works [28, 22, 20, 26] the focus was mostly on dispersal dis- 6, 7, 8]. For simplified landscapes, often described geometri- tance, dispersal rates and dispersal kernels, and how they af- cally by linear or lattice structures, a variety of local environ- fect diversity patterns in relatively simple landscapes. These mental factors have been brought forward as the elements cre- factors, directly affecting the history of community assembly ating and maintaining diversity among habitats [9, 10, 11, 12]. [29, 30], introduce variability in community composition in Many highly diverse landscapes, however, exhibit hierarchical term of abundances and local species richness. We specifically spatial structures that are shaped by geomorphological pro- studied basic mechanisms of dispersal and landscape structure cesses and neither linear nor two-dimensional environmental on diversity patterns in metacommunities mimicking realis- matrices may be appropriate to describe biodiversity of species tic network structures. Thus, our replicated and controlled living within dendritic ecosystems [13, 14]. Furthermore, in experimental design sheds light on the role of connectivity many environments intrinsic disturbance events contribute to in more structured metacommunities, disentangling complex spatio-temporal heterogeneity [14, 15]. Riverine ecosystems, natural systems’ behavior [31]. among the most diverse habitats on earth [16], represent an outstanding example of such mechanisms [17, 18, 19, 7]. Here, we investigate the effects of directional dispersal im- posed by the habitat-network structure on the biodiversity Results and Discussion of metacommunities (‘MC’s), by conducting a laboratory ex- We compared the RN and the 2D landscapes focusing on three periment using aquatic microcosms. Experiments were con- measures of biodiversity: the number of species present in ducted in 36-well culture plates (Figure 1), thus imposing by a local community (훼-diversity), among-community diversity construction a metacommunity structure [20, 21]: each well (훽-diversity) and the number of LCs in which a given species hosted a local community (‘LC’) within the whole landscape is present (species occupancy) [7]. We found a significantly and dispersal occurred by periodic transfer of culture medium broader 훼-diversity distribution (Figs. 2 and 3A, B) in the among connected LCs [22], following two different geometries RN compared to the 2D landscapes (measured as the coeffi- [see Materials and Methods and Supporting Information (SI)]. We compared spatially heterogeneous MCs following a river network geometry (‘RN’; Fig. 1D), with spatially homoge- Reserved for Publication Footnotes neous MCs, in which every LC has 2D lattice four nearest neighbors (‘2D’; Fig. 1E). The coarse-grained RN landscape is derived from a scheme [13] known to reproduce the scaling properties observed in real river systems (Fig. 1A). To single out the effects of connectivity, we deliberately avoided reproducing other geomorphic features of real river networks, such as the bias in downstream dispersal, the grow- ing habitat capacity with accumulated contributing area or other environmental conditions connected to topographic ele-

www.pnas.org/cgi/doi/10.1073/pnas.0709640104 PNAS Issue Date Volume Issue Number 1–9 cient of variation CV, 퐶푉 푅푁 = 0.265, 퐶푉 2퐷 = 0.122, paired of the river network exhibits on average a higher species rich- t-test, 푡5 = 7.05, 푃 = 0.0009). Furthermore 훽-diversity, here ness with respect to peripheral communities. described by the spatial decay of the Jaccard’s similarity in- To explain the variability of the local species richness in dex (Materials and Methods, see also SI ), was higher in the the RN, we included two other factors in our analysis: the RN compared to the 2D landscapes (Fig. 3C). Mean local ‘ecological diameter’ 푙푖 of the LC 푖 (strictly related to its species richness in RN was significantly lower compared to closeness centrality), and the temporal distribution of disturbance events. The ecological diameter is simply defined as 2D landscapes (Fig. 2A-D, ⟨훼⟩푅푁 = 5.72, ⟨훼⟩2퐷 = 6.72, paired t-test, 푡5 = 9.23, 푃 = 0.0003). These results confirm the average distance 푙푖 = ⟨푑푖푗 ⟩푗 of 푖 from all the other LCs theoretical predictions on the role of directional dispersal from 푗 in the RN, where 푑푖푗 represent the shortest (geodesic) dis- both individual- or metacommunity-based models [32, 7, 33]. tance between 푖 and 푗 [34]. We found that connectivity sig- Specifically, we experimentally observe that the anisotropy nificantly affected 훼-diversity in the RN landscape (ANOVA, induced by directional dispersal has a strong impact on the 퐹1,5 = 12.09, 푃 = 0.0006), whereas neither time to the last spatial configuration of the species occupancy, reflected in 훼- disturbance nor network centrality significantly affected local and 훽-diversity (Figs. 2A-D, 3E). This is a direct consequence species richness (ANOVA, 퐹6,5 = 1.66, 푃 = 0.13; and 퐹4,5 = of the radically different distributions of closeness centrality, 0.71, 푃 = 0.59) (see Fig. S3 and SI Text ). i.e., the mean geometric geodesic distance [34] and the mean We obtained 훽-diversity separately for headwaters and distance 푙 between all LCs pairs (Fig. S6) in RN vs. 2D confluences, to test the difference in species composition landscapes (푙푅푁 = 5.33, 푙2퐷 = 3) (see SI ). within the river network structure. Headwaters exhibit not In parallel to the experiment we developed a stochastic only a higher variability in 훼-diversity, but also a higher 훽- model, generalizing across spatial and temporal scales (Mate- diversity compared to confluences (Fig. 4B), confirming pat- rials and Methods). The model embeds spatio-temporal en- terns found in natural river basins [16, 18]. Therefore, the vironmental heterogeneity, and is based on a Lotka-Volterra difference in the loss of spatial correlation relative to lattice competition model. We simulated the dynamics of species landscapes appeared even higher when only headwaters were competing for space and food resources on the same trophic considered in the comparison. These results reveal the cru- level, subjected to periodic perturbation events consisting of cial importance of headwaters as a source of biodiversity for partial habitat destruction. The model is an approximation to the whole landscape. In natural systems other local environ- our experimental system, but does not contain trophic dynam- mental factors may play a role in structuring ecosystems [35]. ics that may occur in the protozoa communities. Dispersal to Nevertheless, our causal approach sheds light on the sole effect neighboring patches can generate recolonization. of directional dispersal on biodiversity. Note that the patterns We measured species-specific intrinsic growth rates and we found in river network geometry are predicted to be even carrying capacities in pure cultures (Fig. S4 and Table S1), stronger in the presence of a downstream dispersal, which is and we used these specific values in the stochastic model, typical for many passively transported riparian and aquatic without fitting parameters (Materials and Methods). Even species in river basins [19, 33]. if estimates on growth rates and carrying capacities were al- We observed a lower mean 훼-diversity in the experiment ready available for some species [21], we repeated these exper- compared to the theoretical predictions ( Δ⟨훼⟩푅푁 = 37%, iments to get direct values for our specific experimental condi- Δ⟨훼⟩2퐷 = 42% ), but a re-scaling to the experimental mean tions, i.e., illumination, nutrient levels, chamber temperature, produced a consistent local species richness distribution (Fig. particular environment provided by well-plates (volume, ratio 3A, B). Species occupancies are presented in Figure 3E as a area/volume). The model confirmed the experimental obser- rank-occupancy curve: both the model and the experiment vations: a higher variability for 훼-diversity (Fig. 2E, F) and a revealed that well-connected 2D landscapes presented higher higher 훽-diversity (Fig. 3C) in dendrites compared to lattice spatial persistence compared to river network environments, landscapes. These patterns were robust over a long time in- but the sharp decrease in experimental rank-occupancy curves terval relative to species intrinsic growth rates (Fig. 3D, Fig. observed in both landscapes suggests that some species are S5 and SI Text). Furthermore, the patterns are consistent disadvantaged. It is likely that species competition in the also at different spatial scales (Fig. 3D). experiment had stronger effects on the persistence of weaker The bimodal shape of the 훼-diversity distribution ob- species, than that generated in the model by pure competition served in both model and experiment for the river network for space (see SI ). geometry (Fig. 3A) called for an analysis based on the degree At this point of the discussion the following question of connectivity, 푑, which gives the number of connected neigh- arises: how does the system react over these spatio-temporal boring nodes to a LC. In the ‘Headwater’ class (H), LCs have scales, without any disturbance-dispersal events? We tested 푑퐻 = 1 and are connected uniquely to their ‘downstream’ species’ ability to coexist in an ‘Isolation’ treatment, under node whereas in the ‘Confluence’ class (C), LCs are character- the same environmental conditions (Materials and Methods). ized by 푑퐶 = 3 and are connected to two ‘upstream’ and one We hypothesized that under stress (space saturation and re- ‘downstream’ nodes. In our scenario, the terms ‘downstream’ duced availability of bacteria) larger protozoans, such as Ble- and ‘upstream’ refer only to the position of the connected LC pharisma and Spirostomum sp., could predate on smaller pro- with respect to the outlet. They do not refer to a mass-flow tozoans, such as Chilomonas, Tetrahymena and Colpidium as dispersal is not directionally biased [7] (see Materials and sp. (Table S1 for species’ traits). The latter appeared to be Methods). The outlet of the network (‘O’), connected only to strongly inferior competitors (Fig. S3). Note that predation its upstream node (푑푂 = 1), falls into the H class. could happen even at low protist densities and high bacterial We found that the 훼-diversity distribution for Hs peaks densities. at a significantly lower value compared to the peak of the Cs’ We found that a consistent subset of four species survived distribution ( ⟨훼⟩퐻 = 5.29, ⟨훼⟩퐶 = 6.10, paired t-test, 푡5 = at the end of the isolation experiment (Fig. S2), whereas all 7.24, 푃 = 0.0008) and exhibits higher variability (Fig. 4A). other species went mostly extinct, resulting in lower values of Figure 2A and 2E shows this pattern, in which the backbone both 훼- and 훽-diversity ( 퐶푉 퐼푠표푙푎푡푖표푛 = 0.086, ⟨훼⟩퐼푠표푙푎푡푖표푛 = 4.17). The results confirmed the importance of dispersal and connectivity for maintaining higher level of biodiversity ob-

2 www.pnas.org/cgi/doi/10.1073/pnas.0709640104 Footline Author served in fragmented landscapes (Fig. 4A) [36, 37], at tem- tailed dispersal events (see SI ). This particular type of density- poral scales over which competitive exclusion dynamics have independent (diffusive) dispersal imposes equal per capita disper- emerged in isolated communities. Clearly, competition, al- sal rates for all different species, and no competition-colonization though stronger than just for space and resources, has not trade-offs occur [41, 42]. We also run three MC replicates (108 LCs) altered the connectivity-induced patterns highlighted by both without any disturbance-dispersal events to test species coexistence the theoretical and the experimental approaches. in isolation (‘Isolation’ treatment, Fig. S2). Biodiversity patterns. On day 24, after six disturbance-dispersal treat- Because the types of dispersal and disturbances employed ments, we checked for species presence-absence in each LC. We in our system are not specific to riverine environments, the screened the entire LC under a stereo-microscope, to avoid false- above results apply to a variety of heterogeneous and frag- absences of the rarer species, obtaining the number of species mented environments. We suggest that species constrained to present in every LC (훼-diversity). Because of the nature of the disperse within dendritic corridors face reduced spatial persis- last disturbance event, a few LCs could not be immediately recolo- tence and higher extinction risks. On the other hand, hetero- nized by neighboring communities. We then determined the spatial geneous habitats sustain higher levels of among-community distribution of 훼-diversity and the number of LCs in which a species biodiversity, that can be altered by modifying the connectiv- is present (species occupancy). To characterize 훽-diversity we con- ity of the system, with implications for community ecology sidered the spatial decay of Jaccard’s similarity index (JSI), defined as 푆 /(푆 +푆 −푆 ), where 푆 is the number of species present in and conservation biology. 푖푗 푖 푗 푖푗 푖푗 both LCs 푖 and 푗, whereas 푆푖 is the total number of species in LC 푖. We considered the topological, rather than the euclidean, distances Materials and Methods between community pairs, because they represent the effective distance an individual has to disperse. The notation in the main text Aquatic communities. Each local community (‘LC’) within a metacommunity ⟨⋅⟩ means a spatial average, while the ⋅ represents an average over (‘MC’) was initialized with nine protozoan species, one rotifer species and a set of the six experimental replicates. common freshwater bacteria as a food resource. The nine protozoan species were . We measured the protozoans Blepharisma sp., Chilomonas sp., Colpidium sp., Euglena gracilis, Species’ traits: size distribution Euplotes aediculatus, Paramecium aurelia, P. bursaria, Spirosto- with a stereo-microscope (Olympus SZX 16), on which a cam- mum sp. and Tetrahymena sp., and the rotifer was Cephalodella era was mounted (DP72), and analyzed photographs via software (cellˆD 3.2). Exposure time and the magnification were optimized sp.). Blepharisma sp., Chilomonas sp., and Tetrahymena sp. were supplied by Carolina Biological Supply Co., while all other species for each species. We measured the length of 50 individuals of each species (longest body-axis) to get size distributions (Table S1). were originally isolated from a natural pond [38], and have also been . For the growth experiment we culti- used for other studies [21, 22]. We use the same nomenclature as in Species’ traits: population growth such studies, except for Cephalodella sp., which has been previously vated protozoan in pure cultures at identical conditions used for the metacommunity experiment. Population density 휙(푡) = ⟨푛(푡)⟩/푉 identified as Rotaria sp. All species are bacterivores whereas Eug. grows in time following the Malthus-Verhulst differential equation gracilis, Eup. aediculatus and P. bursaria can also photosynthesize. Furthermore, Blepharisma sp., Euplotes aediculatus, and Spirosto- (logistic curve) ( ) 푑휙푠 휙푠 mum sp. may not only feed on bacteria but can also predate on = 푟푠휙푠 1 − [ 1 ] smaller flagellates. Twenty-four hours before inoculation with pro- 푑푡 퐾푠 tozoans and rotifer, three species of bacteria (Bacillus cereus, B. where 푠 = 1,..., 10 is the species index, which has the following subtilis and Serratia marcescens) were added to each community. solution: 푟 푡 LCs were located in 10 ml multiwell culture plates containing a 휙0,푠퐾푠푒 푠 휙 (푡) = [ 2 ] solution of sterilized local spring water, 1.6 g l−1 of soil and 0.45 푠 푟 푡 퐾푠 − 휙0,푠(1 − 푒 푠 ) g l−1 of Protozoan Pellets (Carolina Biological Supply). Protozoan where 휙 is the initial number of individuals per ml of medium, Pellets and soil provide nutrients for bacteria, which are consumed 0,푠 for species 푠. For every species we measured the population growth by protozoans. We conducted the experiment in a climatized room curve in time, averaging over six replicates. We started every replica at 21∘C under constant fluorescent light. On day 0, 100 individu- at the same low density. We measured densities daily for the first als of each species were added, except for Eug. gracilis (500 ind.) three days, subsequently we took measurements depending on the and Spirostomum (40 ind.), which naturally occur respectively at species’ growth rate 푟 , till saturation of the curve, i.e. carrying ca- higher and lower densities. We determined species’ intrinsic growth 푠 pacity 퐾 . Figure S4 illustrates the Colpidium growth curve with rate 푟 and carrying capacity 퐾 in pure cultures, at identical condi- 푠 the logistic fit. The complete results for all species are shown in tions (see Species’ traits below for details). Table S1. The landscapes. Each MC consisted of 36 LCs, connected accord- . The stochastic formulation of the logistic process ing to two different schemes: a lattice network in which each LC Stochastic model [the one-step ‘birth and death process’ with space/food limitation has four nearest-neighbors with periodic boundaries (‘2D’ land- [43]] is necessary when volumes of communities and/or number of scape), and a coarse-grained river network structure (‘RN’), ob- individuals considered are small. Each individual has a natural tained from a 200×200 space filling optimal channel network (OCN, death rate 푑 and a probability 푏 per unit time to produce a second [39, 40, 13]), with an appropriate threshold on the drainage area (see one by division. To insure that the Markov property holds, 푑 and 푏 SI for details). In the RN landscape a LC has either three nearest- are assumed to be fixed and independent of the age of the individ- neighbors (‘Confluence’, C) or one nearest-neighbor (‘Headwater’, ual. Moreover, competition gives rise to an additional death rate H). Landscapes of these two dispersal treatments were replicated 훾(푛−1)/푉 , proportional to the number of other individuals present. six times. Furthermore, we had MCs of ‘Isolation’ treatment, repli- For a population of 푛 individuals, the transition probabilities read cated three times. The disturbance-dispersal events. Spatio-temporal heterogeneity was 훾 푇 (푛 − 1∣푛) = 푑푛 + 푛(푛 − 1) [ 3 ] introduced by disturbance-dispersal events: twice a week a 푉 disturbance-dispersal event was set-up, six times in total. Each 푇 (푛 + 1∣푛) = 푏푛 [ 4 ] time, we randomly selected 15 patches to be disturbed per metacommunity (MC). We independently selected these patches for each The master equation is of the six replicates, but paired one RN and one 2D landscape to 푑푝 (푡) [ 훾 ] be disturbed along the same pattern. The total number of links 푛 = 푑(푛 + 1) + (푛 + 1)푛 푝 (푡) + 푏(푛 − 1)푝 (푡) − between the two treatments is different by construction, but the 푑푡 푉 푛+1 푛−1 per site amount of dispersal is kept constant. A disturbance event [ 훾 ] − 푏푛 + 푑푛 + 푛(푛 − 1) 푝 (푡) [ 5 ] consisted of the removing of all 10 ml of medium present in the local 푉 푛 community (LC). After each disturbance event, dispersal was ac- complished by manual transfer from every single LC to its nearest Expansion in 푉 [43] gives the macroscopic equation for concentra- neighbors, without bias in directionality (isotropic dispersal) and tion 휙 = ⟨푛⟩/푉 푑휙 happened simultaneously in well-mixed conditions, avoiding long- = (푏 − 푑)휙 − 훾휙2 [ 6 ] 푑푡

Footline Author PNAS Issue Date Volume Issue Number 3 in which we clearly recognize the logistic equation, provided we The multivariate master equation [43] for the community is given identify the macroscopic carrying capacity 퐾 with (푏 − 푑)/훾, which by [44] 푠 is the metastable stationary solution 휙 for 휙(푡) = √⟨푛(푡)⟩/푉 . Se- (푏−푑)푡 lected a time 푡1 such that 푛0푒 1 is of order 푉 , for time 푡 < 푡 the non-linear competition term in the master equation is −→ ∑ 1 푑푝( 푛 , 푡) { −→ −→ −→ −→ −→ of order 푉 −1/2 and may be neglected. The population is simply = 푇 ( 푛 ∣ 푛 + 푒 )푝( 푛 + 푒 , 푡)+ 푑푡 푖 푖 in its exponential malthusian growth phase ⟨푛(푡)⟩ = 푛 푒(푏−푑)푡 and 푖 [ ] 0 2 2 푏+푑 2(푏−푑)푡 (푏−푑)푡 −→ −→ −→ −→ −→ ⟨푛 ⟩ − ⟨푛⟩ = 푛0 푒 − 푒 . To disentangle the two + 푇 ( 푛 ∣ 푛 − 푒 )푝( 푛 − 푒 , 푡)− 푏−푑 [ 푖 푖 ] } factors 푏 and 푑 hidden inside the macroscopic growth rate 푟 = 푏−푑, −→ −→ −→ −→ −→ −→ −→ − 푇 ( 푛 + 푒푖 ∣ 푛 ) + 푇 ( 푛 − 푒푖 ∣ 푛 ) 푝( 푛 , 푡) [ 11 ] we performed an analysis of variance among our six experimental replicates: by calculating the macroscopic ⟨푛(푡)⟩ and the variance 2 휎 (푡) for time 푡 < 푡1, we can infer 푏 and 푑 separately, knowing their sum and difference. The natural death rate for our protist species The resulting equations for the first moments are: is 푑푠 ≈ 0. Metacommunity model. We generalize the above arguments to the case ⎛ ⎞ of multiple species living in a patchy environment and competing 푆∑=10 푑⟨푛푖⟩ ⟨푛푖푛푗 ⟩ for the same resources. The following discussion is valid for the LC = 푟 ⎝⟨푛 ⟩ − ⎠ [ 12 ] 푑푡 푖 푖 퐾 푉 푘 into the whole metacommunity. The nearest neighbors dispersal 푗=1 푠 along the network is also simulated in a stochastic fashion. We can not assume ‘well-mixed’ conditions for individuals of all species, so we ideally divide each LC in 100 cells and we randomly distribute individuals in each of these cells. Then we randomly choose 20 cells that depends also on the second moments. Due to the limited LC to be dispersed to LCs nearest neighbors. The most conservative volume 푉 = 10 ml and the fact that the species’ carrying capac- choice – in a pure competition for space framework among individu- ity in some cases is small (less than hundred individuals per ml of als of different species – is to consider the following null hypothesis. medium), fluctuations around the macroscopic solutions may not be negligible. Thus, we performed numerical simulations employ- The competition term 훾푖(푛푖 − 1)/푉 ≈ 푟푖(푛푖 − 1)/(퐾푖푉 ), valid for species 푖 in pure growth, changes when taking into account the fact ing the Gillespie algorithm [45], which allows us to produce time that the fraction of space occupied by an individual of species 푗 is series that exactly recover the solution of the multivariate master equation in Eq. (14) with transition probabilities in Eqs. (12) and 퐾푗 /퐾푖 times that of individual of species 푖. The transition probabilities for the birth and the death of an individual of the 푖th species, (13). Edge effects in the lattice landscape are removed by impos- −→ ing periodic boundary conditions. The dynamics of the system are within a community with 푛 = (푛1,푛2,...,푛푖,...,푛푆 ) individuals in species pool 푃 = (1, 2,... ,i,... , 푆) respectively, read: stochastically perturbed to include diffusive dispersal of individuals across patches and spatially uncorrelated environmental distur- −→ −→ −→ bances, reflecting the experimental conditions. A simulation ends 푇 ( 푛 + 푒푖 ∣ 푛 ) = 푏푖푛푖 [ 7 ] ⎛ ⎞ when the system has reached mono-dominance. Actually, at the ∑ (푏푖 − 푑푖)푛푖 푛푗 푛푖 − 1 experimental disturbance regime (and without any speciation pro- 푇 (−→푛 − −→푒 ∣−→푛 ) = 푑 푛 + ⎝ + ⎠[ 8 ] 푖 푖 푖 푉 퐾 퐾 cess taken into account), only the species with the highest growth 푗∕=푖 푗 푖 rate survives in the simulations. −→ where 푒푖 is a unit vector whose only 푖th component is not zero. ACKNOWLEDGMENTS. Funding from: ERC Advanced Grant RINEC 22761 (AR, The transition probabilities, when 푑푖 ≡ 0, ∀푖 ∈ 푃 simplify to: FC); SFN Grant 200021/124930/1 (AR, FC); SNF Grant 31003A 135622 (FA). We −→ −→ −→ thank E. Bertuzzo, T. Fukami, M. Gatto, L. Mari and A. Maritan for invaluable help, 푇 ( 푛 + 푒푖 ∣ 푛 ) = 푟푖푛푖 [ 9 ] ⎛ ⎞ support, comments and suggestions. We also acknowledge the generous support of ∑ F. de Alencastro (CEAL/IIE/EPFL). We thank Sophie Campiche for access to their 푟푖푛푖 푛푗 푛푖 − 1 푇 (−→푛 − −→푒 ∣−→푛 ) = ⎝ + ⎠ [ 10 ] laboratory material, and R. Illi for protozoan pictures. 푖 푉 퐾 퐾 푗∕=푖 푗 푖

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D E

Fig. 1. Design of the connectivity experiment. (A) The river network (‘RN’) landscape (bottom inset: red points label the position of LCs, the black point is the outlet) derives from a coarse-grained optimal channel network (OCN) which reﬂects the 3D structure of a river basin (top inset). (B to E) The microcosm experiment involves protozoan and rotifer species. (B) Subset of the species (for names see SI, the scale bars are 100 휇m). (C) Communities were kept in 36-well plates. Dispersal to neighboring communities follows the respective network structure: blue lines for RN (D), same network as in (A), black for ‘2D’ lattice with four nearest neighbors (E).

6 www.pnas.org/cgi/doi/10.1073/pnas.0709640104 Footline Author A Experiment RNB Experiment 2D 8

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0 Fig. 2. Experimental and theoretical local species richness in river network (‘RN’) and lattice (‘2D’) landscapes. (A, B) Mean local species richness (훼-diversity, color coded; every dot represents a LC) for the microcosm experiment averaged over the six replicates. (C, D) Species richness for each of these replicates individually. (E, F) The stochastic model predicts similar mean 훼-diversity patterns (note diﬀerent scales).

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texp 0 0 10 25 50 75 100 125 150 0 2 4 6 8 10 Time (day) Species Rank Fig. 3. (A, B) Probability density function (pdf ) of 훼-diversity for RN and 2D landscapes, with model distributions re-scaled to experimental averages. (C) 훽-diversity (JSI) in 2D (red) and in RN (blue), as a function of topological distance between LC pairs (mean ± s.d. of experimental data, dotted lines are model predictions). Maximum geodesic distance in a 36 lattice is six, in the RN it is 11. (D) Predicted time behavior of mean ± s.d. 훼-diversity for RN and 2D at two landscapes sizes (36 and 1040 LCs for RN and 36 and 1225 LCs for 2D). Upper inset: 훼-diversity at 푡푒푥푝 = 24 day (black dashed line gives the experimentally measured time point) for a 1040 LCs RN landscape (‘O’ is the outlet), and for a 1225 LCs 2D landscape. (E) Rank-occupancy curve (red for 2D, blue for RN, and cyan for ‘Isolation’), dotted lines are model predictions. Note the sharp decrease in occupancy for some protozoan species that the model does not predict, indicating stronger competition in the experiment (see SI Text).

8 www.pnas.org/cgi/doi/10.1073/pnas.0709640104 Footline Author A B 1

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Fig. 4. (A) Experimentally observed 훼-diversity as a function of the degree of connectivity (푑), e.g. the number of connected neighboring nodes to a LC. For LCs in ‘Isolation’ treatment 푑 = 0, in RN ‘Conﬂuences’ (Cs) have 푑 = 3 and ‘Headwaters’ (Hs) 푑 = 1, whereas in 2D all LCs have 푑 = 4. Larger 푑 results in signiﬁcantly higher species richness. Boxes represent the median and 25/75th percentile, whiskers extend to 1.5 times the interquartile range. (B) JSI for Cs (green), and for Hs (black) separately. Filled symbols represent the mean ± s.d. of the experimental data, dotted lines the model predictions. For comparison, the JSI for the entire RN (blue) and that for the 2D (red) are shown.

Footline Author PNAS Issue Date Volume Issue Number 9