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Disentangling local, metapopulation, and cross-community sources of stabilization and asynchrony in metacommunities Matthew Hammond, Michel Loreau, Claire de Mazancourt, Jurek Kolasa

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Matthew Hammond, Michel Loreau, Claire de Mazancourt, Jurek Kolasa. Disentangling local, metapopulation, and cross-community sources of stabilization and asynchrony in metacommunities. Ecosphere, Ecological Society of America, 2020, 11 (4), pp.e03078. 10.1002/ecs2.3078. hal-02565047

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Disentangling local, metapopulation, and cross-community sources of stabilization and asynchrony in metacommunities 1, 2 2 1 MATTHEW HAMMOND , MICHEL LOREAU, CLAIRE DE MAZANCOURT, AND JUREK KOLASA

1Department of Biology, McMaster University, 1280 Main Street West, Hamilton Ontario L8S 4K1 Canada 2Centre for Biodiversity Theory and Modelling, Theoretical and Experimental Ecology Station, CNRS, 2 Route du CNRS, 09200 Moulis, France

Citation: Hammond, M., M. Loreau, C. de Mazancourt, and J. Kolasa. 2020. Disentangling local, metapopulation, and cross- community sources of stabilization and asynchrony in metacommunities. Ecosphere 11(4):e03078. 10.1002/ecs2.3078

Abstract. Asynchronous ﬂuctuations of populations are essential for maintaining stable levels of biomass and ecosystem function in landscapes. Yet, understanding the stabilization of metacommunities by asynchrony is complicated by the existence of multiple forms of asynchrony that are typically studied inde- pendently: Community ecologists, for instance, focus on asynchrony within and among local communities, while population ecologists emphasize asynchrony of populations in metapopulations. Still, other forms of asynchrony, such as that which underlies the spatial insurance effect, are not captured by any existing analytical frameworks. We therefore developed a framework that would in one analysis unmask the stabilizing roles of local communities and metapopulations and so unify these perspectives. Our framework shows that metacommunity stabilization arises from one local and two regional forms of asynchrony: (1) asynchrony among species of a local community, (2) asynchrony among populations of a metapopulation, and (3) cross-community asynchrony, which is between different species in different local communities and underlies spatial insurance. For each type of stabilization, we derived links to diversity indices and associated diversity–stability relationships. We deployed this framework in a set of rock pool invertebrate metacommunities in Discovery Bay, Jamaica, to partition sources of stabilization and test their dependence on diversity. Cross-community asynchrony was the dominant form of stabilization, accounting for >60% of total metacommunity stabilization despite being undetectable with existing frameworks. Environmental variation inﬂuenced types of stabilization through different mechanisms. pH and dissolved oxygen, for example, increased asynchrony by decorrelating local species, while salinity did so by changing the abundance structure of metapopulations. Lastly, all types of asynchrony depended strongly on different types of diversity (alpha, metapopulation, and beta diversity drove local, metapopulation, and cross-community asynchrony, respectively) to produce multiple diversity–stability relationships within metacommunities. Our new partition of metacommunity dynamics highlights how different elements—from local communities to metapopulations—combine to stabilize metacommunities and depend critically on contrasting environmental regimes and diversities. Understanding and balancing these sources of stability in dynamic landscapes is a looming challenge for the future. We suggest that synthetic frameworks which merge ecological perspectives will be essential for grasping and safeguarding the stability of natural systems.

Key words: asynchrony; community; diversity; diversity–stability; metacommunity; metapopulation; partitioning; stability; variability.

Received 27 August 2019; revised 3 December 2019; accepted 18 December 2019; ﬁnal version received 6 February 2020. Corresponding Editor: Cory Merow. Copyright: © 2020 The Authors. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. E-mail: [email protected]

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INTRODUCTION prevent a deeper understanding of stabilization at the metacommunity scale. Community-level biomass or abundance var- The analytical barrier is that the main local ies over time and governs the rise and fall of community framework used to date (Wang and ecosystem functions in landscapes. Such system- Loreau 2014) does not capture some forms of level fluctuations are stabilized when compo- regional asynchrony that interest ecologists. Asyn- nents (e.g., species) fluctuate asynchronously so chrony among populations of a metapopulation, that declines in one component are compensated for example, helps to stabilize overall metacom- by increases in another (Doak et al. 1998, Yachi munity biomass (Wilcox et al. 2017) and is critical and Loreau 1999, Schindler et al. 2015). Because for species persistence in landscapes (Anderson asynchrony reduces variation of community or et al. 2015, Schindler et al. 2015). But this form of ecosystem properties, it is important for ensuring asynchrony is only implicit in the local commu- their reliability. Alaskan salmon returns, for nity framework (Wilcox et al. 2017), leaving its example, are stabilized by the existence of hun- contribution to stability at the metacommunity dreds of uncoupled populations (Schindler et al. scale unquantified. Another form of asynchrony 2010). Tallgrass prairie biomass is similarly stabi- overlooked by current frameworks is that which lized where fire and grazing create a mosaic of underlies the spatial insurance hypothesis (Yachi asynchronous patches (McGranahan et al. 2016). and Loreau 1999), wherein different species occu- In turn, biomass stabilization can be crucial for pying different patches fluctuate asynchronously stabilizing ecosystem functions like net primary and disperse to maintain ecosystem function production (Wilcox et al. 2017). (Gonzalez et al. 2009). Recent work has isolated the mechanisms by The above gaps may be seen to result from a which asynchrony stabilizes natural systems. conceptual problem: The form of asynchrony Support for the insurance hypothesis (Yachi and measured depends on the organizational hierar- Loreau 1999) highlights the stabilizing effect of chy used to conceptualize and study a metacom- asynchronous species responses to environmen- munity (Fig. 1). Viewed as a set of local tal fluctuations (Leary and Petchey 2009, Hector communities (Fig. 1A), for instance, the meta- et al. 2010, Loreau 2010). Confirmed portfolio community is stabilized by asynchrony among effects (sensu Doak et al. 1998, Tilman 1999), local communities (which we call type I asyn- meanwhile, demonstrate the power of diversity chrony) and asynchrony of species within those to stabilize communities or functional groups local communities (type II; Wang and Loreau when species dynamics are weakly correlated 2014). But if viewed (equally validly) as a set of (Bai et al. 2004, Cardinale et al. 2012). But while metapopulations (Fig. 1B), it is stabilized by stabilization by asynchrony is well understood in asynchrony among species metapopulations local communities (Thibaut and Connolly 2013), (type III) and asynchrony of populations within there is an urgent conservation need to scale that those metapopulations (type IV). understanding up to metacommunities (Wang Progress in stability research depends on and Loreau 2014). bringing these overlapping metacommunity per- In a recent advance, Wang and Loreau (2014) spectives together in a single frame of reference. partitioned the variability of total metacommunity Wang et al. (2019) made an important step in this — c biomass or abundance gamma variability ( CV) direction by relating the local community and —into local and regional components represent- metapopulation hierarchies in an analytical a ing the variability of local communities ( CV)and framework. However, the approach does not rec- asynchrony among those communities (b). Their oncile local communities and metapopulations in approach has rapidly become the most common a single analysis to give their independent contri- in metacommunity asynchrony research and has butions to metacommunity stability. Nor does it underscored the importance of spatial heterogene- capture the fifth form of asynchrony (type V)— ity in stabilizing metacommunity biomass and among different species in different local com- ecosystem function (McGranahan et al. 2016, Wil- munities—that is the generative mechanism for cox et al. 2017). But despite this progress, two bar- spatial insurance (Loreau et al. 2003, Gonzalez riers—one analytical and the other conceptual— et al. 2009).

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Fig. 1. Three views of a metacommunity and their associated forms of asynchrony. Viewing metacommunities

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(Fig. 1. Continued) as (A) a set of local communities emphasizes asynchrony among local communities (type I asynchrony, blue dashed lines) and among species within local communities (type II), both of which stabilize total metacommunity abundance. (B) But viewed as a set of metapopulations, focus is on asynchrony among metapopulations (type III) and among populations of a metapopulation (type IV). (C) Here, we view the metacommunity as a set of local populations (species i in local community k). This bridges the local community and metapopulation perspectives to partition stabilizing asynchrony from species within local communities (type II), from populations within metapopulations (type IV), and from a cross-community form of asynchrony that occurs between different species inhabiting different local communities (type V).

Here, we present a new perspective on meta- The resulting framework exposes how metacom- community stabilization that overcomes the munities are stabilized by one local-scale and two analytical and conceptual barriers left unad- regional-scale forms of asynchrony—among local dressed by past approaches (Fig. 1C). Viewing species (type II), among populations of a metapopu- the metacommunity as a set of asynchronous lation (type IV), and among different species in dif- local populations (i.e., population of species i in ferent communities (type V), which we call cross- local community k) allows a highly resolved community asynchrony. Notably, these forms are view of metacommunity dynamics (e.g., Gouh- wholly consistent with the deﬁnition of metacom- ier et al. 2010). Moreover, it lets us partition munity dynamics (cf. Holyoak et al. 2005:9) as asynchronies that would be hidden if the meta- including a local community component (e.g., type community was analyzed as a set of local com- II), a spatial component (e.g., type IV), and a communities or a set of metapopulations. On the munity x spatial component (e.g., type V). A further conceptual front, the approach uniﬁes the local advantage is that because the framework works at community and metapopulation hierarchies in a the resolution of species populations, it offers ties to single analytical partition by including elements biological mechanism and diversity that other of each. frameworks do not (see Box 1 for details).

Box 1.

Linking stabilization and diversity at the metacommunity scale

Diversity–stability relationships are increasingly well understood within local communities in terms of portfolio and insurance effects (McCann 2000, Leary and Petchey 2009, Thibaut and Connolly 2013). But the links between diversity and stability at the metacommunity scale are only now coming into focus (Howeth and Leibold 2010, Wang and Loreau 2016). Analyzing metacommunity stabilization at the resolution of local populations facilitates this effort because many standard diversity measures (e.g., a diversity) also use populations as the basic unit of analysis (e.g., diversity of local species populations). Viewing the metacommunity as a set of local populations, we can consider the diversity of local populations (i.e., of species i in community k) that contributes to stabilization of total biomass or abundance. Most simply, stabilization always increases with the diversity of local populations when all populations have the same variability (CV) and pairwise correlation (q; Appendix S4):

2 x ¼ HikðÞ1 q CV (B1) P 2 here, Hik is the Gini-Simpson diversity of all populations in the metacommunity, or 1 pik where pik is the relative abundance of a population ik in the metacommunity.In real metacommunities where CVs and correlations dif-

fer among populations, diversity plays a more contingent role. Here, population diversity (Hik) increases total ι stabilization unless counteracted by two other factors: population variability ( CV) and asynchrony per unit of u = diversity (AH which is the ratio of asynchrony to diversity: 1 pop Hik; see Appendix S4):

x ¼ HikAHiCV (B2)

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Similar to stabilization, asynchrony increases with diversity unless the added units of diversity are less effective at buffering change and result in a lower asynchrony per unit diversity (i.e., the poor buffering capacity of extra diversity counters the expected gains in asynchrony): u ¼ 1 pop HikAH (B3)

These expressions highlight two routes to stabilizing metacommunity biomass or abundance (cf. Bluthgen€ et al. 2016), either by increasing population diversity (e.g., portfolio effect) or by increasing asynchrony of that diversity (e.g., increased buffering). The diversity route to stability depends on the number and evenness of populations in the metacommunity. Use- fully, this population diversity can be broken down into contributions from local communities, metapopulations, and cross-community population pairs (Table 2). Similar to species diversity, Gini-Simpson population diversity

(Hik) is the probability of randomly sampling two individuals from different populations in the metacommunity. These individuals can only be of (1) different species within the same local community, (2) the same species in different local communities, or (3) different species in different local communities. Gini-Simpson diversity in a metacommunity thus splits into three components and sampling probabilities reﬂecting how populations are distributed across species and local communities: ¼ a~ þ p~ þ b~ Hik div div div (B4) These diversities are implicit in our measures of local, metapopulation, and cross-community stabilization and, in fact, can be derived from them (Appendix S5). These links, in turn, predict four basic diversity–stabilization relationships that will emerge in metacommunities unless obscured by the modifying terms in Eqs. B2, B3 (i.e., diversity that adds extra synchrony or changes population variability): x First, total stabilization of the metacommunity ( ) increases with population diversity (Hik). d ae Second, local stabilization ( ) rises with a measure of local species diversity, div, which is a weighted alpha diversity emphasizing larger local communities (Table 2). b pe Third, metapopulation stabilization ( mp) increases with the diversity of constituent populations, div. The same ae pe general form as div, div, is an average population diversity of metapopulations and is weighted toward dominant species. b be Finally, cross-community stabilization ( cc) increases with div, a weighted, additive beta diversity (Lande 1996). It represents the average amount of diversity not found in a random local community (Veech et al. 2002) with down-weighting of larger local communities.

The framework thus has strong potential for metapopulation hierarchies. We deﬁne a local synthesizing community and population ecology population ik as the individuals of species i living as well as exposing the stabilizing roles of diver- in a sampled local community k, though we rec- sity. Moreover, its application to empirical data— ognize that these may not constitute a population rock pool metacommunities here—should help in the demographic sense. As shown in Fig. 1C, to resolve the complex stabilization of ecosys- focusing on local populations is the only tems that emerges over many lower levels of approach that avoids an intermediate hierarchi- organization (Proulx et al. 2010). It therefore cal level (e.g., local communities which are offers a tantalizing step toward a full accounting aggregates of local species) to expose all intra- of temporal stability at the metacommunity and interspeciﬁc stabilization occurring at the scale. population level. Using local populations as the unit of analysis, Analytical framework: Disentangling stabilization we can quantify total stabilization from local by local communities, metapopulations, and more population asynchrony, x. This is the degree to Stabilization here is the reduction of variability which variability of metacommunity biomass at the metacommunity scale due to asynchrony. (gamma) is reduced by asynchrony among all Analyzing the metacommunity as a set of local local populations in the metacommunity (i.e., populations is the key to partitioning stabilizing between all populations living in all local com- asynchrony from both the local and munities or, equivalently, between all

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Table 1. New measures of population-level variability and stabilization by asynchrony in metacommunities (see Appendix S1 for derivations).

Related Variance-based Coefficient of asynchrony Statistic Measure formula Variationformula measure P r 2 P ik 2 ɩ Pik CV Weighted-average population variability ik pikCVik - mik P ik jl r r : P ik6¼jl ik jl covik jl jl g g x Stabilization from asynchrony among all local 1 q : CV CV 1 u P P M2 ik6¼jl ik jl ik jl pop populations j r r ik jk covik:jk P P d k i6¼j j q g g d Stabilization from asynchrony among species in 2 6¼ 1 ik:jk CVik CVjk i P P M k i j CV local communities (type II) l r r P P ik il covik:il b b i k6¼l l ðÞ q g g mp mp Stabilization from asynchrony of populations 2 6¼ 1 ik:il CVik CVil i P P M i k l CV within metapopulations (type IV) l j r r P P 6¼ 6¼ ik jl covik:jl j b Β k l i j l q g g cc Stabilization from asynchrony of different 2 6¼ 6¼ 1 : CV CV cc M k l i j ik jl ik jl iCV species in different patches (type V) Notes: Measures can be expressed using elements of the variance–covariance matrix of metacommunity populations or as products of the relative abundances, temporal CVs, and pairwise correlation coefficients of populations—properties known to fl r in uence community-level variability (Cottingham et al. 2001, Thibaut and Connolly 2013). Abbreviations are ik, temporal standard deviation of a population of species i in local community k; cov , covariance of populations ik and jl; m , temporal ik.jl f ik mean biomass of population of species i in local community k; M, temporal mean of metacommunity biomass; CV, coefficient of variation of a population weighted by its relative abundance in the metacommunity (i.e., pikCVik where pik = mik/M); q fi φ , between-population Pearson correlation coef cient; pop, population synchrony index. populations of all species; see Table 1 for formu- communities k and l). It is equivalent to within- lae and Appendix S1 for derivations). species stabilization in the metapopulation hierar- Total stabilization reduces variability of meta- chy (Fig. 1B) and an additive version of Wang community biomass or abundance as et al.’s (2019) partition (see Appendix S2). Lastly, b quantifies cross-community stabilization from c ¼ i x; (1) cc CV CV type V asynchrony between different species in cwhere fi 2 CV is the squared coef cient of variation (CV ) different local communities (species i in local com- of metacommunity biomass or abundance (Wang munity k with species j in local community l). This ι and Loreau 2014). CV is a weighted and squared source of stability reflects the degree to which average variability of all populations in the meta- contrasting dynamics of species spread across the c community. It is also the value of CV when all landscape reduces metacommunity variability local populations are perfectly synchronized and is notably masked in existing hierarchical (Appendix S1: Eq. S6). frameworks (Appendix S2: Fig. S1). Because the There are just three forms of asynchrony that same asynchrony mechanism underlies the spa- b can occur among local populations to stabilize tial insurance hypothesis, cc sheds new light on the metacommunity (Fig. 1C). Total stabilization how species diversity and environmental hetero- (x) thus splits into three components correspond- geneity interact to stabilize metacommunities. ing to the different pairings of populations and Metacommunity biomass or abundance is stabi- covariances possible (Appendix S1: Fig. S1): lized whenever there is asynchrony among local x ¼ d þ b þ b ; populations in the metacommunity. We can mp cc (2) φ φ express this asynchrony as 1 pop, where is d ’ measures local stabilization or stabilization due to Loreau and de Mazancourt s (2008) dimensionless fi type I asynchrony among local species (species i measure of synchrony. Doing so, we nd that sta- x with j in local community k). It is equivalent to bilization ( ) depends on the average variability ι within-community stabilization in the local com- of local populations ( CV) and their asynchrony in the metacommunity (Appendix S3): munity hierarchy (Fig. 1A) and Wang and Lor- ’ eau s (2014) additive partition (see Appendix S2). x ¼ u i : b 1 pop CV (3) mp measures metapopulation stabilization or stabilization from type II asynchrony among pop- Ecologists often study asynchrony as opposed ulations in metapopulations (species i in local to the resulting reduction of metacommunity

❖ www.esajournals.org 6 April 2020 ❖ Volume 11(4) ❖ Article e03078 SYNTHESIS & INTEGRATION HAMMOND ET AL. variability (Thibaut and Connolly 2013, Hautier stabilizes metacommunities from local to regio- et al. 2014). For these applications, we can apply nal scales. the same additive partition of stabilization (Eq. 2) to partition asynchrony (Appendix S3). METHODS fi φ We nd population asynchrony (1 pop)tobe d ι a composite of asynchrony from local ( / CV), Study system and sampling b ι metapopulation ( mp/ CV), and cross-community We sampled 49 coastal rock pools near Discov- b ι pairs of populations ( cc/ CV): ery Bay Marine Laboratory, University of the West Indies, on the northern coast of Jamaica d b b 0 0 u ¼ þ mp þ cc : (18°28 N, 77°25 W) over fourteen annual sur- 1 pop i i i (4) CV CV CV veys (1989–2003). Pools lie on a 25 m radius sec- tion of fossil reef within 1 m of the nearest These components change with the degree of neighbor, on average, and no further than 10 m correlation between populations and enable from the ocean. Pools have volumes ranging deeper analysis of asynchrony in metacommu- from 0.5 to 78.4 L and are refilled by precipita- nities. tion, ocean spray, and, for a few, occasionally Stabilization of rock pool metacommunities large ocean tides. Seventy-eight invertebrate species occur in the system and disperse as propag- We illustrate our analytical framework in a set ules transported by wind, ocean spray, animal of tropical rock pool metacommunities. This sys- vectors, and overflow after heavy rainfall (Sciullo tem has been well-studied and has many positive and Kolasa 2012). We confined analyses to the 26 attributes for testing metacommunity theory, most abundant species. These species are those such as high species diversity, discrete, identifi- with densities of more than five individuals per able local communities, and relatively indepen- pool and constitute 99% of all individuals. They dent annual samples of community composition therefore represent the diversity that contributes and structure (Kolasa and Romanuk 2005). It most to total metacommunity abundance and its thus offers a clear and well-resolved system for stabilization by asynchrony. Analyzed species testing our framework. Our main goal is to included ostracods (8 species), copepods (6), understand how forms of stabilizing asynchrony cladocerans (3), worms (5), aquatic insects (3), that were previously overlooked or considered and other crustaceans (1). separately combine to stabilize metacommuni- We sampled invertebrate communities at low ties. In specific terms, stabilized metacommunity tide in December or January of a sampling year, biomass or abundance has implications for sus- with the exception of an additional June 1997 taining generalist predators in rock pools (e.g., sampling. We withdrew 0.5 L of water after stir- crab larvae Sesarma miersii Rathburn 1897) and ring the pool to dislodge organisms from rock smoothing ecosystem processes (e.g., primary walls and homogenize contents. Each sample productivity; Wilcox et al. 2017). But as a was filtered through 63-lm mesh to isolate inver- broader exploration of stabilization pathways, tebrates, which were immediately preserved in we ask: 50% ethanol. Community samples were sorted, 1. Is metacommunity abundance most stabi- identified, and counted by microscope. Rock lized by local communities, metapopula- pools could not be sampled when pool drying tions, or cross-community combinations of caused volumes to fall below 0.5 L and were species? recorded as blanks (see below for data treat- 2. What environmental factors drive the vari- ment). Environmental variables including tem- ous forms of stabilization? perature, salinity, dissolved oxygen, pH, and 3. How do different forms of diversity influ- chlorophyll-a concentration (a proxy for biologi- ence stabilization at the metacommunity cal productivity) were measured with multiprobe scale? sondes (DataSonde, Yellow Springs Instruments, or Hydrolab). Data were available for 8–11 of the Through a unifying approach, our findings survey years, except for chlorophyll a which was highlight multiple paths by which diversity measured on six annual surveys.

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Identification of replicate metacommunities constituted <10% of total observations. Since We identified seven subsystems within the these blanks introduce errors when partitioning rock pool landscape to serve as replicate meta- variability, we replaced them with zeros which communities. Metacommunities could not be assumes that no living, adult invertebrates occur identified based on rates of organism dispersal in a dry pool. Stabilization and asynchrony met- as these are mostly unknown—a common defi- rics in Table 1 were calculated from rock pool ciency in ecological data sets. Past work in the density data for each replicate metacommunity. same system, however, indicates that dispersal is We used Statistica 8.0 software (StatSoft 2007) to d b b common (Sciullo and Kolasa 2012) and that its test for differences in , mp, and cc asynchrony effects on local communities decay with distance with one-way ANOVAs and Tukey’s post hoc (Pandit et al. 2009). We therefore delineated tests. Data were log- or square-root-transformed metacommunities based on their spatial cluster- when necessary to meet parametric assumptions. ing in the landscape. This approach assumes Nonparametric Kruskal-Wallis tests were used if only that closer pools exchange more dispersers parametric assumptions could not be met. —and so form a more integrated system—than Because environmental variables were measured those that are farther apart and hence less con- with differing frequencies, we calculated tempo- nected by dispersal. But because identified sub- ral means or CVs of a variable for each pool. systems may nonetheless still exchange These measures therefore summarized the long- organisms, it is important to recognize that they term characteristics of pools (e.g., high salinity) may not be completely independent. Still, the as opposed to their instantaneous conditions. We chosen systems provide a reasonable snapshot of employed standard and forward-step bivariate clusters of sites that are more likely to exchange regressions to test for environmental drivers of organisms on account of their proximity. stabilization. We used cluster analysis with complete link- We also used the CV-based formulae in Table 1 c d b age to group pools by geographic position in to calculate benchmark values of CV, , mp, and b the X, Y, and Z (height above sea level) dimen- cc for theoretical metacommunities with differ- sions. The number of statistically justified clus- ent statistical properties. We assessed, for c ters was determined by the elbow in the instance, CV values for (1) zero correlation q amalgamation schedule. Seven clusters were between populations ( ik.jl = 0), (2) even local advanced as putative metacommunities. Meta- populations (pik = 1/Npop, where Npop is the communities ranged in number of local commu- number of populations in the metacommunity), nities (pools) from 3 to 25 (mean = 7.0 8.1 and (3) even populations with zero correlation. standard deviation [SD]) and in regional rich- We used one-way ANOVA to test whether ness from 15 to 26 species (mean = 20.7 4.3). types of stabilization differed in terms of relative Metacommunities spanned a range of environ- abundances and variability of population pairs fl mental in uences, from low-lying seaward (pikpjl and CVikCVjl, respectively). We used an pools to high-lying pools close to the leading alternative method to compare mean pairwise q edge of landward vegetation. correlation ( ik.jl) between stabilization types because means of correlation coefficients are Statistical analysis biased by the number of elements in the correla- Stabilization and asynchrony were analyzed at tion matrix (Loreau and de Mazancourt 2008). interannual timescales—the sampling frequency Corrections for this bias exist (Loreau and de of data. Our analyses therefore omit any sub-an- Mazancourt 2008, Gross et al. 2014, Bluthgen€ nual asynchrony exhibited by pool organisms. et al. 2016) but apply to an entire correlation We note, however, that even though stabilization matrix and not the local, metapopulation, and can occur over multiple timescales (Downing cross-community subsets we averaged. We there- et al. 2008), interannual fluctuations are a large fore used random subsampling to keep the num- source of variation in coastal ecosystems and can ber of correlations constant across groups (types be an important timescale for stabilization. of stabilization or asynchrony). For each meta- Dried up rock pools that could not be sampled community, we retained all N correlation coeffi- and were recorded as blank data entries cients for the smallest group and compared these

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d b d to N correlations randomly selected from the lar- followed by and mp (Fig. 2B). stabilized little ger groups. because, even though each local community was We contrasted regressions of diversity and strongly stabilizing, there were relatively few asynchrony in rock pool metacommunities with local communities in metacommunities (Fig. 2C, b null cases of low and high correlation among D). mp was similarly small because there were metacommunity populations. These cases repre- few metapopulations and each one contributed b sent the extremes of uncorrelated and correlated to little stabilization. cc, on the other hand, was responses to environmental ﬂuctuations, respec- large because metacommunities contained many tively. We simulated uncorrelated responses by pairs of local communities—which give rise to randomizing the order of time series values for cross-community population pairs—and each of each population. Correlated responses were sim- these strongly stabilized the metacommunity ulated by aligning time series values in rank (Fig. 2C, D). Cross-community pairs stabilized order within local communities, within metapop- the metacommunity more effectively than local ulations, or within the whole metacommunity to or metapopulation pairs due to their higher asyn- be as correlated as possible given time series val- chrony (Fig. 3A; F2,18 = 12.81, P < 0.001) and ues. We then explored a wider range of interpop- lower mean correlation (Fig. 3B; F2,18 = 6.96, ulation correlation levels by using equations in P = 0.006). We did not detect any differences in Table 1 to calculate stabilization values for differ- the relative abundances or variability of popula- q ent correlation values from ik.jl = 0to1. tion pairs. Forms of stabilization had different environ- RESULTS mental drivers. d, for instance, correlated positively with mean dissolved oxygen of rock pools Stabilization of rock pool metacommunities in a metacommunity (r = 0.76, t2,5 = 2.64, A varying environment drove the temporal P = 0.046). Further analysis showed this was variability of populations in rock pool metacom- because dissolved oxygen or associated, unmea- ι munities ( CV). Temperature variability (CV) was sured variables acted to decorrelate species and the primary environmental factor retained by stabilize local communities (Appendix S7: Tables 2 b stepwise multiple regression (R = 0.70, F1,5 = S1, S2). mp was positively associated with mean P 11.57, = 0.019). But stabilization from local, salinity (r = 0.84, t2,5 = 3.41, P = 0.019), a factor metapopulation, and cross-community popula- that increased the stabilizing effect of relative b tions reduced variability at the metacommunity scale abundance on metapopulations. cc, on the other substantially by 74.9% 10.3 (SD). Comparisons hand, declined with local invertebrate abun- with theoretical benchmarks showed stabilization to dance (r = 0.84, t2,5 = 3.52, P = 0.017), a result be close to the 97.9% 1.2 reduction expected of weaker stabilization from relative abundance if all populations were even and uncorrelated and variability patterns in high-density pools. (Appendix S6: Fig. S1). Moreover, our measures revealed 1.6 times more stabilization than would be Diversity–asynchrony relationships detected within the local community hierarchy (i.e., Population diversity did not predict stabiliza- using Wang and Loreau’s [2014] framework). This tion (x instead was a function of population was because d, bmp, and bcc captured the stabilizing variability, the third factor determining gamma 2 effects of all asynchronous populations in contrast to variability in Eq. B2; R = 0.83, F1,6 = 28.22, hierarchical frameworks that incompletely capture P = 0.002). Rather, diversity was a strong and these effects (Appendix S2: Fig. S1). positive predictor of asynchrony, consistent with Local, metapopulation, and cross-community Eq. B3 (Fig. 4A). Furthermore, the local, populations differed in their capacity to stabilize metapopulation, and cross-community compo- metacommunities (Fig. 2A). Cross-community nents of this diversity (Table 2) predicted asyn- stabilization dominated and accounted for chrony coming from local, metapopulation, and b – 60.9% 19.0 of total stabilization. Mean cc cross-community sources, respectively (Fig. 4B b d – exceeded that of both mp and (F2,18 = 6.13, D). These diversity asynchrony relationships b P = 0.009). cc involved the largest number of were similar in slope and intercept to a null population pairs and hence covariances, model of weakly correlated populations, created

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3 6 A B b

2 4.5 a ab 1 a 3 Stabilization a b Log (# pop. pairs)

0 1.5 δ βmp βcc δ βmp βcc

4 0.3 C a D a 3 0.2 2 b b

0.1 a Log (# of units) 1

Stabilization per unit b

0 0 Local Meta Cross Local Meta pops. Cross comms. pops. comms. comms. comms.

d b Fig. 2. (A) Mean stabilization of gamma variability arising from local communities ( ), metapopulations ( mp), b and cross-communities ( cc) in rock pool metacommunities. (B) Mean number of population pairs contributing d b b asynchrony to , mp, and cc. (C) Stabilization per sampling unit in the metacommunity, that is per local commu- d b b nity for , per metapopulation for mp, and per local community pair for cc. (D) Mean number of local communities, metapopulations, and local community pairs (cross-communities) represented in metacommunities. Dashed line indicates value for whole landscape of rock pools. Signiﬁcant differences (P < 0.05) of raw or log-transformed values indicated by a and b groupings. by data randomization (Fig. 4, gray lines). Fur- taking a metacommunity as a set of asyn- ther null models showed these relationships to chronous local populations, our analytical frame- be robust to a wide range of population correla- work reveals how metacommunities are tion scenarios (Appendix S8: Fig. S1), disappear- stabilized by one local and two regional forms of ing only when populations were highly asynchrony (local, metapopulation, and cross- correlated or when metacommunities had very community). Not only is this perspective consis- different values of interpopulation correlation tent with the classical conception of metacommu- (Appendix S8: Fig. S1). nity dynamics (see Introduction; Holyoak et al. 2005:9), but it also uniﬁes the local community and metapopulation approaches to studying DISCUSSION metacommunities by capturing stabilization from each (see also Wang et al. 2019). Our empir- We presented a solution for partitioning forms ical results further underscore how diversity and of asynchrony that are partially or wholly hidden environmental variation support the wide range when metacommunities are analyzed as a hierar- of stabilizing mechanisms in natural metacom- chy of local communities or metapopulations. By munities.

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0.8 A 0.16 B )

) a

ρ a ( pop 0.6 0.12 b n o

i t 1 ( a

l y 0.4 e 0.08 n r r o b b r a o c h

a n n 0.2 0.04 a y e s A-ϕ M 0 0 δβmpβcc δβmpβcc Source of stabilization Source of stabilization

d b b Fig. 3. Asynchrony and correlation underlying stabilization by , mp, and cc. (A) Local, metapopulation, and cross-community components of asynchrony, calculated according to Eq. 4. (B) Unbiased mean correlation of local, metapopulation, and cross-community population pairs. Dashed line indicates value for whole landscape of rock pools.

Cross-community stabilization: a hidden source of weak correlation among populations probably stability owes to differential responses of populations to Cross-community stabilization, while a core of environmental changes. Thus, the observed weak our framework, is seldom recognized as a force correlation within local communities (Figs. 2C, 3) smoothing metacommunity variability. This is consistent with the local insurance hypothesis omission is in spite of being deemed necessary (Yachi and Loreau 1999) in which species respond for spatial insurance (Gonzalez et al. 2009) and differently to local environmental cues (Leary being implicit in finely resolved descriptions of and Petchey 2009, Thibaut et al. 2012). Weak cor- metacommunity dynamics (Gouhier et al. 2010). relation within metapopulations, in turn, likely Yet, this particular form of asynchrony domi- reflects the tracking of different environmental nated over all others (Fig. 2A), highlighting its regimes by local populations (Ringsby et al. importance in reducing variation at the meta- 2002). And the very weak correlations we found community scale. Since this source of stability is among cross-community populations likely stem not evident when gamma variability is decom- from differential responses of species across posed as a local community or metapopulation space—the same mechanism of compensatory hierarchy (Fig. 1C), studies using these frame- dynamics in the spatial insurance hypothesis works may underestimate stability arising from (Loreau et al. 2003). The strength of this stabiliz- asynchrony and miss a unique (spa- ing effect may owe to a doubling up of differential 9 species) component of metacommunity tial responses: Different species have contrasting dynamics. In turn, recognizing this component responses to the environment and, by living in will strengthen theoretical and empirical under- different local communities, experience different standing of how spatial heterogeneity and spe- environmental fluctuations. Notably, this effect cies richness interact to stabilize landscapes, such increased with scale as cross-community asyn- as through spatial insurance effects. chrony, pairwise decorrelation and stabilization TTwo factors—one biological and one numeric were accentuated at the whole landscape level —may make cross-community stabilization a (Figs. 2A, 3A, B), presumably and in part as more widespread and potent force in natural ecosys- spatial heterogeneity, and species turnover was tems. First, and biologically, cross-community included in the sampled area. populations were the least correlated (Fig. 3B) Second, the biological causes of high cross-com- likely due to stronger differential responses to munity stabilization are likely to be compounded environment. Since Jamaican metacommunities by the numerical dominance of cross-community are strongly forced by environmental variation, populations. We found that the number of cross-

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– – φ Fig. 4. Diversity asynchrony relationships. (A) Population asynchrony (1 pop) increased with Gini-Simpson population diversity. Components of population diversity (Table 2) predicted different types of asynchrony with: (B) local diversity predicting the asynchrony contributed by local communities; (C) diversity of populations in metapopulations predicting the metapopulation fraction of asynchrony; and (D) cross-community diversity predicting cross-community asynchrony. Accompanying lines represent slopes from null cases of uncorrelated populations (light gray lines from 25 permutations) and perfectly correlated populations (dark gray line), generated by data shuffling (see Methods). Local, metapopulation, and cross-community components of asynchrony are defined in Eq. 4. community population pairs outstripped the will contribute most to metacommunity stability. number within local communities or metapopula- Our framework may also be profitably extended tions (Fig. 2B), with each additional pair adding to include functional groups and their specific stabilizing potential akin to a portfolio effect contributions to stabilization in the local, (Bluthgen€ et al. 2016). Our calculations further metapopulation, and cross-community context. suggest that cross-community pairs will dominate We further note that asynchrony specific to eco- in all but the smallest metacommunities (those logically important interactions—such as with less than three local communities and regio- between predator and prey or plants and pollina- nal species; see Appendix S9: Fig. S1). tors—may also be obscured in current metacom- We propose that further exploration of the munity frameworks. Future and targeted numeric and biological causes of cross-commu- incorporation of these into partitions will bring nity stabilization will bring important insights ecology closer to a full accounting of stabilizing about when and where cross-community pairs forces in metacommunities.

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x d b b Table 2. Components of Gini-Simpson diversity (Hik) that increase , , mp, and cc stabilization when populations have equal temporal variability and pairwise correlations (see Appendices S4 and S5).

Diversity Probability of sampling two Gini-Simpsondiversity Associated component Formula individuals from: formula stabilization type P 2 x Population 1 ik pik Different local populations in the Hik P P metacommunity P j a~ ¼ 2 d Local species k i6¼j pikpjk Different species in the same local div pk Hk P P community Pk l p~ ¼ 2 b Metapopulation i k6¼l pikpil Different populations in the same div pi Hi mp P P metapopulation i l j b~ ¼ c a~ b Cross-community k6¼l i6¼j pikpjl Different species from different div div div cc local communities

Notes: Abbreviations are pik, relative abundance of a population, belonging to species i and local community k, in metacommunity (i.e., pik = mik/M); pk, relative abundance of local community k in metacommunity (i.e., pk = mk/M); pi, relative abundance of species i in metacommunity (i.e., pi = mi/M); Hik, Gini-Simpson diversity index of populations in metacommunity; Hk, b c diversity of species in local community k; Hi, diversity of populations ofP species i; div, additive beta diversity (Lande 1996); div, 2 Gini-Simpson species diversity at regional metacommunity scale (i.e., 1 i pi ). Subscripts are species; i, j; local communities; k, l.

An integrated view of metacommunity metapopulations (e.g., of butterflies; Oliver et al. stabilization 2010) but could promote habitats with factors that Our approach allowed for an integrated view synchronize local species (e.g., generalist preda- of stabilization from local communities and tors; Raimondo et al. 2004). Conversely, commu- metapopulations. Though cross-community sta- nity-based management may prioritize species bilization dominated the metacommunities, sta- with asynchronous dynamics (e.g., in forests; bilization from within local communities and Morin et al. 2014), but these could include species metapopulations was still indispensable and with easily synchronized local populations (e.g., together accounted for nearly half of all stabiliza- masting species; Koenig and Knops 2013). tion (Fig. 2A). This observation promotes the The relative balance of asynchrony forms will unifying view that metacommunities are mean- also likely be relevant to the maintenance of resi- ingfully stabilized by several lower levels of lience in metacommunities. Disturbances or organization and ecological entities. Thus, sort- management actions that dampen local species ing out the relative impacts of local communities, asynchrony, for instance, may weaken local metapopulations, and more will be crucial to insurance effects (Yachi and Loreau 1999). Rescue understanding and managing the stability of effects (Brown and Kodric-Brown 1977) similarly landscapes. depend on metapopulation asynchrony for vig- With multiple forms of stabilization or asyn- orous local populations to subsidize moribund chrony to balance comes the potential for trade- ones via dispersal. Disruption of cross-commu- offs. Most simplistically, this is because forms of nity asynchrony, finally, may impair spatial stabilization or asynchrony are collectively insurance effects (Loreau et al. 2003) in which exhaustive (Eqs. 2, 4). This property means that ecosystem functions are buffered by asynchrony given a fixed amount of total stabilization or asyn- within functional groups (e.g., primary produc- chrony, an increase in one type (e.g., local stabi- ers; Symons and Arnott 2013). Because rescue, lization) comes at the expense of another (e.g., local, and spatial insurance effects depend on dif- metapopulation stabilization). Some real-world ferent types of asynchrony, an important future trade-offs indeed seem possible. Gouhier et al. research question is how these can be optimized (2010), for instance, report differential effects of in managed landscapes. Our framework might environmental variation on local community and prove useful for connecting underlying patterns metapopulation asynchrony at certain levels of of asynchrony with their associated ecological dispersal. Similarly, managing for one type of effects (i.e., rescue, local insurance, and spatial asynchrony may unwittingly modify other types. insurance effects). Species-based management, for example, encour- The multifaceted nature of metacommunity stabi- ages habitat heterogeneity to stabilize lization was also apparent in the variety of

❖ www.esajournals.org 13 April 2020 ❖ Volume 11(4) ❖ Article e03078 SYNTHESIS & INTEGRATION HAMMOND ET AL. environmental controlsoverstabilizationtoo does the weight of cross-community popula- (Appendix S7). Notably, stabilization could be vari- tion pairs and thus their potential contribution to ously promoted or impaired by environmental forc- spatial asynchrony. This, combined with the ing of the correlation, relative abundance, and numerical dominance of cross-community pairs, variability components of stabilization. If such com- suggests that preserving beta diversity may be of plex causation is the norm, ecologists will need to paramount importance for metacommunity sta- move beyond single causes of stabilization (Down- bility—a position supported by positive beta ing et al. 2014) and elucidate how multiple environ- diversity–stability relationships in the literature mental drivers impact different forms of (Mellin et al. 2014, Wang and Loreau 2016). stabilization and asynchrony. A complete picture of The diversity–asynchrony relationships we metacommunity stabilization—similar to the local found can be considered portfolio effects because community case (Thibaut and Connolly 2013)—will rock pool populations were very weakly corre- include understanding how environmental varia- lated (see Figs. 3, 4)—a common assumption of tion differentially affects each statistical component portfolio theory (Doak et al. 1998, Tilman et al. of stabilization (e.g., evenness, correlation, and vari- 1998). They may therefore be expected in simi- ability). Absent this detailed understanding, our larly stochastic metacommunities. But equations analysis suggests that preserving biodiversity may and simulations show they may also emerge in be the most viable route to maintaining asynchrony more deterministic systems where environmen- and stability in changing environments (cf. Ander- tal fluctuations synchronize dynamics. First, son et al. 2015). Eqs. B1–B3 and our null models predict that the main condition for a positive diversity–asyn- Multiple paths from diversity to metacommunity chrony relationship is simply that an added pop- stability ulation has a unique response to environmental Diversity–stability research asks how much fluctuations. Second, diversity–asynchrony rela- and what kind of diversity is needed to support tionships are robust to varying levels of interpop- stable ecosystems. Our results show that popula- ulation correlation and only weaken and tion diversity increases asynchrony (Fig. 4A), disappear as populations approach perfect corre- indicating that large metacommunities buffer lation, as predicted by theory (Appendix S8; see change in the same way that large financial port- also Fig. 5.3 in Loreau 2010). Given this robust- folios enable diversification and variance reduc- ness, the smoothing of metacommunity variabil- tion (Doak et al. 1998, Anderson et al. 2015). ity by multiple diversity–stability relationships Looking deeper, we find that population diver- may be a widespread phenomenon. If so, the crit- sity—and its stabilizing effect—is a composite of ical challenge will be to recognize and conserve, other known types of diversity (Eq. B4). Strik- not just species diversity (e.g., Leary and Petchey ingly, at least three diversity–asynchrony rela- 2009) or patch diversity (Wilcox et al. 2017), but tionships stabilize metacommunities and depend the suite of local community, metapopulation, on how populations are distributed across local and cross-community diversities that collectively communities and metapopulations. stabilize landscapes. Alpha diversity, for instance, predicted the amount of asynchrony generated within local CONCLUSIONS communities. This is consistent with previous work showing that a diverse local species pool Metacommunity dynamics defy simple analy- often buffers community-level variation (Cardi- sis and management, at least in part, because nale et al. 2012, Wang and Loreau 2016). Similarly, they are not tractable by the local community or metapopulation asynchrony grew with the diver- metapopulation perspective alone. Our novel sity of constituent populations and agreed with partition unifies these organizational hierarchies studies showing the variance-reducing effects of to show how asynchrony arises through multiple large metapopulations (Anderson et al. 2015). local and regional pathways of environmental Cross-community asynchrony, lastly, increased variation. A more complete view of metacommu- with additive beta diversity. From its equation in nity stability will come from recognizing the Table 2, we see why: As beta diversity grows, so multiple forms of asynchrony that stabilize

❖ www.esajournals.org 14 April 2020 ❖ Volume 11(4) ❖ Article e03078 SYNTHESIS & INTEGRATION HAMMOND ET AL. metacommunities, gauging their relative impor- statistical inevitability of stability-diversity rela- tance and studying the diversity–stability relationships in community ecology. American Natu- tionships which underlie them. We anticipate ralist 151:264–276. that highly resolved approaches like ours will Downing, A. L., B. L. Brown, and M. A. Leibold. 2014. – prove powerful for disentangling stabilizing Multiple diversity stability mechanisms enhance population and community stability in aquatic mechanisms that span the range of ecological food webs. Ecology 95:173–184. hierarchies (e.g., subpopulations and functional Downing, A. L., B. L. Brown, E. M. Perrin, T. H. Keitt, groups). and M. A. Leibold. 2008. Environmental ﬂuctua- tions induce scale-dependent compensation and ACKNOWLEDGMENTS increase stability in plankton ecosystems. Ecology 89:3204–3214. MH and JK acknowledge support from several Nat- Gonzalez, A., N. Mouquet, M. Loreau. 2009. Biodiver- ural Science and Engineering Research Council sity as spatial insurance: the effects of habitat frag- (Canada) grants. ML and CdM were supported by the mentation and dispersal on ecosystem functioning. TULIP Laboratory of Excellence (ANR-10-LABX-41) Pages 134–146 in S. Naeem, et al., editors. Biodiver- and by the BIOSTASES Advanced Grant, funded by sity, ecosystem functioning & human wellbeing. the European Research Council under the European Oxford University Press, Oxford, UK. Union’s Horizon 2020 research and innovation pro- Gouhier, T. C., A. Gonzalez, and F. Guichard. 2010. gram (grant agreement No 666971). We thank Discov- Synchrony and stability of food webs in metacom- ery Bay Marine Lab, and the many undergraduate and munities. American Naturalist 175:E16–E34. graduate students for contributing to the data bank Gross, K., B. J. Cardinale, J. W. Fox, A. Gonzalez, M. and Bart Haegeman, Jean-Francßois Arnoldi, and Jo Loreau, H. Wayne Polley, P. B. Reich, and J. van Werba for helpful discussions. We also thank several Ruijven. 2014. Species richness and the temporal anonymous reviewers for their suggestions to improve stability of biomass production: a new analysis of the manuscript. All authors contributed equally to recent biodiversity experiments. American Natu- conceiving of the study. MH developed the analytical ralist 183:1–12. framework with help from ML, CdM, and JK. JK col- Hautier, Y., E. W. Seabloom, P. B. Adler, and E. Al. 2014. lected data. MH analyzed data and wrote the text with Eutrophication weakens stabilizing effects of diver- substantial contributions from ML, CdM, and JK on sity in natural grasslands. Nature 508:521–525. analyses and interpretation of results. Hector, A., Y. Hautier, P. Saner, and E. Al. 2010. Gen- eral stabilizing effects of plant diversity on grass- LITERATURE CITED land productivity through population asynchrony and overyielding. Ecology 91:2213–2220. Anderson, S. C., W. M. Jonathan, M. M. Michelle, K. D. Holyoak,M.,M.A.Leibold,N.M.Mouquet,R.D.Holt, Nicholas, and B. C. Andrew. 2015. Portfolio conser- M. F. Hoopes. 2005. Metacommunities: a framework vation of metapopulations under climate change. for large-scale community ecology. Pages 1–31 in Ecological Applications 25:559–572. M. Holyoak, et al., editors. Metacommunities: spa- Bai, Y., X. Han, J. Wu, and Z. Chen. 2004. Ecosystem tial dynamics and ecological communities. Univer- stability and compensatory effects in the Inner sity of Chicago Press, Chicago, Illinois, USA. Mongolia grassland. Nature 431:181–184. Howeth, J., and M. Leibold. 2010. Species dispersal Bluthgen,€ N., et al. 2016. Land use imperils plant and rates alter diversity and ecosystem stability in animal community stability through changes in pond metacommunities. Ecology 91:2727–2741. asynchrony rather than diversity. Nature Commu- Koenig, W., and J. Knops. 2013. Large-scale spatial nications 7:1–7. synchrony and cross-synchrony in acorn produc- Brown, J. H., and A. Kodric-Brown. 1977. Turnover tion by two California oaks. Ecology 94:83–93. rates in insular biogeography: effect of immigra- Kolasa, J., T. Romanuk. 2005. Assembly of unequals in tion on extinction. Ecology 58:445–449. the unequal world of a rock pool metacommunity. Cardinale, B. J., et al. 2012. Biodiversity loss and its Pages 212–232 in M. Holyoak, et al., editors. Meta- impact on humanity. Nature 486:59–67. communities: spatial dynamics and ecological Cottingham, K. L., B. L. Brown, and J. T. Lennon. 2001. communities. University of Chicago Press, Chi- Biodiversity may regulate the temporal variability cago, Illinois, USA. of ecological systems. Ecology Letters 4:72–85. Lande, R. 1996. Statistics and partitioning of species Doak, D. F., D. Bigger, E. K. Harding, M. A. Marvier, diversity and similarity among multiple communi- R. E. O’Malley, and D. Thomson. 1998. The ties. Oikos 76:5–13.

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