Evidence for self-organization in determining spatial patterns …Evidence for self-organization in determining spatial patterns of stream nutrients, despite primacy of the geomorphic

Evidence for self-organization in determining spatialpatterns of stream nutrients, despite primacy of thegeomorphic templateXiaoli Donga,b,1, Albert Ruhíc,d, and Nancy B. Grimma,c

aSchool of Life Sciences, Arizona State University, Tempe, AZ 85287; bNicholas School of the Environment, Duke University, Durham, NC 27708; cJulie AnnWrigley Global Institute of Sustainability, Arizona State University, Tempe, AZ 85287; and dNational Socio-Environmental Synthesis Center, University ofMaryland, Annapolis, MD 21401

Edited by Andrea Rinaldo, Laboratory of Ecohydrology (ECHO/IIE/ENAC), Ecole Polytechnique Federale Lausanne, Lausanne, Switzerland, and approved April24, 2017 (received for review November 4, 2016)

Nutrients in freshwater ecosystems are highly variable in space andtime. Nevertheless, the variety of processes contributing to nutrientpatchiness, and the wide range of spatial and temporal scales at whichthese processes operate, obfuscate how this spatial heterogeneity isgenerated. Here, we describe the spatial structure of stream nutrientconcentration, quantify the relative importance of the physicaltemplate and biological processes, and detect and evaluate the roleof self-organization in driving such patterns. We examined nutrientspatial patterns in Sycamore Creek, an intermittent desert stream inArizona that experienced an ecosystem regime shift [from a gravel/algae-dominated to a vascular plant-dominated (hereafter, “wetland”)system] in 2000 when cattle grazing ceased. We conducted high-resolution nutrient surveys in surface water along a 10-km streamreach over four visits spanning 18 y (1995–2013) that represent differ-ent successional stages and prewetland stage vs. postwetland state.As expected, groundwater upwelling had a major influence on nutri-ent spatial patterns. However, self-organization realized by the mech-anism of spatial feedbacks also was significant and intensified overecosystem succession, as a resource (nitrogen) became increasinglylimiting. By late succession, the effects of internal spatial feedbacksand groundwater upwelling were approximately equal in magnitude.Wetland establishment influenced nutrient spatial patterns only indi-rectly, by modifying the extent of surface water/groundwater ex-change. This study illustrates that multiple mechanisms interact in adynamic way to create spatial heterogeneity in riverine ecosystems,and provides a means to detect spatial self-organization against phys-ical template heterogeneity as a dominant driver of spatial patterns.

ecosystem succession | spatial feedbacks | spatial heterogeneity

The relationship between pattern and process is a long-standingtopic of investigation in ecology (1–3). One of the fundamental

questions underlying the study of pattern–process relationships isto what extent patterns are determined by local environmentalconditions (e.g., soil and climate in terrestrial ecosystems, salinityand currents in oceans) and to what extent they are self-organized(4). A major challenge to understanding spatial heterogeneity isthat multiple processes operating across a range of spatial scalescontribute to it, and their relative contributions may themselvesvary over time (5). Here, we used patterns of nutrient concen-tration in a desert stream as a model system to disentangle therelative influence of physical template and biological processes,evaluate the role of internal spatial feedbacks emerging fromphysical and/or biological processes, identify the spatial scales ofunderlying processes, and compare inferences over short-termsuccession and long-term ecosystem regime shifts.The physical template can be defined as the relatively stable

physical environment in which a pattern of interest develops (3),and is considered an overriding organizer of ecological patterns. Atlarge spatial scales, spatial zonation of vegetation pattern is a classicexample of the environmental template determining plant patternformation in action (6). At smaller scales, microtopography signif-

icantly influences plant distribution (7). In streams, the physicaltemplate influences stream surface-water nutrient patterns (8).Longitudinally, tributary junctions bring water with distinct bio-geochemical signatures into a stream. Laterally, streams are hy-drologically connected to the riparian zone, the floodplain, and theupland portions of catchments (8), with riparian zones acting as“nutrient filters” that remove various chemical constituents as watermoves from uplands to the stream (9). Vertically, subsurface waterfrom the hyporheic zone can also alter the biogeochemical signatureof surface water (10). At broader spatial scales, geomorphic fea-tures, such as slope breaks and canyons, determine the locations ofupwelling and down-welling zones (11). Collectively, such connec-tions among subsystems in the riverine landscape form the physicaltemplate that influences patterns of nutrient concentration instream surface water.Biological processes also contribute to spatial patterns in nutri-

ent concentration. In many arid and semiarid terrestrial ecosys-tems, canopy trees and shrubs produce organic litter and alterwater flows, creating islands of fertility and spatial heterogeneity insoil moisture and nutrients across the landscape (12). Stream nu-trient dynamics are influenced by similar in-stream biologicalprocesses (13). Many studies have documented longitudinal (i.e.,downstream) declines in nutrient concentration (14), and othershave shown that algal uptake represents a primary pathway of ni-trogen (N) retention (15). Riverine wetland patches dominated bymacrophytic vascular plants (“macrophytes”) have more complexrelationships with stream nutrients. During the growing season, a

Significance

Rivers and streams are open, heterogeneous ecosystems. Streamwater chemistry is influenced by organisms and the physical en-vironment, resulting in longitudinal (upstream-downstream) het-erogeneity that can be analyzed with time-series methods.Applying statistical techniques to longitudinal nutrient concen-tration data in a desert stream, we found evidence of substantialinternal regulation of surface-water nutrient patterns, realized viaspatial feedbacks. The strength of these feedbacks increased oversuccession. Although inputs from subsurface zones (a feature as-sociated with the physical template) remained a major factor inexplaining nutrient patterns, by late succession, the effect size ofinternal feedbacks was equal to the effect size of major upwellingzones. Our study demonstrates that multiple processes interact ina dynamic way to create ecosystem spatial heterogeneity.

Author contributions: X.D. and N.B.G. designed research; X.D. and N.B.G. performed re-search; X.D. and A.R. analyzed data; and X.D., A.R., and N.B.G. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.1To whom correspondence should be addressed. Email: [email protected].

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1617571114/-/DCSupplemental.

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substantial amount of N and phosphorus (P) may be taken up byvascular plants (16). However, comparisons of stream reaches withdifferent macrophyte covers showed that macrophytes have limitedinfluence on water-column nutrient concentration (17). Riverinemacrophytes accumulate fine sediments and reduce vertical hy-drological exchange (18), which could dampen the biogeochemicalsignature of groundwater on surface water. N fixation (i.e., N2 toorganic N) is another seasonally variable biological process thatpotentially contributes to variation in surface-water N concentra-tion (19). Biological processes may be controlled, in turn, by factorsthat vary spatially, such as the physical template described above.Last but not least, spatial heterogeneity can also emerge via

self-organization. Broadly defined, self-organization is a processin which pattern at large scales emerges from local interactions(4). Self-organized, regular vegetation patterns have been stud-ied extensively in the past decade in water-limited systems (e.g.,refs. 20–22). Mathematical models (e.g., refs. 23, 24) and fieldobservations (e.g., refs. 21, 22) show that terrestrial plants canform regular patterning driven by the local feedbacks betweenbiomass and the limiting resource (water). In streams, nutrients(N and P) often represent limiting resources (25, 26), and thuscould potentially induce local spatial feedbacks (i.e., self-organization). For example, elevated stream nitrate (NO3

−)concentration at upwelling zones induces the formation of algalpatches that take up NO3

− (27), resulting in low concentrationdownstream. Low stream NO3

− concentration may favor thegrowth of N2-fixing cyanobacteria (28), which then may raiseNO3

− concentrations further downstream, in turn, inducing thedevelopment of algal patches there (29). To what extent suchinternal spatial feedbacks, realized through biological and/orphysical processes, inform nonregular spatial structure in het-erogeneous systems remains unexplored to date.The drivers described above have been studied relatively well

in isolation. However, little is known about how they interactcollectively to influence spatial heterogeneity, and even less isknown about how their relative contributions may change oversuccessional time in ecosystems. Here, we capitalized on twounique features of stream ecosystems: (i) unidirectional flow instreams simplifying the spatial pattern from 2D to 1D, whichallows the use of time-series analyses to understand spatial pat-terns, and (ii) their rapid reorganization and regrowth (1–3 mo)after biomass-reducing floods, which allows investigation ofmultiple successional changes in spatial patterns within a shortperiod (30). Regime shifts, another type of ecosystem change,occur abruptly as thresholds are crossed, and could result indramatic changes that are difficult to reverse [e.g., a lake shiftingfrom a clear-water state with abundant rooted aquatic plants to aturbid state, where shading by abundant algae suppresses rootedplants (31)]. Changes in the dominant species and altered bio-logical processes may have significant biogeochemical conse-quences. Our study system (Sycamore Creek, a desert stream inArizona) experienced a regime shift around 2000 when cattlewere removed from the watershed, with dominant gravel- andbenthic algae-dominated substrates transforming, over the courseof several years, to a state dominated by riverine wetlands (32).The removal of cattle is assumed to have favored the expansion ofwetland plants because the plants were released from grazingpressure. At the time of this study, wetlands dominated 40% of thechannel length (33). This situation contrasted with essentially nowetland cover over 20 y of prior research. Thus, the system pro-vides an opportunity to evaluate short-term successional changesin stream nutrient patterns and longer term changes associatedwith an ecosystem regime shift.We collected chemical concentration data [NO3

−-N, soluble re-active P (SRP), and conductivity (COND)] every 25 m along a10-km stream segment in Sycamore Creek at four postflood suc-cessional stages (early-, mid-, mid- to late-, and late-successionalstages), three of them before wetland establishment (1990s) and

one afterward (2013). Comparing different successional stages be-fore and after the ecosystem regime shift, we asked the followingquestions:

i) Are spatial patterns of nutrient concentration influenced bywetland establishment?

ii) What is the relative importance of physical and biologicaldrivers, and what role do internal feedbacks play (if any) ininfluencing spatial patterns of nutrients?

iii) How do the underlying processes and the manifested pat-terns change over successional time?

These questions were answered by applying time-series models toevenly spaced, longitudinal (spatial) nutrient data. We used waveletanalysis to describe the scales at which the underlying processesoperate. To quantify the relationships between the putative driversand nutrient spatial heterogeneity, we used multivariate autore-gressive state-space (MARSS) models, a time-series analysis method.The MARSS modeling framework is commonly used in populationand community ecology to understand long-term trends in pop-ulations (e.g., refs. 34, 35) and the relative importance of internalregulation or species interactions vs. the effects of exogenous envi-ronmental variables on population dynamics (e.g., ref. 36). In thisstudy, we applied MARSS models to one-dimensional chemical datato partition the relative importance of the physical template, biologicalprocesses, and internal concentration regulation over succession.Two important findings emerge from our results. First, the

physical template (here, groundwater upwelling) was a dominantfactor influencing nutrient spatial patterns, about one order ofmagnitude higher than biological effects. The most visually obvi-ous (biological) change in the system over the nearly two decadesencompassed by the study, establishment of riverine wetlands, didnot have a direct effect on nutrient spatial patterns. Second, in-ternal spatial feedbacks, feedbacks that indicate self-organizationbut have not been considered in stream biogeochemical research,became stronger over succession as a resource becoming in-creasingly limiting, and were as important as the physical templateby late succession. We conclude that research on stream nutrientspatial patterns requires an explicit consideration of the interplaybetween the physical template and the system’s internal self-organization, as well as how this interplay may change over suc-cessional or greater time scales.

ResultsPatterns of Nutrient Heterogeneity. Nutrient concentrations were ex-tremely variable in space (Fig. 1 and Table 1). Over 23 y (1976–1999) of approximately biweekly surface-water nutrient monitoringin Sycamore Creek at a single location yielded a coefficient ofvariation (CV) of NO3

− concentration that was only twice the NO3−

concentration over 10 km of space in midsuccession on a single day(CV over 23 y = 207% for 434 samples, CV over 10 km = 104% for399 samples). The pattern of overall spatial variation in concen-trations (CV) was highest for NO3

−, followed by SRP, and lowestfor conductivity, regardless of successional stage.A large sine-wave curve was observed across all four surveys for

conductivity (Fig. 1). Mean SRP concentration was 60% higher afterwetland establishment (same successional stage). In contrast, meanNO3

− concentration was similar before and after wetland establish-ment (Table 1). Spikes in NO3

− concentration were found in thesame upwelling locations, regardless of timing of the survey (Fig. 1).For NO3

−, net uptake length (a measure of tightness of nutrientcycling, with shorter lengths indicating tighter cycles) was shortestin late succession. Net NO3

− uptake length after wetland estab-lishment was similar to NO3

− uptake length in early succession,much longer than in late succession (SI Appendix, Fig. S1). The netSRP uptake length with wetlands present was shortest during mid-to late succession after wetland establishment, even shorter thanin late succession before wetland establishment.

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Wavelet analysis revealed a strong influence of upwellingzones on NO3

− patterns (Fig. 2). The global wavelet spectrum(GWS) is the space-integrated version (i.e., across the entirestream length) of the wavelet power spectrum, and it identifies thedominant scales of spatial variation (by peaks in GWS). The GWSof NO3

− signals showed two distinct spectrum peaks at spatialscales of ∼1 km and 3 km, except during early succession, whenthe 1-km peak was absent (Fig. 3 and SI Appendix, Table S1). ForSRP and conductivity, only one peak, between 1.5 and 1.8 km, wasobserved in the GWS over successional time (Fig. 3 and SI Ap-pendix, Table S1). Wavelet analysis of wetland abundance distri-bution and its GWS showed that the spectrum powers peaked atspatial scales of ∼700 m and ∼2,500 m at downstream distances of5–7 km and 7–10 km, respectively (Figs. 2 and 3). Wavelet analysisfor nutrient spatial heterogeneity and wetland distribution showeddifferent patterns (Figs. 2 and 3 and SI Appendix, Fig. S2), sug-gesting different underlying contributing processes. By comparingthe mean dissimilarities in the space-spatial scale plane (i.e.,spatial locations on the x axis, spatial scale on the y axis) for dif-ferent solutes, we found that SRP patterns varied most with suc-cessional stage, followed by NO3

− and then conductivity (SIAppendix, Fig. S3A). Differences in spatial patterns among solutesincreased with successional stage (SI Appendix, Fig. S3B).

Relative Importance of Drivers over Successional Time. The explanatoryvariables in MARSS include three physical variables (water perma-nence, reach types, and presence/absence of upwelling zones), threebiological variables (presence/absence of algae, presence/absence ofcyanobacteria, and macrophyte abundance), and internal spatialfeedbacks. We constructed two models. In the first one (model I), wecompared the local effects of physical variables and biological driverson nutrient concentration. In the second one (model II), we focusedon partitioning internal spatial feedbacks and physical drivers(template) by leaving out processes (variables) that could potentiallycontribute to the internal spatial feedbacks to avoid double counting(Methods and SI Appendix, SI Materials and Methods).Upstream wetland abundance was not a significant factor in

explaining the SRP, NO3−, or conductivity [in 2013, we measured

chloride (Cl−), also a nonreactive metric] spatial patterns. We ex-plored wetland abundance across a variety of upstream distances(scales: 25 m, 50 m, 75 m, 100 m, 125 m, and 150 m), but at none ofthese scales was a wetland effect statistically significant (only resultsat 100-m scales are shown in Fig. 4). Algal communities showed asignificant negative effect on NO3

− in 2013 (Fig. 4). In late suc-cession, the effect of cyanobacteria on NO3

− was positive and sig-nificant (Fig. 4).

The influence of upwelling (physical template) on NO3−

concentration was approximately one order of magnitude greaterthan the influence of upwelling of biological processes [i.e., thevalue of the coefficient for upwelling was at 10° (Fig. 5), and itwas at 10−1 for biological processes (Fig. 4)]. The upwelling ef-fect on NO3

− and SRP was significantly positive in three suc-cessional stages before wetland establishment, and its effect sizeincreased from early to late succession (Fig. 5). For NO3

−, beforewetland establishment, the upwelling effect was negatively cor-related with the amount of surface water in the stream (Fig. 6).However, following wetland establishment, this effect size de-creased, showing significantly lower values than predicted by theamount of surface water at the time the survey was conducted(Fig. 6B). Similarly, for SRP patterns, after wetland establish-ment, the effect of upwelling zones became nonsignificant (Fig.5). Other physical drivers, including water permanence andreach type, influenced nutrient spatial patterns in some surveys,

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Fig. 1. Spatial patterns of nutrient concentration in Sycamore Creek over 10 km across four stages of postflood succession and two ecosystem states (early successioninMarch 1997, midsuccession inMay 1995, late succession in December 1995, andmid- to late successionwithwetlands present inMay 2013). In 2013, wemeasured Cl−

concentration instead of conductivity. Small and large red dots denote minor and major upwelling locations, respectively. Data from Dent et al. (10).

Table 1. Water chemistry characteristics over the 10-km stretchof Sycamore Creek

Characteristics Unit of measurement n Mean SD CV, %

Early succession (2 wk postflood)/March 1997NO3

−-N μg L−1 398 219 158 72SRP μg L−1 398 17 7 42Conductivity μS cm−1 396 379 14 4N/P — 398 28 11 —

Midsuccession (2 mo postflood)/May 1995NO3

−-N μg L−1 399 6 6 104SRP μg L−1 399 28 6 20Conductivity μS cm−1 399 402 19 5N/P — 399 0.5 0.5 —

Late succession (9 mo postflood)/December 1995NO3

−-N μg L−1 260 35 51 145SRP μg L−1 260 28 13 44Conductivity μS cm−1 260 488 68 14N/P — 260 3 4 —

Mid- to late succession (2 mo postflood)/May 2013NO3

−-N μg L−1 449 7 10 144SRP μg L−1 449 44 19 43Cl− μg L−1 449 15 2 17N/P — 449 0.3 0.16 —

All values are calculated across the n sample locations; values at eachsample location are means of two analytical replicates. Data for 1995 and1997 are from Dent and Grimm (54).

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but none of these physical drivers had an explanatory power asstrong as the explanatory power of upwelling (SI Appendix, Ta-bles S2 and S3).The effects of internal spatial feedbacks were quantified with the

b coefficient in univariate autoregressive state-space models(model II; Methods). When dealing with population time seriesdata, this coefficient quantifies internal regulation of a populationvia density dependence [Ives et al. (37)]. Here, the b coefficientquantified the strength of concentration-dependent effects: Valuesof 1 indicate no concentration-dependent effects, and values closerto 0 suggest strong concentration dependence, or processes causingdownstream concentration to return to its mean level quickly. Forall b coefficients, the 95% confidence intervals did not include 1(Fig. 7), indicating significant regulation of nutrient concentrationvia internal spatial feedbacks (self-organization) in the system.Values decreased from early to late succession for NO3

−, indicatingstronger concentration-dependent effects toward late succession(Fig. 7). The strength of internal regulation increased by a factor ofeight from early to late succession for NO3

−; meanwhile, the effectsize of upwelling increased by a factor of four. The ratio betweenthe effects of internal regulation and external geomorphic controlincreased from 0.5:1 in early succession, to 0.7:1 in midsuccessionand mid- to late succession, and up to 1:1 in late succession (Figs. 7and 8). Such successional trends did not exist for SRP or COND(Fig. 7 and SI Appendix, Table S4).

DiscussionThe central question of which processes generate spatial hetero-geneity in terrestrial and aquatic ecosystems has received attentionfrom ecologists for decades, but the challenge of disentangling thesimultaneous effects of exogenous drivers and internal feedbackson the spatial structure of elements or biota remains unmet (1–4).Here, using recent advances in time-series methods applied to adesert stream, we identified the spatial scales of drivers underlyingobserved patterns of solute concentrations, partitioned the relativeinfluences of physical drivers and biological processes, quantifiedinternal spatial feedbacks, and compared inferences over short-term succession and a long-term ecosystem regime shift. The ob-servation that internal spatial feedbacks contribute to regulatingbiogeochemical patterns in rivers and streams is novel and couldinfluence how stream ecosystems respond to environmental per-turbations (38, 39). Our study also illustrates that data and

methods capable of appraising this complexity and dynamism areessential for understanding pattern–process relationships in rivers,lending importance to long-term data coming online in the UnitedStates and elsewhere, such as the National Ecological ObservatoryNetwork’s stream monitoring program.

Effects of Wetlands on Spatial Heterogeneity of Nutrients. Wetlandsare considered biogeochemical hotspots (40), in the sense thatriverine macrophyte patches exhibit significant nutrient retention(41). However, studies quantifying biogeochemical influences ofwetlands typically integrate large downstream distances (or areas)to calculate total nutrient uptake; hence, the particular contribu-tion of macrophytes to nutrient spatial patterns remains un-resolved. In our study, although wetland plants covered ∼40% ofthe stream in 2013, we found no evidence of wetland patches af-fecting spatial patterns of NO3

− or SRP concentrations directly. Incontrast, algae had a significant negative effect on NO3

− (but noton SRP; Fig. 4), even though the amount of N stored in algae isonly about a third of the amount of N stored in vascular plants (SIAppendix, SI Materials and Methods). Concentration of SRP isadditionally affected by physical adsorption/desorption and solu-bility processes, which may explain why SRP concentration is notnegatively associated with algae in this system. Vascular macro-phytes do assimilate these nutrients and, in fact, represent a muchgreater nutrient storage pool than algae. We suggest that local

Fig. 2. Wavelet power analysis of the three types of solutes in four surveys (four rows) and of the wetland abundance distribution in June of 2013. Sta-tistically significant results (based on red noise) inside the labeled 95% confidence interval are enclosed in black solid lines. Image colors are a representationof the wavelet power spectrum. The dashed white U-shaped line is the cone of influence, below which edge effects limit confidence in results. The x axisshows downstream location (meters), and the y axis shows spatial scale (meters). For the dry section, we used the ARIMA (autoregressive integrated movingaverage) model to generate the missing data in those sections (SI Appendix, SI Materials and Methods).

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and GWS for wetland abundance distribution (D). Global spectrum powerpeaks identify the dominant spatial scales at which the processes that con-trol nutrient spatial heterogeneity occur.

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effects of wetlands on surface water nutrients are undetectablecompared with local effects of algae because macrophytes obtaintheir nutrients via root uptake (42), which is not reflected insurface-water concentration.We observed no direct effect of wetlands on surface-water spatial

patterns of nutrients, but wetlands indirectly affected nutrient spatialpatterns through their influence on surface–subsurface hydrologicalexchange. After wetland establishment, the effect size of upwelling onNO3

− in 2013 was significantly lower than predicted by the amount ofsurface water (Fig. 6) and its effect on SRP was no longer significant(Fig. 7). This shift in the importance of upwelling is likely a result ofbiogeomorphic changes that occurred during wetland development.Upwelling zones feature a high abundance of vascular plants (33),which trap and accumulate fine sediments, leading to a reduced ver-tical hydrological gradient, and thus to a lower hydrological exchangethan would otherwise occur (18). In addition, wetlands may create ahypoxic hyporheic environment, which favors denitrification in hypo-rheic sediments, leading to low NO3

− (18). Reduced exchange andenhanced denitrification are consistent with the observed reducedeffect of upwelling zones on NO3

−. As a consequence of reducedupwelling, nutrient dynamics associated with the plant rooting zonewould be reflected in surface water concentrations even less, if at all.

Changes in the Spatial Scales of Underlying Drivers over SuccessionalTime. The geomorphic template determines the spatial scales atwhich geomorphic drivers operate; it was relatively stable over thetime scale of this study. The NO3

− and SRP peaks occurred atmajor upwelling zones, repeating approximately every 3 km (Fig.1). This distance between major upwelling zones corresponded toa stable peak at the ∼3-km spatial scale in the GWS over foursuccessional stages (Fig. 3).In contrast, the spatial scale of the influence of biological pro-

cesses is determined by the process rates and by the propagationrate of the results of processes (43), both of which may change oversuccessional time. The 0.75- to 1.5-km spatial scale (Fig. 3) couldbe attributed to the accumulation of NO3

− due to N2 fixation.According to Grimm and Petrone (28), N2 fixation in late suc-cession in Sycamore Creek is about 2 mg·m−2 h·−1. This fixationrate translates to a distance of ∼1.5 km for NO3

− to accumulate apeak of 50 μg·L−1 (SI Appendix, Table S1), about the size of thesmall peaks observed in late succession (Fig. 1). Cyanobacteria areusually absent in early spring (28), but over seasonal and succes-sional time, rates of N2 fixation, flow velocity, and areal coverage ofN2 fixers tend to increase (28). These changes explain why thespatial scales of N2 fixation changed over successional time (Fig. 3).

Alternatively, the 0.75- to 1.5-km signal could also be generated byminor upwelling spots (not the major reach-scale upwelling zonesused as the physical template in the model) caused by a decrease inchannel slope that may cause subsurface water to upwell to thesurface (44). This signal became stronger as surface water (dilutionwater) declined toward late succession (45).For SRP, the first maximum GWS was reached at a spatial scale

of 1.2–1.8 km (Fig. 3B). Adsorption/desorption equilibrium betweensediments and the overlying water column often plays an importantrole in P dynamics (46). A desorption rate of 1.7–2.5 μg·L−1·d−1

would increase SRP concentration by μg·L−1 within a 1.2- to 1.8-kmdownstream distance (SI Appendix, Table S1). This desorptionrate is within the range observed in other streams and rivers (e.g.,refs. 47, 48).

Relative Influences of Exogenous Factors and Internal SpatialFeedbacks. Rivers and streams are open ecosystems, highly influ-enced by their physical environment. This characterization issupported in our study: The effect size of upwelling on NO3

−

concentration was about one order of magnitude higher than thedirect effect of biological processes (Figs. 4 and 5), indicating adominant role for the geomorphic template in shaping patternsof NO3

− in Sycamore Creek. However, patchiness in any land-scape is likely to result from a mixture of both exogenous driversand internal feedbacks (49). Variability in nutrient concentrationinduces internal spatial feedbacks, realized through interaction

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Fig. 5. Maximum likelihood (ML) estimates of the MARSS model coefficientsrepresenting upwelling effect on three surface-water chemistry parametersacross four surveys (results from model I). Associated 95% CIs were obtained viabootstrapping. CIs not overlapping with 0 indicate statistical significance. The xaxes indicate successional stages. E, early succession; L, late succession; M, mid-succession in 1995; M–L, mid- to late succession with wetland patches in 2013.

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between local biological and/or physical processes and local nutrientconcentrations and by the propagation of that influence in space(43). Such propagation of influence in space has been documentedin streams at the local scale (e.g., ref. 29), but its effect on largerscale nutrient patterns has not been quantified, as is the case forchanges over time. Here, we show that such internal spatial feed-backs could be as important as the geomorphic template in theirinfluence on NO3

− concentration in the stream: By late succession,the ratio of control of nutrient concentration variability by internalregulation and by geomorphic template was 1:1 (Fig. 8).The intensification of the internal spatial feedbacks means that

the system became more responsive to changes in NO3− concen-

tration in late succession (i.e., a small fluctuation in concentrationinvoked a quick return to an equilibrium concentration). Thisresponsiveness likely results from intensified N limitation in latesuccession in Sycamore Creek, as observed in previous empiricalresearch on the system (15). Resource limitation increasing thestrength of internal feedbacks has been described in arid terres-trial ecosystems, where water constitutes the constraining resourceand gives rise to self-organized vegetation patterns (e.g., refs. 20,22). Sheffer et al. (49) showed that a semiarid shrub-grasslandlandscape exhibited self-organized vegetation patchiness onlywhen water was limiting; in contrast, the physical template de-termined vegetation patchiness under sufficiently high pre-cipitation. Although these regular patterns are formed via scale-dependent feedbacks, a mechanism different from the feedbackswe describe here, both studies demonstrate the role of broadlydefined spatial self-organization (4) in forming spatial heteroge-neity and show that the strength of self-organization intensifieswith increasing resource limitation. Concentration-dependent ef-fects were also observed for SRP, which suggests the existence ofregulation mechanisms. However, no successional trend was ob-served for SRP, likely because SRP is subject to an additionalcontrol pathway (50) of sediment adsorption and desorption (51)that masks biological uptake.The current paradigm for understanding nutrient spatial het-

erogeneity has almost exclusively focused on the effects of ex-ogenous environmental drivers, considered for a snapshot intime. Although our study did support the importance of thegeomorphic template in establishing spatial pattern (Fig. 5), wehighlight here that internal regulation played an equally signifi-cant role in surface water chemical patterns (Fig. 8). Over suc-cessional time with a progressive reduction of surface discharge,the effect of groundwater inputs (i.e., groundwater is a higherfraction of total flow) was amplified by fourfold. However, the

intensity of internal spatial feedbacks of NO3− increased by a

factor of eight, from 49% of the effect size of groundwater up-welling in early succession, to about 70% in midsuccession andmid- to late succession, up to 98% in late succession (Fig. 8).Meanwhile, biological uptake, an intensely studied and oftenpronounced mechanism driving spatial pattern in streams, hadonly a limited effect on longitudinal variation in nutrient con-centrations (Fig. 4). Rivers and streams have generally beenconsidered as open systems, subject to strong external environ-mental influences (38). We can therefore infer that it is highlylikely that the kind of internal spatial feedbacks demonstrated inour study may play an even more important role in other eco-system types where the effect of template heterogeneity is notas strong.

MethodsStudy Site. This study was carried out in Sycamore Creek, a tributary of theVerde River located 32 km northeast of Phoenix, Arizona. The stream drains acatchment of 505 km2 that ranges in elevation between 427 m and 2,164 m.The study site is a 10-km stretch of stream ranging from 600 to 700 m in el-evation. Stream substrata consist of coarse sand and gravel that can be up toseveral meters deep in runs, as well as boulders and cobble in riffles, withlimited reaches of exposed bedrock. The long-term (1905–2014) mean annualprecipitation varies with elevation from 39 to 51 cm·y−1, but varies greatlyacross years (ranging from 2 to 92 cm·y−1). Precipitation is bimodally distrib-uted through the year, with rainy seasons in winter (December–March) andsummer (July–September); thus, the stream is frequently intermittent, withisolated perennial sections separated by large sections that dry out completely,especially in summer (52). N limits algal primary production during base flow,but P limitation has not been demonstrated and is unlikely (25). Growth ofwetland vegetation (post-2000) also is N-limited (53).

Sycamore Creek experienced an ecosystem regime change around 2000,whencattle were removed from the watershed, with dominant gravel- and benthicalgae-dominated substrates transforming to a state with abundant riverinevascular macrophytes (wetlands) (32). By 2013, around 40% of the 10-km mainstem of Sycamore Creek was covered by patchily distributed wetland plants (33).Before wetland establishment (in the late 1990s), three surveys of the spatialpatterns of water chemistry were completed in the 10-km main stem of Syca-more Creek by Dent and Grimm (54). These sampling dates represent threepostflood successional stages (i.e., they differ in time after large winter floodsthat removed biomass, initiating succession) in the algae-dominated ecosystemstate. In May 2013, after the ecosystem regime shift (wetland state), we re-peated the water chemistry of Dent and Grimm (54) in the same 10-km streamreach, with the timing of the survey capturing a mid- to late (postflood)-successional stage. These surveys collectively represent four successional stages(early to late) and two ecosystem states (algae- vs. microphyte-dominated).

Sample Collection and Analysis. The nutrient data used in this study were fromtwo sources: existing data (51) and new data collected on May 31, 2013, allfrom the same section of Sycamore Creek. We replicated field techniques ofDent and Grimm (54), collecting duplicate samples of surface water in 60-mLtubes from the stream’s thalweg. Samples were taken at points 25 m apart,

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Fig. 7. Concentration-dependent effects of the surface water solutes acrossfour surveys (dots are maximum likelihood estimates of the b coefficient inMARSS model II, and whiskers indicate associated 95% CIs obtained via1,000 bootstrap samples. All values fall between 0 and 1. Within this range,smaller values denote stronger concentration-dependent effects [or the influ-ence of the concentration on the rate of change in concentration downstream(i.e., stronger internal feedbacks)]. The x axes indicate successional stages.

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concentration (model I) before wetland establishment (1990s) and afterwetland establishment (2013). After wetland establishment, the coefficientof upwelling was significantly lower than predicted by surface water volume(in red dashed-lined box).

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and were collected as simultaneously as possible by 14 people arrayed alongthe 10-km stream segment. Each person walked upstream as he or she col-lected samples over ∼700 m. All samples were filtered in the field within 2 h,between 0800 hours and 1000 hours. Locations at each 700-m overlap pointwere sampled at both the beginning and the end of the collection period tocheck for diel variation in nutrient concentrations. The magnitude of dielchange was <10% of the range of concentrations observed and 2.5-fold theaverage variation between replicates, so we are confident that the spatialpatterns we report were not confounded by temporal variation.

Filtered water samples were frozen until analysis. All water samples wereanalyzed within 3 wk for NO3

−-N (hereafter, NO3−, but concentration is

reported as mass N per volume), SRP (concentration reported as mass P pervolume), and Cl−. NO3

− and SRP were determined using a Lachat QC8000Flow Injection Analyzer. We measured NO3

− using the cadmium reductionmethod (55) and SRP using the molybdate blue method (56). Cl− was alsodetermined on the QC8000 Flow Injection Analyzer.

We then organized and reanalyzed the data collected from the same 10-kmsegment of Sycamore Creek studied by Dent and Grimm (54) in the 1990s. Thosesurveys represent three stages of postflood succession, 2.5 mo after a flood onMarch 6, 1995 (peak discharge = 113 m3·s−1); 9 mo after the same flood; and2 wk after a flood on February 28, 1997 (peak discharge = 83 m3·s−1) (SI Ap-pendix, Fig. S4). These dates were representative of mid-, late-, and earlypostflood successional conditions in the stream, respectively. Data in 2013 werecollected 2.5 mo after a flood and corresponded to midsuccession (comparabletoMay 1995 data); however, the peak discharge of the flood inMarch 1995wasthreefold larger than in May 2013. Moreover, there was a sustained relativelyhigh flow in 1995 before the May survey (the mean daily discharge was0.45 m3·s−1 on the survey date in 1995), whereas in 2013, dischargedropped to 0.45 m3·s−1 as early as March 28 and declined to 0 on the surveydate. As a result, although both surveys were conducted 2.5 mo after the lastflood, the 2013 survey was judged to be at a mid- to late-successional stage.Whereas Dent and Grimm (54) measured conductivity, we analyzed Cl− insteadin 2013. Both measures represent variation in a biologically inert constituent.

Data for Covariates. Two types of covariate data were collected. The first typewas biological data. We surveyed the location, species (dominant species:Equisetum laevigatum, Paspalum distichum, Schoenoplectus americanus,Typha domingensis, and Juncus torreyi), and sizes of wetland patches alongthe 10-km study reach 2 wk after the 2013 water chemistry survey (SI Ap-pendix, Fig. S5). One week before the survey, we recorded the presence orabsence of filamentous algae and cyanobacteria at 25-m flagged intervalswhere water samples were to be taken. Dent and Grimm (54) recorded thepresence or absence of filamentous algae and cyanobacteria in late succes-sion in 1995 in the same way. The second type of covariate data collectedwas data used to describe the physical template. Water permanence datawere provided by E. Stanley, University of Wisconsin, Madison, WI (52). From

May 1988 to February 1990, Stanley surveyed the same 10-km stream stretchand recorded the spatial extent and average depth of water monthly(22 consecutive monthly measures). We calculated water permanence (per-centage of time with surface water present within the 22-mo study period)along the stream using these survey data. The spatial locations of upwellingalong the 10-km stretch of the stream were obtained from Dent et al. (10);they recorded upwelling zones at the reach, channel unit, channel subunit,and particle scale. Upwelling zones at the reach scale occur at transitionsfrom unconstrained to constrained valleys. Dent et al. (10) identified threesuch transitions as major upwelling zones in the system (Fig. 1). Addition-ally, they used locations where water emerged downstream of a drystreambed as reach-scale upwellings, which they mapped during a dryperiod when the stream had not flooded for more than 18 mo. The up-welling locations at smaller spatial scales were also mapped; however,here, we assumed that only the reach-scale upwelling locations remainspatially fixed through bed-moving floods and only used these data. Fi-nally, we recorded reach types (riffle, run, and pool; categorical) in the2013 survey, as did Dent and Grimm (54).

Statistical Methods.Wavelet analysis. We performed a wavelet analysis to decompose spatial scales oflongitudinal variation in nutrient concentration, the results of which were used toinfer putative environmental drivers. Wavelet analysis does not require the dataseries to be stationary, and is therefore particularly attractive, given the non-stationary nature of most ecological data (57). A full description of the wavelettechnique can be found in an article by Torrence and Compo (58). Waveletanalyses were applied to all 12 nutrient series (i.e., three nutrient types × foursurveys). A global assessment of the scale-specific properties of the decomposedsignal was achieved by summing the mean of the squared wavelet coefficientsacross all locations to produce a scalogram or GWS. After obtaining the corre-sponding wavelet spectra generated from wavelet analysis, we compared themusing a multivariate method that defines an orthonormal basis maximizing themutual covariance for each pair of wavelet spectra (59). Comparing the de-composition of the wavelet spectra onto this orthonormal basis enabled us toquantify the dissimilarity of space- and spatial-scale patterns (i.e., both the spatialscales and the spatial positions) among different nutrient species and amongsuccessional stages. We then used the constructed 12 × 12 dissimilarity matrix tocalculate themean dissimilarity exhibited by themain factors [i.e., nutrient species(NO3

−, SRP, and Cl−), successional stages], which allowed us to evaluate the rela-tive importance of the main factors [similar to the method of Rouyer (59)].Wavelet analyses were carried out using the “biwavelet” package (60) in R (61).MARSS models. To quantify the relationships between the putative drivers andnutrient heterogeneity, we used MARSS models. We fitted MARSS models usingthe “MARSS” R-package (62), which provides support for fitting MARSS modelsto multivariate data via maximum likelihood, using an expectation-maximizationalgorithm. We constructed two different MARSS model structures: Model Iquantified the relative influences of biological processes and the physical tem-plate on nutrient spatial patterns, and model II was used to quantify effects ofthe relative contribution by physical template and by internal spatial feedbacks.

Model I. A MARSS model includes a process model (Eq. 1) and an obser-vation model (Eq. 2):

xs =Bxs−1 +Ccs +ws;ws ∼MVNð0,QÞ [1]

ys = Zxs +A+ vs; vs ∼MVNð0,RÞ [2]

Data enter the model in y (with ys being the log-transformed and z-scorednutrient concentration at sampling site s) and in c (with cs being the cova-riate data at sampling site s, z-scored for continuous covariates). The totalnumber of covariates included in MARSS models for different years varied,as detailed in the following paragraph. The data ys are a linear function ofthe “hidden” or true nutrient concentration xs. Each element in ys is theobserved concentration for three chemical species, each with two replicates(i.e., a 6 × 1 vector). Each element in xs is the true concentration for eachchemical species (i.e., a 3 × 1 vector). The effect of exogenous variables (i.e.,the covariates representing physical drivers and biological processes) onconcentration changes is C, a matrix of the linear effects of cs on xs. B is a 3 ×3 interaction matrix that models the effect of nutrients on each other (off-diagonal values) and on themselves (diagonal values). The covariate ws is a3 × 1 vector of process error, representing the effects of environmentalstochasticity and being modeled with a multivariate normal distribution(mean of 0, covariance matrix Q). In the observation model (Eq. 2), vs is a 6 ×1 vector of nonprocess (observation or measurement) errors, with errors atsampling site s being multivariate normal with mean 0 and covariance matrix R.At each sampling point, we collected replicate samples, which allowed the

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model to separate the two sources of error variance (observation vs. processerror). Z is a 6 × 3 matrix that relates time series to the different state processes.Finally, A is a 6 × 1 “scaling” vector that allowed us to combine, in the samemodel, z-scored continuous covariates and non–z-scored categorical covariates.

Covariates (cs) included three physical variables [water permanence(continuous, unit [%]), reach types (pool, run, and riffle; categorical), andpresence/absence of upwelling zones (binary)] and three biological variables[presence/absence of algae (binary; available for late succession in 1995 and2013 surveys), presence/absence of cyanobacteria (binary; available for latesuccession in 1995 and 2013 surveys), and macrophyte abundance (i.e.,percentage of cover of wetland patches 100 m upstream from each samplingsite; available only in 2013; continuous, unit [%])]. At the time of the early-successional survey in 1997, water was being pumped from a gravel pitbeside the stream into the stream channel at a location in the middle of thestudy section. The chemistry of the pumped water differed significantly fromthe stream water at that point (54). We included the effect of the gravel pitas an additional covariate by designating all of the sampling upstream of thegravel pit as 0 and all of the points downstream as 1.

We selected the best model structure using AICc (Akaike information cri-terion with a correction for finite sample sizes) (63). In the Q matrix (Eq. 1), wecompared models considering nutrient-specific process error with modelsconsidering a single process error across nutrients. In the B matrix (Eq. 1), wecompared models with and without nutrient interactions. In the R matrix(Eq. 2), we compared models considering nutrient-specific observation errorswith models considering constant observation errors (i.e., equal across all nu-trient types). The best model structure (i.e., the one delivering the lowest AICc)was one that assumed both concentration-dependent effects and interactionsamong nutrients, plus nutrient-specific process and observation errors (SI Ap-pendix, Table S5 on model comparison and selection).

Model II.Model II was a set of univariate state-space models constructed topartition the relative importance of internal spatial feedbacks and geo-morphic template. To do so, we built a model for each chemical species ateach successional stage (three chemical species × four successional stages =12 models). Each model incorporated two types of drivers: variables de-scribing the physical template and internal concentration-dependent spatialfeedbacks. All of the covariates (continuous, water permanence; categorical,reach types and presence/absence of upwelling zones) in the model andnutrient concentration data were z-scored (SI Appendix, SI Materials andMethods). The first-order autocorrelation coefficient b in model II canquantify internal spatial feedbacks of nutrients in a way that is analogous todensity dependence in ecological communities (37), as we articulate below.A univariate autoregressive process can be expressed as

xt = a+bxt−1, [3]

where xt is the log species abundance. Provided b ≠ 1, this model has anequilibrium point given by

x∞=a

1−b. [4]

Starting from the initial point x0, the following can be derived via recursion,after Ives et al. (37):

xt = x∞ +btðx0 − x∞Þ. [5]

The value of xt will converge to equilibrium x∞, provided jbj < 1. The variable bmeasures density dependence, or how fast the system is drawing populationsback to equilibrium [more stability properties of the model can be found in thestudy by Ives et al. (37)]. A jbj value closer to 0 produces rapid returns to equi-librium point x∞ (i.e., increasing density dependence). In our study, b describeshow the concentration of a chemical species upstream influences the rate ofconcentration change of the same chemical species immediately downstream.This phenomenon is a “concentration-dependent effect” in space, analogous tothe long known density-dependent effects over time. Whereas b values close to0 suggest strong concentration dependence and quick return to an equilibriumconcentration level, values close to 1 suggest concentration independence. Astochastic version of Eq. 5 is the univariate autocorrelation process:

Xt = a+bXt−1 + Et . [6]

Here, Xt is the log abundance at t and Et is the normal random variable with

mean 0 and variance σ2, and represents process error (model II is furtherdescribed in SI Appendix, SI Materials and Methods).

Concentration-dependent feedbacks are an emergent property of bi-ological and/or physical processes and can arise from several mechanisms. Ifnutrient concentration is high, biological consumption and/or physical ad-sorption may reduce downstream concentration; if nutrient concentration islow enough, nutrients may increase further downstream due to biological(e.g., N2 fixation) and/or physical processes (e.g., desorption of P from sed-iments). To quantify such spatial feedbacks, model II excluded biologicalcovariates because concentration-dependent feedbacks are realized viathese processes. We kept the covariates describing the physical template(i.e., water permanence, reach types, presence/absence of upwelling zones)because these covariates are not controlled by nutrient concentration insurface water, but rather by geomorphic processes at much larger scales. Wehypothesize that NO3

− spatial feedbacks have a biological nature (explainedby biological uptake and release via decomposition-nitrification and N2

fixation-mineralization-nitrification), whereas the spatial feedbacks of SRPare physical (explained by adsorption and desorption). Based on these pre-mises, we tested the predictions with model II: (i) the b value for NO3

− up-stream–downstream interaction would be significantly lower than 1, and (ii)as NO3

− becomes more limiting toward late succession, the b value woulddiminish and approach 0. For conductivity and SRP, (iii) the b value would besignificantly lower than 1 and (iv) there would not be a linear trend overecosystem successional time. AICc was used to compare models, includingphysical template and internal spatial feedbacks, models with only internalspatial feedbacks, and models including only physical template (SI Appendix,Table S6).

We note that like most rivers and streams in arid and semiarid areas,Sycamore Creek is an intermittent stream; therefore, part of the stream wasdry during the survey and no data were collected there. Methods foraddressing these missing values in the dry sections for wavelet analysis andMARSS models (model I and model II) are described in SI Appendix, SI Ma-terials and Methods. We compared the extent to which our inferenceswould change by different approaches to deal with missing values. If in-ferences varied with the approach, we pointed out these differences. For allmodel I and model II results, 95% confidence intervals around maximum-likelihood covariate effects were obtained via 1,000 parametric bootstraps(62). Model residuals were examined via the autocorrelation function (62)(no significant autocorrelation remained in the model residual; SI Appendix,Figs. S6 and S7).

Net Uptake Length. To assess the intensity of biological activity, we appliedan index, net uptake length (64), that reflects the rate of nutrient ex-change with biota. To perform this assessment, we analyzed longitudinalnutrient concentration declines. We computed the first derivative of nu-trient concentration (above a threshold value to filter out noise in thedata) over moving window sizes of 100 m, 150 m, 200 m, and 250 m. Wethen extracted all of the positive values (so that concentration was de-creasing downstream) and computed their mean. The result was an aver-age downstream distance (in meters) required to see a concentrationdecline of 1 μg·L−1. This definition is different from uptake length in thenutrient spiraling concept (65), which is defined as the average down-stream distance traveled by a nutrient molecule in dissolved form beforebeing removed from the water column, because it likely includes bothuptake and release processes. Our estimate of net uptake length usingonly decreasing downstream concentrations is conservative, because itmight also include nutrient release from mineralization or groundwaterinputs (i.e., groundwater concentrations of NO3

− and SRP are usuallyhigher than surface water concentrations of NO3

− and SRP).

ACKNOWLEDGMENTS. We thank members of the Urban and StreamEcosystems Laboratory and many other volunteers at Arizona State Univer-sity for their essential assistance in the field and laboratory. We thank StuartG. Fisher for constructive review of this manuscript. This research wassupported by Grants DEB-0918262 and DEB-1457227(to N.B.G.) from theNational Science Foundation (NSF), by a Facilities Initiative Grant for Grads,and by the Lisa Dent Memorial Fellowship (to X.D.) from the School of LifeSciences at Arizona State University. A.R. was supported by the NationalSocio-Environmental Synthesis Center, under funding received from NSFGrant DBI-1052875.

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