Spatial early warning signals in a lake manipulationVINCE L. BUTITTA,1,� STEPHEN R. CARPENTER,1 LUKE C. LOKEN,1,2 MICHAEL L. PACE,3 AND EMILY H. STANLEY

1

1Center for Limnology, University of Wisconsin, 680 North Park Street, Madison, Wisconsin 53706 USA2Wisconsin Water Science Center, U.S. Geological Survey, Middleton, Wisconsin 53562 USA

3Department of Environmental Sciences, University of Virginia, 291 McCormick Road, P.O. Box 400123,Charlottesville, Virginia 22904 USA

Citation: Butitta, V. L., S. R. Carpenter, L. C. Loken, M. L. Pace, and E. H. Stanley. 2017. Spatial early warning signals in alake manipulation. Ecosphere 8(10):e01941. 10.1002/ecs2.1941

Abstract. Rapid changes in state have been documented for many of Earth’s ecosystems. Despite a grow-ing toolbox of methods for detecting declining resilience or early warning indicators (EWIs) of ecosystemtransitions, these methods have rarely been evaluated in whole-ecosystem trials using reference ecosys-tems. In this study, we experimentally tested EWIs of cyanobacteria blooms based on changes in the spatialstructure of a lake. We induced a cyanobacteria bloom by adding nutrients to an experimental lake andmapped fine-resolution spatial patterning of cyanobacteria using a mobile sensor platform. Prior to thebloom, we detected theoretically predicted spatial EWIs based on variance and spatial autocorrelation, aswell as a new index based on the extreme values. Changes in EWIs were not discernible in an unenrichedreference lake. Despite the fluid environment of a lake where spatial heterogeneity driven by biologicalprocesses may be overwhelmed by physical mixing, spatial EWIs detected an approaching bloom suggest-ing the utility of spatial metrics for signaling ecological thresholds.

Key words: algal bloom; critical transition; early warning indicators; ecosystem experiment; regime shift; resilience;spatial analysis.

Received 20 June 2017; accepted 26 June 2017. Corresponding Editor: Debra P. C. Peters.Copyright: © 2017 Butitta et al. This is an open access article under the terms of the Creative Commons AttributionLicense, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.� E-mail: vincent.butitta@wisc.edu

INTRODUCTION

Ecosystem transitions can result in drasticchanges in composition, structure, and internalprocesses (Scheffer et al. 2001, 2012). Desertifica-tion of grasslands (K�efi et al. 2007), collapse ofcoral reefs (Hoegh-Guldberg et al. 2007), andblooms of harmful cyanobacteria in freshwaters(Scheffer et al. 1997) represent examples of nota-ble state transitions. Models of transitions areoften characterized by bifurcation points (or tip-ping points), in which a small perturbationcauses the ecosystem to quickly and easily “tip”from one dynamical pattern to another (Lentonet al. 2008, Scheffer et al. 2009).

Recent work in ecology has explored how toidentify when an ecosystem is at risk of undergo-ing a critical transition (Scheffer et al. 2009, 2012,

2015). Modeling suggests that there are commonstatistical characteristics of spatial or temporaldata near a tipping point between alternativeecosystem states. Identifying these statisticalcharacteristics—often referred to as early warn-ing indicators (EWIs)—could make it possible todetect an approaching tipping point before it iscrossed. Many EWIs assess an ecosystem’s weak-ening attraction to its current state, which is rep-resented by a decreasing ability to recoverquickly after perturbations. Slower recovery rateof an ecosystem to a local equilibrium is referredto as critical slowing down and is the foundationof many EWIs (Wissel 1984, Dakos et al. 2011,Scheffer et al. 2015). Critical slowing down hasbeen detected from changes in temporal dynam-ics in mesocosm experiments (Drake and Griffen2010, Veraart et al. 2012, Dai et al. 2013) and in

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whole-lake experiments (Carpenter et al. 2011,Pace et al. 2017). Simple spatially explicit modelsof critical transitions indicate that characteristicsof spatial structure can also signal loss of resili-ence, and thus might be useful for early warnings(review by Scheffer et al. 2015). The mechanismsfor spatial early warnings are diverse and are stillactive subjects of research. In many cases, appro-priate spatial indicators are based on measures ofvariance, skewness, spatial autocorrelation, orpatch size.

Although temporal and spatial EWIs may befundamentally linked (Dakos et al. 2010), spatialanalysis may sometimes be more powerful forassessing risk of critical transition (Guttal andJayaprakash 2009, Dakos et al. 2010, Donangeloet al. 2010, Dai et al. 2013). Time series useful fordetecting EWIs require unbroken series of fre-quent observations sustained for long periods oftime. Existing time series that were collected forother purposes may not meet these requirementsand thus can yield ambiguous results (Gsell et al.2016). Spatial analysis at a few points in time(e.g., by remote sensing) may provide greatersensitivity at less cost than high-frequency timeseries.

While there are clear demonstrations of spatialEWI behavior drawn from theoretical examples(van Nes and Scheffer 2005, Guttal and Jaya-prakash 2008, Carpenter and Brock 2010), and ahandful from microcosm experiments (Drake andGriffen 2010, Dai et al. 2013), field experiments onspatial early warnings are rare (but see Carpenteret al. 2011, Cline et al. 2014, Ratajczak et al. 2016,Rindi et al. 2017). Physical processes that influ-ence spatial patterning such as mixing or otherhomogenizing forces may limit detection of earlywarnings (Carpenter and Brock 2010, Dakos et al.2010, Dai et al. 2013, Eby et al. 2017). For this rea-son, field studies exploring detection of EWIsunder natural conditions are needed.

Lakes are a potentially useful ecosystem forevaluating spatial EWIs. Transitions of lakes tocyanobacterial bloom states, a common phe-nomenon of eutrophic lakes, can involve severaltypes of critical transitions (Scheffer et al. 1997,2000, Gragnani et al. 1999, Veraart et al. 2012,Batt et al. 2013). Many of these critical transitionscould generate EWIs, and at least one modelanalysis has shown that this is the case (Battet al. 2013). Spatial models of bloom formation

by cyanobacteria exhibit complex changes in spa-tial patterns that may generate spatial earlywarnings (Serizawa et al. 2008). Blooms areeasily detected in surface waters with automatedsensors capable of gathering high-frequencymeasurements. Time series from automated sen-sors successfully anticipated a cyanobacteriabloom in a whole-lake experiment (Pace et al.2017). Cyanobacteria blooms are also of practicalinterest as they can create serious economic andhuman health problems (Dodds et al. 2009) aswell as extensive alterations to aquatic ecosys-tems (Paerl et al. 2001). Their frequency andintensity are increasing in freshwaters globally—a trend that is expected to continue (O’Neil et al.2011, Taranu et al. 2015).Modeling studies cited above, especially the

work of Serizawa et al. (2008), suggest that spa-tial patterns of cyanobacteria on lake surfacesmay generate early warnings of blooms, but thisphenomenon has yet to be tested under field con-ditions. Here, we induced a cyanobacteria bloomby adding nutrients to an experimental lake toinvestigate whether spatial early warnings aredetectable prior to harmful cyanobacterialblooms. Cyanobacteria were mapped using amobile sensor platform to measure the spatialstructure of the cyanobacteria and attempt todetect early warnings of the bloom. We tested forincreased spatial variance (Guttal and Jaya-prakash 2009, Reinette et al. 2009), increasedskewness (Guttal and Jayaprakash 2008), increasedfrequency of extreme events, and increased spatialautocorrelation (Dakos et al. 2010).

METHODS

In two consecutive years, we measured lake-wide spatial patterning of cyanobacteria usingthe FLAMe platform (Crawford et al. 2015). Toevaluate EWIs of a critical transition, in the firstyear we induced a cyanobacteria bloom throughnutrient addition in an experimental lake whileusing a nearby unmanipulated lake as a refer-ence ecosystem (Pace et al. 2017). During the sec-ond year, both lakes were left unmanipulated.Proposed detection methods for EWIs were com-pared between the manipulated and referencelakes to test for their ability to accurately detectstatistical signals before the cyanobacteria bloomdeveloped.

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Lake descriptionPeter and Paul Lakes are small, oligotrophic lakes

(Peter, 2.5 ha, 6 m, 19.6 m; and Paul, 1.7 ha, 3.9 m,15 m, for surface area, mean, and max depth,respectively) located in the Northern HighlandsLake District in the Upper Peninsula of Michigan,USA (89°320 W, 46°130 N). These lakes have similarphysical and chemical properties and are connectedvia a culvert with Paul Lake being upstream. Bothlakes stratify soon after ice-off and remain stratifiedusually into November (for extensive lake descrip-tions, see Carpenter and Kitchell 1993).

In the first year, Peter Lake (hereafter “manipu-lated lake”) was fertilized daily starting on 1 June2015 (day of year [DOY] 152) with a nutrient addi-tion of 20 mg N�m�2�d�1 and 3 mg P�m�2�d�1

(molar N:P of 15:1) through the addition of H3PO4

and NH4NO3 until 29 June (DOY 180). The deci-sion to stop nutrient additions required meetingfour predefined criteria based on temporalchanges in phycocyanin and chlorophyll concen-trations indicative of early warning behavior of acritical transition to a persistent cyanobacteriabloom state (Pace et al. 2017). Nutrients uniformlymix within 1–2 d after fertilization based on priorstudies (Cole and Pace 1998). No nutrient addi-tions were made to Paul Lake (hereafter “refer-ence lake”). In the second year (2016), neither lakereceived nutrient additions.

Field samplingWe mapped the surface water characteristics

of both experimental lakes to identify changes inthe spatial dynamics of cyanobacteria. In 2015,mapping occurred weekly from 4 June to 15August (11 sample weeks). In 2016, when neitherlake was fertilized, the lakes were mapped threetimes in early to mid-summer. In both years,mapping occurred between the hours of 07:00and 12:00 (before the daily nutrient addition). Werotated the order that we sampled the lakes toavoid potential biases due to differences in timeof day. Each individual lake sampling event wascompleted in approximately one hour.

The FLAMe platform maps the spatial patternof water characteristics. A boat-mounted sam-pling system continuously pumps surface waterfrom the lake to a series of sensors while geo-referencing each measurement (complete descrip-tion of the FLAMe platform in Crawford et al.2015). For this study, the FLAMe was mounted

on a small flat-bottomed boat propelled by anelectric motor and was outfitted with a YSI EXO2multi-parameter sonde (YSI 2015). We focusedfor this study on measures of phycocyanin (a pig-ment unique to cyanobacteria) and temperature.Phycocyanin florescence was measured using theoptical EXO Total Algae PC Smart Sensor. TheTotal Algae PC Smart Sensor was calibrated witha rhodamine solution based on the manufac-turer’s recommendations. Phycocyanin concen-trations are reported as lg/L; however, theseconcentrations should be considered as relativebecause we did not calibrate the sensor to actualphycocyanin nor blue–green algae concentra-tions. Geographic positions were measured usinga Garmin echoMAP 50s (Garmin International,Olathe, Kansas, USA). Sensor data were collectedcontinuously at 1 Hz and linked via timestampto create spatially explicit data for each lake.Each sampling produced approximately 3500measurements in the manipulated lake and 2000in the reference lake. The measurements weredistributed by following a gridded pattern acrossthe entire lake surface to characterize spatial pat-terns over the extent of the lake (Fig. 1).

Statistical analysisPhycocyanin concentration were transformed

to log10(x + 1) units for statistical analysis. Q-Qplots indicated that transformation improved fitto a normal distribution. Reported concentrationsand ranges were back-transformed for ease ofinterpretation; lower bounds included negativesbecause the range of sensor output extends fromslightly negative to positive values. We analyzedthe statistical and spatial properties of phyco-cyanin to calculate proposed EWIs of a cyanobac-terial bloom. Specifically, we were interested inestimates of spatial variance, spatial skewness,frequency of extreme events (as indicated by theshape parameter of the extreme value distributionor EVD-shape), and spatial autocorrelation. Basedon models (Guttal and Jayaprakash 2009, Carpen-ter and Brock 2010, Dakos et al. 2010) and a labo-ratory experiment (Dai et al. 2013), we expectedincreases in spatial variance, skewness (in thepositive direction), and spatial autocorrelationprior to the bloom. In addition, we expected thefrequency of extreme values to increase as themanipulated lake approached a bloom. Extremevalues were assessed using the shape parameter

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of the generalized EVD (Gilleland and Katz 2016).This parameter increases with the frequency andmagnitude of extreme events, assessed relative tothe expectation from the normal distribution.

To check for spurious responses unrelated to acyanobacteria bloom, we compared (1) statisticalproperties of cyanobacteria between the manipu-lated lake and reference lake, (2) years with andwithout fertilization in the manipulated lake,and (3) statistics for cyanobacteria to an abioticvariable, temperature. Temperature patternsshould reflect physical processes that were notdirectly affected by nutrient addition nor biology.Thus, temperature provides an internal referencefor abiotic effects on spatial pattern. Temperaturewas not transformed as it appeared to be nor-mally distributed in Q-Q plots. The referenceecosystem tests the possibility that factorsimpinging on both lakes, such as weather, gener-ated patterns we observed in the manipulatedlake (Carpenter and Kitchell 1993).

High winds could potentially influence advec-tive mixing of the lakes and thus the spatial struc-ture of cyanobacteria. Comparisons between the

reference lake and the manipulated lake are likelyminimally affected by differences in mixing giventhat they were sampled on the same day, are adja-cent to each other, and are of similar size. How-ever, to evaluate possible differences in windbetween sampling dates, wind speeds from anearby tower (3.2 km from the lakes) managedby the National Ecological Observatory Network(http://www.neonscience.org) were analyzed forhigh average wind speeds and gust speeds (aver-age and maximum wind speed over 5-min win-dows) from a 4-h window that immediatelypreceded each day’s sampling.

Data handlingAll data are publicly accessible through the

LTER data repository (Butitta et al. 2017). Allstatistical analyses were computed using R statis-tical software (R Core Team 2016). Aggregatestatistics such as standard deviation (SD), med-ian absolute deviation (MAD), and skewnesswere estimated across the spatial extent of theentire lake. Standard deviation and MAD werecalculated using the “stats” package (R CoreTeam 2016). Skewness was calculated using the“moments” package (Komsta and Novomestky2015). Extreme value distributions were fittedusing the “extRemes” package in R using blockmaxima from bins of 16 consecutive data points(Gilleland and Katz 2016). Bin size is a compro-mise between precision of the block maxima andthe number of bins for fitting the EVD. Extremevalue distribution fits were based on an averageof 200 bins for the manipulated lake and no <100bins for the reference lake.Non-parametric bootstraps of 1000 resamples

were employed to calculate 99% confidence inter-vals for estimates of SD, MAD, skewness, andEVD-shape.Semivariogram models and correlograms were

used to evaluate changes in spatial structuring ofindividual lake variables. For both semivariogramand correlogram analysis, we used the geographicpositions of point measurements. Semivariogramsand correlograms were calculated at approxi-mately 3-m intervals up to a distance of 60 m(approximately half the diameter of the manipu-lated lake). Model semivariograms were fit usingfit.variogram function in the gstat package in R(Pebesma and Graeler 2016), using either an expo-nential or linear model (depending on goodness

Fig. 1. A representative sampling day during the lakemanipulation for both the manipulated lake (N = 4169)and reference lake (N = 2422). Each point represents asampling location (sampling at 1 Hz), and the color ofthe point relates to the phycocyanin concentration.

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of fit) with weighting equal to Nj/(c(hj)2), where Nj

is the number of observations in a distance classand c(hj) is the estimated semivariance at distanceclass hj. These models and parameterization werechosen because they consistently characterizedsample semivariograms well and highly weightobservations that are close in space. Correlogramswere calculated using the correlog function inthe “ncf” package in R (Bjornstad 2016). Standarddeviations for correlograms (Figs. 4, 5) were calcu-lated using 250 random resamples of 80% of obs-ervations from each sampling event. All reportederror terms in the text are SDs.

RESULTS

We successfully initiated a cyanobacterialbloom during the experimental treatment (year 1)in the manipulated lake. Phycocyanin concentra-tions increased three orders of magnitude, reach-ing a peak lake-wide average of 4.8 lg/L on 25–26of June (DOY 176–177; Fig. 2a). After nutrientadditions stopped on 29 June (DOY 180), cyano-bacteria concentrations steadily dropped until 30July (DOY 211), after which they remained similarto the reference lake for the final three weeks ofsampling. We used the date of peak phycocyaninconcentration as the reference date for evaluatingthe spatial indicators, consistent with the interpre-tation of Pace et al. (2017). Phycocyanin concen-trations in the reference lake (median � 1 SD)were 0.0 lg/L (�0.02, 0.02) throughout both yearsof the study (Fig. 2a). In the second year, with nonutrient additions, the manipulated lake hadconsistently low phycocyanin concentrations,0.0 lg/L (�0.07, 0.07). The manipulation thatcaused the cyanobacterial bloom allowed us toexplore possible EWIs at a whole-lake areal scale.Standard deviation and MAD of phycocyanin

had similar temporal and within-treatmentpatterns. Standard deviation and MAD of phyco-cyanin concentrations were consistently low for the

Fig. 2. Early warning statistics of cyanobacteria formanipulated and reference lakes during 2015 (left;with nutrient addition) and 2016 (right; no manipula-tion). For both the polygons and the lines, red and bluecolors represent the manipulated and reference lake,respectively. Vertical gray lines represent the datenutrient addition stopped. Phycocyanin concentrationsare displayed in the top panel (a). Lines are the follow-ing statistics based on phycocyanin: (b) standard devi-ation (SD), (c) median absolute deviation (MAD), (d)skewness, (e) shape parameter of the extreme valuedistribution (EVD-shape), and (f) autocorrelationrange. Dotted gray line at 60 m in panel (f) representsthe range of sample variograms, and estimated ranges

≥60 m were plotted at 60 m (lines jittered to see both).Polygons in panels (b–e) represent 99% confidenceintervals computed from a non-parametric bootstrap.All estimates are based on 13 sampling events over11 weeks in 2015 and three sampling events over asimilar period in 2016.

(Fig. 2. Continued)

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reference lake during both years. In contrast, dur-ing nutrient additions in the manipulated lake, SDand MAD doubled at least one week prior to thecyanobacteria bloom (Fig. 2b, c). During nutrientaddition, SD and MAD generally increased untilnutrient additions halted, after which both quicklyreturned to low levels comparable to the referencelake. In the unfertilized year, SD and MAD in themanipulated lake remained low and were compa-rable to the reference lake. There were no earlywarnings of critical transitions nor discernible dif-ferences in the SD or MAD of temperature betweenthe two lakes in either year (Fig. 3a, b).Cyanobacteria displayed positively skewed

spatial distribution before, during, and shortlyafter the bloom (Fig. 2d). During fertilization,increased skewness of cyanobacteria in themanipulated lake—however variable—wasnoticeably higher than in the reference lake atleast one week prior to the bloom occurring.After nutrient additions halted, skewness in themanipulated lake decreased within a week tolevels comparable to the reference lake andremained consistently low for the rest of the year.Skewness of cyanobacteria in the reference lakewas consistently low during both years of thestudy. The skewness of temperature remainedconsistently low for both lakes which were indis-tinguishable from one another (Fig. 3c).The shape parameter of the EVD was consis-

tently higher for the manipulated lake comparedto the reference lake leading up to the bloom,indicating a greater frequency and magnitude ofextreme phycocyanin concentrations in themanipulated lake during enrichment. After halt-ing nutrient additions, EVD-shape estimatesreturned to low levels comparable with the refer-ence lake within a week (Fig. 2e). There was nodifference in EVD-shape between the two lakesin the year with no cyanobacteria bloom. TheEVD-shape of temperature was similar betweenthe two lakes and showed no relationship to thecyanobacteria bloom (Fig. 3d).Spatial autocorrelation in the reference lake

was consistent and relatively weak throughout

Fig. 3. Early warning statistics of temperature formanipulated and reference lakes during (2015) andafter (2016) manipulation. For both the polygons andthe lines, red and blue colors represent the manipulatedand reference lake, respectively. Vertical gray lines rep-resent the date nutrient addition stopped for reference.Lines are the following statistics based on temperature:(a) standard deviation (SD), (b) median absolute devia-tion (MAD), (c) skewness, (d) shape parameter of theextreme value distribution (EVD-shape), and (e) auto-correlation range. Polygons in panels (a–d) represent99% confidence intervals computed from a non-parametric bootstrap. Dotted gray line at 60 m in panel(e) represents the range of sample variograms, and esti-mated ranges ≥60 m were plotted at 60 m. For 2015data, all spatial temperature measurements were ana-lyzed as deviations from a temperature probe mountedon a stationary central buoy to account for diel changesduring the course of a sampling run (2016 data are not

similarly corrected for lack of high-resolution buoy tem-perature measurements). All estimates are based on 13sampling events over 11 weeks in 2015.

(Fig. 3. Continued)

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the study (mean autocorrelation distance = 8.2 �3.8 m). In the manipulated lake, semivariancemodels showed increased autocorrelation rangesduring nutrient addition (mean = 33.2 � 26 m)compared to baseline phycocyanin concentra-tions in 2016 (mean = 5.1 � 3.6 m; range esti-mates larger than semivariogram fitting wererounded down to the sample semivariogramrange of 60 m; Fig. 2f). Autocorrelation rangeswere variable but generally higher during ele-vated phycocyanin levels. We detected no differ-ences in autocorrelation between the two lakes inthe non-manipulation year. This finding suggeststhat there is no inherent lake-specific differencebetween lakes in spatial patterning with respectto spatial autocorrelation. Also, analysis of auto-correlation of temperature showed no evidenceof changes in the physical mixing between thetwo lakes in the first year that might be used toexplain the changes observed in cyanobacteria(Fig. 3e).

Correlograms depicted detailed spatial pat-terns of cyanobacteria consistent with autocorre-lation range estimates. During nutrient addition,we observed generally higher autocorrelation ofcyanobacteria over a wide range of distances(10–60 m) in the manipulated lake compared tothe reference lake (Fig. 4a). After phycocyaninconcentrations in the manipulated lake returnedto levels comparable to the reference lake, therewere no noticeable differences in autocorrelationbetween the two lakes (Fig. 4b). Similarly, inthe non-manipulation year, autocorrelation ofcyanobacteria was indistinguishable between thetwo lakes (Fig. 4c). Correlogram characteristicsof temperature were consistent between the twolakes and showed no relationship to the timingof cyanobacteria bloom (Fig. 5).

DISCUSSION

We detected spatial EWIs in the experimentallake before the onset of the cyanobacteria bloom.We observed changes in spatial variance, skew-ness, EVD-shape, and autocorrelation distancethat were consistent with expected EWIs of criti-cal transitions between alternative ecosystemstates. On the other hand, autocorrelation dis-tance was often at the maximum value and lessuseful as an early warning. Although the indica-tors differed in sensitivity to the approaching

bloom, these findings show that spatial EWIscould predict an impending regime shift, even ina dynamic fluid environment with patterns thatcould change within hours.

Fig. 4. Correlograms of phycocyanin for manipulated(red) and reference lake (blue) for each sampling date.Data were binned into distance classes of 3 m, anddistance classes over 60 m were omitted. Correlationcoefficients (y-axis) were calculated using Moran’s I. Thecorrelograms for both lakes are shown during the 2015enrichment (top), baseline cyanobacteria concentrationsafter the bloom in 2015 (day of year 205–225; middle),and all dates in 2016 when there was no enrichment. Fourdates (spanning two weeks) that immediately followedhalting nutrient additions in 2015 were omitted from themiddle panel as cyanobacteria concentrations remainedelevated relative to the reference lake. Polygons representone standard deviation around each estimate based on250 random resamples of 80% of each sampling event.

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We found marked increases in spatial SD,MAD, and skewness of cyanobacteria in themanipulated lake as it approached the bloom(Fig. 2). In a spatially heterogeneous situation,exponential growth of cyanobacteria in patchescould generate extremely high concentrations. Weobserved increases in the frequency of extremeevents (EVD-shape) as the manipulated lakeapproached the bloom, likely reflecting these highand patchy cyanobacterial concentrations (Fig. 2).To our knowledge, this is the first study thatshows the potential usefulness of the EVD as anEWI. The high rate of change between samplingdates of some statistics suggests a high sensitivityof the statistical indicators to changes in the spa-tial structure over a few days. Nonetheless, weobserved no discernible differences in any of theEWI statistics in the reference lake in either year.Also, spatial statistics for temperature did notexhibit changes consistent with early warningsand remained similar for the manipulated and ref-erence lakes. Lack of response in the referencelake suggests that responses in the manipulatedlake were the result of enrichment rather thansome regional factor, such as weather, that wouldhave affected both lakes equally. Lack of spatialpattern in temperature suggests that responses ofphycocyanin to enrichment were biological, or acombination of physical and biological processes.Spatial autocorrelation, like temporal autocor-

relation, is expected to increase near critical tran-sitions (Dakos et al. 2010, Dai et al. 2013, Rindiet al. 2017). Correlograms during the period ofenrichment showed that spatial autocorrelationof phycocyanin was higher in the manipulatedlake than in the reference lake at nearly all spatialdistances (Fig. 4). In contrast, correlograms ofphycocyanin were similar in the manipulatedand reference lakes during the unenriched periodof 2015 and all samples from 2016. Correlogramsof temperature were similar in both lakes in bothyears (Fig. 5). These results are consistent withexpected responses near a tipping point (Dakoset al. 2010, Dai et al. 2013). In contrast, autocor-relation range was more ambiguous in relationto nutrient enrichment. Autocorrelation rangesof phycocyanin and temperature were frequentlynear the maximum discernible value (Figs. 2, 3).In this study, at least, autocorrelation range didnot appear to provide consistent early warningsof the cyanobacterial bloom.

Fig. 5. Correlograms of temperature for manipulated(red) and reference lake (blue) for each sampling date.Data were binned into distance classes of 3 m, anddistance classes over 60 m were omitted. Correlationcoefficients (y-axis) were calculated using Moran’s I.The correlograms for both lakes are shown during the2015 enrichment (top), baseline cyanobacteria concen-trations after the bloom in 2015 (day of year 205–225;middle), and all dates in 2016 when there was noenrichment (bottom). For 2015 data, all spatial tempera-ture measurements were analyzed as deviations from atemperature probe mounted on a stationary centralbuoy to account for diel changes during the course of asampling run. 2016 data are not similarly corrected dueto lack of high-resolution buoy temperature measure-ments. Four dates (spanning two weeks) that immedi-ately followed halting nutrient additions were omittedfor direct comparison to Fig. 3. Polygons represent onestandard deviation around each estimate based on 250random resamples of 80% of each sampling event.

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Interestingly, most of the EWI statistics wererelatively higher when transitioning to the bloomcompared to the shift back to low cyanobacteriaconcentrations. This was most notable in SD,MAD, and EVD-shape where the statisticsreturned to low levels (comparable to the refer-ence lake) within days after halting nutrientinputs. In theoretical phytoplankton models,temporal EWIs can differ depending on thedirection of transition between alternative states(Batt et al. 2013). Nutrient addition stopped priorto a critical transition to cycling blooms, but ourresults suggest an asymmetry of spatial EWIssimilar to theory that are related to the directionof the transition. This suggests that our detectionof early warnings is not merely a product of ele-vated phycocyanin concentrations, but is alsorelated to whether the bloom is rising or falling.Thus, the indicators responded differently fromphycocyanin concentration itself.

Spatial EWIs are likely influenced by many dif-ferent factors, including diffusion/advection ratesdue to stochastic processes of wind and othermixing events, population or community interac-tions (e.g., clustered areas of high growth ofcyanobacteria, trophic interactions), or lake-speci-fic characteristics such as hydrology, surfaceshape, and bathymetry (van Nes and Scheffer2005, Serizawa et al. 2008). These factors maycause differences among lakes and dates in theperformance of early warning statistics. Therefore,multiple methods may provide diverse informa-tion, greater rigor, and more insight about charac-teristics of ecosystems near thresholds and thepotential for critical transitions. While our resultsshow that spatial statistics are promising tools forthe study of developing blooms in lakes, furthertesting and comparisons on a wider variety oflake ecosystems are advisable.

The patterns suggestive of approaching thresh-olds in this study could potentially have beenmeasured using remote sensing. The possibilityof using remote sensing to detect changes incyanobacteria at potentially relevant scales forEWIs is appealing (though currently limited bythe availability to accurately differentiatecyanobacteria spectral properties). Future workshould explore the usefulness of remote sensingto detect spatial EWIs in aquatic ecosystems.

This study is the first application of spatialindicators to detect impending blooms of

harmful cyanobacteria in lakes and addresses agrowing call for testing the usefulness of earlywarnings approaches in ecosystems (Schefferet al. 2009, Dakos et al. 2011, 2012). Surprisinglyin the small lakes we considered, many spatialEWIs were detected under the manipulationdespite the potential for physical mixing tohomogenize conditions. We are far from a com-plete understanding of critical transitions in spa-tially structured ecosystems, and the findingspresented here support the need for further testsof these ideas in the field.

ACKNOWLEDGMENTS

Stephen R. Carpenter, Michael L. Pace, VinceL. Butitta, and Emily H. Stanley designed the study,and Vince L. Butitta and Luke C. Loken collected thedata. Vince L. Butitta and Stephen R. Carpenter per-formed the analysis. Vince L. Butitta wrote the firstdraft of the manuscript, and Stephen R. Carpenter,Michael L. Pace, Luke C. Loken, and Emily H. Stanleycontributed significantly to revisions. The authorsdeclare no conflict of interest with production or publi-cation of this work. This work was supported by grantsprovided by the North Temperate Lakes Long TermEcological Research (DEB-1440297), National ScienceFoundation (DEB-1144683, DEB-1144624), and HilldaleProfessorship Research Funds. The authors would liketo thank Anders Uppgaard for helping collect and visu-alize the data and Patrick Dowd for also helping collectthe data. The authors would also like to thank CalBuelo, Grace Wilkinson, and Jason Kurtzweil for fieldsupport. Jon Cole contributed to design of the ecosys-tem experiment. The authors would also like to thankthe Center for Limnology’s Trout Lake Station and theUniversity of Notre Dame’s Environmental ResearchCenter for the use of facilities. Any use of trade, firm, orproduct names is for descriptive purposes only anddoes not imply endorsement by the U.S. Government.

LITERATURE CITED

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