Early Warnings of Regime Shifts: Evaluation of Spatial Indicators from a Whole-ecosystem Experiment

warnings of regime shifts: evaluation of spatial indicators from a whole-ecosystem experiment. Ecosphere 5(8). 102. Abstract. Critical transitions between alternate ecosystem states are often preceded by increased variance and autocorrelation in time series of ecosystem properties. Analogous changes may occur in spatial statistics as ecosystems approach thresholds for critical transitions. Changes in spatial statistics near thresholds have been described using models, laboratory experiments, and remotely sensed data, but there have been no tests using deliberate manipulations of whole ecosystems in the field. We previously documented a whole-lake manipulation resulting in a transition to predator dominance, a type of critical transition. The food web of an experimental lake was forced via cascading trophic interactions from a stable state characterized by abundant prey fish, small zooplankton, and high chlorophyll concentrations to an alternative state dominated by predatory fish, large zooplankton and low chlorophyll concentrations. Time series of zooplankton and chlorophyll concentrations provided early warning of the regime shift. Here we test if similar early warning signals were present in space by applying spatial variance and the discrete Fourier transform to spatially distributed prey fish catch data from this regime shift. Prey fish spatial distributions were monitored daily using minnow traps deployed around the lake perimeter. Added predators reduced prey fish populations and altered their spatial distributions. Increases in spatial variance and shifts to low frequency spatial variance were observed up to a year in advance of the shift. There was no response in an adjacent reference lake. Our results demonstrate that spatial signals of approaching thresholds can be detected at the ecosystem scale. Copyright: Ó 2014 Cline et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.


INTRODUCTION
Critical transitions between alternative ecosystem states can result in large changes to ecosystems and the services they provide (Scheffer et al. 2001, Folke et al. 2004).Regime shifts are difficult to predict, but theoretical (e.g., Carpenter and Brock 2006, van Nes and Scheffer 2007, Scheffer et al. 2009, Seekell et al. 2011) and experimental (e.g., Ke ´fi et al. 2007, Drake and Griffen 2010, Carpenter et al. 2011, Veraart et al. 2012, Dai et al. 2013) results indicate that certain statistical patterns occur as ecosystem conditions approach critical thresholds.Increasing autocorrelation, rising variance, and conditional heteroskedasticity have been identified in ecological time series prior to simulated and experimental regime shifts (Carpenter et al. 2008, Drake and Griffen 2010, Carpenter et al. 2011, Seekell et al. 2012) as well as paleoclimate time series (Dakos et al. 2008).If these signals are detected far enough in advance, management actions could potentially avert unwanted shifts (Biggs et al. 2009, Contamin and Ellison 2009, Carpenter et al. 2013).
While most research on statistical signals of approaching thresholds has employed ecological time series, spatial dynamics of ecosystems may also reflect approaching thresholds and declining resilience (Ke ´fi et al. 2007, Guttal and Jayaprakash 2009, Ke ´fi et al. 2014).For instance, as shortgrass steppe is exposed to drying climate and increased grazing, patch structure disappears as the ecosystem becomes a desert (Ke ´fi et al. 2007).In marine fisheries, exploited populations have reduced spatial heterogeneity and recover more slowly from climate shocks (Hsieh et al. 2008).Therefore, changes in the spatial characteristics of stressed populations within ecosystems may provide information about stability and proximity to potential thresholds, and may be useful as an early warning signal.
Numerous statistical approaches have been applied to understand critical transitions in spatial patterns.Increasing spatial variance, increasing spatial autocorrelation, shifting spatial skewness, and shifts to low frequency spatial variance have been observed prior to simulated regime shifts in stochastic models of spatially coupled ecosystems (Guttal and Jayaprakash 2009, Carpenter and Brock 2010, Dakos et al. 2010, Dakos et al. 2011).Spatial indicators of approaching thresholds may have many applications in ecology because spatial information may, in some cases, be more accessible than detailed time series.Spatial indicators can be computed from observations of many spatial sites but on relatively few occasions in time (Guttal and Jayaprakash 2009).Additionally, the spatial observations need not be equally spaced through time, unlike requirements for many time series statistics (Bestelmeyer et al. 2011).Highresolution spatial data are widely available from remote sensing platforms making spatial indicators a potentially powerful tool for detecting changes as ecosystems approach critical thresholds.
Previous tests of spatial indicators for approaching thresholds have generated mixed results.Ke ´fi et al. (2007) found that power-law patch size distributions in semi-arid grasslands break down prior to transitions to desert.Drake and Griffen (2010) found clear signals in time series but not in spatial autocorrelation prior to experimentally induced extinctions of laboratory populations of the crustacean, Daphnia magna.In contrast, Dai et al. (2013) found clear spatial indicators preceding collapse of stressed yeast populations in a laboratory array.In marine food webs, Litzow et al. (2008) found increases in spatial variance in the ratio of predator to prey fish prior to a transitions induced by overfishing in the Gulf of Alaska and the Scotian Shelf, but acknowledged that the observed changes in variance could be due to several factors.Hence, spatial indicators may have important applications, but there continues to be a need to evaluate spatial early warning indicators at scales relevant to ecosystem managment.
We previously reported an experimentally induced critical transition in the food-web of a small lake (Carpenter et al. 2011, Pace et al. 2013, Seekell et al. 2013).We added top predators to an ecosystem dominated by prey fish to reduce planktivory and induce a trophic cascade, thereby restructuring the zooplankton community and altering phytoplankton concentrations (Carpenter et al. 2011).There was strong evidence for a critical transition in the manipulated system with no evidence for change in an adjacent reference system (Carpenter et al. 2011, Seekell et al. 2012, Seekell et al. 2013), consistent with expectations from a model based on long-term data from the experimental lake and nearby lakes (Carpenter et al. 2008).Changes in the fish community were associated with shifts to larger bodied species of Daphnia (Pace et al. 2013) and reduced chlorophyll concentrations (Carpenter et al. 2011).Prior to the regime shift, we found early warning signals (e.g., increased autocorrelation, increased variance, and significant conditional heteroskedasticity) in time series of chlorophyll, pH, dissolved oxygen, and zooplankton (Carpenter et al. 2011, Seekell et al. 2012, Batt et al. 2013, Pace et al. 2013).These results provide robust evidence for early warning of critical thresholds using time series.In this study we examine prey fish spatial distributions for evidence of the approaching threshold, and in doing so test for spatial indicators of critical transition using this deliberate ecosystem-scale manipulation.We tested if increased spatial variance and shifts to low frequency variance in space were present in the manipulated system prior to the transition, with no similar signals in an adjacent reference system.

METHODS
Study sites and trophic structure.-PeterLake and Paul Lake (89832 0 W, 46813 0 N) are small, deep, oligotrophic lakes located at the University of Notre Dame Environmental Research Center in Michigan's upper peninsula near Land O'Lakes, Wisconsin.The lakes are separated by an earthen dike and Paul Lake is upstream of Peter Lake.The lakes have similar physical and chemical characteristics.A detailed description of both systems can be found in Carpenter and Kitchell (1993).
Prior to the study, the fish community in the manipulated system (Peter Lake) was composed of a diversity of small bodied prey fish including pumpkinseed Lepomis gibbosus, golden shiner Notemigonus crysoleucas, fathead minnow Pimephales promelas, dace Phoxinus spp., brook stickleback Culaea inconstans, and central mudminnow Umbra limi.We refer to these species collectively as planktivores while recognizing they are omnivorous, feeding mainly on a variety of benthic and pelagic invertebrates.Pumpkinseed dominated the fish community both numerically and by biomass.Also present was a small population (n , 40) of piscivorous adult (.150 mm) largemouth bass Micropterus salmoides.We refer to adult M. salmoides as piscivores, while recognizing they are omnivorous, because they feed preferentially on the prey fish noted above.
The fish community in the reference system (Paul Lake) was dominated by largemouth bass (.95% of total fish biomass).There were small populations of prey fishes including L. gibbosus, Phoxinus spp., and U. limi.
Experimental manipulation and monitoring.-Foodwebs with these trophic structures are known to take two alternative states, dominated by either predators or prey fish (Carpenter et al. 2008).In a predator-dominated state, adult predators reinforce their control through direct predation on prey fish that compete with juvenile predators (Walters andKitchell 2001, Carpenter et al. 2008).This encourages recruitment of juvenile predators into the adult predator population, promoting predator dominance.In a prey fish-dominated state, small numbers of predators cannot control prey fish abundance.Prey fish compete with juvenile predators for food but may also consume predator eggs and fry preventing juvenile predators from recruiting into the adult population.These feedbacks reinforce prey fish dominance.
We added adult largemouth bass to change Peter Lake from a state of prey fish dominance to a state of predator dominance.The threshold population of largemouth bass required to trigger a regime shift and transition the system to predator dominance was unknown, therefore; largemouth bass were added slowly to maximize the potential to test for early warning indicators.First, we added 1200 golden shiners on 28 May 2008 to reinforce the initial state of prey fish dominance and extend the transition long enough to assess indicators of declining resilience.Then we added 12 adult largemouth bass on 7 July 2008, 15 adult largemouth bass on 18 June 2009, and 15 adult largemouth bass on 21 July of 2009 to induce the shift to predator dominance.These additions resulted in a decline in prey fish abundance and changes in prey fish behavior, reducing competition for food and predation risk on juvenile predators by prey fish.As a consequence, largemouth bass produced a large year class in 2009 and many of these offspring survived the following winter to recruit into the adult largemouth bass population in 2010.The transition to predator dominance in Peter Lake was largely complete by the second half of the summer season of 2010 and the lake appeared to stabilize in this new state in 2011.We added an additional 32 adult largemouth bass after the transition on 23 June 2011 to reinforce the predator-dominated state (see Seekell et al. 2013).
We estimated fish densities in mid May and late August in each lake for the period of 2008-2011 (except for late August of 2008).We used Schnabel mark-recapture estimates (Schnabel 1938) with a variety of sampling gear (boat electrofishing and minnow traps for prey fish; boat electrofishing and angling for predators).Prey fish were also monitored daily through a spatially distributed set of minnow traps (6-mm mesh with standardized 25-cm openings) deployed about 45 m apart along the edge of the lake.Thirty traps were deployed in the manipulated system and 20 traps in the reference system (except in 2008 when 10 traps were used in the reference system).All traps were placed adjacent to shore in ,1 m of water.Traps were emptied and captured fish were enumerated by species between 10:00 and 13:00 daily from mid-May to early September 2008 to 2011.
Statistical analysis.-Meanfish catch and variance in fish catch are strongly related (cf.Thompson 1976).Here we are most interested in variance in trap catch arising from usage of spatial sites.Consequently, we standardized prey fish catch-per-trap-day to the prey fish abundance in the lake to remove dynamics in trap catch that may be related to changes in biomass alone.Daily population estimates were computed by linear interpolation from the independent mark-recapture estimates measured in the spring and the fall of each year.We used these daily abundance estimates to standardize catch-perday (CPUE) to catch-per-day-per-thousand minnows (Standardized CPUE) for each trap (note effort is one day).This procedure minimizes variability due to changing fish biomass and increases the potential for identifying early warning indicators driven by animal responses to predation risk.All statistics were applied to these standardized data.All statistical programming and analysis was performed in R (R Development Core Team 2013).
We calculated spatial variance (Oborny et al. 2005, Guttal andJayaprakash 2009) of minnow trap standardized CPUE.Spatial variance is expected to increase prior to a regime shift and should be relatively small in a stable system (Guttal and Jayaprakash 2009).We applied this statisitic to 28-day moving window where each day's computation includes that day's catch from all spatial sites and the catch from all spatial sites of the previous 27 days (e.g., one window has 28 days of 30 spatial sites; 840 total values).Varying the window length did not change our conclusions (see discussion).
We calculated the discrete Fourier transform (DFT) to measure shifts in the frequency and magnitude of spatial variance.The DFT decomposes variance into separate frequencies (Carpenter and Brock 2010).The DFT results in complex numbers, which relate to magnitude and phase of the signals.The DFT ordinate (or amplitude) was measured as the distance from the origin, in the complex plane.We plotted frequencies calculated as the natural logarithm of 1/n, 2/n, . . ., 1/2, where n is the number of spatial sites.DFT ordinates were included from k where k is the index of the Fourier transformed spatial vector.We applied this statistic using a 28-day rolling window where individual trap catches were summed across time within the window before the DFT was calculated.The values used to calculate the spatial metric were the sum of that day's catch and the previous 27 days' catch for each trap, still resulting in 30 spatial sites.This approach minimizes short-term fluctuations associated with environmental changes such as weather and short-term behavioral changes such as spawning while capturing the characteristic temporal scale of variability of an impending regime shift.A warning signal would be evident in increased DFT ordinates (variance) especially at low frequencies (Carpenter and Brock 2010).The DFT was computed using the 'fft' function in R.
We assessed the strength of the shift to low frequency spatial variance by comparing DFT ordinates with expectations from a null model of white noise.Normal white noise with variance r 2 has a periodogram (DFT ordinates vs. frequency) that is flat (i.e., no frequency dominates the variance).Twice the periodogram ordinates divided by r 2 are chi-square distributed with two degrees of freedom (Hinich 1982).We divided twice the periodogram ordinates computed from the observed data by the variance in the data for each moving window.We then calculated the probability of each peak being greater than or equal to the observed value using a chi-square distribution with two degrees of freedom.A shift to low frequency variance would be pronounced by periodogram peaks much larger (low probability) than expected given the null model.

RESULTS
As a result of largemouth bass additions and natural reproduction, predator abundance in the manipulated lake increased from about 40 adults in 2008 to more than 140 in 2011.Prey fish abundance declined from more than 13,000 to less than 2,500 (Fig. 1).Predator populations in the reference lake ranged from about 191 to 314, 2-3 times the densities seen in the manipulated system.Prey fish populations in the reference lake were consistent through time ranging from 338 to 850.Populations in the manipulated system converged to the reference system by the end of 2011 (Fig. 1).
Prey fish CPUE in the manipulated lake was high in early 2008 then declined after the initial predator addition (Fig. 2a).Throughout 2009 and 2010, CPUE fluctuated between periods of high catch and low catch before declining to near zero in 2011 (Fig. 2b, c, d).The decline in prey fish catch to near zero after day 230 of 2010 closely followed the critical transition, which occurred between days 210 and 230 (Carpenter et al. 2011, Batt et al. 2013, Carpenter et al. 2013).Standardized CPUE was variable early in 2008 but declined and became less variable after the first predator addition (Fig. 2e).There was a general increasing trend in standardized CPUE through 2009 and the first half of 2010 punctuated by oscillatory dynamics.Standardized catch declined sharply after day 200 of 2010 just prior to the critical transition (Fig. 2f, g).Standardized CPUE remained low through 2011, except for four days in early spring due to spawning aggregations (Fig. 2h).In the reference system, CPUE and standardized CPUE were consistently low throughout the experiment (Fig. 2).Prey fish CPUE and standardized CPUE in the manipulated and reference systems were similar at the end of 2010 and the majority of 2011 (Fig. 2).
The spatial distribution of prey fish catch changed from fairly uniform to more aggregated as the manipulation proceeded (Fig. 3).In 2008, the distribution of catch was even in space and time, with most sites characterized by moderate catch values.Through 2009 and 2010 as the ecosystem moved toward the regime shift, catch become patchy in space and time with only a few sites constituting the majority of catch.In the final year, a short period of high catch was distributed over a large proportion of sites.For most of the final year, low catch was common at all sampling locations.The spatial distribution of prey fish catch in the reference lake was even and there were no general patterns or distinct changes throughout the experiment (Appendix: Fig. A1).
Spatial variance of standardized CPUE was low through the first year of the manipulation (Fig. 4a).Around day 200 of 2009, variance spiked, increasing almost three fold (Fig. 4b).Spatial variance in 2010 was high, more than four times the base line variance in 2008, and reached its highest value just prior to the critical transition around day 210 of 2010.In 2011, spatial variance was generally low with the exception of a strong peak around the spawning period (Fig. 4d).Spatial variance in the reference lake was generally low in all years of the experiment (Fig. 4).
Prey fish did not show strong aggregation (shoaling) in 2008, signified by low DFT variance  v www.esajournals.orgshort period of moderate clustering (light blues), and was most pronounced in mid frequencies (Fig. 5d).There was a clear shift of spatial variance toward low frequencies prior to the regime shift signified by highly unlikely spectral peaks (Fig. 5e-h).Shoaling was largely absent (cool colors) throughout the remainder of the experiment.DFT variance across all frequencies was low in the reference system and there were no persistent low probability spectral peaks throughout the study (Appendix: Fig. A2).

DISCUSSION
The manipulated lake crossed a threshold from prey fish dominance to predator dominance (Carpenter et al. 2011, Seekell et al. 2013).This transition was clearly evident through changes in prey fish biomass and shifting prey fish spatial distributions.Clear statistical changes were observed in spatial data more than a year in advance of the critical transition.Changing prey fish spatial distributions increased spatial variance prior to the regime shift in 2010 (Fig. 4).These signals were most strongly pronounced in shifts to low frequency variance (Fig. 5).The dynamics observed in the manipulated system contrast with the stable prey fish spatial distributions seen in the reference system (Fig. 4 and Appendix: Fig. A2).These spatial statistics signaled declining ecosystem resilience in the experimental lake.
Spatial patterns observed in this study may arise from complex tradeoffs between predation risk and competition from conspecifics.Minnow trap catch is a function of both prey fish biomass and habitat choice (cf.Dupuch et al. 2011).Sampling locations in this study varied in their habitat characteristics from open shoreline to thick woody debris, each offering differing levels of refuge.Increased predation pressure from predator additions directly reduced prey fish biomass but also forced prey fish from open water habitats into near shore refuge.This is evident in an increase in standardized-CPUE as the system approached the threshold (Fig. 2f, g).We also observed small-scale shifts in habitat usage.Prior to the manipulation, low predation created widespread low risk habitat and prey fish were more evenly spread across sites (Fig. 3; 2008).When predation increased, low refuge sites were abandoned (e.g., sites 12-16, Fig. 3).Shoaling and use of only high refuge sites are reflected in high catch rates at limited sampling locations (e.g., sites 1-4, 19-23, Fig. 3).There were no changes in habitat in this experiment.The emergence of prey fish patchiness in the manipulated system was due to predation levels approaching a critical threshold.These changes increased spatial variance and shifted variance to v www.esajournals.orglow frequencies as the ecosystem approached the critical transition.This shift to low frequencies provides an example of a general mechanism of spatial slowing down (Ke ´fi et al. 2014).
Previous research has evaluated early warning signals in space for ecosystems that were not manipulated deliberately.Spatial sampling prior to a marine food web transitions noted increased coefficients of variation but other factors could have affected the variance (Litzow et al. 2008).In our study, the experimental manipulation deliberately reduced resilience, which is expected to increase variance.In addition, we corrected for mean-variance relationships by standardizing the catch data by the abundance estimates.The observed changes in spatial variance corresponded with the timing of the critical transition as estimated using diverse analyses of independent time series (Carpenter et al. 2011, Batt et al. 2013, Carpenter et al. 2013, Seekell et al. 2013).Shifts in v www.esajournals.orgspatial variance in our study were associated with shifts toward lower frequencies in space, as expected for critical transitions but not for other causes of spatial variance (Carpenter and Brock 2010).Finally, we noted no changes in spatial variance or the DFT in the reference lake, indicating that regional drivers that affected both lakes (such as weather) are not likely explanations of the changes observed in the manipulated lake.
A challenge for early warning indicators is evaluating the strength of signals (Seekell et al. 2011, Dakos et al. 2012, Ke ´fi et al. 2014).Here we applied a probability-based approach to help assess the magnitude of a shift to low frequency variance (spectral reddening).As the system approached the tipping point, spectral density peaks at low frequencies become extremely unlikely (probabilities , 0.001; Fig. 5).A small number of spectral peaks early in the manipulated system and in the reference system also exhibit low probability values (probability ; 0.05), but this is expected based on chance alone (Fig. 5 and Appendix: Fig. A2).Importantly, this test incorporates the overall change in variance and therefore offers an auxiliary line of evidence.
In this experiment we used a reference ecosystem as a baseline with which to compare changes in indicators, but not all studies have this luxury.Other methods for comparing the magnitude of changes in variance are using longterm observations to establish expectations for reasonable patterns in variance.Most importantly using multiple lines of inference can help rule out spurious signals (e.g., evaluating changes in spatial variance together with a shifts to low frequency variance).Here, we combined premanipulation measurements, information from the reference system, multiple indicators, and a probability based approach to demonstrate compelling spatial early warning signals of the approaching tipping point.
Not all proposed early warning tools provide consistent signals of tipping points in all systems (Ke ´fi et al. 2014).A commonly applied metric for detecting regime shifts in space is spatial correlation (Dakos et al. 2010).We applied spatial correlation (data not shown), but the results were difficult to interpret and this metric was not a consistent indicator of the impending transition in this ecosystem.In some ecosystem models, transfers or flows of populations or nutrients can muffle statistical signals of approaching thresholds (Carpenter andBrock 2010, Dakos et al. 2011).Strong changes in one patch may be mediated by flows to or from adjacent patches, potentially reducing variance.Connectivity is essential to produce spatial correlation (Dakos et al. 2010).In this ecosystem, while shoaling and restricted habitat use may increase correlation among a few sites, habitat contrasts between neighboring sites prevented diffusion into adjacent sites and created mixed responses of spatial correlation.Further research is needed to understand how different spatial indicators perform among a variety of ecosystems and resilience conditions.
An important consideration for applying early warning signals is the spatial and temporal scale of sampling.In spatial systems some sites may shift earlier or later than average (Dakos et al. 2010).For example, in this experiment, low refuge sites were abandoned early and therefore time series methods applied to this site alone would yield few early warning signals.Thus adequately monitoring at the spatial scale of the critical transition and capturing a representative set of the heterogeneity is important for observing early warning signals.Issues of temporal scale are also important.Here we used highresolution sampling, which generates a substantial amount of data and this allowed us to apply a 28-day temporal moving window.Moving windows provide several key benefits.First, many early warning indicators including the DFT can be sensitive to zero values.Here, a moving window allowed us to incorporate zero catch days yet still capture the critical dynamics of the system.Second, the key observations of an approaching tipping point are slow moving dynamics occurring at low frequencies.Longer windows allowed us to reduce spurious signals created by high-frequency variability in time.While longer windows may create more consistent and easily interpretable signals, the tradeoff is sensitivity of the indicator to change.
Tools for detecting early warning signals are developing rapidly in both time and space (Dakos et al. 2012).Methods now range from variance (Carpenter and Brock 2006) and autocorrelation (Dakos et al. 2010) to more complex tests for conditional heteroskedasticity (Seekell et v www.esajournals.org al. 2011) as well as model-based methods (Dakos et al. 2012).From this manipulation we have now evaluated the efficacy of several temporal (Carpenter et al. 2011, Seekell et al. 2012, Batt et al. 2013, Pace et al. 2013) and spatial indicators.Signals were detected in both time and space more than a year in advance of the transition.Time series methods were effective using single site measurements for well-mixed pelagic phytoplankton and zooplankton (Carpenter et al. 2011, Batt et al. 2013, Pace et al. 2013).Indicators computed across space (this study) and for aggregates of many spatial sites in time (Seekell et al. 2012) captured early warning signals in mobile and heterogeneously distributed prey fish.However, all of these indicators require many data points that can be expensive and time consuming to collect especially for mobile consumers like fish.Spatial indicators offer a potential advantage as data that are richly detailed in space and cover spatially extensive ecosystems can often be collected by remote sensing.Automated measures and remote sensing will play a critical role in expanding understanding of critical transitions and exploring applications to management.
Spatial indicators may provide important information about nearby thresholds, and could perhaps be used to prevent catastrophic loss of ecosystem services.These tools have proven effective in ecosystem model simulations (Dakos et al. 2010, Carpenter andBrock 2010) and controlled laboratory settings (Dai et al. 2013).Nonetheless, as research on indicators of critical transitions evolves both the limitations and opportunities will become more clearly defined (Boettiger et al. 2013).Further research is needed to evaluate spatial signals of ecosystem thresholds and their strengths and limitations under field conditions.Based on our results spatial early warning signals can be observed in a real ecosystem subject to significant environmental variability and measurement error.This is a critical step toward expanded use of these approaches in research and management.

Fig. 1 .
Fig. 1.Change in prey fish (circles) and predator (squares) abundance in Peter and Paul Lakes from 2008 to 2011.Peter Lake population estimates are in black and Paul Lake estimates are in gray.Estimates taken from mark-recapture surveys in late May and August of 2008-2011 (see Methods).Error bars represent 95% confidence intervals computed from the Schnabel multiple mark-recapture method.Confidence intervals on predator abundance in the manipulated lake cannot be computed due to low population densities.

Fig. 3 .
Fig. 3. Spatial distribution of ln-standardized daily prey fish catch in minnow traps along the lake edge in Peter Lake (manipulated system) between 2008 and 2011.Each circular plot is the spatial distribution of catch within an individual year.Each segment of a circle represents an individual trap location located along the lake perimeter.The color scale indicates daily ln-standardized catch.Daily measurements through time at each location proceed along each segment from the perimeter toward the center of the circle.Dashed circles indicate dates of predator additions.As the system approaches the regime shift prey fish catch should become patchier in space and time.

Fig. 4 .
Fig. 4. Spatial variance (a-d) computed from standardized trap catch values for all spatial sites over 28-day moving windows in Peter (black) and Paul (gray) lakes from 2008 to 2011.Vertical dashed lines indicate predator additions.Increasing variance would signal an impending regime shift.The critical transition occurred around day 230 in 2010 (Seekell et al. 2013).

Fig. 5 .
Fig. 5. (a-e) Discrete Fourier transform (DFT) of prey fish spatial catch distributions in Peter Lake 2008-2011.Standardized catch from each site is summed across a 28-day moving window before the DFT is computed.The color corresponds to the amplitude of a signal at each particular frequency.(e-h) The probability of observing a spectral peak that large or greater given a null hypothesis of normal white noise (see Methods).The color bar indicates significance thresholds not continuous probability values.High DFT amplitudes, especially at low frequencies, would signal an impending regime shift.Vertical dashed lines indicate predator additions.The critical transition occurred around day 230 in 2010 (Seekell et al. 2013).
Fig. A1.Spatial distribution of ln-standardized daily prey fish catch in minnow traps along the lake edge in Paul Lake (reference system) between 2008 and 2011.Each circular plot is the spatial distribution of catch within an individual year.Each segment of a circle represents an individual trap location located along the lake perimeter.The color scale indicates daily ln-standardized catch.Daily measurements through time at each location proceed along each segment toward the center of the circle.Note that there are only 10 sampling sites in 2008 and 20 in the other three years.

Fig
Fig. A2.(a-e) Discrete Fourier transform (DFT) of prey fish spatial catch distributions for Paul Lake 2008-2011.Standardized catch from each site is summed across a 28-day moving window before the DFT is computed.The color corresponds to the amplitude of a signal at each particular frequency.(e-h) The probability of observing a spectral peak that large or greater given a null hypothesis of normal white noise (see Methods).The color bar indicates significance thresholds not continuous probability values.Note that there are only 10 sampling sites in 2008 and 20 in the other three years.Note that the color ramp for this reference lake figure is almost an order of magnitude less than the manipulated system.