1. Usefulness of Spatial Analysis in predicting Early
Warning Indicators of Regime Shifts in Lakes
Anders Uppgaard
uppgaard@wisc.edu
5/2/16

2. Abstract
Ecosystem tipping points are notoriously hard to predict. Theoretical models have shown that
spatial characteristics of an ecosystem may inform us of an upcoming tipping point before it
occurs, however only a few empirical tests of this idea have been performed. In order to test
these ideas in a complex ecosystem, we induced a tipping point to cyanobacteria dominance in
an experimental lake and mapped spatial characteristics of cyanobacteria using a mobile sensor
platform. We analyzed commonly proposed detection methods for their usefulness in detecting
the tipping point of our manipulated system. Variance based statistics were elevated prior to the
bloom. Spectral reddening was associated with transitions of of a non cyanobacteria dominated
state to a cyanobacteria dominated state. These characteristics are consistent with theoretically
derived characteristics of ecosystems nearing a tipping point. We show that variance based
statistics and spectral analysis of spatial data may be useful in detecting early warning indicators
(EWI). Because of the variability in detecting the approaching tipping point, we suggest that a
suite of detection methods is necessary for accurate EWI detection.
Introduction
Many ecosystems are able to exist in alternative stable states. Ecosystem transitions between
alternative states may exhibit a critical threshold (or a tipping point), which means that at a
certain point, a system may quickly and easily transition to an alternative state which can
severely change or disrupt ecosystem services (Scheffer et al 2009). Humans depend on Earth’s
ecosystems to provide essential resources, and critical transitions that impair ecosystem ability to
provide these resources can threaten human health and wellbeing (Ecosystems and Human Well-
being: General Synthesis)
Because of the catastrophic nature of transitions of these transitions, it may be beneficial to avoid
tipping points in ecosystems altogether. Theoretical, modeling, and recently empirical studies
have shown that simple systems may show common changes in statistical properties of their
spatial structure before a tipping point (often referred to as early warning indicators or EWI)
(Carpenter and Brock 2006). Ecologists have proposed methods to identify whether early
warning indicators are detectable in complex ecosystems as well.
Multiple methods have been proposed to detect EWIs in ecosystems. These include increases in
variance-based statistics such as standard deviation (SD) and median absolute deviation (MAD)
(Carpenter and Brock 2006, Guttal and Jayaprakash 2009). Also, a shift toward lower
frequencies in spectral properties (spectral reddening), has been suggested as an EWI (Carpenter
and Brock 2010).
Until recently, it has been difficult to measure aquatic ecosystems with spatially high resolution
sensing. However, recent developments such as the FLAMe (a mobile sensor platform) has made
it possible to measure spatial water characteristics at fine resolutions. This technology may allow
us to detect spatial EWIs in aquatic ecosystems.
To test the usefulness of spatial EWIs in aquatic ecosystems, we induced a cyanobacteria bloom
in an experimental lake and measured spatial characteristics of cyanobacteria before, during, and
after the bloom. Associated with the transition to cyanobacteria dominance, we predict that SD
and MAD would increase as the bloom approached. Additionally, we hypothesized that spectral
analysis would show a shift toward lower frequencies.

3. Methods
The study took place on two experimental lakes–Peter and Paul Lakes, located in the Northern
Highlands Lake District of the Upper Peninsula of Michigan. Peter Lake (hereafter “manipulated
lake”) received daily nutrient addition consisting of 3 mg P m-3d-1 at molar N:P of 10:1 through
the addition of H3PO4 and NH4NO3. Paul Lake (hereafter “reference lake”) had no nutrient
addition. The addition of nutrients to Peter Lake was done to induce a cyanobacteria bloom.
The lakes were sampled using the FLAMe platform (a mobile, flow-through, sensor platform)
mounted on a flat bottomed boat with a trolling motor (Crawford et al. 2015). The boat was
driven in a loose grid pattern across the entire lake (Figure 1). The lakes were sampled twice a
week on consecutive days from 4 June to 15 August 2015 (11 sample weeks) between 7am-
12pm, before daily nutrients were added. The order of lakes sampled was rotated so that there
was no bias from possible diurnal shifts. Additionally, each lake was sampled for approximately
1 hour for consistency.
The FLAMe platform was outfitted with a YSI EXO2 multi-parameter sonde (EXO2; Yellow
Springs, OH) to measure phycocyanin (a pigment unique to cyanobacteria) and temperature.
Geographic position were measured using a Garmin echoMAP 50s. All sensor-collected data
were collected at 1 Hz and linked via timestamp to create a spatially explicit data set of lake
characteristics (complete description of the FLAMe platform in Crawford et al. 2015).
Data analysis
One sampling event (6/5/15) was thrown out due to obvious sensor drift. On all other sampling
days, all data were used for analysis and phycocyanin were log transformed to more closely
resemble a normal distribution as determined by a QQ plot. For each sampling day, estimates of
SD and MAD were calculated using the data set created that day.
Spectral analysis used a discrete Fourier transform of the time series of each lake’s sampling
event.
Spectral variation statistics were calculated using the average of the area of “red” low frequency
spectrum waves, compared to the average of the area of “blue” high frequency spectral waves.
The cutoff between red and blue frequencies was decided at a frequency of 0.05 (approximately
25 meters). All statistical analysis was done using R statistical software. SD, MAD, and ratios of
spectral variation were calculated “stats” package in R. Spectrum were calculated using the
multitaper package in R (R Core Team (2015)
Results
In the reference lake, phycocyanin concentrations were consistently low during the entire study
(µ = 0.004 +/- 0.03 µg/l). At the peak bloom phycocyanin concentrations in the manipulated
lake reached a lake-wide average of 4.8 µg/l during the 25-26 of June. Phycocyanin
concentrations were elevated in the manipulated lake relative to the reference lake for a total of

4. eight weeks surrounding peak bloom, we refer to this duration as the transition period throughout
the text. The weeks before and after the transition period are referred to as the baseline
conditions of the manipulated lake.
As shown in Figure 1, SD of phycocyanin in the manipulated lake was elevated during the
transition period (µ = 0.048 +/- 0.039 ug/l) compared to the reference lake (p-value = 0.0088, df
= 9), and was also significantly higher than baseline conditions in the manipulated lake (p-value
= 0.0081, df = 9). Variance based statistics for the reference lake were low throughout the entire
study. We also saw consistent changes in median absolute deviation (MAD) (a more
conservative estimate of variance in the data). In Figure 1, MAD of phycocyanin concentrations
during the eight-week transition period (µ = 0.030ug/l +/- 0.02) was significantly higher than
both in the reference lake (p-value = 0.0038, df = 9) and compared to the baseline conditions in
the manipulated lake as well (p-value = 0.0037, df = 9). Figure 2 shows that before and after the
bloom, the reference lake’s spectral pattern was marked by sharp peaks and troughs, When the
bloom occurred, the spectrum smoothed out, and lost its sharp peaks and troughs. Spectral
analysis of the reference lake showed sharp peaks and troughs throughout the entire study, with
no smoothing out, and no elevation of mean spectrum. We saw no changes in spectral properties
of temperature that related to the bloom. Figure 3 shows a ratio of spectral variation, which was
calculated to quantify changes in spectral frequencies during the shift from a non cyanobacteria
dominated state to a cyanobacteria dominated state. In the manipulated lake, red/blue ratio was
elevated compared to the reference lake (p-value = 0.04, df = 9), and was also significantly
higher than baseline conditions in the manipulated lake (p-value = 0.05, df = 9).
Throughout the entire study the reference lake had no significant red/blue ratio changes.
Discussion
Our analysis suggest that spatial EWI are detectable in aquatic ecosystems. We found that
variance based statistics and spectral analysis showed significant differences in bloom and non-
bloom periods. These findings are consistent with other statistical based analysis of regime shifts
(citation). Increases in variance were expected as the system approached the tipping point.
Approaching cyanobacteria blooms, systems become patchy and are characterized by areas of
high or low algae concentrations. Our manipulated system showed these symptoms as the lake
shifted to a cyanobacteria dominated system. Variance increased as the bloom approached, and
decreased quickly after the bloom. This spike in variance supports our understanding of how a
system will behave when experiencing critical slowing down where the system will fluctuate
more widely as it approaches a transition.
Variance characteristics in systems with high physical mixing are likely to be “muffled”
(carpenter and Brock 2010). This may limit the detectability of variance-based EWIs in
ecosystems such as lakes. Unlike variance estimates, spectral analysis focus on spatial
patterning, which may be more sensitive to detecting characteristics we would expect of EWI in
an aquatic system of mixing.
Our manipulated system showed changes in the spectral properties of phycocyanin associated
with bloom formation. However, there was no early indication of the changes in spectral
properties before the bloom. The lateness of the spectral analysis detecting EWI highlights the

5. sensitivity in different EWI detection methods. Spectrum was also applied to lake temperature
data, to ensure that spectral patterns were caused by biological factors rather than non biological
factors. Temperature spectrum did not show any red shifts. This supports that the deviations in
spectral properties for phycocyanin are biological and were not caused by physical, non-
biological drivers. As a system shifts from one stable state to another, its spectral properties are
expected to shift toward lower frequencies. The shift is quantified using a ratio of red (low
frequency) waves to blue (high frequency) waves. As a cyanobacteria bloom occurs, it is
expected to have more of its spectrum in a red, low frequency wave. We saw this shift toward
lower frequencies in the manipulated lake. Before the bloom, there was a noticeable rise in the
amount of spectrum at low frequencies. The red/blue ratio peaked sharply directly before and
after the bloom occurred, and tapered off in the weeks following the bloom (Figure 3).
Throughout the entire study the reference lake had no significant red/blue ratio changes.
Conclusion
We found that spatial EWIs are detectable in ecosystems that are subject to shifting between
stable states due to environmental variability. Detecting EWI signals was variable throughout the
study, highlighting the importance of using a suite of detection methods for real world
applications. Future studies should consider: Are spatial EWIs useful in larger aquatic
ecosystems? Can more frequent spatial sampling allow for a better chance of predicting a regime
shift? Answering these questions would allow us to better understand and predict ecological
regime shifts.

6. FIGURES
Figure 1: Phycocyanin concentrations are indicated by the polygons, with the manipulated lake
shown in red, and the reference lake in blue. The lines correspond to SD (left panel) and MAD
(right panel) over time and follow the same color scheme. As the manipulated lake approaches
the bloom, there is increased SD and MAD. The reference lake does not show these properties.

7. Figure 2: Maps of phycocyanin concentrations and their corresponding spectral signatures. From
left to right: 2 pre-bloom dates, 2 bloom dates, and 2 post-bloom baseline dates. The top panels
show phycocyanin concentrations of the two lakes where light colors correspond with higher
values. The manipulated lake can be seen shifting from non bloom to bloom to non bloom
showing highly elevated spectrum during the cyanobacteria bloom. The reference lake had
consistent spectral properties throughout the entire study.

8. Figure 3: Red/blue ratio of manipulated lake (red) and reference lake (blue). This is a ratio
comparing the integrated values from a discrete Fourier transform of frequencies below 0.05
(“red” frequencies) to frequencies above 0.05 (“blue” frequencies) (high ratio values correspond
to relatively increased variance at broader spatial extents). The reference lake showed consistent
red/blue ratio throughout the entire study, while the manipulated lake showed a red shift
(relatively increasing variance at broader spatial scales) during the transition period to and from
high phycocyanin concentrations.