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Papers in Natural Resources Natural Resources, School of
2021
Panarchy and management of lake ecosystems Panarchy and management of lake ecosystems
D. Angeler
C. Allen
University of Nebraska - Lincoln
A. Garmestani
L. Gunderson
R. Johnson
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Angeler, D.; Allen, C.; Garmestani, A.; Gunderson, L.; and Johnson, R., "Panarchy and management of lake
ecosystems" (2021).
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Angeler, D. G., C. R. Allen, A. Garmestani, L. Gunderson, and R. K. Johnson. 2021. Panarchy and management of lake ecosystems.
Ecology and Society 26(4):7. https://doi.org/10.5751/ES-12690-260407
Research, part of a Special Feature on Panarchy: the Metaphor, the Theory, the Challenges, and the Road Ahead
Panarchy and management of lake ecosystems
David G. Angeler 1, Craig R. Allen 2, Ahjond Garmestani 3,4, Lance Gunderson 5 and Richard K. Johnson 1
ABSTRACT. A key challenge of the Anthropocene is to confront the dynamic complexity of systems of people and nature to guide
robust interventions and adaptations across spatiotemporal scales. Panarchy, a concept rooted in resilience theory, accounts for this
complexity, having at its core multiscale organization, interconnectedness of scales, and dynamic system structure at each scale. Despite
the increasing use of panarchy in sustainability research, quantitative tests of its premises are scarce, particularly as they pertain to
management consequences in ecosystems. In this study we compared the physicochemical environment of managed (limed) and
minimally disturbed reference lakes and used time series modeling and correlation analyses to test the premises of panarchy theory:
(1) that both lake types show dynamic structure at multiple temporal scales, (2) that this structure differs between lake types due to
liming interacting with the natural disturbance regime of lakes, and (3) that liming manifests across temporal scales due to cross-scale
connectivity. Hypotheses 1 and 3 were verified whereas support for hypothesis 2 was ambiguous. The literature suggests that liming is
a “command-and-control” management form that fails to foster self-organization manifested in lakes returning to pre-liming conditions
once management is ceased. In this context, our results suggest that redundance of liming footprints across scales, a feature contributing
to resilience, in the physicochemical environment alone may not be enough to create a self-organizing limed lake regime. Further research
studying the broader biophysical lake environment, including ecological communities of pelagic and benthic habitats, will contribute
to a better understanding of managed lake panarchies. Such insight may further our knowledge of ecosystem management in general
and of limed lakes in particular.
Key Words: cross-scale; lakes; liming; management; panarchy; resilience; time series modeling
INTRODUCTION
The biophysical environment is hierarchically structured and
dynamically changing (Allen et al. 2014). Theories have been
developed that have this complexity at their core and that are
crucial for understanding the resilience of complex systems of
people and nature in times of rapid social-ecological change. For
example, panarchy theory, a branch of complexity science
incorporating resilience, accounts for the multiscale organization,
interconnectedness of scales, and dynamic system structure in
social-ecological systems (Gunderson and Holling 2002).
Panarchy captures the cross-scale structure envisioned in
hierarchy theory (Allen and Starr 1982) and acknowledges the
transmission of information (matter, energy) not only from higher
to lower scales (top–down processes) but also from lower to higher
levels (bottom–up effects) in complex systems (Carpenter 1988).
Such organization is ubiquitous and observed, for instance, in
lake food webs, regional ecosystem management, and the global
climate (Power 1992, Angeler et al. 2016, Garmestani et al. 2020).
Panarchy recognizes extrinsic and intrinsic factors that influence,
and are influenced by, interrelated phenomena such as innovation,
novelty, and regime shifts in social-ecological systems (Allen et
al. 2014). Panarchy therefore is critical for providing a holistic
view, and informing, ecosystem management (Garmestani et al.
2020). Ecosystem management is often unsuccessful at emulating
natural disturbance regimes constrained by the overwhelming
complexity inherent in systems of people and nature (Mori 2011).
Such shortcomings of ecosystem management have been recently
discussed in the context of coerced regimes (Angeler et al. 2020),
which are social-ecosystem states that are not self-organizing but
exclusively maintained by management to facilitate the
production of selected ecosystem services. Coerced regimes thus
only mimic desired system regimes through management but
either shift or revert to an undesired regime with limited provision
of services once management is ceased.
Lake liming as a management form fits the notion of coerced
regimes since, as suggested in the literature, lakes fall back into a
pervasive pre-liming regime when liming is discontinued (e.g.,
Clair and Hindar 2005). Liming is a management intervention
for lakes, streams, wetlands and their catchments intended to
counteract the effects of anthropogenic acidification, a major
environmental problem during the industrial epoch in eastern
North America and northern Europe (e.g., Wright et al. 1976,
Schindler 1988, Henriksson and Brodin 1995, Bradley and
Ormerod 2002). Liming consists of the application of limestone
sand or powder to mitigate acidification impact in the abiotic (low
pH, aluminum toxicity) and biotic (biodiversity and ecosystem
service loss) environment.
Many countries implemented large-scale liming projects
(Henriksson and Brodin 1995, Sandøy and Romunstad 1995) to
facilitate the recovery of acid-sensitive biota, protect and enhance
existing fish populations, and maintain aquaculture and
recreational fishing (Appelberg and Svensson 2001). Although
some positive outcomes of liming have been reported (Eriksson
et al. 1983, Hasselrot and Hultberg 1984, Nyberg et al. 1986,
Henriksson and Brodin 1995), reviews show that overall liming
effects have been equivocal (Clair and Hindar 2005, Ormerod and
Durance 2009, Mant et al. 2013) and often confounded by abiotic,
ecological, and historical factors. These factors include episodic
fluctuations in water chemistry caused by recurring liming and
re-acidification events, limited dispersal of organisms, habitat
characteristics, and altered food webs (Yan et al. 2003, Binks et
al. 2005, Lau et al. 2017). These results suggest that the
effectiveness of liming is riddled with spurious certitude (Bishop
et al. 2001, McKie et al. 2006, Angeler and Goedkoop 2010).
1Swedish University of Agricultural Sciences, Department of Aquatic Sciences and Assessment, 2University of Nebraska-Lincoln, Center for
Resilience in Agricultural Working Landscapes, School of Natural Resources, 3United States Environmental Protection Agency, Office of Research
and Development, 4Utrecht Centre for Water, Oceans and Sustainability Law, 5Department of Environmental Sciences, Emory University
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Limed ecosystems provide opportunities to study coerced regimes
from a panarchy perspective. There have been diverse and
successful applications of panarchy in social and ecological
systems, predominately in metaphorical discourse and qualitative
analyses (Berkes and Ross 2016, DeWitte et al. 2017, Wilcox et
al. 2019) that have informed vulnerability and risk assessments
(Angeler et al. 2016) and ecosystem management (Garmestani et
al. 2020). However, panarchy offers more than a heuristic for
qualitative research (Sundstrom and Allen 2019); it also allows
for empirical analyses. We used time series modeling of the
physicochemical environment of limed lakes and unmanaged,
minimally disturbed reference lakes (sensu Stoddard et al. 2006)
to infer scale-specific temporal patterns, indicative of hierarchical
structuring over time, in individual lakes (Baho et al. 2015).
Specifically, panarchy describes hierarchical and dynamic system
change, portrayed as a nested set of adaptive cycles (Gunderson
and Holling 2002). Such dynamic system change in lakes can be
exemplified with, for instance, fast (e.g., diurnal fluctuation of
temperature), slower intra-annual (plankton seasonality), and
more gradual, inter-annual patterns (lake browning). Such
patterns are expected to be detected by time series modeling
because many boreal lakes have experienced a monotonic
decrease of total phosphorus and an increase of dissolved organic
carbon since the early 1990s due to catchment processes related
to changes in climate, catchment soil properties, and recovery
from acidification (i.e., slow, gradual dynamic; Huser et al. 2018).
Such decadal patterns of monotonic change are uncoupled from,
for example, seasonal change, which is manifested in variables
such as water temperature and oxygen concentration (e.g., faster
intermediate temporal dynamics). Also, more complex patterns
of combined inter- and intra-annual variability during specific
cycles can be observed (Baho et al. 2015), which shows that
biophysical dynamics in lakes are more complex relative to the
simplified adaptive cycle dynamics invoked by the panarchy
heuristic. That is, in addition to hierarchical temporal structuring
(scales), orthogonal (statistically independent) patterns of
temporal change within defined cycles can be revealed by our time
series models (Legendre and Gauthier 2014). More generally,
temporal structure of the abiotic environment in individual lakes
can integrate and thus arise from environmental processes, which
are themselves structured at, and interacting across, different
spatiotemporal scales in catchments (e.g., Strahler 1964, Soranno
et al. 2014).
Studying the abiotic environment is deemed especially suitable
given the strong and direct physicochemical footprints of liming
in freshwater ecosystems. Panarchy theory allows formulating
hypotheses for individual premises that can be empirically tested.
This is useful for studying liming from a complex systems
perspective, which can further our knowledge of the resilience of
aquatic ecosystems (Pelletier et al. 2020). Panarchy theory holds
the potential to answer lingering questions about the interactions
of natural and anthropogenic/management disturbances and
provide information about the magnitude and scale-specificity of
recurrent liming impacts on the abiotic lake environment. We
tested the following hypotheses:
1. In accordance with previous studies (Angeler et al. 2011,
Baho et al. 2015), we hypothesized that distinct hierarchical
and orthogonal temporal patterns of the physicochemical
environment manifest within individual lakes. Verifying this
hypothesis is essential to test the premise of panarchy theory
that complex systems dynamics are compartmentalized.
2. Following the first hypothesis, and given the alteration of
natural disturbance regimes by liming (Bishop et al. 2001,
McKie et al. 2006), we postulated that the hierarchical and
orthogonal temporal patterns of physicochemical variables
differ between limed and reference lakes. Verifying this
hypothesis will allow testing the premise of dynamic system
change of panarchy theory, and whether management, as
opposed to natural dynamics, can alter such patterns.
3. We further hypothesized that, in order to verify the aspect
of linked scales of panarchy, the impacts of liming will be
manifest across modeled hierarchical and orthogonal
temporal dimensions in the lakes. We used Ca:Mg ratios as
a surrogate of liming to assess the strength of management
footprints across temporal scales and contrasted with
reference lakes.
We tested these conjectures relative to the null hypothesis that no
liming effects are evident in significant time series models relative
to models of reference lakes (liming effects are absorbed and thus
undetectable in the complex systems structure of lakes). Verifying
either the null hypothesis or alternative conjectures will provide
mechanistic insight about limed lakes as coerced regimes. That is,
whether limed lakes are robust to management (null hypothesis)
or whether cross-scale manifestations of liming footprints alone
are not enough for attaining stable, self-perpetuating liming
regimes (alternative hypotheses).
METHODS
Study lakes
We used an ecosystem experiment approach and environmental
monitoring data for assessing lake management panarchies. Four
limed lakes and four circumneutral reference lakes with the most
exhaustive time series data were selected (Appendix 1). All lakes
are situated in the boreonemoral ecoregion of southern Sweden
and were chosen to avoid confounding effects due to idiosyncratic
biophysical features of other ecoregions. The limed lakes were
integrated in the national liming program initiated in 1989 by the
Swedish Environmental Protection Agency (Appelberg and
Svensson 2001). Liming was carried out prior to the start of the
program between 1974 and 1985 and consisted of application of
limestone powder by boat or helicopter at different intervals
across lakes (Appendix 1). The minimally disturbed reference
lakes were chosen to assess the footprints of management on
temporal patterns of water quality relative to unmanaged
conditions. These reference systems have a high buffering capacity
and were thus robust against acidification (Fölster et al. 2014).
Sampling procedures
Mid-lake water samples were taken in near-equidistant sampling
intervals (early spring, summer, and late autumn) over a 30-y study
period between 1990 and 2019 in the epilimnion (0-2 m) using a
Ruttner sampler. Samples were kept cool during transport to the
laboratory where they were analyzed for alkalinity,
concentrations of calcium (Ca), magnesium (Mg), sodium (Na),
potassium (K), total phosphorus (P), silicon (Si), total organic
carbon (TOC), and water color. Water temperature, dissolved
oxygen concentration, electrical conductivity, and potential of
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Fig. 1. Temporal patterns of physicochemical variables in reference lakes (blue lines) and
limed lakes (red lines). Trend lines (full, limed lakes; dashed, reference lakes) indicate
significant components of monotonic change revealed by Kendall tau correlation analysis.
Shown are means ± standard deviations.
hydrogen (pH) were measured in situ. All physicochemical
analyses were performed at the Department of Aquatic Sciences
and Assessment following international (ISO) or European (EN)
standards (Fölster et al. 2014).
Statistical analysis
Kendall tau rank correlation analyses were carried out to assess
whether individual physicochemical variables changed monotonically
over time. The entire set of physicochemical variables for each
lake was subsequently analyzed using redundancy analysis
(RDA) where time was modeled using Asymmetric Eigenvector
Maps (AEM; Baho et al. 2015). When used in time series
modeling, this analysis is useful for extracting independent
temporal patterns and scaling relationships necessary for
assessing the panarchic organization of lakes from the data. That
is, the analysis is capable of discerning, for example, between
seasonal, inter-annual, and decadal patterns (and their
combinations) inherent in the dynamics of the environment. It
also allows for detecting orthogonal patterns that can arise from
differentiated temporal variability within defined cycles of
periodicity (Legendre and Gauthier 2014). This analysis is
therefore useful for testing hypothesis 1, that there is, following
the premise of panarchy, hierarchical structure in the
physicochemical environment, while accounting for orthogonality
as an additional factor capturing ecological complexity.
The time series analysis was conducted by first converting the
linear time vector consisting of 90 steps between years 1990 and
2019 in a set of independent temporal AEM variables. These
AEMs comprise a set of sine waves ranging from long to short
frequencies that allow the modeling of fluctuation patterns
together with a linear vector, which simultaneously accounts for
monotonic trends in the data (Blanchet et al. 2008, Legendre and
Legendre 2012). These AEMs are then used as explanatory
variables in the time series models using redundancy analysis
(RDA). Time series models were constructed individually for each
lake, resulting in eight time series models, four for the limed lakes
and four for the reference lakes, using the 13 physicochemical
variables (Fig. 1) as response variables. The RDA selects
significant temporal variables (AEMs) using forward selection,
and these variables are linearly combined to extract temporal
structures from the matrices containing physicochemical
variables. The modeled temporal patterns that are extracted from
the data are collapsed onto significant RDA axes, which are tested
through permutation tests. These RDA axes are then used to
distinguish independent temporal (hierarchical and orthogonal)
patterns in the data, which can be visualized through linear
combination (lc) score plots. All physicochemical variables were
standardized prior to the analysis.
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Table 1. Summary statistics of AEM-RDA models. Not applicable (na) because axes were not significant.
Adjusted R²
min. model
No. of vectors
selected
No. of
significant
axes
Variance RDA 1 Variance RDA 2 Variance RDA 3 Variance RDA 4 Variance RDA 5
Reference lakes
Allgjuttern 49.60 15 3 15.10 6.36 2.53 na na
Fiolen 66.07 16 4 23.00 11.96 6.33 2.87 na
Stora Skärsjön 45.84 14 4 9.56 8.09 3.02 1.94 na
Stora Envättern
45.29 15 4 9.27 6.09 4.17 1.83 na
Limed lakes
Ejgdesön 48.08 15 4 12.77 6.14 2.88 2.08 na
Gyslättasjön 40.67 8 5 7.43 3.51 3.32 1.92 1.19
Stengårdshultasjön 62.86 25 5 21.01 8.49 5.34 4.17 2.05
Stora Härsjön 53.22 15 5 13.92 7.28 3.86 3.34 1.71
To test hypothesis 2, that temporal patterns differ between limed
and reference lakes, two ANOVA analyses were conducted. First,
one-way ANOVA was used to compare RDA-AEM model
structure and performance between limed and reference lakes
contrasting the following variables: adjusted R² of the minimum
models, their numbers of significant axes, numbers of vectors
selected, and the variances explained by individual RDA axes.
Second, repeated measures analysis of variance (rm-ANOVA)
was used to compare the temporal patterns of individual RDA
axes, and their interaction, between reference and limed lakes. For
this we used a mixed model approach, based on restricted
estimation of maximum likelihood (REML), accounting for the
temporal autocorrelation structure of order one, AR(1), of the
time series. Lakes were treated as random variables in this model
to allow for more generalized inference about liming impacts on
temporal patterns of water quality beyond the set of lakes used
in this study. Significant lake “Type” (reference lakes vs limed
lakes) terms and interaction terms between lake “Type” and
“Time” (90 time steps between 1990 and 2019) are considered
crucial for inferring that liming alters natural patterns of temporal
variability of lake physicochemical conditions. Because of
unbalanced designs caused by different numbers of significant
RDA axes across time series models (Table 1), comparisons were
made only for the first three RDA axes.
Finally, to test hypothesis 3, assessing the strength of liming
impacts on the modeled hierarchical and orthogonal temporal
patterns, Spearman rank correlation analysis was used to relate
lc scores of individual RDA axes with Ca:Mg ratios. These ratios
serve as surrogates of the management regime imposed by liming
on the natural dynamics of lake physicochemistry, which is
manifested in substantial inter-annual variation relative to
unmanaged lakes (Fig. 2). The strength and nature of the
interference of liming with natural fluctuation patterns across
temporal scales revealed by the RDA analyses can be assessed
through significant correlations across individual axes.
Specifically, correlation analysis can reveal whether monotonic
or fluctuating patterns of change of water quality are associated
with liming within and across lakes. These correlations are also
carried out for reference lakes to assess the degree of associations
between modeled temporal patterns and Ca:Mg ratios unbiased
by liming. All statistical analyses were carried out in R Studio
1.1.383 (https://www.rstudio.com/) using the “cor.test” function
and packages vegan, adespatial, tidyverse, reshape, ade4,
quickMEM, nlme, data table, and car.
Fig. 2. Temporal patterns of Ca:Mg ratios as a surrogate of
management disturbance imposed by liming compared to
patterns of reference lakes.
RESULTS
Individual physicochemical variables showed significant
monotonic change (Kendall tau rank correlations; p < 0.05) in
limed and reference lakes over the study period, except water
temperature and total P in both lake types and pH and TOC in
limed lakes (Fig. 1). Alkalinity and water color in limed and
reference lakes and pH and TOC in reference lakes significantly
increased while ions, Si, oxygen concentration and conductivity
significantly decreased in both lake types over time (Fig. 1).
These patterns of change were reflected in the AEM-RDA time
series models, which explained 41% to 66% of the adjusted
variance (Fig. 3; Appendix 2). RDA axis 1, which captured the
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component of monotonic change over time (i.e., slow dynamics
at the highest panarchy level), explained a large part of the
variance across the lakes studied relative to the other axes revealed
by the models, although the range of variance was variable
(7%-23%; Table 1). The time series models also revealed seasonal
patterns reflecting the sampling periods in early spring, summer,
and late autumn and different degrees of inter-annual variation
across RDA axes (i.e., faster cycling at lower panarchy levels; Fig.
3). Some of these RDA axes showed orthogonal patterns (for
instance, at roughly 15-year fluctuation cycles at RDA 2 and RDA
3 of reference lakes and broadly 20-year cycles at RDA 3 and
RDA 4 of limed lakes) in addition to hierarchical (slow to fast)
temporal structure (Fig. 3).
In total, temporal patterns were manifested at three to four RDA
axes in reference lakes and four to five RDA axes in limed lakes
(Table 1; Appendix 2). Despite limed lakes tending to have an
apparent “finer” temporal structure relative to reference lakes, it
was too subtle to be significant in the mixed model. ANOVA
comparisons also revealed no significant differences (P > 0.05)
regarding model structure and performance, indicating that the
number of AEM vectors selected for modeling temporal patterns
and the variance explained by the models and individual RDA
axes were similar between limed and reference lakes (not
highlighted in Table 1).
Within reference lakes, Ca:Mg ratios correlated significantly with
RDA 1 in Allgjuttern and Fiolen and with RDA 4 in Stora
Skärsjön and Stora Envättern. In contrast, within limed lakes,
significant correlations between Ca:Mg ratios and linear
combination scores of RDA axes from the time series models (a
management surrogate of liming) were more prevalent.
Specifically, significant correlations were found between Ca:Mg
ratios and RDA 1 and 2 for lake Ejgdesjön, RDA 1, 2 and 4 for
lake Gyslättasjön, RDA 2 and 4 for lake Stengårdshultasjön, and
RDA 1 to 4 for lake Stora Härsjön (Table 2). Despite these
differences between limed and reference lakes, the mixed models
revealed no significant interaction terms or lake type (limed vs
reference lakes) effects comparing individual RDA axes (Table 3).
Only significant time effects were found for RDA 1 and 2 (Table 3).
DISCUSSION
Panarchy has clear implications for the management of social-
ecological systems (Garmestani et al. 2020). As environmental
change accelerates, it becomes increasingly important to
understand ecosystem dynamics at different spatiotemporal
scales, cross-scale interactions, and the consequences of the
structures and processes in lake systems. This study quantitatively
tested three hypotheses related to core aspects of panarchy theory:
hierarchical structuring, dynamic system changes, and cross-scale
connectivity (Gunderson and Holling 2002). The panarchy
analysis revealed that lakes have structure at multiple temporal
(hierarchical and orthogonal) scales and that the effects of liming
manifests at different temporal scales.
The results of our study supported our first hypothesis that the
physicochemical environment in individual lakes shows dynamics
at distinct temporal scales, including seasonal, inter-annual and
monotonically changing patterns and their combinations. This
fits the premise of panarchy theory that complex system dynamics
are bound, both hierarchically (Allen et al. 2014), and, as revealed
by our study, orthogonally. These results are in agreement with
previous studies showing such compartmentalized temporal
variation in lake biogeochemistry (Baho et al. 2015) and biota
(phytoplankton [Baho et al. 2014], macroinvertebrates [Angeler
et al. 2011]).
Fig. 3. Linear combination (lc) score plots showing distinct
temporal patterns modeled by RDA analyses. These temporal
patterns correspond to different scaling patterns indicative of
hierarchical and orthogonal structuring of lake panarchies.
Shown are the averages ± standard deviations of four reference
(blue lines) and limed (red lines) lakes; except RDA 4, which is
based on the average of three reference lakes and RDA 5, which
was significant only in three limed lakes (See Table 1).
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Table 2. Spearman rank correlation analysis associating temporal
patterns determined by AEM-RDA and Ca:Mg ratios. Shown are
correlation coefficients (rho). Significant correlations (highlighted
in bold) where * p < 0.05; ** p < 0.01; *** p < 0.001. Not applicable
(na) because axes were not significant.
RDA 1 RDA 2 RDA 3 RDA 4 RDA 5
Reference lakes
Allgjuttern 0.26* -0.06 0.15 na na
Fiolen -0.37*** 0.16 0.14 0.06 na
Stora Skärsjön 0.18 -0.13 0.09 0.24* na
Stora Envättern
0.09 0.08 -0.01 -0.27** na
Limed lakes
Ejgdesjön 0.75*** -0.35*** 0.17 0.11 na
Gyslättasjön 0.34*** 0.05 -0.61*** 0.27* 0.13
Stengårdshultasjön -0.08 -0.78*** -0.04 -0.31** -0.02
Stora Härsjön -0.29** -0.74*** -0.30** 0.32** 0.15
Table 3. Results of linear mixed models showing main effects of
lake type (“Type”; Reference lakes vs limed lakes) and period of
study (“Time”; 1990–2019) and their interactions for dominant
temporal scales (RDA 1–3) in the time series models. Note: no
contrasts were made for subordinate scales (RDA 4 and RDA 5),
present only in limed lakes, resulting in an unbalanced design (see
Table 1). Significant factors are highlighted in bold.
Factor Chi square P
RDA 1 Type 0.008 0.93
Time 39.51 > 0.001
Type x Time 2.27 0.13
RDA 2 Type 0.006 0.98
Time 22.25 > 0.001
Type x Time 2.62 0.11
RDA 3 Type < 0.001 0.99
Time < 0.001 0.94
Type x Time 1.54 0.21
Although catchment processes related to changes in climate,
catchment soil properties, and recovery from acidification have
been reported to influence local lake biogeochemistry (Huser et
al. 2018) our study is agnostic about mechanisms leading to the
hierarchical and orthogonal temporal scaling structures in lakes.
That is, our study prevents us from determining the influence of
spatially scaled processes in the catchments and the interactions
that may arise between such landscape effects and local lake
conditions (Soranno et al 2014). It also does not account for social
aspects (governance, environmental laws) that influence social-
ecological water panarchies (Pope et al. 2014, Cosens and
Gunderson 2018). Notwithstanding, all lakes studied here are
situated in near-pristine catchments and in the same ecoregion.
Assuming that unmeasured environmental processes are similar
across limed and reference lakes, we are confident that the
hierarchical and orthogonal structures observed are not
confounded by potential catchment scale (land use and other
anthropogenic disturbances) processes. This suggests that our
comparisons between lake types are suitable, especially for
assessing liming effects on the lakes’ panarchy structure.
This brings us to our second hypothesis, for which support was
ambiguous. We expected liming to substantially alter the temporal
patterns and scaling structure in the physicochemical environment
given its profound disturbance on biophysical conditions of
aquatic ecosystems (Bishop et al. 2001, McKie et al. 2006). It can
be particularly expected that liming footprints manifest strongly
at scales that are associated with the temporal fluctuations of
variables that are directly affected by liming (Ca concentrations,
pH, alkalinity). This in turn should be captured by model
performance of the RDA, a method sensitive to different patterns
in the data (Baho et al. 2015). However, RDA model performance
was similar across limed and reference lakes. Also, the lack of
significant interaction terms (lake type x time) in the ANOVA
suggests that scale-specific temporal patterns were similar between
limed and reference lakes. A subtle difference was that limed lakes
generally had a more differentiated temporal structure, manifested
in additional temporal scales (RDA axes) in comparison with
reference lakes. A similar observation contrasting these lake types
has been made in previous comparisons using phytoplankton
(Baho et al. 2014). However, sample sizes are currently too low for
attributing this differentiation unambiguously to liming.
We speculate that the similar temporal patterns of dominant scales
(RDA 1-RDA 3) between limed and reference lakes may partly be
due to liming frequencies not being aligned with lake sampling.
This may lead to the wrong impression that liming effects dissipate
quickly after application indicative of fast re-establishment of
temporal dynamics in limed lakes similar to reference conditions.
Liming partly correlated to different degrees with subordinate
scales in the time series models (RDA 4-RDA 5; see below).
However, the unequal number of such subordinate scales
prevented statistical comparisons with the temporal structure of
reference lakes and therefore the unambiguous detection of
potential liming effects given our sampling design. Although
methods for such comparisons exist (PERMANOVA, ANOSIM),
ambiguity remains an issue because they perform unreliably with
unbalanced designs (Anderson and Walsh 2013).
More generally, the weak evidence of liming in our time series
models and ANOVA comparisons suggests that the natural
disturbance regimes mitigate anthropogenic impacts, as has been
shown in systems exposed to high natural variation (intermittent
streams [Soria et al. 2020], Mediterranean coastal lagoons [Franzo
et al. 2019]). However, this interpretation is at odds with pervasive
impacts on physicochemical variables, especially Ca, alkalinity,
and pH, as long as lakes are limed (Fig. 1). It also contradicts many
lake studies reporting anthropogenic stress (e.g., acidification or
eutrophication) and management forms to “override” natural
disturbance regimes, as is the case with command-and-control
management (Holling and Meffe 1996). Such profound
anthropogenic effects in the environment, of which liming is an
example, fit interpretations of acidification mitigation as an
anthropogenic perturbation (e.g., McKie et al. 2006). We speculate
that the relatively high standard deviations of lc-scores describing
AEM-RDA temporal patterns resulted in high within-group
variability of limed and reference lakes. This variability may have
obscured the statistical detection of liming effects, providing
unambiguous support for hypothesis 2. Further research, using
more lakes with greater resolution of temporal structure than three
sampling events per year and potentially longer time series with
periods before and after liming, might help to more clearly detect
Ecology and Society 26(4): 7
https://www.ecologyandsociety.org/vol26/iss4/art7/
and accurately describe liming effects on the temporal dynamics
in managed lakes.
Although liming effects were ambiguous in the time series and
ANOVA analyses, there is stronger evidence of liming footprints
in the physicochemical lake environment in our correlation
analyses. This is manifested in the significant correlations of Ca:
Mg ratios, which are substantially altered by and thus serve as a
surrogate of liming, and the temporal patterns identified by the
RDA. Ca:Mg ratios correlated across different modeled
hierarchical and orthogonal scales in the limed lakes, which
supports our third hypothesis that “(management) information”
manifests across different scales, more specifically across the
independent significant temporal patterns revealed by time series
modeling. Interconnectedness is a fundamental aspect of
panarchy theory, and its ubiquity is evident in the flow of matter
and energy in nature, ranging bottom-up and top-down effects in
lake food webs (Gruner et al. 2008) to the global climate (Angeler
et al. 2016) to biochemical cycling (Friedl and Wüest 2002).
Interconnectedness of scales and cross-scale interactions in a
panarchy invoke dynamic processes (Gunderson and Holling
2002). Our results, rather than describing dynamic processes,
show static pattern manifestations of liming footprints at
individual temporal dimensions in the time series models.
However, the detection of patterns in this study is not at odds
with the premise of dynamic information flow in a panarchy.
These patterns suggest that liming, because of its significant
impact on the biophysical environment of lakes, can have parallel
and independent effects on multiple time scales.
We acknowledge that Ca:Mg ratios are not only a surrogate of
liming effects but also inherent in the natural variability of lakes.
Both elements originate from weathering of rocks and leaching
from soils in catchments. It is therefore not surprising that these
ratios also correlated with temporal patterns in reference lakes.
Contrary to limed lakes, lake- significant correlations only
occurred at a single scale in the unmanaged lakes (Table 2). This
finding provides support for a classical notion of ecological
complexity: that a few key variables, such as, Ca and Mg
concentrations, manifest at specific scales in ecosystems (Holling
1992). This scale-specificity in reference lakes versus the cross-
scale manifestation of Ca:Mg ratios in limed lakes provide insight
into management footprints on lake panarchies.
There is increasing evidence that limed lakes comprise coerced
regimes that fail to restore baseline conditions of self-
organization and ecosystem services (i.e., lake restoration), and
are maintained exclusively through management (Angeler et al.
2020). That limed lakes comprise coerced, rather than self-
organizing regimes is supported by a body of research that
documents that limed lakes revert to acidified conditions once
liming is discontinued (Clair and Hindar 2005). Such patterns
have been specifically observed in the abiotic environment
(Lydersen et al. 2002, Hindar et al. 2013, Hindar and Skancke
2014) and are supported by geochemical modeling of pH and
aluminum concentrations in a large number of Swedish lakes
(Sjöstedt et al. 2013). Also, evidence of coerced regimes has been
revealed by research showing that lake internal phosphorus
cycling in limed lakes and their susceptibility to re-acidification
events limit their restoration (Dickson et al. 1995, Hu and Huser
2014).
Taken together our results suggest that management footprints
are evident but become diluted in limed lake panarchies. From a
coerced regime perspective, our results suggest that redundance
of liming footprints across scales—a feature considered to
contribute to resilience (Allen et al. 2005)—in the physicochemical
environment alone may not be enough to create self-organizing
limed lake regimes. Our results reject the null hypothesis that
liming effects are absorbed and therefore undetectable in the
abiotic environment. However, potential verification of our null
hypothesis cannot be completely discarded at this preliminary
stage as liming footprints in the biotic lake environment may
differ. Further research studying the broader biophysical lake
environment, including ecological communities of pelagic and
benthic habitats, shall contribute to a better understanding of
managed lake panarchies.
We conclude with highlighting that the abiotic environment of
managed and unmanaged lakes strikingly fit the premises of
panarchy theory. This theory has so far only been used to describe
“living” (ecological, social, combined social-ecological, including
economic) systems (Holling 2001, Garmestani et al. 2009, 2020).
This study reveals for the first time that the organization of the
abiotic environment of lakes also fits the premises of panarchy
theory. Our study suggests that further quantitative evaluations
of panarchy across different types of social-ecological systems
may be useful to inform ecosystem management and resilience
science in general.
Responses to this article can be read online at:
https://www.ecologyandsociety.org/issues/responses.
php/12690
Author Contributions:
DGA conceived this study, analyzed the data, and wrote the paper.
All co-authors contributed to the writing.
Acknowledgments:
This study was financed by the Department of Aquatic Sciences
and Assessment (SLU). The research was not performed or funded
by EPA and was not subject to EPA’s quality system requirements.
The views expressed in this manuscript are those of the authors and
do not necessarily represent the views or the policies of the U.S.
government. This material is based upon work supported by the
National Science Foundation under Grant Nos. DGE-1735362 and
1920938. Any opinions, findings, and conclusions or
recommendations expressed in this material are those of the author
(s) and do not necessarily reflect the views of the National Science
Foundation.
Data Availability:
All data are freely available at: https://www.slu.se/en/departments/
aquatic-sciences-assessment/data-host/. The R script for analysis
is available in Appendix 3.
Ecology and Society 26(4): 7
https://www.ecologyandsociety.org/vol26/iss4/art7/
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Appendix 1 Water quality of lakes and their location in Sweden. Shown are geographical positions and
morphological characteristics of study lakes. Shown are also features of liming management in
individual lakes. Abbreviations: na, not applicable
SMHI X
SMHIY
Lake area (km2)
Max. Depth (m)
Liming
period
Liming
events
Delivery
Liming quantity
(metric tons;
means/SD
Reference lakes
Allgjuttern
642489
151724
0.19
40.70
na
na
na
na
Fiolen
633025
1.65
10.50
na
na
na
na
142267
Stora Envättern
655587
0.38
11.20
na
na
na
na
158869
St Skärsjön
628606
0.31
11.50
na
na
na
na
133205
Limed lakes
Ejgdesjön
653737
0.83
28.60
1982-2018
16
Boat
60/32
125017
Gyslättasjön
633209
0.33
9.80
1985-2019
32
Helicopter
11/7
141991
Stengårdshultasjön
638317
4.98
26.80
1981-2019
23
Boat
235/325
138010
Stora Härsjön
640364
2.57
42.00
1977-2011
13
Boat
294/145
129240
Appendix 2 Linear combination score plots of individual lakes
Reference lakes
Allgjuttern
Fiolen
Stora Envättern
Stora Skärsjön
Limed lakes
Eigdesjön
Gyslättasjön
Stengårdshultasjön
Stora Härsjön
Appendix 3 RScript
#load packages
library(vegan)
library(adespatial)
library(tidyverse)
library(reshape)
library(ade4)
library(readxl)
##get quickMEM function (replacement of old quickPCNM function)
source ('http://www.davidzeleny.net/anadat-r/doku.php/en:numecolr:sr.value?do=export_code&codeblock=1')
source ('http://www.davidzeleny.net/anadat-r/doku.php/en:numecolr:sr.value?do=export_code&codeblock=1')
source ('https://raw.githubusercontent.com/zdealveindy/anadat-r/master/scripts/NumEcolR2/quickMEM.R')
source ('https://raw.githubusercontent.com/zdealveindy/anadat-r/master/scripts/NumEcolR2/scalog.R')
#Lakes data
#Time 90 steps, 30 years with 3 steps per year (1990-2019); this time vector is use for the
individual time series models of all lakes
Timesteps <- read_excel("file_location_on_disk.xlsx", sheet = "Time vector 90 steps")
#Lakes: Example of data import with explanatroy (water quality) variables
Lake <- read_excel("file_location_on_disk.xlsx.xlsx", sheet = "Lake_name")
#Standardization of water quality variables
Lake_scaled <- scale(Lake, center = TRUE, scale = TRUE)
# TIME SERIES MODELING
#creating AEM variables
out <- aem.time(90, moran = TRUE)
#AEM-RDA models using quickMEM function
modelLake <- quickMEM(Lake_scaled, Timesteps, myspat=out$aem[,1:70], alpha=0.05, perm.max=999, detrend
= FALSE)
#Extract lc scores for significant RDA axes; note: choices=1:X refers to significant RDA axes in
the models, where X stands for the number of significant axes
fitted.scores.Lake <- data.frame(scores(modelLake$RDA,display="lc",choices=1:X))
#LINEAR MODEL
#ANOVA for significant RDA axes, folllowing https://rcompanion.org/handbook/I_09.html
rmANOVA_RDA1 <- read_excel("file_(significant_axes)_import_from_file_location_on_disk.xlsx", sheet = "rm-
ANOVA RDA1")
rmANOVA_RDA2 <- read_excel("file_(significant_axes)_import_from_file_location_on_disk.xlsx", sheet = "rm-
ANOVA RDA2")
rmANOVA_RDA3 <- read_excel("file_(significant_axes)_import_from_file_location_on_disk.xlsx", sheet = "rm-
ANOVA RDA3")
rmANOVA_RDA4 <- read_excel("file_(significant_axes)_import_from_file_location_on_disk.xlsx", sheet = "rm-
ANOVA RDA4")
library(nlme)
if(!require(psych)){install.packages("psych")}
if(!require(nlme)){install.packages("nlme")}
if(!require(car)){install.packages("car")}
if(!require(multcompView)){install.packages("multcompView")}
if(!require(lsmeans)){install.packages("lsmeans")}
if(!require(ggplot2)){install.packages("ggplot2")}
if(!require(rcompanion)){install.packages("rcompanion")}
#accounting for temporal autocorrelation structure; finds value for corAR1 function
#RDA1
model.RDA1 = gls(RDA1 ~ Type + Time + Type*Time,data=rmANOVA_RDA1)
ACF(model.RDA1, form = ~ Time | Lake)
#RDA2
model.RDA2 = gls(RDA2 ~ Type + Time + Type*Time, data=rmANOVA_RDA2)
ACF(model.RDA2,form = ~ Time | Lake)
#RDA3
model.RDA3 = gls(RDA3 ~ Type + Time + Type*Time, data=rmANOVA_RDA3)
ACF(model.RDA3, form = ~ Time | Lake)
#RDA4
model.RDA4 = gls(RDA4 ~ Type + Time + Type*Time, data=rmANOVA_RDA4)
ACF(model.RDA4,form = ~ Time | Lake)
#Lake (i.e. replicates) treated as random variable, using lme function; without random effects
the gls function can be used
model.RDA1 = lme(RDA1 ~ Type + Time + Type*Time, random = ~1|Lake, correlation = corAR1(form = ~ Time |
Lake, value = 0.8210608), data=rmANOVA_RDA1, method="REML")
model.RDA2 = lme(RDA2 ~ Type + Time + Type*Time, random = ~1|Lake, correlation = corAR1(form = ~ Time |
Lake, value = 0.17883266), data=rmANOVA_RDA2, method="REML")
model.RDA3 = lme(RDA3 ~ Type + Time + Type*Time, random = ~1|Lake, correlation = corAR1(form = ~ Time |
Lake, value = 0.059594695), data=rmANOVA_RDA3, method="REML")
model.RDA4 = lme(RDA4 ~ Type + Time + Type*Time, random = ~1|Lake, correlation = corAR1(form = ~ Time |
Lake, value = 0.0328), data=rmANOVA_RDA4, method="REML")
#car package not working without loading data.table package
install.packages("data.table")
library(data.table)
install.packages("car")
library(car)
#display ANOVA tables
Anova(model.RDA1)
Anova(model.RDA2)
Anova(model.RDA3)
Anova(model.RDA4)
Anova(model.RDA1.gls)
Anova(model.RDA2.gls)
Anova(model.RDA3.gls)
Anova(model.RDA4.gls)
# adj. R2 of RDA axes
RsquareAdj(modelLake)$r.squared
coef(modelLake)
##CORRELATION ANALYSES
#All analyses carried out at: https://www.socscistatistics.com/tests/spearman/default2.aspx
