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).
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:
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).
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).
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 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).
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.
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.
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 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).
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]).
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 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.
DGA conceived this study, analyzed the data, and wrote the paper. All co-authors contributed to the writing.
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.
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.
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