Continental-scale effects of phytoplankton and non-phytoplankton turbidity on macrophyte occurrence in shallow lakes

Abstract

Submerged macrophytes are key components of shallow lake biological communities, and their presence has been associated with a predominantly clear-water state. Conversely, lakes lacking macrophytes are often turbid with elevated phytoplankton abundance. One main mechanism that influences the presence or absence of submerged macrophytes is turbidity that reduces the light available to macrophytes. Increases in turbidity can be caused by increased phytoplankton abundance and by increased concentrations of suspended inorganic sediment and understanding the relative contributions of these two factors can inform efforts to manage the effects of increased turbidity on macrophyte occurrence. Here, a continental scale data set is analyzed to quantify the effects of macrophytes on turbidity that originates from phytoplankton and from non-phytoplankton sources (e.g., inorganic sediment). Effects of phytoplankton assemblage composition on turbidity are also estimated. Based on this model, illustrative examples of chlorophyll concentrations needed to maintain or restore macrophytes to shallow lakes are calculated, and the difference in the magnitude of these concentrations illustrates the stabilizing effect of macrophytes on lake condition.

Introduction

The effects of macrophytes on shallow lake biological communities has been the subject of intense research, much of which has focused on the mechanisms that maintain two, often alternating stable states in a lake: a clear water state in which macrophytes are present and a turbid state in which macrophytes are absent (Scheffer 2004; Scheffer and Jeppesen 2007). A variety of biotic and abiotic processes have been proposed as stabilizing mechanisms, and among these, the effects of macrophytes on light availability may be one of the most important. That is, the presence of abundant macrophytes is often associated with increased water clarity, a relationship that has been attributed to both a reduction in the amount of suspended, inorganic sediment and a reduction in the density of phytoplankton in the water column. Increased light availability may then help maintain a lake in a clear water state.

Macrophytes stabilize bottom substrates and reduce the potential for resuspension of sediments, and when macrophytes are lost, increased concentrations of suspended inorganic sediment reduce light availability, making it difficult to re-establish macrophytes (Scheffer 2004). Measurements that characterize suspended sediment concentrations (e.g., turbidity and total suspended sediments) include contributions from both non-phytoplankton and phytoplankton sources, so quantifying the increase in turbidity that is attributable to resuspended sediments can be difficult (Yuan and Jones 2020). One approach for estimating these distinct contributions is to measure the volatile fraction of suspended sediments (Jones and Knowlton 2005) and assume that this organic fraction characterizes the contribution from phytoplankton, while the remaining fraction provides an estimate of the inorganic contribution. However, these measurements are not commonly collected (Buiteveld 1995).

Increased turbidity due to a greater abundance of phytoplankton has also been associated with a loss of submerged macrophytes in shallow lakes. The underlying mechanism for this association may be identical to that described for inorganic sediment, as increased turbidity due to phytoplankton reduces light available to macrophytes. However, other mechanisms have been suggested in which reductions in macrophytes cause increases in phytoplankton abundance. For example, when macrophytes are lost, zooplankton may lose an important refugia from predation and their abundance decreases. Then, top-down control of phytoplankton provided by grazing zooplankton decreases, and phytoplankton abundance increases (Jeppesen et al. 1999). Macrophytes can also compete with phytoplankton for available nutrients by directly absorbing them from the water column (Kufel and Kufel 2002) or by stabilizing nutrient-laden bottom sediments (Horppila and Nurminen 2003). Finally, allelopathic effects of certain macrophyte species may also suppress phytoplankton growth (Hilt and Gross 2008).

Many of the insights regarding the effects of macrophytes in lakes have been derived from intensive studies conducted on individual lakes (Hargeby et al. 2004; Hilt et al. 2013), and characterization of the effects of macrophytes over a larger population of lakes can help generalize these findings and provide useful information for guiding management decisions. However, only a few broad scale studies have been conducted (Jeppesen et al. 2000; Bayley and Prather 2003). Here, I ask whether the quantitative effects of submerged macrophytes on turbidity via reductions in non-phytoplankton sediment and decreases in phytoplankton abundance can be estimated from monitoring data collected at a continental spatial scale. To this end, a Bayesian network model is used to analyze data collected by the US EPA’s National Lakes Assessment (NLA) to estimate separate contributions to turbidity from phytoplankton and non-phytoplankton sources. Based on the model, I then predict conditions that would maintain macrophytes in a lake and conditions necessary for restoring macrophytes to lake where they are absent.

Methods

Data

Data was collected during the NLA in the summer (May-September) of 2012. The NLA consists of data collected from a random sample of lakes from the U.S. Lakes greater than 1 hectare were selected using a stratified random sampling design (US EPA 2012a). The overall sampling design of the NLA was synoptic, but 10% of sampled lakes were randomly selected and resampled on a different day after the initial visit. Shallow lakes, defined as lakes with maximum depths less than or equal to 4 m were selected for further analysis (Padisák and Reynolds 2003) (Figure 1).

Figure 1.

Map of sampled lakes. Open circles: lakes with mean annual air temperature greater than 8° C, grey filled circles: lakes with mean annual air temperature less than 8° C.

During each visit, an extensive suite of abiotic and biological variables was measured (US EPA 2011), but details are only provided here regarding measurements used in the present study. At each lake, a sampling location was established in open water at the deepest point of the lake (up to a maximum depth of 50 m) or at the mid-point of reservoirs. A water sample was collected using a vertical, depth-integrated methodology from the photic zone of the lake (to a maximum depth of 2 m). Multiple sample draws were combined in a rinsed, 4 liter (L) cubitainer. When full, the cubitainer was gently inverted to mix the water, and an aliquot was taken as the water chemistry sample. This subsample was placed on ice and shipped overnight to the Willamette Research Station in Corvallis, Oregon. A second aliquot was taken to characterize the phytoplankton community and preserved with Lugol’s solution. The presence or absence of submerged macrophytes was recorded at each of ten littoral sites, approximately equally spaced around the perimeter of each lake. These data were summarized as the proportion of the ten sites at which submerged macrophytes were observed. The presence of emergent macrophytes was also recorded but this analysis focuses on submerged macrophytes due to their clearer association with water clarity (but see Horppila and Nurminen 2001).

To measure Chl a concentration, 250 mL of lake water was pumped through a glass fiber filter in the field and quantified in the lab to pre-specified levels of precision and accuracy. Turbidity was also measured in the lab with nephelometry. To characterize the phytoplankton community, at least 400 natural algal units were identified under 1000× magnification to the lowest practical taxonomic resolution (usually species). In each sample, the dimensions of the taxa that accounted for the largest proportions of the observed assemblage were measured and used to estimate biovolume. Biovolumes of the most abundant taxa were based on the average of measurements from at least 10 individuals, while biovolumes for less abundant taxa were based on somewhat fewer measurements (US EPA 2012b). Mean annual air temperatures at each lake location were extracted from 30-year averaged climatic data (Daly et al. 2008).

Statistical analysis

Statistical analysis consisted of two steps. First, contributions to turbidity from phytoplankton and non-phytoplankton components were estimated for each of the samples with a Bayesian network model (Figure 2). Second, a relationship between macrophyte occurrence and turbidity was estimated and used to estimate a illustrative turbidity thresholds for maintaining macrophytes in different lakes. Chl a concentrations necessary to achieve these turbidity levels were then calculated for lakes with and without macrophytes.

Figure 2.

Schematic for Bayesian network model. Turb: turbidity, Chl: chlorophyll a concentration, TNP: non-phytoplankton turbidity, V_n: relative biovolume for the n^th phytoplankton division, Macrophytes: variable indicating the presence or absence of macrophytes, d_n, k, d_a, μ_i, σ_i: model parameters. Measured variables are shown in rectangles and variables estimated in the model are shown in ovals. Numbers in parentheses refer to equation numbers in the text.

Measured turbidity is directly related to the scattering coefficient, an inherent optical property of a water sample (Effler 1988). Each turbidity measurement is modeled as the sum of contributions from phytoplankton and non-phytoplankton components (which can be attributed primarily to inorganic suspended sediment). This approach is consistent with models for the light scattering coefficient that decompose contributions from different sources (Van Duin et al. 2001). The phytoplankton component is modeled as a power function of phytoplankton biomass, estimated here as chlorophyll (Chl) concentration (Morel 1987), giving the following relationship for total turbidity:

$$Tur{b}_{mn}=d_{a}Ch{l}^k+TNP$$ (1)

Where Turb_mn is the mean value of turbidity for a sample and TNP is estimated non-phytoplankton turbidity. I initially expected that mean turbidity would be directly proportional to phytoplankton biomass, as quantified by Chl, so the prior distribution of k was assumed to be normal with a mean value of 1 and standard deviation of 1. This standard deviation is much greater than expected range of values of k, and so the prior just limits the occurrence of extreme values during model fitting.

The amount of turbidity associated with each unit of Chl a is expected to vary with different phytoplankton species because of differences in size and morphology (Davies-Colley et al. 1986). Hence, the value of the coefficient d_a was modeled as the weighted average of values estimated for each of six major divisions of phytoplankton taxa (Cyanophyta, Chlorophyta, Heterokontophyta, Cryptophyta, Euglenophyta, and Chrysophyta). A final group, designated as “Other”, accounted for all taxa that did not belong to one of the six groups. The aggregate value, d_a, for each sample i was calculated as the average of division-specific values of d_n, weighted by the relative biovolume of each taxonomic grouping, as follows:

$$d_{a,i}=\sum _{n=1}^7{d}_n{V}_{n,i}$$ (2)

Where the index, n, accounts for each of the modeled divisions of phytoplankton and V_n,i is the relative biovolume of division n in sample i. The distribution of each d_n was assumed to be log-normal to restrict it to positive values, and the prior distribution for the log-transformed value of d_n was assumed to be normal with a mean value of zero and a standard deviation of 3. Here again, the standard deviations of the prior distributions of d_n were specified as large values relative to the range of expected values, so they only weakly influenced the posterior distributions and acted primarily to limit the occurrence of extreme values during model fitting (Gelman and Hill 2007).

Phytoplankton biovolume is quantified by the summing the measurements of many individual specimens in a sample, and therefore, substantial measurement uncertainty is associated with these values (Yuan and Pollard 2018). To account for the effects of the measurement uncertainty in the model, the observed biovolume for each phytoplankton division n in sample i (D_n,i) is modeled as being drawn from a log-normal distribution of possible values with a mean value of μ_n,i and an standard deviation of s_D:

$$\text{log}(D_{n,i})=\mathit{\text{Normal}}\left(\text{log}\left({\mu }_{n,i}\right),s_D\right)$$ (3)

The value of s_D was fixed at 1 for all D_n based on previous analysis of the variability of biovolume measurements (Yuan and Pollard 2018). Relative biovolume for each phytoplankton division was calculated as follows,

$$V_{n,i}={\mu }_{n,i}/{\sum }_n{\mu }_{n,i}$$ (4)

That is, relative biovolume for each division was the ratio between the estimated mean biovolume of division n and the sum of all estimated mean biovolumes for all phytoplankton divisions.

Limiting relationships between Chl a and turbidity can be calculated by setting TNP to zero in Equation (1), which gives the following log-transformed relationship: log(Turb) = log(d) + k log(Chl). This simplified expression quantifies the amount of turbidity that can be attributed to phytoplankton in absence of TNP and is a straight line in a log-log plot of Chl a vs. turbidity that is located at the bottom of distribution of points.

The presence of macrophytes is known to influence the amount of suspended, inorganic sediment, and this phenomenon is reflected in the model by estimating two mean values of TNP: for lakes with and without macrophytes. Lakes were designated as having macrophytes if submerged macrophytes were observed in at least one of the 10 littoral observations in all samples collected at a particular lake. TNP within each sample was then modeled as a log-normal distribution about a mean value and standard deviation specific to lakes with and without macrophytes:

$$\text{log}\left(TNP\right)~\mathit{\text{Normal}}\left({\mu }_{TNP,j},{\sigma }_{TNP,j}\right)$$ (5)

Where μ_TNP,I is the mean value of log(TNP) for lakes with and without macrophytes (j = 1,2), and σ_TNP,j is the standard deviation of the distribution of individual measurements of TNP within each group of lakes. Prior distributions for all values of μ_TNP were assumed to be zero with a standard deviation of 3, while the prior distributions of all values of σ_TNP were assumed to half-Cauchy with a scale of 3. These priors are also only weakly informative.

Finally, sampling variability for the log-transformed measurement of turbidity in sample i (Turb_i) was assumed to be distributed according to a Student-t distribution with 4 degree of freedom, to provide a robust fit in the presence of outliers (Lange et al. 1989):

$$\text{log}\left(Tur{b}_i\right)~\mathit{\text{StudentT}}\left(\text{log}\left(Tur{b}_{mn,i}\right),{\sigma }_T\right)$$ (6)

Where σ_T is the standard deviation of log-transformed turbidity measurements. The Bayesian model was fit with a Markov Chain/Monte Carlo sampling using “stan” (Stan Development Team 2016) and all other statistical calculations were performed in R (R Core Team 2017).

To calculate illustrative targets for turbidity and Chl a, the relationship between macrophyte occurrence and turbidity was first estimated with a logistic regression, assuming a linear relationship between logit-transformed macrophyte occurrence and log-transformed turbidity. Exploratory analysis indicated that macrophyte occurrence was only weakly associated with turbidity in lakes with mean annual air temperatures less than 8° C (see Supplemental Information), a finding that was consistent with other observations that water temperature can strongly influence macrophyte occurrence (Barko and Smart 1981). Because the intent of this second part of the analysis was only to illustrate possible turbidity targets, to simplify the analysis, these lakes were excluded from the model. Then, illustrative targets for turbidity to maintain macrophyte occurrence were calculated as the turbidities associated with 0.5 and 0.65 probabilities of macrophyte occurrence. Equation (1) was then used to compute illustrative targets for chlorophyll concentration that corresponded with the turbidity targets in lakes with and without macrophytes.

Results

A total of 505 samples collected from 468 shallow lakes were available for fitting the Bayesian network model. In 365 of the lakes, submerged macrophytes were observed in at least one of the littoral surveys in all samples. Measured turbidity ranged from 0.05 to 445 NTU with a median value in all lakes of 4.7 NTU and a mean value of 5.6 NTU (computed from log-transformed values). Mean turbidity in lakes with submerged macrophytes was 3.8 NTU, while in lakes without macrophytes mean turbidity was 20.2 NTU (left panel, Figure 3). Measured Chl a ranged from 0.1 to 764 μg/L with a mean value of 16.3 μg/L (middle panel, Figure 3). The mean Chl a concentration in lakes with macrophytes was 12.5 μg/L while in lakes without macrophytes it was 38.8 μg/L. The composition of the phytoplankton assemblage was also associated with the present of macrophytes. For example, the relative biovolume of cyanobacteria was greater in lakes where macrophytes were absent (right panel, Figure 3).

Figure 3.

Distributions of turbidity (left panel), Chl a (middle panel), and proportion cyanobacteria (right panel) in lakes with macrophytes absent and present.

The Bayesian model accurately predicted observed turbidity with a root mean square error on predictions of log-transformed turbidity of 0.46. The estimated values of the coefficients, d_n, varied significantly among phytoplankton divisions, with mean values ranging from a low of 0.31 for Heterokontophyta to a high of 1.00 for Cyanophyta (Figure 4). The value of the exponent, k, for the relationship between turbidity and Chl a was estimated as 0.73 (0.68, 0.79). (Values shown in parentheses here and for the remaining text are the 90% credible intervals.) Examples of limiting relationships between Chl a and turbidity calculated for two different taxonomic groups are shown in Figure 5. Turbidity per unit of Chl a is significantly greater for an assemblage that is dominated by cyanobacteria compared to one dominated by chlorophytes.

Figure 4.

Estimates of the coefficient, d, for the relationship between Chl a and turbidity for different phytoplankton divisions. Open circles: mean value, thick line segments: 50^th credible intervals, thin line segments: 90% credible intervals.

Figure 5.

Turbidity vs. Chl a. Open circles: observed values of turbidity and Chl a. Solid line: limiting relationship using parameter estimate for Cyanophyta, dashed line: limiting relationship using parameter estimate for phytoplankton other than Cyanophyta, grey shading: 90% credible intervals.

The estimated mean value of TNP among all lakes with macrophytes was 0.10 NTU (0.02, 0.27). In lakes without macrophytes mean TNP was estimated as 5.0 NTU (2.9, 7.6). The standard deviations of the distributions of estimated log-transformed TNP in each sample were similar in lakes with and without macrophytes (2.5 and 1.9, respectively). In individual sites, model estimated values of TNP ranged from near zero to almost 300 NTU, and a strong difference was apparent between sites with and without macrophytes (right panel, Figure 6).

Figure 6.

Comparisons of d_a and non-phytoplankton suspended sediment in sites with macrophytes present and absent.

The phytoplankton contributions to turbidity in any single sample is predicted by a combination of the limiting relationships for each taxonomic group. The overall mean estimated value of d_a in samples collected from lakes with macrophytes was 0.67 whereas in lakes without macrophytes it was 0.77, so the phytoplankton assemblage in lakes without macrophytes caused somewhat more turbidity per unit Chl a than in lakes with macrophytes. However, distributions of d_a in sites with and without macrophytes overlapped with one another (left panel, Figure 6).

A total of 299 samples collected from shallow lakes with annual air temperatures greater than or equal to 8° C were available for the illustrative model relating turbidity and macrophyte occurrence. In these lakes, the logistic relationship modeled between turbidity and macrophyte occurrence corresponded closely with the pattern observed in the measurements (Figure 7). Based on the modeled relationship, the turbidity target for maintaining a 0.5 probability of macrophyte occurrence was 19 (15, 25) NTU. This turbidity target can be achieved by maintaining Chl a concentrations at low enough levels such that the sum of contributions of turbidity due to phytoplankton and turbidity due to non-phytoplankton suspended sediment are less than the total turbidity target. Following this logic, Chl a targets that correspond to the turbidity target were computed using Equation (1) with the mean values of TNP for lakes with and without macrophytes. Initially, phytoplankton assemblage composition was assumed to be the same for all lakes, and therefore, overall mean estimates for d_a and k were used in the calculation. In lakes without macrophytes, mean TNP was 5.0 NTU, and so, the Chl a target was 93 μg/L to achieve a total turbidity of 19 NTU. The 90% credible intervals for this Chl a target were 70 and 114 μg/L. The broad range spanned by the credible intervals arises from compounded uncertainty of the many estimated parameters incorporated in the calculation. In lakes in which macrophytes are present, mean TNP was 0.10 TNP, and the Chl a target was 141 (123, 165) μg/L.

Figure 7.

Relationship between turbidity and probability of macrophyte occurrence for lakes with mean annual air temperatures greater than 8 C. Open circles: average probability of macrophyte occurrence computed in 15 samples around the indicated turbidity; solid line: estimate mean relationship, gray shading: 90% confidence limits on mean relationship; dashed line segments: illustrative turbidity targets corresponding to a 50% and 65% probabilities of macrophyte occurrence.

Lakes with and without macrophytes also differed in their phytoplankton assemblage composition and incorporating differences in the value of d_a between lakes with and without macrophytes yielded a greater disparity in Chl a targets. After accounting for differences in d_a in lakes without macrophytes, the mean Chl a target was 82 (63, 101) μg/L, and in lakes with macrophytes the target was 147 (127, 173) μg/L.

Turbidity and Chl a targets were very sensitive to selected probability of macrophyte occurrence. The turbidity target for maintaining a 0.65 probability of macrophyte occurrence was 10 (8, 13) NTU. In lakes without macrophytes, this turbidity target corresponds with a Chl a target of 23 (9, 35) μg/L, while in lakes with macrophytes the Chl a target is 64 (58, 73) μg/L. Selection of the probability used for calculating target values for different areas would reflect local risk management decisions.

Discussion

Macrophytes in shallow lakes exert strong effects on turbidity both by reducing the degree to which bottom sediments are resuspended and by reducing the density of phytoplankton (Scheffer and van Nes 2007). In the present analysis, measurements of turbidity collected at a continental spatial scale were decomposed into phytoplankton and non-phytoplankton components. The resulting model estimates were used to calculate illustrative quantitative targets for Chl a concentrations necessary for maintaining or restoring macrophytes in shallow lakes. More specifically, the occurrence of macrophytes was associated with a critical turbidity level, and because levels of non-phytoplankton turbidity are elevated in lakes lacking macrophytes, the Chl a concentration needed to restore macrophytes is relatively low to compensate for the increased concentrations of non-phytoplankton turbidity. Conversely, in lakes with macrophytes, levels of non-phytoplankton turbidity are low, and the Chl a concentration needed to maintain macrophytes is relatively high. The difference in Chl a targets is consistent with the idea of alternate stable states existing in shallow lakes, a phenomenon that has been observed in other studies (Ibelings et al. 2007).

Many approaches of varying complexity have been used to model the relationship between suspended particles in the water column and light availability, but the present model provides a new approach that combines empiricism with known theoretical relationships. Linear regression models relating turbidity or Secchi depth to measurements of Chl a, inorganic sediment, and detritus have provided a practical approach for estimating the relative contributions of different factors to light attenuation (Kirk 1984; Xu et al. 2005; Devlin et al. 2008). However, predictions from these models can be unrealistic at low concentrations of Chl a (Scheffer 2004), and the formulation is not consistent with the underlying theoretical relationships between particle density, light scattering, and absorption (Van Duin et al. 2001). Models have also been described that are closely aligned with theories for light scattering and absorption but they require calibration data that are unavailable at broad spatial scales (Buiteveld 1995). In the present study, turbidity was used as the response variable, a choice that facilitated the formulation of a statistical model that was consistent with theory because only relationships between scattering and particle density needed to be estimated. Turbidity, however, provides no information on absorption, which can account for a substantial proportion of light attenuation. As others have noted, including absorption in the model substantially increases the complexity of the model (Davies-Colley and Smith 2001), so I opted to retain the simplicity of the model for turbidity and assumed that it provided an unbiased estimate of the effects of suspended particles on light attenuation. A close relationship between Secchi depth and turbidity in the current data set (not shown) confirmed this assumption (Spearman ρ = −0.89).

The difference in mean non-phytoplankton turbidity of 4.9 NTU between lakes with and without macrophytes accounted for most of the difference in the calculated Chl a targets. The increase in non-phytoplankton turbidity is consistent with observations in many lakes that overall turbidity increases in the absence of macrophytes (Scheffer et al. 1992; Horppila and Nurminen 2005). The estimated difference may seem small, but a small change in mean value corresponds with much higher values in individual samples when coupled with the inherent variability and log-normal distribution of suspended sediment observations. For example, TNP estimates in lakes with macrophytes exceed 10 NTU in fewer than 1% of the samples, whereas TNP estimates in lakes without macrophytes exceed 10 NTU in greater than 24% of samples. Across the entire data set, occurrences of elevated TNP occurred relatively infrequently compared to occurrences of elevated phytoplankton turbidity, a trend that is consistent with a mechanism in which bottom sediments are episodically re-suspended by wind events (Cristofor et al. 1994; Cózar et al. 2005). Experiments have also shown that relatively large, inorganic suspended sediments settle more quickly from the water column than smaller organic particles (Blom et al. 1995). Even though large contributions of TNP to turbidity were relatively rare, the overall difference in mean TNP between lakes with and without macrophytes exerted a substantial effect on the Chl a targets.

Another factor that contributed to the difference in Chl a targets was the difference in phytoplankton assemblage structure between lakes with and without macrophytes. The model described here provided a practical approach for accounting for differences in the effects of different phytoplankton species on turbidity by aggregating taxa into major taxonomic groups and calculating a different effect on turbidity for each group. Scattering of light by phytoplankton cells is a function of cell biovolume (Agustí 1991), and has been modeled as a function of Chl a (Morel 1987) and estimated for different phytoplankton species (Davies-Colley et al. 1986; Bricaud et al. 1988). The current approach provides less information than detailed studies of scattering at different light wavelengths (Snyder et al. 2008), but by estimating turbidity attributed to different taxonomic groups, the effects of shifts in phytoplankton community structure can be broadly quantified and incorporated into estimates of target concentrations.

Changes in the phytoplankton community structure have been observed previously with the loss of macrophytes, where dominance of cyanobacteria and the frequency of blooms both increase (Jensen et al. 1994). On average in this study, cyanobacteria were associated with greater levels of turbidity per unit Chl a than other phytoplankton divisions and were more abundant in lakes without macrophytes, and so, the changes in phytoplankton structure contributed an additional stabilizing mechanism for shallow lakes (Scheffer et al. 1997), although the magnitude of this effect was less pronounced than that of TNP. Several mechanisms have been proposed to explain the change in phytoplankton structure. For example, the increased turbidity in lakes without macrophytes may favor cyanobacteria that can regulate their buoyancy and migrate to shallower depths (Ibelings et al. 1991). Also, higher nutrient concentrations may favor certain cyanobacterial taxa (Downing et al. 2001).

The inherent stability of different lake regimes is further magnified by differences in Chl a concentration observed among lakes. If we assume for simplicity that average nutrient loads to lakes in the dataset are similar, then the greater Chl a concentration observed in lakes without macrophytes suggests that available nutrients are preferentially converted to the standing stock of phytoplankton in these systems. As described above, several mechanisms may account for this difference, including competition for nutrients by macrophytes, allelopathic effects, and trophic interactions. Regardless of the mechanism, the higher Chl a concentration in lakes without macrophytes suggests that the magnitude of the management actions required to reduce Chl a to targeted concentrations is greater in lakes without macrophytes.

Macrophytes were assessed only as being present or absent in the littoral zone in the data set used for this analysis. This characterization of macrophytes is coarse, and measurements of areal coverage of macrophytes may be more strongly related to turbidity measured at the center of the lake. However, the relationship between turbidity and the presence and absence of macrophytes was consistent with expectations, suggesting that the qualitative observations do provide useful information. Furthermore, these observations are more easily collected in large-scale monitoring efforts, yielding a data set that spans a wide range of different lakes, so this simpler assessment of macrophyte occurrence may be more appropriate in large-scale monitoring studies. Another inherent assumption of this model is that turbidity and Chl a measurements collected at the center of the lake sufficiently characterize conditions throughout the lake. This assumption likely holds true with regard to average trends across the entire data set, but variations in conditions at different locations in large lakes may introduce additional uncertainty to the estimate relationships.

The effects of turbidity were examined in the present study, but a host of other factors can affect the persistence of macrophytes in different lakes (Phillips et al. 2016). Large scale perturbations, including climate change (Hargeby et al. 2004; Kosten et al. 2009), invasive species that disturb bottom sediments (Zambrano et al. 2001), the availability of propagules (Bakker et al. 2013), changes in hydrology (Blindow 1992; Loverde-Oliveira et al. 2009), water chemistry (Koch 2001), and epiphyte density (Jones and Sayer 2003) have all been observed to influence macrophyte persistence. Many of these factors would be expected to heighten differences in Chl a targets between lakes with and without macrophytes beyond those described here and make it much more difficult to restore lakes by only controlling nutrients. Indeed, documented restoration attempts have initially focused on reductions in nutrient loads, but many have subsequently or simultaneously introduced biological manipulations to help trigger regime change (Hosper and Jagtman 1990).

Understanding the direction of causality is an important component for interpreting the targets derived in this analysis, and cause-effect relationships occur in both directions regarding macrophytes and turbidity. That is, the presence of macrophytes causes reductions in turbidity, while increased turbidity also causes a decrease in the occurrence of macrophytes. The statistical relationship between turbidity and macrophyte occurrence reflects patterns that occur in the data, and as such, arise from both of the relationships described above. Isolating separate relationships, one in which macrophytes cause increased turbidity and one in which turbidity reduces the occurrence of macrophytes, is not possible with monitoring data. Instead, the targets derived from these empirical relationships simply provide turbidity and Chl a concentrations that are associated with different probabilities of macrophyte occurrence. Furthermore, interventions that result in long-term decreases in turbidity and Chl a concentrations are likely to yield an increased likelihood of macrophytes.

The analysis of large-scale data affirms that findings derived from lake-specific studies apply to a much broader variety of lakes across very different geographic settings. Target values calculated in this study are average values that characterize the population of lakes in the study and may provide a useful starting point for management decisions. Additional data from individual lakes or smaller study areas can refine the models and yield more precise predictions of conditions in individual lakes (Yuan and Pollard 2019). However, some management decisions need to apply to many lakes, and the current analysis approach can inform such decisions.

Availability of data and material:

All data used in this manuscript are presently available on the National Lakes Assessment website