The emergence and dominance of Planktothrix rubescens as an hypolimnetic cyanobacterium in response to re‐oligotrophication of a deep peri‐alpine lake

Toxic cyanobacteria, such as Planktothrix rubescens, came to dominate temperate lakes in the mid‐to‐late 20th century, as a result of eutrophication. Even after decades of re‐oligotrophication, where phosphorus levels were reduced by 1–2 orders of magnitude, P. rubescens remains present in various lakes. In this study, we examine the persistence and changes of P. rubescens deep chlorophyll maximum (DCM) in Lake Hallwil (Switzerland) over 35 yr of steadily decreasing phosphorous concentrations. Although lake transparency increased and the euphotic layer deepened during this period, the P. rubescens population maximum moved even deeper. It is now found ca. 7.7 m deeper than its shallowest position in the 2000s, and this depth no longer coincides with the depth of maximal water column stability. P. rubescens neutral buoyancy has now driven it beneath the stable metalimnion into the hypolimnion, where buoyancy regulation is restricted due to reduced metabolic activity at low light and low temperature. If P. rubescens DCM continues to deepen each year, it will eventually reach a region of lower stability in the hypolimnion where turbulent conditions are strong enough to disperse the DCM. We also explore the mechanisms that ensure P. rubescens ongoing presence in peri‐alpine lakes despite strong re‐oligotrophication and ongoing climate change. We find that P. rubescens in the lake is mainly sustained by growth during fully mixed conditions in winter, not during stratification in summer. This may contradict another commonly made prediction that periods of longer stratification will promote future blooms of this cyanobacterium.

The widespread occurrence of P. rubescens is generally attributed to its ability to use buoyancy regulation to form a deep chlorophyll maximum (DCM) at a stable depth in the metalimnion during the stratified season (Walsby et al. 2004).
P. rubescens maintains near-neutral buoyancy, where filaments neither float nor sink minimally, since its cellular density is very close to the density of water (Walsby et al. 2004). Buoyancy regulation is achieved through the equilibrium between gas vesicles content (positive buoyancy) and the amount of carbohydrate ballast (negative buoyancy), which accumulates through photosynthesis and is depleted through respiration Kinsman et al. 1991;Walsby 1994). Being filamentous and not colonial, the vertical displacement rate of P. rubescens due to its flotation or sinking velocity is relatively low, from 0.4 m to 1 m per day (Walsby 1994). P. rubescens forms metalimnetic DCMs through buoyancy regulation as a result of intersecting resource gradients of light and nutrients (Konopka 1987(Konopka , 1989Brookes and Ganf 2001). In the metalimnion, light levels are low but still sufficient for P. rubescens to photosynthesize and avoid photoinhibition (Dokulil and Jagsch 1992;Micheletti et al. 1998;Zotina et al. 2003). At the same time, metalimnetic nutrient concentrations are higher than in the surface mixed layer, which is often nutrient depleted before the end of the stratification period (Reynolds et al. 1987;Walsby 2001;Walsby et al. 2004).
Although, the light availability at the depth where DCMs are formed seems to differ between lakes , the euphotic depth (Z eu ), defined as the depth where 1% of surface photosynthetic active radiation (PAR) remains, has often been associated with DCMs (Leach et al. 2018). P. rubescens can live in low light conditions (Bormans et al. 1999;Oberhaus et al. 2007) and contains the red accessory pigment, phycoerythrin, which captures light energy at wavelengths between 540 and 570 nm where chlorophyll is not efficient (Frank and Cogdell 2012;Lauceri et al. 2019). In mesotrophic lakes Zurich (Switzerland) and Ledro (Italy), P. rubescens maximum forms close to the euphotic depth (Boscaini et al. 2017;Knapp et al. 2021), while in the meso-oligotrophic Lake Mondsee (Austria) the DCM occurs deeper, at lower irradiance levels between 0.1% and 1% of the surface irradiance (Dokulil and Jagsch 1992). In the early 1980s, Feuillade et al. (1984) documented a 5 m gradual deepening of P. rubescens DCM as phosphorus was reduced by 75% over 8 yr in Lake Nantua (France). These results indicate that the irradiance at which P. rubescens maintains near-neutral buoyancy may vary with the trophic state of the lake. Scofield et al. (2020) compared DCM characteristics across a trophic state gradient in the North American Great Lakes and found that oligotrophic lakes had thicker DCMs located at greater depths when compared to eutrophic lakes. Their results showed that in eutrophic lakes a DCM formed at shallower depths due to higher phytoplankton biomass, and steeper light attenuation in the epilimnion (Scofield et al. 2020). Nutrients (phosphorus and nitrogen) also modulate buoyancy in cyanobacteria (Konopka 1987(Konopka , 1989Brookes et al. 1999;Brookes and Ganf 2001). Under nutrient-limited conditions, cells accumulate more ballast and sink (Konopka 1987(Konopka , 1989. However, if light limitation becomes more important, then the ballast is respired, the number of gas vesicles increases, and the proportion of floating individuals subsequently increases. Therefore, we assume that the depth at which P. rubescens reaches neutral buoyancy varies with trophic state, which is reflected in the nutrients and light availability as well as in the size of the metalimnion, considered being the perfect habitat for P. rubescens during the summer (Walsby and Schanz 2002).
We expect that as re-oligotrophication of a lake advances, lower nutrient conditions in the metalimnion and increased lake transparency will drive P. rubescens neutral buoyancy to deeper layers. If the DCM shifts below the metalimnion, buoyancy regulation will be restricted for two main reasons: (1) reduced metabolic activity at low temperature, as seen in experiments with other cyanobacteria, slows down ballast adjustments (You et al. 2018) and (2) increasing vertical turbulent diffusivity with depth in the hypolimnion, enhanced by higher shear stress, hinders P. rubescens buoyancycontrolled positioning . Thus, the likelihood of stronger turbulent diffusivity resulting in the vertical spread of P. rubescens DCM increases with depth in the hypolimnion.
This study examines the dynamics of P. rubescens DCM in the peri-alpine Lake Hallwil (Switzerland) over 35 yr of re-oligotrophication. We focus especially on the deepening of P. rubescens DCM and the decline of its summer biomass since the 2000s. Using monthly time series between 1985 and 2020, we investigate how changes in the euphotic depth, the metalimnion size, vertical mixing, and the distribution of phosphorus in the water column determine the position of the DCM and whether these new conditions influenced P. rubescens biomass levels. Understanding the ecological mechanisms behind the persistence and dominance of toxic cyanobacteria during and after re-oligotrophication can have important implications in lake modeling as well as water quality management and decision-making processes.

Study site
Lake Hallwil is situated on the central suisse plateau in canton Aargau, northern Switzerland (449 m above sea level 47.2772 N, 8.2173 E). The lake has a surface area of 10.3 km 2 , a volume of 0.28 km 3 , a maximum depth of 47 m and a residence time of 3.8 yr (BUWAL 1994). The lake is of glacial origin, like nearby eutrophic Lake Baldegg from which Lake Hallwil receives an inflow through the Aabach River. They are both situated in the Seetal Valley (Luzern and Aargau cantons) surrounded by mountains that shelter them from easterly and westerly winds, which limits the winds' capacity to completely mix the lake during fall overturn (BUWAL 1994). In the 1960s and 1970's, the lake was considered eutrophic due to the high phosphorus inputs from human settlements, industry, agriculture, and from Lake Baldegg (Bürgi and Stadelmann 1991). By the end of the 1970's phosphorus concentrations were as high as 300 μg P L À1 . As a response, the local authority implemented a remediation program consisting of a wastewater treatment plant (1964)(1965)(1966)(1967)(1968)(1969)(1970)(1971)(1972)(1973)(1974)(1975)(1976)(1977)(1978)(1979)(1980) and reduction of agricultural sources of phosphorus (2001) (Holzner et al. 2012).
The lake was oligomictic (only rarely mixing) until 1985 when the aeration system was installed to guarantee winter vertical mixing of the water column each year and to avoid anoxic conditions in the hypolimnion (McGinnis et al. 2004;Holzner et al. 2012). The system has two modes; destratification mode during winter using coarse air bubbles, and hypolimnetic oxygenation during summer using fine oxygen or air bubbles, which does not disrupt thermal stratification. The aeration system is still in use to this day in order to guarantee the legal water quality requirement of ≥ 4 mg L À1 of oxygen at any depth (OEaux 2014).

Lake Hallwil long-term monitoring program
Lake Hallwil has been monitored since 1985 by the Environmental Department of Canton Aargau (Umwelt Aargau). Water column profiles of temperature , turbidity , chlorophyll a (Chl a; 2010-2020), and the cyanobacteria pigment phycocyanin (2016-2020), among other parameters, have been taken on a monthly basis with multiparameter probes (specifications in Supporting Information S1), as well as light climate variables such as Secchi depth and euphotic depth .
Integrated water samples are collected monthly at two depth intervals, 0-13 (since 1985) and 13-45 m depth (since 2010) for microscopy counts of the main phytoplankton and zooplankton groups. Biovolume estimations are performed on Lugol preserved samples and since 1997 also on filters, exclusively for P. rubescens. Biomass is then calculated from these results (detailed methods in Supporting Information S1). Additionally, P. rubescens monthly net growth rate μ (d À1 ) was calculated as: Where B 0 and B i are the initial and final P. rubescens integrated biomass from 0 to 45 m, and Δt is the number of days between measurements. Net growth represents the balance of gains and losses during the period evaluated. A negative sign means losses were higher than gains; a positive sign the opposite.
In this study, we perform a time series analysis of the data between 1985 and 2020. Thermal structure parameters such as the depth of the thermocline, top and bottom boundaries of the metalimnion, and the Brunt-Väisälä buoyancy frequency (N, s À1 ) were calculated from the temperature and density monthly profiles (1 m interval; 1985-2020) using the R package "rLakeAnalyzer" (Read et al. 2011). The metalimnion was defined as the region in the water column with a minimum density gradient of 0.1 kg m À3 per m, and with a minimum change between the top and bottom boundaries of 1 C.
Given that no PAR data were available after 2010, we recalculated the euphotic depth for each sampling date between 1985 and 2020 based on the Secchi depth. After testing different methods recommended in Luhtala and Tolvanen (2013), a power regression was selected as the best fit. This method gave us the highest correlation (R 2 = 0.79, p < 0.001) and the lowest error indicators (MAE = 1.03 m, MRE = 13.3%, RRMSE = 0.16%). Further details of the fit and the goodness of the fit are available in Supporting Information S2. Therefore, based on the Secchi depth (Z s ) and 1% surface PAR depth between 1985 and 2010, we obtained the following equation to calculate the euphotic depth in Lake Hallwil (Z eu , m) as: In addition, we calculated the percentage of surface irradiance (I%) at P. rubescens DCM depth (Z DCM ), relative to the euphotic depth and its corresponding light attenuation coefficient (Kd zeu ) based on Beer-Lambert's law, using the following equations: P. rubescens deep maximum parameters estimation Planktothrix scatters light more strongly than other phytoplankton due to their gas vesicles (Ganf et al. 1989;Scheffer et al. 1997) and was the dominant phytoplankton species by biomass for much of the time series in Lake Hallwil (Fig. S5). Therefore, we used turbidity profiles (Nephelometric Turbidity Units, NTU) as a proxy for P. rubescens distribution in the water column . The validity of this assumption is supported first by a strong correlation between the depths where maximum turbidity and phycocyanin (cyanobacteria pigment) values occurred between 2016 and 2020 (R 2 = 0.95, p < 0.001, Fig. S2) and second, by a positive and linear association over the top 13 m of the water column between P. rubescens biomass and average turbidity (r = 0.82, R 2 = 0.68, p < 0.001, Fig. S3). Therefore, from May to September (thermal stratified period) between 1998 and 2020, P. rubescens DCM depth was defined as the exact depth where the turbidity maximum occurred, between the epilimnion limit and 25 m depth. Below this depth, we assumed that there is not enough light for a DCM to form, although we also verified whether this was true by visual inspection of each profile. To resume, the region where the subsurface turbidity peak occurs, the proxy for Planktothrix abundance peak of both pigments concentration and biomass, will be referred to in the text as P. rubescens DCM. Furthermore, we interpreted variations in the turbidity maximum value as probable changes in P. rubescens abundance peak.
Moreover, a Gaussian curve was fit to each turbidity profile between 5 and 25 m depth to calculate the thickness, in meters, of the P. rubescens layer, DCM, from May to September (for further details see Supporting Information S3), as has been done previously with chlorophyll profiles (Lewis et al. 1983;Leach et al. 2018;Scofield et al. 2020). We used the "Gauss" curve fitting function from Originpro (v.2021, OriginLab Corporation, Northampton, MA, USA) to fit 138 turbidity profiles. For each fitted curve, the thickness of the DCM was calculated as 2 standard deviations from the curve mean (Leach et al. 2018). The average R 2 for the fitted curves was 0.914 and ranged from 0.75 to 0.99 (Supporting Information S4).
Furthermore, all the physicochemical conditions at the DCM depth (temperature, nutrients, Chl a, and phycocyanin) were utilized to characterize P. rubescens DCM during the stratification period.

Turbulence conditions at Planktothrix DCM
To study the effect of turbulence on the persistence of the P. rubescens layer, we related changes in the DCM to vertical turbulent diffusivity field measurements and modeled time series. The objective was to verify if the DCM was moving toward a higher turbulence region, resulting in a widening of the DCM and/or affecting P. rubescens buoyancy regulation and vertical migration.

Buoyancy frequency Vertical shear of the horizontal velocity ð5Þ
First, we calculated the Richardson number (Ri) using Eq. 5. This parameter indicates the regions where the water column becomes dynamically unstable and turbulence is likely to form. We used Acoustic Doppler current velocity profiles (Sentinel V50 ADCP 492 kHz, Teledyne RDI) between 2.5 and 25 m depth during the summer of 2011 (647 h; 13 Jun-10 Jul) and 2015 (263 h; 10-21 Aug) to calculate the vertical shear velocity. The frequency of unstable flow was calculated as the time where Ri ≤ 0.25, as this is the condition for an unstable flow where the vertical shear velocity overcomes water column stability. We used the Richardson number to verify if the deepening of the DCM between 2011 and 2015 resulted in the entrainment of P. rubescens into a turbulent region. The buoyancy frequency N (s À1 ), which is a measure of the strength of the water column stratification, was calculated from water column density profiles and indicates at which depth stability was maximal.

Ozmidov length scale
Second, we observed the changes in the size of the overturning eddies at the location of the DCM. To do so, we calculated the maximum eddy size, or Ozmidov length scale L O (m) (Ozmidov 1965;Bouffard and Wüest 2019). In our case, L O would be an indicator of the viability of buoyancycontrolled vertical positioning. For P. rubescens to be able to remain at a stable depth, L O must be smaller than the flotation rate, 0.4-1 m day À1 (Walsby et al. 2004).
To calculate L O (Eq. 6), we utilized the available time series between 2013 and 2019 on vertical diffusivity K z (m 2 s À1 ) and buoyancy frequency modeled by EAWAG using the 1D lake model Simstrat (v2.0, Model quality: R 2 = 0.992, RMSE = 0.85 C, available at: simstrat.eawag.ch/LakeHallwil). We calculated the maximum eddy size and the vertical diffusivity at the DCM during the thermal stratification period, on the same sampling day and time of the cantonal monitoring data.

Time series analysis and statistics
Given the nature of re-oligotrophication, we expected changes in the physico-chemical and biological parameters over time. Therefore, we used the seasonal Kendall test to check whether there was an overall significant trend in each of the time series (increasing or decreasing) despite the seasonal component of these Limnological data (Hirsch and Slack 1984). The seasonal Kendall test evaluates a trend within each season (e.g., months or climatic stations) and combines the results to give the overall trend within the study years (Helsel et al. 2020). The associated correlation coefficient is denoted as Tau. If there was a significant trend we then calculated the associated Sen's slope, which is an estimation of the rate of change of the trend (Sen 1968). It is calculated as the median of the pairwise slopes. Compared to other methods, these methods are valid regardless if the variation is linear or not. In addition, since disturbances in the lake are not always continuous in time, for some parameters, it was necessary to check whether there were abrupt changes in the time series trend. We used the rank-based Pettitt method to detect if there was a point (year) where the time series trend of a specific parameter changed significantly (Pettitt 1979). We selected the Kendall test, Sen's slope, and Pettitt method as they are robust against outliers, missing values, and heteroscedasticity, and do not require a specific distribution of the data (Hirsch and Slack 1984). All of the aforementioned statistical tests were performed using the functions available in the R package "Trend" (Pohlert 2020).
For the time series visualization, we added a centered moving average smoothing using the "MA" function from the R package "forecast" (Hyndman et al. 2021). This method allows us to visualize the overall trend of the time series without the seasonal component. The frequency of the time series (e.g., monthly or quarterly data) determined the order of the moving average smoothing and it is specified in the figures as m-MA. Given that the trend of the physico-chemical and biological parameters changed over time and was not always linear, a least-squared regression would have not been informative.

Total phytoplankton and Planktothrix biomass dynamics over the last 35 yr
The eutrophic state of the lake and the return of complete water column mixing during winter with the aeration system installed in 1985, overlaps with the rise of phytoplankton biomass during the first 17 yr of the re-oligotrophication program (Fig. 1a). From 1985 to 2002, the total phytoplankton biomass increased from 14 to 75 g m À2 (0-13 m), the highest annual average biomass ever recorded in the lake (Fig. 1a). Although it is important to note that the biomass of non-Planktothrix phytoplankton increased by 13 g m À2 during the same period, the rise in total phytoplankton biomass was mainly a consequence of P. rubescens growth, which started with an inoculum of 0.009 g m À2 (winter 1985) and jumped to an annual average of 48 g m À2 in 2002. In other words, while the non-Planktothrix phytoplankton biomass doubled, the Planktothrix biomass went up $ 5000-fold. The relative abundance of Planktothrix increased from 0.1% to 67% and thus became the dominant phytoplankton species in Lake Hallwil over this period (Fig. S5).
After 2002, total phytoplankton biomass began to decline along with the continued phosphorus reduction (Figs. 1a and S6). In 2005 non-Planktothrix biomass had already decreased to 7.5 g m À2 , which is below the biomass levels at the onset of re-oligotrophication efforts in 1985. Since then, non-Planktothrix biomass has remained around this value with no increasing or decreasing trend (Tau = À0.08, p = 0.1, Fig. S7). Diatoms, cryptophytes, and dinophytes are the most abundant groups after P. rubescens (Fig. S8). There is no evidence of other emerging species in the last 5 yr (2015-2019). P. rubescens relative abundance has remained above 50% and its average annual biomass, 9.9 g m À2 (2019), has decreased at a slower rate than other phytoplankton taxa in Lake Hallwil (Fig. 1, Tau = À0.54, p < 0.001).
Estimation of P. rubescens net growth rate (0-45 m), only available from 2010, revealed that there was only positive net growth (median = 0.007 d À1 ) from November to March when water column stratification was not present. Negative net growth (median = À0.008 d À1 ) occurred from April to October when there was a DCM and the water column was stratified (Fig. S16).

Planktothrix DCM
Since lake turbidity monitoring began in 1998, a P. rubescens layer has formed every year (no years without DCM), initially from May to September but extending to October since 2007 (Fig. 1b). In 1998, the DCM depth was at 9 AE 1.4 m (average May to Sep). As P. rubescens reached its biomass peak between 1999 and 2002, the DCM depth was found at shallower depths around 6.2 AE 0.8 m (Tau = À 0.19, p = 0.33). However, since 2002, the DCM depth has been deepening at a rate of 0.33 m yr À1 (Tau = 0.73, p < 0.001). Indeed, from 1999 when the DCM depth was positioned at 5.3 AE 1.8 m (shallowest point) to 2020, the DCM depth has moved deeper by 7.7 m (Figs. 1b and S9).
Furthermore, as the DCM deepened, it shifted to colder water conditions. From 1998 to 2002 when the DCM was at its shallowest depth (4-11 m), the temperature at the peak was between 7 C and 21 C (Fig. S10). In July and August, the warmest months, the mean temperature at the DCM depth was 17 C. As the DCM deepened in the metalimnion (2003- 2010) the mean temperature decreased to 11 C. Later when the DCM formed between 9 and 17 m (2010-2020) the mean temperature decreased to 9 C (min = 6 C and max = 14 C).
The thickness of the DCM has increased over time (Tau = 0.26, p < 0.001, Fig. 2). Between 1998 and 2006, when P. rubescens DCM was located at depths between 5.3 to 10.3 m, the DCM was around 2 m thick (average from May to September). As the DCM deepened and extended to October (2007), it also became thicker at an average rate of 5 cm yr À1 (Tau = 0.19, p < 0.05). In 2020, the average DCM thickness was 3.4 AE 1.6 m, the maximum average thickness observed in the time series.
The turbidity at the DCM has also decreased (Tau = À0.32, p < 0.0001). This parameter is an indicator of P. rubescens biomass peak (see Methods). The highest turbidity values were found from 1998 to 2006 (Fig. S11), which is the period with the highest P. rubescens biomass (Fig. 1). On average, the turbidity maximum was 20 AE 6.8 NTU, with no tendency to increase or decrease (Tau = 0.04, p > 0.1). Later, in 2007, the turbidity maximum decreased to 12.4 AE 6.4 NTU and since then it has remained stable at low values (Tau = À0.0147, p > 0.1). Overall, the DCM turbidity maximum decreased by 44% between 1998 and 2020.

Planktothrix deep maximum positioning related to light attenuation and thermal structure
The DCM depth has typically been associated with the euphotic depth (Fig. 3). We found that seasonal variations in the euphotic depth corresponded with changes in the depth where the DCM was positioned (Fig. S12). They both migrate deeper from May to July and upwards from July to September/ October, without necessarily being at the same depth. This seasonal pattern persisted over the years.
In Lake Hallwil, even during the eutrophic period, the euphotic zone usually extended deeper than the thermocline and approached the lower boundary of the metalimnion (Fig. 3). In fact, the thermocline, the DCM, and the euphotic depths were aligned during the years with the highest phytoplankton biomass production, 1999-2002 (Fig. 3). As total phytoplankton biomass declined, both the euphotic and P. rubescens DCM depths moved deeper (R 2 = 0.77, p < 0.001, Fig. S13). However, starting in 2010, the euphotic depth and P. rubescens DCM depth began to diverge: the euphotic zone showed no significant trend, while the DCM continued to deepen at a rate of 0.33 m yr À1 .
P. rubescens DCMs are usually found within the metalimnion as it is the most stable region of the water column. Between 1998 and 2020, the metalimnion deepened by approximately 0.1 m yr À1 (Tau = 0.45, p < 0.001, Figs. 3 and S9). The thickness of this thermal layer has however remained stable, at around 6 AE 2 m (Fig. S9). As a result, since 2010 the DCM peak is beneath the lower boundary of the metalimnion, given that the metalimnion has not increased in size and is deepening at a slower rate than the DCM. Indeed, the DCM depth did not correlate with the thermocline ( p > 0.1) or with the maximum buoyancy frequency depth ( p > 0.1, Fig. S14). In the warmest months of 2020 (May to July) the DCM depth was 1.5-5.9 m below the lower boundary of the metalimnion (Fig. 3).
To summarize, between 1998 and 2010 the DCM was positioned within the metalimnion close to the euphotic depth. Between 2010 and 2020, although the euphotic depth and the metalimnion deepened (meaning that light penetrated deeper into the lake) at a rate of 0.1 m yr À1 , the DCM deepened even faster, 0.33 m yr À1 . The DCM has crossed the lower limits of the metalimnion and of the euphotic region, and since 2010 it has been positioned in the upper part of the hypolimnion (Fig. 3).

Variation of the turbulence conditions at the DCM
Although the DCM is now located below the metalimnion (Fig. 3), it is still positioned in a relatively stable region (Richardson number > 0.25, red zone in Fig. 4b). Outside of this region the system becomes dynamically unstable and turbulence is likely to form, preventing P. rubescens remaining at a steady depth. The region where the DCM forms, remains stable for several weeks (Fig. 4b). Hence, P. rubescens has enough time to develop a biomass peak.
Stable conditions at the P. rubescens deep layer were observed for both summers of 2001 (highest biomass peak and metalimnetic DCM) and 2015 (DCM at the top of the hypolimnion). Turbidity profiles, as a proxy for P. rubescens distribution, revealed that most of its layer stratifies at a region where the instabilities were infrequent, indicated by the critical Richardson number (Ri ≤ 0.25) (Fig. 4a). The main difference between the two periods was that the DCM moved from the upper to the lower boundary of the non-turbulent zone. Further deepening of the DCM inside the turbulent region would result in the spread of the layer by turbulent diffusivity. The DCM was thicker but the turbidity peak was smaller (Fig. 4a), showing how it is spreading out. However, we observed that the boundaries of the stable flow region have also deepened. The region where Ri > 0.25, and therefore where turbulent mixing is suppressed, extended below 15 m depth in 2015 (Fig. 4b), which was the limit of the non-turbulent zone in 2001.
The DCM was situated at a depth where the vertical diffusivity was on average 10 À6 m À2 s À1 , which is almost an order of magnitude higher than molecular diffusivity for heat 1.4 Â 10 À7 m À2 s À1 (Campeau et al. 2021), and where the largest (Ozmidov-scale) eddies were around 1.6 cm. P. rubescens flotation velocity at present is still higher than the maximum eddy size: 0.4-1 m d À1 (Walsby et al. 2004) vs. 1-4 cm eddies (Fig. 5), so the frequency of the overturning events becomes important. Time series of vertical diffusivity and L O at the DCM depth from 2013 to 2020, also showed that the deepening of the DCM was not reflected in higher turbulence or larger eddy size. In fact, there is no detectable decreasing or increasing trend in these parameters at the DCM depth. Furthermore, correlations between the physical variables (vertical diffusivity and L O at the DCM depth) and P. rubescens biomass, Chl a, or with the turbidity maximum, were all weak (Fig. S15).
Changes in phosphorus concentration in Lake Hallwil and at P. rubescens deep layer DIP, the biologically available form of P, has undergone large and important changes in Lake Hallwil (Fig. 6b). Between 1998 and 2003 (Fig. 1a), DIP levels in the water column were regularly replenished (27 AE 6 μg P L À1 ) during winter overturn, but then gradually declined above the hypolimnion from spring through fall due to phytoplankton uptake (Fig. 6b). As re-oligotrophication continued, DIP replenishment in winter declined rapidly. By 2009, DIP had already been reduced by 80% (5 AE 5 μg P L À1 ) compared to 2003 (Fig. 5b). In the same period during thermal stratification, a DIP-depleted layer (< 1 μg P L À1 ) started to expand below the metalimnion. First only in late spring (May 2004), then until late summer (August 2007), and finally until October in 2009 (Fig. 6b).
The concentration of DIP in the DCM and the euphotic depth, during thermal stratification, has oscillated between 0 and 3 μg P L À1 without showing an increasing or decreasing trend (Fig. 6a). Conversely, the average concentration of DIP in the hypolimnion has dropped from 55 AE 58 μg P L À1 in 2001 (biomass peak) to 2 AE 1 μg P L À1 in 2020. There is no longer a gradient of DIP below the metalimnion, therefore less and less P is available to be consumed below the DCM. By 2020, the "nutricline", the depth where the DIP concentrations start to increase (rapidly), was situated below 30 m (Fig. 6b) and full water column DIP in winter was close to detection limits (3 AE 2 μg P L À1 , Fig. 5b).

Discussion
Lake Hallwil has now experienced 35 yrs of re-oligotrophication efforts. Although DIP has been reduced by two orders of magnitude, P. rubescens and its DCM persist in the lake. However, the position and thickness of the DCM have changed during this transition from eutrophic to oligotrophic conditions. Between 1999 and 2020, the DCM deepened by 7.7 m and increased its thickness by 1.3 m. Contrary to expectations, our results show that the DCM depth increased at a faster rate, 0.33 m yr À1 , than the deepening of the metalimnion and of the euphotic depth, 0.1 m yr À1 , which both are the result of increased lake transparency through re-oligotrophication. This difference in the deepening rates has resulted in the DCM moving further away from the euphotic zone, toward the upper part of the hypolimnion. Furthermore, the increase in DCM thickness from 2 to 3.5 m (1998-2020) could be related to this displacement of the DCM out of the metalimnion and, most importantly, to the distancing from the most stable part of the water column as the DCM moves deeper in the hypolimnion. However, we did not find a significant increase in vertical turbulent diffusivity or Ozmidov length scale where the DCM moved between 2012 and 2020, a period when the DCM was already in the upper part of the hypolimnion.

Variations of DCM drivers during re-oligotrophication
Two major drivers control the DCM depth: DIP and light co-limitation. Re-oligotrophication probably exacerbated phosphorus limitation, causing a higher build-up of ballast compounds (carbohydrates) in P. rubescens, causing the filaments to lose buoyancy and sink. This possibly explains why the DCM deepened at a faster rate than the euphotic depth. In Lake Hallwil, since 2015, the mean concentration of DIP in the hypolimnion (1-3 μg P L À1 ), where the DCM now forms, is within the same range as the concentration of DIP in the epi-and metalimnion (0-3 μg P L À1 ). Indeed, there is no longer a nutrient gradient, at least in the upper 30 m depth, and there is probably not enough DIP upwelling to the metalimnion for P. rubescens to form a biomass peak at the euphotic depth. The decrease of DIP in the hypolimnion corresponds with the displacement of Planktothrix biomass from the top (0-13 m) to the bottom (13-45 m) layer that has been observed since 2015 (Fig. 7). These observations are in good agreement with previous experimental studies showing ballast accumulation in other cyanobacteria under P-limited conditions (Konopka 1987;Kleiner et al. 1996;Brookes and Ganf 2001;Chu et al. 2007).
P. rubescens filaments will sink until light becomes limiting. Under low light, cells would respire their ballast as well as increase their gas vesicle content, and thus regain buoyancy. Several studies have shown that a reduction in irradiance or an extension of the dark period in P-limited cultures resulted in increased gas vesicle content and a higher proportion of floating cells or filaments (Konopka 1987;Brookes and Ganf 2001;Chu et al. 2007). Therefore, we hypothesize that in Lake Hallwil the variation in P. rubescens neutral buoyancy depth, where 50% of the filaments are floating, and 50% are sinking, is the reflection of an equilibrium between phosphorus and light limitation. This explains why P. rubescens in Lake Hallwil still forms a DCM during thermal stratification and does not fully sediment despite very low DIP concentrations.

Implications of further DIP removal in the DCM
Indeed, our results show a relationship between the amount of DIP in the hypolimnion and the percentage of surface irradiance at the DCM (Fig. 8). At high nutrient levels (DIP > 30 μg P L À1 ) P. rubescens regained buoyancy above 1% surface irradiance (Z eu ), while under oligotrophic conditions (DIP < 3 μg P L À1 ) P. rubescens was neutrally buoyant only at surface irradiance levels between 1% and 0.1%. Previous lake and laboratory experiments indicate that cyanobacteria neutral buoyancy occurred at a lower irradiance as nutrient concentrations decreased (Konopka 1987(Konopka , 1989Brookes et al. 1999). If P reduction in Lake Hallwil continues and DIP concentration in the hypolimnion goes below 1 μg P L À1 , the irradiance threshold for P. rubescens to maintain neutral buoyancy, with 50% floating, would be < 0.1% of the surface irradiance (Fig. 8). This would result in decreased P. rubescens growth rates due to lower light and lower temperature conditions occurring deeper in the hypolimnion.
In Lake Hallwil, the DCM depth might be defined by the lower limit of irradiance that can sustain P. rubescens net photosynthesis under the most stringent P-limited conditions, driving Planktothrix to deeper depths, and lower light conditions. In Lake Bourget (France), a lake that also went through a re-oligotrophication process, P. rubescens went from being the dominant species for 13 yrs to disappearing completely from the lake (Jacquet et al. 2014). P. rubescens was only detected again in 2016 and 2017, possibly due to incomplete mixing and high amounts of P entering the lake from tributary rivers (Moiron et al. 2021). Once the temporary peak in P levels ended Planktothrix disappeared again (Moiron et al. 2021). Other phytoplankton species like dinophytes, cryptophytes, and diatoms have emerged in the meanwhile (Jacquet et al. 2014). So, while in Lake Bourget, and other lakes like Mondsee (Austria), P. rubescens was only present in mesotrophic conditions and disappeared when P-levels dropped to oligotrophic levels, in Lake Hallwil, P. rubescens persist even under very low phosphorus concentrations. The different responses to re-oligotrophication between the two lakes may be linked to a large difference in maximum depth: 45 m for Lake Hallwil vs. 145 m for Lake Bourget. P. rubescens annual relative abundance has remained above 50% until 2020 (Fig. 1). Nevertheless, P. rubescens biomass has been decreasing since 2002, particularly during thermal stratification when this species is present as a DCM (Fig. 7).

Effect of thermal stratification variations in the DCM
Between 2010 and 2020, P. rubescens net growth rate was negative during thermal stratification but positive during the rest of the year (December to March) (Figs. 8 and S16). This means that this species is just surviving the stratified period, estivating, to provide a large enough inoculum for winter mixing when water column P is replenished and filaments are brought back to the light for a period of renewed growth. This could explain why P. rubescens is almost the sole competitor during the non-thermal stratification period. Thus, P. rubescens inoculum or in this case the biomass of the layer during the stratification period, is important for the survival of the species and competition with other phytoplankton.
Negative net growth rates during thermal stratification could be explained by low light, low phosphorus, and also low temperature in the hypolimnion where the DCM forms. The temperature at the DCM depth was between 7 C and 21 C during the biomass peak (1999)(2000)(2001)(2002) vs. 6-15 C during P. rubescens decline in 2015-2020 (Fig. S10). Controlled experiments have shown that P. rubescens can survive for multiple weeks at 4-5 C in the dark (Holland and Walsby 2008), although its growth rate increases from 6 C to 25 C (Davis and Walsby 2002;Oberhaus et al. 2007;Wierenga et al. 2022).
Slowed metabolism by P. rubescens at low temperatures could condition filaments to neither float nor sink, but to stabilize at a given depth. Whereas one would assume that under low light or in the dark, cyanobacteria would regain buoyancy by respiration of the stored carbohydrate ballast, experiments in Microcystis showed that while this was true at 20 C, cells failed to regain a buoyant state at 8 C (Thomas and Walsby 1986). This was attributed to the slower carbohydrate metabolism and lower gas vesicle production at low temperatures (Thomas and Walsby 1986). In addition, the energy available to invest in the production of new, energetically costly, gas vesicles in the hypolimnion is limited. P. rubescens would have to invest primarily in maintenance energy until winter mixing, when the filaments regain access to light.
Water column stability at the DCM If future nutrient reduction leads to a further increase in the lake transparency and therefore an expansion of the euphotic region, P. rubescens DCM could be entrained in deeper turbulent regions of the hypolimnion causing population dispersal. Results from field measurements on the vertical turbulent diffusivity and the Ozmidov length scale showed that even with the recent deepening of the DCM, it is still formed in a stable region with low turbulence and small eddies (< 3 cm; Figs. 4 and 5). Simstrat-1-D model time series of Lake Hallwil between 2013 and 2020 showed that there has been no increase in vertical diffusivity or L O at the depth where the P. rubescens peak forms (Fig. 5). This explains why we did not find a correlation between P. rubescens biomass decline and the turbulence parameters. Other studies on the microstructure of P. rubescens DCM in Lake Zurich found similar values (same order of magnitude) of the Ozmidov scale at the Planktothrix peak . However, in Lake Zurich the population of P. rubescens is still found in the metalimnion ). In Lake Hallwil, the deepening of the DCM-caused by finding neutral buoyancy at greater depth, linked to improved light conditions and P-limitationresulting from re-oligotrophication, has not yet led to a loss of buoyancy-controlled depth positioning of P. rubescens. It is still capable of forming a deep biomass layer at the top of the hypolimnion without being entrained into deeper, more turbulent regions (Fig. 4).

Conclusion
This study highlights the importance of extending the monitoring of toxic cyanobacteria to the hypolimnion of oligotrophic lakes. A high biomass and toxin concentration are not necessarily restricted to the surface mixed layer and metalimnion of a lake. Filamentous species, such as P. rubescens, can to respond to lower nutrient conditions by positioning deeper in low turbulent regions of the hypolimnion that are rich in phosphorus, up to the depth where light becomes limiting. This strategy might be restricted to low-light adapted species with buoyancy regulation abilities. Different species would fall into deeper and darker regions and eventually sediment. Moreover, in a global warming scenario, P. rubescens and other buoyant species might prevail in this unusual hypolimnetic niche, as longer thermal stratification periods are expected, as well as more years with incomplete mixing (Butcher et al. 2015;Woolway et al. 2020;Råman Vinnå et al. 2021). Yet, our results also show that in Lake Hallwil it is not the stratified summer period but the mixed winter period that sustains P. rubescens growth. Therefore, longer stratification may in certain lakes work against the persistence of this cyanobacterium, contradicting previous studies.

Data availability statement
The data that support the findings of this study are available from the corresponding author, E.L.S, upon reasonable request.