Dominance of free-floating plants such as duckweed is undesirable as it indicates eutrophication. The objectives of this study are to investigate whether the onset of duckweed dominance is related to weather conditions by analysing field observations, to evaluate the effect of different climate scenarios on the timing of duckweed dominance using a model and to evaluate to what extent nutrient levels should be lowered to counteract effects of global warming.
To analyse the onset of duckweed dominance in relation to weather conditions, duckweed cover in Dutch ditches was correlated with weather conditions for the period 1980–2005. Furthermore, a model was developed that describes biomass development over time as a function of temperature, light and nutrient availability, crowding and mortality. This model was used to evaluate the effects of climate change scenarios and the effects of lowering nutrients.
The onset of duckweed dominance in the field advanced by approximately 14 days with an increase of 1 °C in the average maximum daily winter temperature. The modelled biomass development correlated well with the field observations. Scenarios showed that expected climate change will affect onset and duration of duckweed dominance in temperate ditches. Reducing nutrient levels may counteract the effect of warming.
Synthesis and applications. Global warming may lead to an increase in the dominance of free-floating plants in drainage ditches in the Netherlands. The expected reductions in nutrient-loading to surface waters as a result of different measures taken so far are likely not sufficient to counteract these effects of warming. Therefore, additional measures should be taken to avoid a further deterioration of the ecological water quality in ditches.
Global temperatures are rising and predictions for the twenty-first century range from an increase of 1·1–6·4 °C (IPCC 2007) and 2–4 °C increase for the temperate climate in the Netherlands (Van den Hurk et al. 2006). An important indicator of climate warming is changes in phenology (Bradley et al. 1999; Menzel 2002; Sparks & Menzel 2002). Higher temperatures, for example, affect the timing of events like leaf bud burst (Linkosalo et al. 2009) and flowering of terrestrial plants (Tooke & Battey 2010) and may lengthen the growing season of terrestrial (Menzel & Fabian 1999) and aquatic primary producers (Thackeray, Jones & Maberly 2008; Meis, Thackeray & Jones 2009). Warming showed to result in altitudinal and pole-ward shifts in terrestrial vegetation (e.g. Parmesan & Yohe 2003; Walther 2003) as well as the pole-ward shift of emergent aquatic macrophytes in Finland (Alahuhta, Heino & Luoto 2011).
Vegetation data from drainage ditches in the Netherlands revealed that cover of free-floating and evergreen overwintering submerged macrophytes in summer was positively related to mild winters, whereas higher cover of submerged macrophytes that die back in winter occurred after cold winters (Netten et al. 2011). Another study in shallow lakes showed that fewer frost days during winter may lead to lower submerged macrophyte cover in favour of higher phytoplankton biomass (Kosten et al. 2009). Other studies indicate that warming may affect aquatic ecosystems in a similar way as eutrophication (Moss et al. 2011).
Floating plants like duckweeds are in close contact with the atmosphere, and therefore, any effects of climate warming on the phenology of aquatic vegetation will be particularly visible in this group of plants. Phenological changes due to warming are most obvious in events that occur relatively early in the year (Aerts, Cornelissen & Dorrepaal 2006) because observed changes in temperature so far have been more pronounced in winter and early spring (Sparks & Menzel 2002). The onset of duckweed dominance might be such an event that can be related to warming.
Duckweed species occur world-wide, ranging from tropical to boreal regions as long as it is not too cold, too dry or too wet (Landolt 1986). They inhabit relatively small and shallow waters (Landolt 1986) like ponds, pools, small lakes, ditches and wetlands. These ecosystems are found world-wide (e.g. Downing et al. 2006) and can be remarkably rich in biodiversity (Scheffer et al. 2006). Nutrient availability in the water column is essential for free-floating plants as they have no direct access to the sediment nutrient pool, unlike submerged and emergent macrophytes (Hutchinson 1975). Small and shallow drainage ditches in agricultural areas often receive excessive loads of nutrients from the surrounding terrestrial environment, leading to the development of dense mats of duckweed (Landolt 1986; Kočić, Hengl & Horvatić 2008). The mats interfere with the exchange of oxygen between atmosphere and water (Pokorný & Rejmánková 1983) and limit photosynthesis below the mat (Morris et al. 2004) resulting in very low oxygen content (Janes, Eaton & Hardwick 1996; Villamagna & Murphy 2010). Those anoxic conditions strongly reduce the survival of macroinvertebrates and fishes (Davis 1975). Duckweed mats can thus be considered as good indicators of low water quality. In larger aquatic ecosystems in the tropics, such dense mats are often formed by water hyacinth, whereas species of the Lemnaceae family may dominate in smaller and sheltered ecosystems in all climatic regions.
Regional waterboards in the Netherlands have a long tradition of collecting data on aquatic ecosystems. As many drainage ditches are covered by free-floating plants, these systems offer the opportunity to explore effects of weather conditions on the timing of phenological events of these floating plants and whether effects of higher temperature can be compensated by lower nutrient levels.
The first objective of this study is to investigate whether changes in weather conditions over the period 1980–2005 resulted in an earlier start of dominance of floating plants in ditches in the Netherlands by analysing a large data set with field observations. The second objective is to evaluate the effect of different climate scenarios on (timing of) duckweed development and to evaluate the effect of lowering nutrients under the different climate scenarios by means of a duckweed biomass model.
Materials and methods
Data on daily minimum, maximum and mean temperature and on daily solar irradiance were obtained from the Royal Dutch Meteorological Institute (KNMI; http://www.knmi.nl/klimatologie/daggegevens/) for a central and representative location in the Netherlands (De Bilt/Utrecht, 52 °06′N, 05 °11′E) for the period 1958–2009. Weather conditions changed during this period (see Fig. S1 in Supporting Information) with an increase in minimum, maximum and average daily temperature of 1·5, 2·0 and 1·9 °C, respectively, and an increase in mean daily irradiance from 368 up to 394 μmol m−2 s−1. The following variables were calculated for each year: mean daily average and maximum air temperature and mean daily irradiance for the periods January–December (whole year), March–May (start of growing season), March–August (growing season) and November–March (previous winter). Also the number of frost days in the preceding winter was determined.
Duckweed Data in Drainage Ditches
Since 1980, regional waterboards have collected data on macrophytes in various freshwater ecosystems in the Netherlands that were stored in the database Limnodata Neerlandica (STOWA; http://www.limnodata.nl). All recordings on duckweed cover (including the genera Lemna, Spirodella, Wolffia and Azolla) in drainage ditches (>2000 locations, Fig. S2, Supporting Information) in the period 1980–2005 were retrieved. The locations were all situated within a distance of 180 km from the meteorological station. Recordings, measured on the Braun–Blanquet or Tansley scale, were transformed into the following cover classes 0, 1–5%, 6–12%, 13–25%, 26–50%, 51–75% and >75%. It appeared that approximately 65% of the locations were sampled only in 1 year during this period, 30% in 2 or 3 years and <5% in more years. Usually one inventory per year was made, but in approximately 10% of the cases, 2 inventories were made in 1 year. Dominance (cover >75%) did not occur in all locations due to a number of factors, for example, nutrient limitation. Data from all locations were pooled per year, and then, the earliest recording for each cover class was selected in each year. Thus, the earliest day of registration for each cover class in each year was determined. If a higher cover class was recorded earlier in a specific year than a lower cover class, this indicates that the earliest recording of this lower cover class has been missed, and for proper analysis, this should be avoided. Therefore, in these situations, the lower cover class of that year was disregarded. Furthermore, only those recordings that were preceded by recordings of lower cover classes made earlier in that year were used. Observations in 1980 and 1989 were excluded as recordings were only carried out late in the season. The selection criteria resulted in 24 observations on the first day of duckweed dominance (highest cover) in a year in the period 1980–2005 and 63 observations for all cover classes (8, 4, 10, 17 and 2 observations for, respectively, 51–75%, 26–50%, 13–25%, 6–12% and 1–5% cover).
Unfortunately, the database did not provide the last day a cover class was observed in a year, as recordings late in the year (e.g. October–December) were sparse.
Statistical Analyses of Duckweed Observations
Pearson's correlation analyses were performed to identify which weather variables were related to the onset of duckweed dominance in drainage ditches. Stepwise forward linear regressions were performed to determine which variables (air temperature variables, number of frost days, irradiance variables and sampling year) explained dominance best. The analyses were performed using psaw Statistics 17·0 (SPSS Inc, Chicago, Il, USA).
A model was constructed to describe the development of duckweed biomass (B in g DW m−2) over time, based on the concept of maximum growth rate (r in day−1) achievable under optimal conditions for temperature, light and nutrient saturation, and under long photoperiods (Nicklisch, Shatwell & Köhler 2008). Biomass development was further modified by a limitation function that takes into account suboptimal conditions with respect to air temperature [f(Tair)], light availability and intensity [f(L)], nutrients [f(N,P)] and the effect of crowding [f(B)]. Losses (l) due to mortality, grazing and respiration were also included. The model has the following general form:
The temperature experienced by floating plants is better described by the daily maximum air temperature than by mean air or water temperature (Driever, Van Nes & Roijackers 2005). The effect of temperature on the growth rate was assumed to be linear from the minimum temperature up to the optimum temperature (Landolt 1986; Landolt & Kandeler 1987). As maximum air temperature may exceed the optimum temperature, temperature limitation also increased linearly from the optimum to the maximum temperature. The limitation function for temperature [f(Tair)] was defined as:
with Tair: maximum daily air temperature (°C); Tmin: minimum air temperature for growth (°C); Topt: optimum air temperature for growth (°C); Tmax: maximum air temperature for growth (°C).
Both quality and duration of light are important for plant growth. Reddy and DeBusk (1985) observed a strong correlation between growth rate of duckweeds and solar radiation. Photosynthetic rates increased linearly with light to a saturation level (Cosby, Hornberger & Kelly 1984), and the upper range of saturation was approximately 450 μmol m−2 s−1 for species of the genus Lemna (Filbin & Hough 1985). Limitation function for light [f(L)] was, therefore, defined as:
with I: irradiance (μmol m−2 s−1); Imax: saturation for Lemna (μmol m−2 s−1); Daylength = day length (min); MaxDaylength = maximum day length in a year (min).
The daily incoming solar radiation (300–3000 nm) was converted into PAR (450–700 nm) by assuming that 1 W m−2 s−1 equals 1·90 μmol m−2 s−1 (Sattin et al. 1997). To obtain the average amount of available PAR during the photoperiod, the measured solar radiation was divided by day length obtained from the formula given by Park, Na and Uchrin (2003).
Limitation by nutrients [f(N,P)] was modelled as Monod-type function for orthophosphate (P) with a half-saturation value hP of 0·05 mg P L−1 and for nitrogen as ammonium and nitrate with a half-saturation value hN of 0·04 mg N L−1 (Lüönd 1980). The limitation function for nutrients was defined as:
with P = orthophosphate (mg P L−1); hP = half-saturation value of orthophosphate (mg P L−1); N = ammonium plus nitrate nitrogen (mg N L−1); hN = half-saturation value of nitrogen (mg N L−1).
Loss rate (l) was set at 0·05 per day (e.g. Scheffer et al. 2003; Driever, Van Nes & Roijackers 2005). The limiting effect of crowding (presence of own biomass) [f(B)] was also assumed to be a Monod-type function (Driever, Van Nes & Roijackers 2005), defined as:
with B = duckweed biomass (g DW m−2); hB = half-saturation biomass constant (g DW m−2).
The carrying capacity for floating species is around 180 g DW m−2 in shallow waters (Bloemendaal & Roelofs 1988; Monette et al. 2006), and preliminary modelling results showed that the half-saturation value of 42 g DW m−2 yielded the carrying capacity as observed in the field. Default values and dimensions for the parameters are given in Table 1.
Table 1. Default values and dimensions for the parameters used in the duckweed model
The model performance was evaluated in multiple ways. First, the model was run with weather data for the period 1980–2005 to correlate the model output with the first day in a year the duckweed cover classes were observed in the field. For this, model results were translated into cover classes, assuming that 1 g DW m−2 equals a cover of 1% (Janse 1998), and the mid-value of the cover classes was used as translation points to obtain more robust model outcomes.
Second, the model was also run with averaged weather conditions for each day of the year, obtained by averaging temperature and irradiance for each day over the period 1980–2005. The output of this run and the output of the run with variable weather conditions were correlated with field cover observations to evaluate which weather input performed best.
Third, the modelled yearly first and last day of duckweed dominance and minimum and maximum biomass were related to weather conditions. For this, the model was run over the period 1959–2009. Pearson's correlation coefficients were calculated, and stepwise forward linear regression was applied to identify the most important variables using psaw Statistics 17·0 (SPSS Inc).
Fourth, the effect of nutrient limitation was evaluated using a different set of field observations from 42 ditches in the periods 26 June–17 July and 14 September–5 October in 2007 (J.P. Van Zuidam & E.T.H.M. Peeters, unpublished data) further referred to as the duckweed–nutrient data set. In both periods, duckweed biomasses (wet weight) were determined; however, orthophosphate, ammonium and nitrate were only measured in September–October. Wet weight was converted to dry weight assuming that dry weight was 6% of wet weight (Monette et al. 2006). Biomass was modelled in each ditch starting from the day the ditch was visited in June–July 2007. The model was run with the determined biomass as initial biomass, with weather data from 2007 and nutrient data from September to October. The model stopped at the day of the second visit in September–October, and the modelled biomass was determined. Results were plotted against field observations, and linear regression was applied to assess the performance of the model.
Finally, sensitivity and uncertainty analyses were performed to show which parameters are most sensitive and how uncertainties in parameter values translate to the model outcomes (see Appendix S1 in Supporting Information).
The KNMI developed four scenarios for temperature effects of global warming on the temperate climate in the Netherlands (Table S1, Supporting Information), based on the predicted climate change according to the IPCC (2007). The duckweed model was run to evaluate these climate change scenarios. For this, weather data from the period 1990–2005 were used, and the assumed increases in temperature were added according to the scenarios. The model was run for the period 1990–2005 without and with the assumed increases in temperature and for comparisons also for the periods 1960–1975 and 1975–1990.
Furthermore, the model was also run to investigate how much nutrient concentrations have to be reduced in the scenarios to obtain similar onset of duckweed dominance as for the contemporary weather data. For this, the model was run for the scenarios with different nutrient concentrations, and paired t-tests were applied to determine the concentration that gave no statistical difference in onset of duckweed dominance between the scenario and the contemporary scenario. Only results of the analyses of phosphorus will be presented as for nitrogen, similar patterns were obtained, and phosphorus is the most limiting nutrient in drainage ditches (Van Liere, Janse & Arts 2007). The analyses were performed using pasw Statistics 17·0 (SPSS Inc).
Timing of Duckweed Dominance in the Field
First day of year with duckweed dominance (>75% cover) showed significant negative correlations with all temperature variables, a positive correlation with number of frost day and no correlation with irradiance and year of sampling (Table 2). Mean temperature in the preceding winter correlated better with the onset of duckweed dominance than daily mean annual, spring or growing season temperatures. The stepwise regression included only mean daily maximum temperature from the period November–March. A 1 °C increase in the average maximum daily winter temperature advanced the timing of duckweed dominance by approximately 14 days (Fig. 1).
Table 2. Pearson's correlation results of the relation between the first day in a year dominance of duckweed (cover >75%) was observed in the field and weather variables or year of sampling (n = 24)
Pearson's correlation coefficient
Year of sampling
Daily mean air temperature
Daily maximum air temperature
Number of frost days
Duckweed Biomass Model
The modelled first day of year with duckweed dominance correlated well with field observations. Excluding variability in weather conditions in the period 1980–2005 resulted in a much lower explained variance (Fig. S3, Supporting Information), and including nutrient limitation in the 2007 data set gave better results than without this limitation (Fig. S4, Supporting Information). Biomass was especially overestimated by the model without nutrient limitation at locations where low biomasses in the field coincided with low nutrient concentrations.
The modelled first day of year with duckweed dominance in the period 1959–2009 correlated best with average temperature over the period March–May (Table S2, Supporting Information). Mean maximum temperatures performed better than mean daily temperatures. Last day and total number of days with duckweed dominance correlated best with average temperature of the period April–September, especially with maximum air temperatures. Modelled average biomass correlated equally with maximum air temperature in the periods January–December, March–May and April–September, whereas mean maximum temperature and mean irradiance in the growing season (April–September) correlated best with maximum modelled biomass. Minimum modelled biomass correlated best with mean maximum winter air temperature.
Regression showed that some of the duckweed characteristics can be well predicted (up to 84%) from the weather conditions (Table S3, Supporting Information) and also that different aspects of duckweed development are explained by different weather variables. For most duckweed characteristics, both temperature and irradiance were included, except for last day and number of days of dominance and minimum biomass. Interestingly, regression analyses for the last day with dominance suggested that the decrease in cover was not related to weather variables.
Monte Carlo sensitivity analysis clustered duckweed characteristics related to biomass production in one group, and characteristics for the seasonal pattern in a second group and uncertainty did not increase over time (Appendix S1, Supporting Information).
Evaluating Climate Scenarios
All climate change scenarios lead to an earlier start of duckweed dominance (Fig. 2, Table S4, Supporting Information). Duckweed dominance started 5–23 days earlier, depending on the scenario and nutrient availability. With nutrient limitation, duckweed dominance occurred later in the year than without nutrient limitation. Orthophosphate concentrations below 0·05 mg PO4 L−1 did not allow for duckweed dominance in any scenario. In the most extreme scenario (Wplus), the start of dominance advanced approximately 3 weeks, which was in the same order of magnitude as the advancing that occurred between the periods 1950–1975 and 1990–2005. The shift in onset from the period 1975–1990 to 1990–2005 is in the same order as the shift due to the Gplus scenario. The earlier start of duckweed dominance also led to a longer period with dominance (Fig. 3, Table S4, Supporting Information). The importance of this elongation depends on the duration of dominance under the current scenario. Interestingly, for 0·10 mg PO4 L−1, not only the start of dominance occurred earlier, but also the chance of obtaining dominance of duckweed increased (Fig. 4, Table S4, Supporting Information) from 33·3% (five of 15 years) for the present weather conditions to 66·7% for the G scenario. The additional increase in years with dominance is rather small for the other scenarios.
Evaluating Lowering Nutrients
Reduction in orthophosphate concentration to counteract the effect of warming on duckweed dominance depended on the initial concentration and the scenario (Fig. 5). For (current) nutrient concentrations of 0·50 mg PO4 L−1, a reduction from 40% (G scenario) up to 60% (Wplus scenario) is needed to compensate for warming effects, whereas the lower concentration of 0·10 mg PO4 L−1 still needs a reduction of 10% (G scenario) to 20% (Wplus scenario).
Field observations on duckweed cover indicated that due to warmer weather conditions, dominance of duckweed (cover >75%) occurred earlier in the year. This study clearly showed that the start of duckweed dominance is well related to winter temperature and number of frost days. This finding supports the already recognized importance of winter conditions for terrestrial (Kreyling 2010) and aquatic (Kosten et al. 2009; Netten et al. 2011) plants. The model applied in the present study revealed a similar pattern: earlier start together with a longer duration of duckweed dominance. Although weather conditions in winter were significantly correlated with these results, spring conditions showed better correlations. This seems to support the conclusion of Alahuhta, Heino and Luoto (2011) that conditions during growing season were more important for the distribution of boreal helophytes than winter conditions. The observed earlier start of duckweed dominance is comparable with the earlier onset of algal blooms in Lake Washington, USA, which was also attributed to changes in climate conditions (Winder & Schindler 2004). Lengthening of the growing season as an effect of warming seems to be due to the earlier start of the growing season.
Winter weather conditions are important for duckweed development. Duckweed can overwinter as free-floating plant on the water surface or as frond resting on the sediment (Hillman 1961). Fronds on the sediment usually start to develop later in the season than plants on the water surface because they need a higher temperature (Jacobs 1947). In severe winters, frost may kill floating plants (Whiteman & Room 1991) and duckweed development mainly depends on fronds resting on the sediment delaying the start of duckweed dominance. Prognoses are, however, that severe winters will occur less frequently (IPCC 2007) potentially leading to an increased survival of duckweed floating on the water surface, resulting in a higher initial biomass at the beginning of the growing season leading to an earlier dominance of duckweed. Increasing spring temperatures may even further accelerate the start of duckweed dominance.
Floating plants have a primacy for light due to their position on top of the water column and prevent warming of the water column below the mats while enhancing temperature in their own habitat (Netten et al. 2010). An earlier start of duckweed dominance, therefore, may impede germination and development of submerged macrophytes due to lack of light or lower temperatures. Dense duckweed mats impede the exchange of oxygen between atmosphere and water, and under those mats, oxygen is no longer produced through photosynthesis. This leads to a situation with strong anoxic conditions offering no opportunities for most macroinvertebrate and fish species to survive (Davis 1975). Dominance of floating plants thus decreases diversity of macrophytes (Janes, Eaton & Hardwick 1996) as well as biodiversity of macroinvertebrates (Cremona, Planas & Lucotte 2008). Global warming and the associated earlier dominance of floating plants will probably lead to a further reduction in species diversity in drainage ditches, and this is different from the observations in mountain ponds by Rosset, Lehmann and Oertli (2010), who predict an increase in species diversity due to warming. These contrasting results may potentially be explained by the difference in climate regimes.
The model presented describes growth of duckweed over different seasons and years in semi-natural ecosystems based on a few, simple equations. Other duckweed models are either complex (e.g. Janse 1998), developed for only the growing season (e.g. Driever, Van Nes & Roijackers 2005), or applicable only under controlled situations with high nutrient load (e.g. Monette et al. 2006; Lasfar et al. 2007). The present model performed best when nutrient limitation was incorporated. Nutrient concentrations are constant in the model, although in the field they follow a seasonal pattern with usually higher concentrations of total nitrogen and, to a lesser extent, total phosphorus in winter and lower concentrations of these nutrients in summer (De Klein & Koelmans 2011). For ditches covered with a dense duckweed layer, this nutrient pattern might be different as additional phosphorus may be released from the sediment under anoxic conditions because binding by iron will no longer occur (Geurts et al. 2008). Furthermore, changes in climate conditions may also affect ecosystem nutrient-loading through increased run-off (Jeppesen et al. 2009) potentially leading to stronger effects.
The most important factors regulating biomass development of floating plants were included in the model, but some other factors like dispersal and competition were not. Although dispersal can be a relevant factor, it is not likely to be a limiting factor in drainage ditches as distances between ditches are very short within a drainage area and seeds can be transported by wind up to 250 m per day (Soomers et al. 2010). Competition between floating and submerged plants is assumed to be asymmetric with submerged plant depleting water nutrient concentrations (Scheffer et al. 2003). Effects of competition due to submerged plants might therefore be mimicked with lower nutrient concentrations in the model. The model was tested and validated for the temperate climate region. Blooms of duckweed are, however, a serious problem in most eutrophicated, small and shallow water systems around the world (Landolt 1986). Although the model can easily be modified to other regions by adapting the duckweed parameters to those species present in that region and by running the model with local weather conditions, it remains questionable whether it will work in all situations. In contrast to the temperate region is, for example, seasonal variation in temperature in the tropics weak. Seasonal dormancy induced by, for example, light might need to be included in the model, and this requires more fundamental changes to the model. Furthermore, changes in duckweed phenology due to warming might be undetectable in the tropics with the present model because the increase in temperature is relatively small in comparison with, for example, temperate and boreal regions.
The present results indicated that effects of warming seem to be similar to those of eutrophication suggested in previous studies (Jeppesen et al. 2009; Moss et al. 2011). Even under lower nutrient concentrations, duckweed dominance may probably occur more frequently under future climate scenarios. A similar pattern has been suggested for shallow lakes where cyanobacteria, another group of problematic primary producers, are expected to bloom more frequently even at relatively low nutrient concentrations under future climate scenarios (Wagner & Adrian 2009). Reducing nutrient concentrations, therefore, might mitigate the unwanted effects of warming on duckweed dominance. The modelling results demonstrate that this is possible and that the effort to reduce nutrients increases with warming but also depends on the current orthophosphate concentrations. The latter is in line with observations in Lake Geneva by Tadonléké (2010) where eutrophication status determined the response of phytoplankton productivity to warming. Simulations in the present study showed that at concentrations around 0·10 mg PO4 L−1, a reduction of 10–20% seems to be required, and this increases to up to 40–70% for orthophosphate concentrations of 0·50 mg PO4 L−1. However, the Netherlands Environmental Assessment Agency (PBL 2008) predicted that as a result of measures already taken to reduce nutrient-loading to surface waters in the Netherlands, phosphorus concentrations in surface waters will decrease by only 3% in 2025. This reduction is much less than needed according to the simulations and will probably not be sufficient to counteract warming effects. To prevent earlier onset of duckweed dominance and thus longer duration of duckweed dominance as a result of warming, management strategies have to be adapted.
The authors thank three anonymous reviewers and the associate editor for their valuable comments and suggestions on the manuscript.