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1 loating Plant Dominance as a Stale State Author(s): Marten Scheffer, Sándor Szaó, Alessandra Gragnani, Egert H. van es, Sergio Rinaldi, ils Kautsky, Jon orerg, Rudi M. M. Roijackers, Ro J. M. ranken Source: Proceedings of the ational Academy of Sciences of the United States of America, Vol. 00, o. 7 (Apr., 2003), pp Pulished y: ational Academy of Sciences Stale URL: Accessed: 08/03/20 22:37 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, availale at. JSTOR's Terms and Conditions of Use provides, in part, that unless you have otained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the pulisher regarding any further use of this work. Pulisher contact information may e otained at. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and uild upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. or more information aout JSTOR, please contact ational Academy of Sciences is collaorating with JSTOR to digitize, preserve and extend access to Proceedings of the ational Academy of Sciences of the United States of America.

2 loating plant dominance as a stale state Marten Scheffer*t, Sandor Szao*, Alessandra Gragnani?, Egert H. van es*, Sergio Rinaldi?, ils Kautsky', Jon orerg", Rudi M. M. Roijackers*, and Ro J. M. ranken* *Aquatic Ecology and Water Quality Management Group, Department of Environmental Sciences, Wageningen University, P.O. Box 8080, 6700 DD, Wageningen, The etherlands;?comisio Interdepartamental de Recerca i Innovacio Tecnologica, Politecnico di Milano, Via Ponzio 34/5, 2033 Milan, Italy; $Department of Systems Ecology, Stockholm University, S-06 9 Stockholm, Sweden; and tdepartment of Botany, College of yiregyhaza, P.O. Box 66, H-440, yiregyhaza, Hungary Communicated y Stephen R. Carpenter, University of Wisconsin, Madison, WI, Decemer 20, 2002 (received for review June 5, 2002) Invasion y mats of free-floating plants is among the most important threats to the functioning and iodiversity of freshwater ecosystems ranging from temperate ponds and ditches to tropical lakes. Dark, anoxic conditions under thick floating-plant cover leave little opportunity for animal or plant life, and they can have large negative impacts on fisheries and navigation in tropical lakes. Here, we demonstrate that floating-plant dominance can e a self-stailizing ecosystem state, which may explain its notorious persistence in many situations. Our results, ased on experiments, field data, and models, represent evidence for alternative domains of attraction in ecosystems. An implication of our findings is that nutrient enrichment reduces the resilience of freshwater systems against a shift to floating-plant dominance. On the other hand, our results also suggest that a single drastic harvest of floating plants can induce a permanent shift to an alternative state dominated y rooted, sumerged growth forms. ense mats of free-floating plant have an adverse effect on freshwater ecosystems ecause they create anoxic conditions that strongly reduce animal iomass and diversity (). Invasions y introduced exotic species are partly responsile for the increase of floating plant dominance. The prolems caused y Eichhornia crassipes, Pistia stratiotes, and Salvinia molesta are notorious: they hamper fish production and navigation in tropical regions around the world (2-4). However, eutrophication is likely to have oosted the spread of free-floating plants, too. In temperate climate zones, it is known that dense eds of duckweeds (Lemnaceae) and small, floating water ferns (Azollaceae) are a symptom of high-nutrient loading in small water odies, such as ponds and canals (5, 6). Just as in the case of tropical plant eds, the dark and anoxic conditions under thick duckweed cover leave little opportunity for animal or plant life (). The dependence of free-floating plants on high nutrient concentrations in the water is an ovious consequence of their growth form. They have no direct access to the sediment pool of nutrients, and they have a large portion of their leaf surface exposed to the atmosphere rather than to the water, therey reducing the possiility of taking up nutrients other than caron through their leaves. By contrast, rooted sumerged macrophytes may take up a large part of their nutrients from the sediment (7, 8) and also use their shoots effectively for nutrient uptake from the water column (9, 0). Although floating plants are oviously superior competitors for light, sumerged plants may affect the growth of free-floating plants through a reduction of availale nutrients in the water column. Competition is likely to e especially strong for nitrogen. Although phosphorus availaility in the water column can e reduced ecause of uptake y sumerged macrophytes (), many studies show unaltered or even increased ortho-p levels after increased macrophyte cover (2-5). By contrast, sumerged nitrogen concentrations in the water column of sumerged vegetation stands are often elow detection levels (5, 6). Methods Model. The asymmetry in competition etween free-floating and rooted sumerged plants has three essential features: (i) floating plants have primacy for light, whereas (ii) sumerged plants can grow at lower water-column nutrient concentrations, and (iii) they reduce water column nutrients to lower levels. We construct a simple model to explore the potential implications of this specific asymmetry: ds d n dt rfn + hf + af - f, n dt r n + h, + a,s + + W Changes over time of the iomass of floating plants,, and sumerged plants, S, are modeled as a function of their maximum growth rates, rf and rs, modified y nutrient and light limitation, and of their losses, If and Is, caused y processes such as respiration and various mortality factors. utrient limitation is a saturating function of the total inorganic nitrogen concentration, n, in the water column, which is assumed to e a decreasing function of plant iomass: [] [2] + qss + qf' [3 where the maximum concentration () in the asence of plants depends on the nutrient-loading of the system, and the parameters qs and qf represent the effect of sumerged and floating plants on the nitrogen concentration in the water column. Light limitation is formulated in a simple fashion (7): where /af and /as are the densities of floating and sumerged plants at which their growth rates ecome reduced y 50% ecause of intraspecific competition for light. In addition to this intraspecific competition, irradiation of sumerged plants is reduced y light attenuation in the water column (W) and y shading y floating plants scaled y the parameter. Default values and dimensions for parameters are given in Tale. The default value for hs is 0, to mimic the situation in which nutrient supply from the sediment is sufficient to make sumerged plant growth essentially independent of the nutrient concentration in the water column. The half-saturation concentration, hf, for floating plants is chosen in the middle of the range of values reported in the literature on duckweed growth (8, 9). The default value for qs implies that a sumerged vegetation of 20 g of dry weight m-2 can reduce the nitrogen concentration in the water y 50% (5), whereas floating plants have a smaller impact (qf < qs). The self-shading parameters for floating and sumerged plants af and a, are set as equal and tuned in such a way that the maximum iomass in the asence of any nutrient limitation approaches a realistic value. Because, unlike the case of self-shading, in which all iomass of floating plants contriutes to shading of all sumerged plants, we chose the corresponding parameter larger than the intraspecific competition tto whom correspondence should e addressed. wkao.wau.nl PAS I April,2003 I vol. 00 I no. 7

3 Tale. Default values and dimensions of parameters and variales of the model Variale S n af as hf hs If Is qf qs rf W rs Value Units g dw m-2 g dw m-2 mg liter- mg liter-' mg liter-' mg liter-' day- day-' day- day- See text for parameter definitions and the way in which default values were otained. dw, dry weight. coefficient a. ote that, the default parameter values are just a starting point, as we will systematically analyze the sensitivity of the model to parameter values. a S xi e. i"'t Results Analysis of this model indicates that the competition is likely to lead to alternative stale states over a range of conditions (ig. ). At low-nutrient concentrations, the only stale state is an equilirium with sumerged plants (Es). With increasing nutrient level, a monoculture of floating plants (Ef) appears as an alternative equilirium. However, the sumerged-plantstate (Es) also remains (locally) stale. Therefore, provided that no large disturances occur, the system will remain dominated y sumerged plants, until at the next ifurcation, floating plants start to coappear with the sumerged plants in a stale mix (Em). With increasing nutrient load, the share of floating plants in the mix increases gradually, until a ifurcation point (fm) is reached at which the mixed equilirium disappears and the system moves (ig., doule arrow upward) to the only remaining stale state, the monoculture of floating plants. If, susequently, the nutrient concentration is reduced, the system will not return to the mixed equilirium along the same path. Instead, it remains on the floating plant-dominated upper ranch of the folded curve until a ifurcation point (xf) is reached where staility of the floatingplant monoculture ends, and the system switches ack to the sumerged plant-dominated state. Roustness. The default parameter values are chosen in such a way that they seem likely to mimic certain field situations in a reasonale way. However, plant species and their environments differ widely, and different sets of parameter values or model formulations are oviously needed to represent different field settings. Here, we analyze how the results are affected y different assumptions aout the competition for nutrients and light, and y taking a different model formulation. Changing Competition for utrients. We have assumed that sumerged plants reduce nutrient availaility in the water column a 800 q, = "sumerked x mif sumerged Xm. c I "~..-.-'"f~~~~~~~~~~~~~~~~~~~~~~~~~ 400 _ l sum. I I,fm floatil g r ig.. Effect of nutrient loading on the equilirium iomass of floating plants (a) and sumerged plants (). The arrows indicate the direction of change if the system is out of equilirium. They illustrate that the dashed equilirium (the saddle) is unstale. The vertical transitions with doule arrows correspond to catastrophic shifts to an alternative equilirium. 2 ig. 2. Effect of nutrient loading on the equilirium iomass of floating plants as in ig. 3a ut for moderate (a: qs = 0.025) and small (: qs = 0.005) reduction of nutrients in the water column y sumerged plants. PAS I April,2003 I vol. 00 I no

4 a C d 0 * ig. 3. Bifurcation graphs showing the effect of parameters q5, h,, W, and (a,, c, and d, respectively) on the nutrient loading () at which the different ifurcations (xm, Xf, and fm) in the model occur. The ifurcation lines delineate sections in the parameter plane with different sets of equiliria. loating plant dominance (), sumerged plant dominance (S), or a stale mix of these groups (M) can occur as a unique equilirium, ut in some sections also as one of two alternative equiliria (indicated as S/, /M, or S/M). All depicted ifurcations are computed with the program LOCBI (4). to a greater extent than do floating plants (qs > qf), and that, essentially, growth of sumerged plants does not depend on nutrients in the water column (hs = 0). Relaxing the first assumption has several effects (ig. 2). If the impact of sumerged plants on nutrients is moderately ut sufficiently reduced, a floating plant-dominated system switches first to a mixed equilirium rather than directly to a pure sumerged plant state in response to a decrease in nutrients. Secondly, hysteresis ecomes less pronounced as the distance etween the ifurcations xf and fm ecomes smaller. Indeed, if we assume that the effect of sumerged plants on nutrients is equal to that of floating plants, the hysteresis disappears entirely (ig. 2). A more systematic way to analyze such effects of parameter values on the model ehavior is to perform a ifurcation analysis (20). The idea in our case is to plot the critical nutrient levels at which the ifurcations occur as a function of the parameter of interest (ig. 3). The first graph (ig. 3a) shows the effect of altering the parameter (qs) that represents the impact of sumerged plants on nutrients (note that igs. and 2 represent the model ehavior at different horizontal cross sections: qs = 0.075, 0.025, and 0.005). The main thing to note is that the hysteresis ecomes smaller if the effect of sumerged plants on nutrient levels (qs) is reduced, and eventually disappears elow the point where the two ifurcation curves (xs and fm) meet. Similarly, hysteresis ecomes smaller if the dependence of sumerged plant growth on nutrients (h5) is increased (ig. 3). Other ifurcation analyses (not shown) reveal that decreasing qj has qualitatively similar effects as increasing qs, whereas increasing hf is equivalent to decreasing hs. In conclusion, the asymmetry in competition for nutrients (qs > qf and hf > hs) is essential for causing the hysteresis. Changing Competition for Light. Competition for light is the other major ingredient of our model. Although we did not model phytoplankton explicitly, a first point to note is that the chances decrease for sumerged macrophytes to out-compete freefloating plants if light attenuation in the water column (represented y parameter W) ecomes larger (ig. 3c). Thus, lakes that are deeper and/or more turid are predicted to have a lower proaility of eing dominated y sumerged vegetation and show hysteresis. The asymmetry in light competition etween the two plant 4042 )

5 - E Q).J Y-0s itrogen (mg I ) 0.0 ig. 4. Hysteresis in dominance y floating plants predicted from an elaorate seasonal simulation model of the competition etween floating and sumerged plants. types is represented in our default parameter setting y assuming the shading effect () of floating plants on sumerged plants to e twice as strong as intraspecific shading effects (a). The rationale is that, on average, only 50% of the iomass of sumerged plants casts shade on a given sumerged plant leaf, whereas all floating plant iomass contriutes to shade on a sumerged leaf. This logic sounds reasonale at first, ut holds exactly only for the unlikely case in which the photosynthesis decreases linearly with shading iomass. Reducing to relax this assumption moves the hysteresis to higher nutrient levels (ig. 3d). However, it is not easy to assess what would e the most realistic value for. In fact, there are more fundamental prolems with the formulation of light competition. The way in which photosynthesis decreases with shading iomass depends upon light attenuation in plant iomass and the photosynthetic response to light. Changing the Model. To check whether the predicted hysteresis is an artifact of simplifying assumptions such as the simple formu- lation of light competition and the asence of seasonality and reproduction, we formulated an elaorate individual-ased spatially explicit simulation model for the competition etween rooted sumerged plants and duckweed. This model is an extension of an earlier sumerged plant growth model (2), and its characteristics and analysis will e presented elsewhere in detail. The model descries the seasonal dynamics of aquatic plant growth in temperate regions, including overwintering as dormant stages and regrowth in spring. Although nutrient competition is formulated simply as in our simple model, light competition is descried in a much more realistic way in the simulation model. Irradiance follows a sine wave over oth a year and a daily cycle. Photosynthesis on a given part of the plant depends on in situ light and the distance from the tissue to the top of the plant; the latter is ecause of the decrease in activity with tissue aging. In situ light on any site depends on shading y plant iomass in higher strata and turidity in the water layer. The response of this elaorate model to nutrient loading (ig. 4) is characterized y hysteresis that does not include the mixed state ut is otherwise much like the one found in the simple model (ig. ). This result indicates that the hysteresis is at least not an artifact of the simple formulation of light competition used in the simple model, nor of the asence of seasonality in the simple model. Evidence Competition Experiments. To test whether alternative equiliria may really result from competition etween the two growth forms, we performed a set of controlled experiments in which we let the sumerged plant Elodea nuttallii and the floating duckweed Lemna gia compete. All plants were acclimatized for 4 days in nutrient poor (0.5 mg per liter of, 0.08 mg per liter of P) water under the same temperature and light regime efore the experiments. Susequently, plants were allowed to compete for 57 days in 8-liter containers. The initial nutrient level was the same for all tanks (5 mg per liter of, 0.83 mg per liter of P). Water temperature was maintained at 23-25?C, and the tanks were exposed to a daily 6-h dark/8-h light cycle (80/Imolm-2- s- ). Parallel experiments were started from four different initial conditions, each one represented y two replicate aquaria. If there is only one equilirium, such experiments are expected to a Alternative stale states C 0 ill A 0D r- (o Ll- Sumerged Sumerged ig. 5. (a) If two stale states exist, trajectories of simulations with our model end in either of the two states, depending on initial conditions. () By contrast, trajectories of simulations converge to the same point if there is a single equilirium. The latter simulations are performed with hs = 0.2, rs =.2, and the other parameters at default values (see Tale ). PAS I April,2003 I vol. 00 no

6 6 5 ; ii. < (' Tale 2. Spearman rank correlations: dense vegetation Dense vegetations loating plants Sumerged plants Sumerged plants -0.58** (204) tot +0.28** (4) -0.24** (4) Ptot +0.34** (69) -0.29** (69) +0.49** (4) <: E A Spearman rank correlations etween percentage coverage of free-floating and sumerged plants and the total and P water column concentrations in densely vegetated ditches (total coverage of floating and sumerged plants >50%). Doule asterisks denote two-tailed P < 0.0; numers of ditches are given in parentheses. - O - 0 Elodea DW (g) ig. 6. Growth trajectories in competition experiments of a sumerged plant (Elodea) and a floating plant (Lemna) tend to different final states, depending on the initial plant densities. All experiments were performed under the same conditions. Biomass is plotted for all experiments at the st, 23rd, and 57th day. Dashed ellipses indicate SDs of replicate experiments. converge to it, whereas they are predicted to end in either of the alternative equilirium states if those exist (ig. 5). Our replicated experiments clearly ended in alternative states, depending on the initial iomass of oth species (ig. 6), thus confirming the alternative equilirium hypothesis. Similar experiments performed at various nutrient levels showed that Lemna was increasingly likely to out-compete Elodea at higher nutrient levels (not shown), which is also in line with the model predictions. Patterns of Duckweed Dominance in Dutch Ditches. To check whether evidence of alternative stale states can also e found in the field, we analyzed an extensive dataset of vegetation censuses and water quality from 64 Dutch ditches. Routinely, vegetation is nonselectively removed from such ditches once or twice a year to prevent them from ecoming clogged y vegetation. Oviously, vegetation iomass, and therefore competition, increases steadily from the (not recorded) moment of removal. Therefore, we aritrarily divided the dataset in a sparsely vegetated suset (total cover of all taxa <50%), a o O 30 E 20 Z loating plant cover (%) ig. 7. Bimodal frequency distriution of free-floating plants in a set of 58 densely vegetated (total vegetation cover >80%) Dutch ditches. densely vegetated suset (total cover >50%) and a very densely vegetated suset (total cover >80%). In line with the theory, the frequency distriution of free-floating plants at higher vegetation densities was i-modal (ig. 7). Also, as predicted, cover y floaters was negatively correlated to sumerged plant aundance, and floaters showed a positive correlation to nutrient levels of the water column, whereas sumerged plants were negatively related to nutrient levels (Tale 2). By contrast, in the sparsely vegetated suset of ditches (Tale 3), correlations etween growth forms and nutrient concentrations are less pronounced, and aundances of floating and sumerged plants are positively correlated as would e expected in a phase of regrowth after removal of vegetation, when iomass reflects the recovery time since clearing rather than competition etween growth forms (ig. 5a). Shifts Between loating and Sumerged Plants in an African Lake. On a completely different scale, the tendency to alternative stale states is illustrated y the history of Lake Karia, the largest manmade African lake, created y the damming of the Zamezi river in 958. During the filling, there was a population explosion of floating Salvinia molesta and other floating plants (22-24). loating vegetation remained aundant until a decade later, when an explosion of enthic vegetation and mussels occurred that locked up large amounts of nutrients (24). Salvinia cover rapidly dropped to <5% in 973 and to <% from 980 onward (23). In , there was a new increase of floating vege- tation, this time of Eichhornia crassipes. Most proaly, the shifts etween the alternate states had een driven y the amplitude of water-level fluctuations. Strong fluctuations favor floating plants as they suppress sumerged plants (25) and enhance nutrient input from flooded land (23, 26). The history of this lake again illustrates a tendency to dominance y either sumerged or floating plants, the latter eing associated with high-nutrient levels and increased mortality of sumerged plants driven, in this case, y water-level fluctuation. Discussion Although alternative stale states are considered essential to the understanding and management of ecosystems ranging from Tale 3. Spearman rank correlations: sparse vegetation loating Sumerged Sparse vegetations plants plants tot Sumerged plants +0.23** (436) tot +0.5** (454) -0.7** (354) Ptot +0.25** (382) (382) +0.54** (353) Spearman rank correlations etween percentage coverage of free-floating and sumerged plants and the total and P water column concentrations in sparsely vegetated ditches (total coverage of floating and sumerged plants <50%). Doule asterisks denote two-tailed P < 0.0; numers of ditches are given in parentheses

7 coral reefs (27) and open ocean systems (28) to dry lands (29) and forests (30), their presence in field situations has een remarkaly hard to prove. Typically, strong cases require a comination of approaches (3, 32). This has een the approach in this study. The models form the asis of our analysis. However, even though the individual-ased simulation model contains more detail than the simple model, many mechanisms that may affect the competition have still not een included. or instance, anoxia under floating plant eds may oost the decline of sumerged plants. Also, growth of duckweed species can e inhiited at higher ph (33-35), which may arise from photosynthesis in sumerged weed eds. Although these specific mechanisms will tend to enhance rather than weaken the hysteresis, other mechanisms that we did not consider could potentially work the opposite way. An important factor that we have not addressed is the role of phytoplankton. In temperate shallow lakes, sumerged plants are out-competed y phytoplankton at higher nutrient levels, and a phytoplankton-dominated state and sumerged-plant dominance seem likely to represent alternative attractors (25, 36-38). Thus, an important question is whether sumerged plants will e replaced y floating plants or phytoplankton at high-nutrient loading. Oviously, floating plants are in the est position for competition for light. Therefore, one should logically expect floating plants to ultimately ecome dominant when nutrients are not limiting. Although this may indeed e the case in tropical lakes (2) and temperate ponds and ditches (5), free-floating plants never seem to ecome dominant in larger temperate lakes. The most likely explanation is that the small duckweeds and other free-floating plants that occur in temperate regions are simply washed ashore in exposed waters, restrict- ing their distriution to sheltered sites. By contrast, the larger growth forms of free-floating plants that can develop massively in tropical lakes apparently survive much more exposed conditions (2). Oviously, development of a truly general framework for predicting which conditions give rise to dominance y floating plants, phytoplankton, or sumerged plants remains a major challenge. Meanwhile, the results of our current study apply to situations in which dominance y floating plants is not prevented y factors other than nutrients. Overall, the different lines of evidence we present seem to make a rather strong case for the hypothesis that competition etween floating and sumerged plants can cause alternative attractors. The model approach shows that this hypothesis can e deduced in a roust way from the assumptions that floating plants have primacy for light, whereas sumerged plants can grow at lower water column-nutrient concentrations and reduce water-column nutrients to lower levels. The controlled competition experiments demonstrate alternative attractors in a straightforward way on a small temporal and spatial scale, and the patterns in Dutch ditches and Lake Karia suggest that the phenomenon also may e important in field situations. one of these approaches in themselves can e seen as proof. Interpretations of models, controlled experiments, and field patterns all have their specific caveats (39). Thus, our central result is merely an approximation of "truth as the intersection of independent lies" (40). Proaly the most useful complementary type of evidence could e otained through large-scale field experiments. Because the final state of the system depends on the initial iomass of floating plants (igs. 6 and 7), our results imply that in shallow waters that have some sumerged plants and are not too high in nutrient level, a single harvest of floating plants may lead to a permanent switch to sumerged-plant dominance. The critical harvest needed for a shift is predicted to increase with the nutrient level. Actual critical levels will differ etween ecosystems, ut could e detected experimentally. In general, the est way to manage ecosystems with alternative stale states is to enhance the resilience of the preferred state (32). Translated to our case, this conclusion implies that nutrient control may e an important strategy to reduce the risk of invasion y native or exotic floating plants.. Jansen, J. H. & Van Puijenroek, P. J. T. M. (998) Environ. Pol. 02, Gopal, B. (987) Water Hyacinth (Elsevier, ew York). 3. Oliver, J. D. (993) J. Aquat. Plant Manage. 3, Mehra, A., arago, M. E., Banerjee, D. K. & Cordes, K. B. (999) Resource Environ. Biotechnol. 2, Portielje, R. & Roijackers, R. M. M. (995) Aq. Bot. 50, De Groot, W. T., De Jong,. M. W. & Van den Berg, M. M. H. E. (985)Arch. Hydroiol. 09, Hutchinson, G. E. (975)A Treatise on Limnology: Limnological Botany (Wiley, ew York), Vol Chamers, P. A., Prepas, E. E., Bothwell, M. L. & Hamilton, H. R. (989) Can. J. isheries Aquat. Sci. 46, Roach,., Merlin, S., Rolland, T. & Tremolieres, M. (996) Ecol. Brunoy 27, Sculthorpe, C. D. (967) The Biology of Aquatic Vascular Plants (Edward Arnold, London).. Kufel, L. & Ozimek, T. (994) Hydroiologia 276, Perrow, M. R., Moss, B. & Stansfield, J. (994) Hydroiologia 276, Moss, B., Stansfield, J. & Irvine, K. (990) Verh. Int. Ver. Theor. Angew. Limnol. 24, Van den Berg, M. S., Coops, H., oordhuis, R., Van Schie, J. & Simons, J. (997) Hydroiologia 342, Van Donk, E., Gulati, R. D., Iedema, A. & Meulemans, J. T. (993) Hydroiologia 25, Goulder, R. (969) Oikos 20, Scheffer, M., Rinaldi, S., Gragnani, A., Mur, L. R. & Van es, E. H. (997) Ecology 78, Landolt, E. & Kandeler, R. (987) The amily of Lemnaceae: A Mongraphic Study (Veroff. Geoot. Inst. ETH, Zurich), Vol Hurlimann-luond, A. (990) olia Geoot. Phytotaxonomica 25, Kuznetsov, Y. A. (995) Elements ofapplied Bifurcation Theory (Springer, ew York). 2. Scheffer, M., Bakema, A. H. & Worteloer,. G. (993) Aquat. Bot. 45, Mitchell, D. S. (969) Hydroiologia 34, Marshall, B. E. & Junor,. J. R. (98) Hydroiologia 83, Machena, C. & Kautsky,. (988) reshwater Biol. 9, Scheffer, M. (998) Ecology of Shallow Lakes (Chapman & Hall, London), pp Machena, C. (989) Ecology of the Hydrolittoral Macrophyte Communities in Lake Karia, Zimawe, Acta Universitatis Upsaliensis 96 (Uppsala University, Uppsala, Sweden), pp ystrom, M., olke, C. & Moerg,. (2000) Trends Ecol. Evol. 5, Steele, J. H. (998) Ecol. Appl. 8, S33-S oy-meir, I. (975) J. Ecol. 63, Holmgren, M. & Scheffer, M. (200) Ecosystems 4, Carpenter, S. R. (200) in Alternate States of Ecosystems: Evidence and Some Implications, eds. Press, M. C., Huntly,. & Levin, S. (Blackwell Scientific, Oxford), pp Scheffer, M., Carpenter, S. R., oley, J. A., olke, C. & Walker, B. (200) ature 43, Loeppert, H. & Kronerger, R. (977) in Correlation Between itrate Uptake and Alkalinisation y Lemna paucicostata, eds. Thellier, M., Monnier, A. & Demarty, M. (Centre ational de la Scientifique, Paris), pp ovacky, A. & Ullrich-Eerius, C. I. (982) Plant Physiol. 69, Ullrich-Eerius, C. I., ovacky, A., isher, E. & Luettge, U. (98) Plant Physiol. 67, Scheffer, M., Hosper, S. H., Meijer, M. L. & Moss, B. (993) Trends Ecol. Evol. 8, Blindow, I., Hargey, A. & Andersson, G. (998) in Alternative Stale States in Shallow Lakes: What Causes a Shift?, eds. Jeppesen, E., S0ndergaard, M., S0ndergaard, M. & Kristoffersen, K. (Springer, Berlin), Vol. 3, pp Meijer, M. L., Jeppesen, E., Van Donk, E., Moss, B., Scheffer, M., Lammens, E. H. R. R., Van es, E. H., Berkum, J. A., De Jong, G. J., aafeng, B. A. & Jensen, J. P. (994) Hydroiologia 276, Scheffer, M. & Beets, J. (994) Hydroiologia 276, Levins, R. (966) Am. Sci. 54, Khinik, A. I., Kuznetsov, Y. A., Levitin, V. V. & ikolaev, E. V. 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