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On the dominance of filamentous cyanobacteria in shallow, turbid lakes.


Several physiologically distinct groups of cyanobacteria can be discerned, but in limnology large colony-forming cyanobacteria like Microcystis, Oscillatoria, Anabaena, and Aphanizomenon have received particular attention, because they often dominate the plankton in eutrophic lakes (e.g., Berger 1975, Schindler 1975, Reynolds 1984, Smith 1986, Trimbee and Prepas 1987, Sas 1989).

It has been argued that cyanobacteria are favored by high pH and low C[O.sub.2] availability because of their low half-saturation constant for C[O.sub.2] uptake (Talling 1976, Shapiro and Wright 1984). In shallow lakes and ponds, however, chlorophytes rather than cyanobacteria are often found to dominate under highly productive conditions when pH values are high (DeNoyelles and O'Brian 1978, Jeppesen et al. 1990, Jensen et al. 1994). Probably, C[O.sub.2] limitation is rare in shallow lakes because of the relatively large input of this nutrient from the atmosphere as well as from the sediment (Jensen et al. 1994).

Under certain conditions some cyanobacteria (e.g., Anabaena and Aphanizomenon) form specialized cells (heterocysts) that can fix atmospheric nitrogen. A widely cited idea is that such blue-greens become dominant when the N:P ratio is low (Schindler 1977, Smith 1983). However, the correlation of cyanobacteria to this ratio may well be spurious, stemming from an increase in P rather than a decrease in the N:P ratio (Trimbee and Prepas 1987). In a thorough analysis of data from 210 Danish shallow lakes, no relationship between abundance of heterocystous cyanobacteria and nitrogen availability was found (Jensen et al. 1994).

In this paper we analyze the mechanisms behind the often observed dominance of the filamentous cyanobacteria of the Oscillatoria group in shallow lakes. The most important genera in this family are Oscillatoria, Planktothrix, Lyngbya, and in saline lakes at lower latitudes Spirulina, but probably the most important bloom-forming species in temperate shallow lakes is Planktothrix agardhii (formerly Oscillatoria agardhii). Lakes dominated by Oscillatoriaceae are typically very turbid, and when winters are not too cold the dominance can even persist throughout the year (Berger 1975, Sas 1989). Blue-green dominance is considered an important problem by water quality managers. Although the phenomenon is associated with eutrophication, attempts to restore the original phytoplankton community in shallow lakes by means of reduction of the nutrient loading are often unsuccessful (Sas 1989).

In the following sections, we first analyze field data and construct a graphical model on the basis of the observed patterns that explains the hysteresis and discontinuous responses to nutrient management. Subsequently, we present and analyze a simple mathematical model based on laboratory data, showing that the graphical model is well in line with the expectations based on our knowledge of the physiology of Oscillatoria. In the discussion we link our results to classical competition theory, and discuss the role of seasonality, herbivorous zooplankton, and the recently reported effects of allelopathic substances from macrophytes on cyanobacteria.
TABLE 1. Significance of the relation between relative abundance of
Oscillatoriaceae expressed as a fraction of the total algal
biovolume and various environmental factors.

Environmental factor        [P.sub.r]        [P.sub.c]         n

Shade (EZ)                    0.001           0.00001         118
Secchi                        0.092           0.0015          118
Mean depth                    0.55            0.91            118
Total P                       0.38            0.45            118
Total N                       0.79            0.11            103
Total N/Total P               0.64            0.69            103

Note: [P.sub.r] denotes the significance of the regression
coefficient of a sigmoidal logistic regression model through the
data (e.g., the regression line in [ILLUSTRATION FOR FIGURE 1
OMITTED]). [P.sub.c] denotes the significance of the Spearman rank
correlation. n = number of observations.


We analyzed data from 55 Dutch lakes shallower than 3 m to check the relation between nutrients and light conditions and the abundance of Oscillatoriaceae. Data were averaged per lake over the period July-August for a given year. For most lakes information is available over several years, and the total data set encompasses 118 lake-years. Relative abundance of Oscillatoriaceae is expressed as percentage of the total algal biovolume. The vertical light extinction coefficient, E ([meters.sup.-1]), is estimated from Secchi depth, S (meters), and the chlorophyll a concentration, Chl (micrograms per liter), using a regression model (E = 0.79 + 0.016 Chl + 0.46/S) that has been shown to predict light attenuation in shallow lakes better than Secchi depth or algal biomass alone (M. Scheffer et al., unpublished manuscript). To describe the light climate experienced by algae, the depth (Z) of the mixed layer needs to be taken into account. In shallow lakes, thermal stratification does not occur for long periods, and the mixed depth can therefore be considered equal to the (average) lake depth. In this paper we characterize shade as the product EZ. This measure is inversely proportional to the ratio of euphotic depth to mixed depth ([]/[Z.sub.mix] [approximately equal to] 4.5/EZ) that is sometimes used to characterize the light climate experienced by algae (Reynolds 1984).

There is no significant relationship between the relative abundance of Oscillatoriaceae and the concentration of phosphorus in our data set (Table 1). Also the total N concentration and the total N/total P ratio are unrelated to the Oscillatoriaceae dominance (Table 1). Light conditions under water, however, are clearly related to the relative abundance of Oscillatoriaceae (Table 1, [ILLUSTRATION FOR FIGURE 1 OMITTED]). The correlation with Secchi depth is significant, but an even stronger relation is found with the more sophisticated shade indicator EZ. High abundance of Oscillatoriaceae occurs predominantly under shady conditions [ILLUSTRATION FOR FIGURE 1 OMITTED]. This correlation of cyanobacterial blooms with low light levels is in line with the results of an analysis of 22 lakes worldwide by Smith (1986) and with recent Danish findings for shallow lakes (Jensen et al. 1994). Analyzing semi-quantitative data from a set of 178 lakes and quantitative data from 32 lakes, Jensen and co-workers found that in both sets, correlation of dominance by (nonheterocystous) cyanobacteria to the []:[Z.sub.mix] ratio was more than twice as high as the correlation of dominance to the total phosphorus concentration. Note that the points in Fig. 1 are not clustered around the (logistic) regression line. Instead, most points are found at very high or very low Oscillatoria abundance. This impression is confirmed by the frequency distribution of the relative abundance of Oscillatoriaceae [ILLUSTRATION FOR FIGURE 2 OMITTED]. In the majority of the cases these cyanobacteria are either a minor component of the phytoplankton community or strongly dominant. The regression line [ILLUSTRATION FOR FIGURE 1 OMITTED] roughly characterizes an average Oscillatoria abundance at different shade levels. However, the pattern might be more appropriately described as a high and a low band of data points, with high points being more frequent at high shade levels. Oscillatoriaceae tend to be either scarce or dominant, and the probability of the latter rises steeply with shade.

It is commonly noted that Oscillatoria dominance is associated with eutrophication (Berger 1975, Sas 1989, Romo and Miracle 1994) and that these cyanobacteria can disappear again in response to a reduction of the nutrient loading (Sas 1989, Mur et al. 1993). The above results suggest that it is the low light level rather than the high nutrient availability per se that leads to dominance by Oscillatoriaceae in eutrophic situations. If this is indeed the main causal link between Oscillatoria dominance and eutrophication, disappearance of these cyanobacteria in response to a reduction of the nutrient concentration should occur at comparable shade levels rather than at comparable nutrient levels in different lakes. Indeed, this pattern has been described for a couple of well-studied Oscillatoria-dominated lakes (Mur et al. 1993). Sharp drops in the percentage of cyanobacteria (Planktothrix) have occurred in the lakes Schlachtensee and Veluwemeer where phosphorus concentrations have gradually decreased due to a reduction in loading. In Veluwemeer, cyanobacteria disappeared at a considerably lower phosphorus level than in the approximately three times deeper Schlachtensee ([ILLUSTRATION FOR FIGURE 3 OMITTED], upper panel). However, the light climate (expressed as the ratio []:[Z.sub.mix]) at which the cyanobacteria collapsed was practically the same in both lakes.

The abrupt character of the changes in these lakes [ILLUSTRATION FOR FIGURE 3 OMITTED] seems typical for the transition between Oscillatoria dominance and other algal assemblages (Sas 1989). Interestingly, remarkably abrupt switches have also been described for tropical lakes. Here the species involved is Spirulina platensis, another representative of the Oscillatoria family. Accurate data are scarce, but some of these lakes are actually known to switch back and forth repeatedly. Melack (1980), who described these patterns, noted that the relatively stable states of the community between the switches persisted for [greater than]10 generations, indicating that they represent disjunct equilibrium states.

Analysis of the Dutch data set in a slightly different way reveals another important pattern. Lakes where Oscillatoriaceae dominate tend to be shady compared to lakes of the same nutrient level where these algae are rare [ILLUSTRATION FOR FIGURE 4 OMITTED]. The difference is especially marked for lakes with a total P concentration of [less than]0.3 mg/L ([ILLUSTRATION FOR FIGURE 4 OMITTED], lower panel). This suggests that Oscillatoriaceae dominance is not only favored by shady conditions, but also promotes such conditions. Obviously, this sounds like a chicken and egg problem and causality cannot be inferred from correlations alone. Other differences between lakes may simultaneously influence shade and cyanobacteria in such a way that the same pattern is produced. Therefore, it is informative to see that individual lakes that alternate between cyanobacterial dominance and another algal community tend to show the same pattern [ILLUSTRATION FOR FIGURE 5 OMITTED]. In Lake IJsselmeer, for instance, filamentous cyanobacteria have been rare over the past 20 yr. However, during the summers of 1976 and 1989 the summer algal community has been dominated entirely by Planktothrix agardhii. In both summers chlorophyll a was exceptionally high. Another Dutch lake, Eemmeer, is usually dominated by Planktothrix. In 1991, however, the cyanobacterial density was low most of the summer. This coincided with a drop in chlorophyll a.


The patterns in the field data suggest that shade promotes Oscillatoria dominance [ILLUSTRATION FOR FIGURE 1 OMITTED], but that Oscillatoriaceae also promote shady conditions [ILLUSTRATION FOR FIGURES 4 AND 5 OMITTED]. This would imply an interesting positive feedback in the development of blooms of Oscillatoriaceae. The consequences can be seen more clearly by setting up a simple graphical model [ILLUSTRATION FOR FIGURE 6 OMITTED], based on the empirically derived patterns.

As argued above, shade experienced by the algae depends on the (mixed) depth and the vertical light attenuation coefficient. In a given lake, however, depth is fixed and shade therefore depends only on the light attenuation coefficient (E), termed "turbidity" in the following. Normally turbidity will increase with the phosphorus level, starting at a background value ([E.sub.b]) and levelling off at high P concentrations when light becomes limiting ([ILLUSTRATION FOR FIGURE 6 OMITTED], lower curve). When cyanobacteria dominate, turbidity will be higher at the same nutrient concentration (cf. [ILLUSTRATION FOR FIGURE 4 OMITTED]); thus a separate turbidity-nutrient relationship should apply to Oscillatoria-dominated situations ([ILLUSTRATION FOR FIGURE 6 OMITTED], upper curve).

The field patterns further suggest that the probability that Oscillatoriaceae will dominate the community depends strongly on the shade level. Since many other factors may have an effect on the probability of cyanobacterial dominance, it would be surprising if the response to shade would be identical in all situations. The fact that there is not one unique critical shade level that separates Oscillatoria-dominated states from other data points in Fig. 2 will at least in part be attributable to differences in various factors between lakes and errors in estimating shade. The graphical model refers to the behavior of one hypothetical lake. The simplest assumption in this case is that there is a single critical shade level, which because of the fixed depth translates into a critical turbidity, [E.sub.crit], above which cyanobacteria will become dominant ([ILLUSTRATION FOR FIGURE 6 OMITTED], horizontal line). Above this critical shade level Oscillatoriaceae will become dominant; at lower turbidities other algae will dominate. This implies that below the horizontal line the cyanobacterial turbidity-nutrient relation is irrelevant, whereas above the critical level the other turbidity-nutrient relation is irrelevant. Neglecting these irrelevant (dashed) parts, the two curves combine with the middle segment of the horizontal line to form an s-shaped curve of steady states that is typical of so-called catastrophic systems. The figure suggests that at low total P levels only the noncyanobacterial state is possible, whereas at very high total P levels only the cyanobacteria-dominated state exists. However, over a range of intermediate nutrient levels ([P.sub.1] [less than] P [less than] [P.sub.2]) both states are possible. Here, the community will tend to settle in either of the two states depending on whether the turbidity in the initial state is above or below the critical value ([E.sub.crit]).

This graphical model implies that the response to changes in the nutrient level should be discontinuous ("catastrophic") rather than smooth. When, starting from a low total P level, the nutrient loading of the lake is slowly increased, turbidity will gradually increase too. This smooth response ends when the critical total P value ([P.sub.2]) is reached, since above this level only the blue-green dominated state exists. When this "breakpoint" is passed the system will jump to a higher turbidity at the Oscillatoria-dominated upper branch of the diagram. If from this point the total P concentration is gradually reduced, the algal community will stay on the cyanobacteria-dominated branch until the lower critical nutrient concentration ([P.sub.1]) is reached, and then jump back to the lower branch. It can also be inferred that Oscillatoria will not easily disappear from lakes that have a high background turbidity ([E.sub.b]).


The above reasoning is based solely on the patterns observed in the field. In this and the next paragraph we construct a competition model and use it to analyze a completely independent set of information, namely the physiological characteristics of algae that can be measured in the laboratory. Instead of analyzing competition between many species as it occurs in the field, we simplify the problem by considering only one typical blue-green (b) and one typical green (g) algal species. For parameterization we use data from experiments with Planktothrix agardhii and Scenedesmus protuberans as examples of the two respective groups.

To build up the growth equations we assume that the productivity of the algae depends on the availability of nutrients and light. Losses due to mortality, respiration, and flushing are subtracted from the gross productivity. For the dependence upon the nutrient concentration (n) we take the classical Monod form with a half-saturation concentration (h):

n/n + h. (1)

For simplicity we consider the total nutrient concentration in the system (P) to be constant, and define it as the sum of free nutrients (n) and nutrients present in blue-green (b) and green (g) algae:

n = P - g - b. (2)

The dependence of productivity upon the underwater light climate is more difficult to write in a simple form. Obviously, light intensity varies in the course of the day and decreases also with depth. For an idealized well-mixed system of homogeneous depth, the integration of photosynthesis over the light gradient can be treated elegantly (Huisman and Weissing 1994). However, in real lakes the situation is always much more complex. Since it is, nonetheless, obvious that available light and therefore relative productivity in the lake declines with turbidity, we directly describe this in a simple pragmatic light limitation function:

1/1 + qE (3)

where q is the sensitivity to turbidity and E is the Lambert-Beer light extinction coefficient. This coefficient depends on algal biomass as well as on other components of the seston such as resuspended sediment particles. For our minimal model we omit background turbidity and write E simply as a function of the density of algae and their specific extinction coefficients ([k.sub.g] and [k.sub.b]):

E = [k.sub.g]g + [k.sub.b]b. (4)

Note that the sensitivity coefficient (q) is not solely dependent on the physiology of the algae, as it will [TABULAR DATA FOR TABLE 2 OMITTED] decrease with increasing incoming irradiation and increase with the mixed depth of the lake. Assuming the effect of nutrient limitation and light limitation to be multiplicative, the complete model becomes:

dg/dt = g[[r.sub.g](1/1 + [q.sub.g]([k.sub.g]g + [k.sub.b]b)) P - b - g/h + P - b - g - [d.sub.g] - f] (5a)

db/dt = b[[r.sub.b](1/1 + [q.sub.b]([k.sub.g]g + [k.sub.b]b)) P - b - g/h + P - b - g - [d.sub.b] - f] (5b)

where [d.sub.s] and [d.sub.b] are the typical rates of losses due to respiration, sinking, and mortality of both groups, and f is a species-independent loss rate due to flushing of the lake. The incoming water is assumed to be free of algae and have a nutrient concentration equal to P in order not to affect our mass balance.

The dimensions of the parameter and the default values used to produce the figures that follow are listed in Table 2. The points we make in our formal model analysis, however, depend only on inequalities of pairs of parameters, not on the specific values that we assigned to produce the figures. All qualitative results follow from the assumption that blue-green algae have a lower maximum productivity (r), loss rate (d), and sensitivity to turbidity (q), but cause a higher turbidity per unit of nutrients (k) than other algae. Thus the four basic inequalities are:

[r.sub.b] [less than] [r.sub.g] [d.sub.b] [less than] [d.sub.g] [q.sub.b] [less than] [q.sub.g] [k.sub.b] [greater than] [k.sub.g] (6)


To analyze the behavior of the model we first write it in a compact form:

dg/dt = gG(g, b, f, P) (7a)

db/dt = bB(g, b, f, P) (7b)

where the functions G and B are the ones presented in Eqs. 5a and 5b, respectively.

Like all competition models, our model (Eq. 5) has three trivial equilibria:

absence of both species (g = 0; b = 0)

absence of blue-green algae (g = [g.sup.*] [greater than] 0; b = 0)

absence of green algae (g = 0; b = [b.sup.*] [greater than] 0)

The values of [g.sup.*] and [b.sup.*] can be computed by solving the equations:

G(g, 0, f, P) = 0 B(0, f, P) = 0

with respect to g and b.

Since G and B are decreasing functions of g, b, and f and increasing functions of P, it follows from the implicit function theorem that [g.sup.*] and [b.sup.*] are increasing with P and decreasing with f, as one should expect.

For suitable values of the control parameters (f, P) the model can also have a nontrivial (i.e., strictly positive) equilibrium ([g.sup.+], [b.sup.+]) that can be obtained by solving the equations

G(g, b, f, P) = 0 (8a)

B(g, b, f, P) = 0 (8b)

with respect to g and b. This equilibrium corresponds to coexistence of both groups. It can be formally proven that such a coexistence is always unstable, and that the corresponding equilibrium ([g.sup.+], [b.sup.+]) is a saddle for all parameter values satisfying inequalities (6).

The results can be illustrated by three state portraits [ILLUSTRATION FOR FIGURE 7 OMITTED]. These graphs summarize the model properties by showing the trajectories of simulations starting from many different initial states. Fig. 7A and C correspond to situations where the same species wins the competition irrespective of the initial conditions, while Fig. 7B illustrates the situation in which both trivial equilibria, ([g.sup.*], 0) and ([b.sup.*], 0), are stable. In this case, the boundary of their basins of attraction is the stable manifold of the saddle. This is the dashed trajectory connecting the origin with ([g.sup.+], [b.sup.+]). Simulations end in either of the trivial "monoculture" equilibria depending on which side of this boundary they start.

The next step is to explore how the mode of behavior (i.e., state portrait) depends on the total P level and the flush rate. Let us assume that for a given pair (f, P) both monoculture equilibria are stable [ILLUSTRATION FOR FIGURE 7B OMITTED]. If, departing from this situation, we slightly perturb the parameters, the equilibria of the system will change. However, when the perturbation is sufficiently small the two equilibria will remain on the axis and, by continuity, the saddle ([g.sup.+], [b.sup.+]) will remain in the positive quadrant. Consequently, the trajectories of the system will be perturbed, but qualitatively the state portrait remains the same. For a change of the qualitative properties of this system it is necessary that the saddle ([g.sup.+], [b.sup.+]) disappears from the positive quadrant, which can only happen through a collision with one of the monoculture equilibria. This occurs when ([g.sup.+], [b.sup.+]) = ([g.sup.*], 0), i.e., when the two equations:

G(g, 0, f, P) = 0 B(g, 0, f P) = 0 (9)

have a solution with g [greater than] 0, or when ([g.sup.+], [b.sup.+]) = (0, [b.sup.+]), i.e., when the two equations:

G(0, b, f, P) = 0 B(0, b, f, P) = 0 (10)

have a solution with b [greater than] 0. The Eqs. 9 with g [greater than] 0 implicitly define a curve, called a bifurcation curve, in the parameter space (f, P). On one side of this curve we have systems with only the noncyanobacterial monoculture equilibrium [ILLUSTRATION FOR FIGURE 7A OMITTED], while on the other side of the curve both monocultures are stable [ILLUSTRATION FOR FIGURE 7B OMITTED]. Similarly, Eqs. 10 with (b [greater than] 0) define another bifurcation curve. This curve separates situations with two alternative stable states [ILLUSTRATION FOR FIGURE 7B OMITTED] from those in which only the cyanobacterial monoculture is stable [ILLUSTRATION FOR FIGURE 7C OMITTED].

The two bifurcation curves can be obtained by means of any computer package suitable for drawing implicitly defined curves. The result is shown in Fig. 8 where the labels [g], [g/b], [b] identify which equilibria are stable. The qualitative response of the system to changes in total P concentration and the flush rate can be seen from this bifurcation graph. Starting in the region [b] where a cyanobacterial monoculture is the only stable state, a shift to the alternative state will only occur after the lower bifurcation line is passed. On the other hand, starting from the region [g] where the cyanobacterial monoculture is unstable, a switch to cyanobacteria will only occur after the upper bifurcation line is crossed. In the region [g/b] where two alternative equilibrium states are stable, the system will stay in its current equilibrium state, unless perturbations bring it within the basin of attraction of the alternative state. Note that beyond a flush rate of [approximately equal to] 18% of the lake volume per day, cyanobacteria are predicted to be absent irrespective of the nutrient level. This fits well with the observation of Danish workers that large cyanobacteria are not found in lakes with a hydraulic residence time of [less than]5 d (E. Jeppessen, personal communication).

An alternative and more classical way of looking at the problem is to show the dependency of the systems equilibria upon the control parameters. Fig. 9 shows how the extinction E in equilibrium (in fact a linear combination of g and b) varies with the total P concentration and the flush rate. Note that Fig. 9A represents a vertical and Fig. 9B a horizontal cross section of the bifurcation graph [ILLUSTRATION FOR FIGURE 8 OMITTED]. The values [P.sub.1] and [P.sub.2] in the first hysteresis and [f.sub.1] and [f.sub.2] in the second hysteresis correspond to the intersections with the two bifurcation curves. It can be seen from those diagrams that a transition from blue-green to green dominance is always associated with a conspicuous drop in turbidity, and that in the vicinity of the breakpoints a small variation of a control parameter can be sufficient to induce the transition. Note that the hysteresis with respect to P corresponds well to the graphical model derived from the field data [ILLUSTRATION FOR FIGURE 6 OMITTED].

The figures also show that although the upper branch of the hysteresis is entirely above the lower branch, extinction associated with cyanobacterial dominance is not always greater than that associated to green algae dominance. For example, Fig. 9A (f = 0.1) shows that for P = [P.sub.1] the extinction [E.sub.b] associated with cyanobacterial dominance [approximately equal to] 1, while Fig. 9B (P = 0.3) shows that for f [greater than] [f.sub.1] the extinction [E.sub.g] associated to green algae dominance is greater than that. This supports the idea that in analysis of data from different lakes (cf. [ILLUSTRATION FOR FIGURE 1 OMITTED]) it is unlikely to find one critical shade level that separates cyanobacterial dominance from other states, because the critical level can depend on other factors, such as flushing, that affect the competitive balance.


In the first part of this paper we show that the presence of hysteresis in the algal community can be inferred from the patterns observed in the field. In the second part we use a mathematical model to show that competition between Oscillatoriaceae and other algae is a plausible explanation for this hysteresis in view of their physiological characteristics measured in the laboratory. The model results are robust in the sense that they require only qualitative inequalities between the two groups and do not depend on specific parameter values. It is reassuring to note that these inequalities are comparable to the requirements for hysteresis in other simple models.

As argued earlier, hysteresis occurs if the nontrivial equilibrium is unstable. This "unstable coexistence" case is also one of the qualitative possibilities in standard Volterra competition models. In such models the mechanisms of competition are not specified. Instead, the intensity of inter- and intra-specific competition is defined directly. Unstable coexistence occurs in Volterra models if inter-specific competition is stronger than intra-specific competition. Indeed, in our case green algae have a competitive advantage in an environment dominated by green algae because there is more light in that situation, whereas cyanobacteria have an advantage in the turbid condition caused by their own dominance.

Our general result is also analogous to that obtained from the graphical models of competition for two resources elaborated by Tilman (Taylor and Williams 1975, Tilman 1977, 1982, 1985). Tilman's resource-ratio theory predicts that the coexistence between two competing species is unstable if each species consumes relatively more of the resource of which it also tolerates the lowest levels. In our case competition is for light and nutrients. Blue-greens cause a higher turbidity at the same nutrient level. In resource-ratio terms, this means that they use relatively more light. Since they are also the most shade-tolerant group, this fits with the resource-ratio requirement for unstable coexistence.

Clearly, the model is a minimal model; i.e., it does not cover all possibly important mechanisms. Many other factors than the ones included in the minimal model will operate in real lakes. Some may enhance the hysteresis, while others will tend to promote coexistence instead.

A mechanism that has been suggested before to explain the absence of filamentous blue-green algae in relatively clear water is the fact that their photosynthesis is reduced at high light intensities (Van Liere and Walsby 1982). Photo-inhibition, which is not included in the model, will tend to enhance hysteresis, as it emphasizes the competitive inferiority of blue-greens in situations of low turbidity. In extreme cases hysteresis could even arise from it in the absence of any competing species (Toha et al. 1981), as the net growth of blue-greens in shallow clear water may be negative due to too-high light intensities.

Another topic of much discussion with respect to cyanobacteria is their inedibility. Even large herbivorous zooplankters are unable to effectively consume filamentous cyanobacteria under most conditions (Arnold 1971, Schindler 1971, Gliwicz and Lampert 1990). Viewed in more detail the interaction of filamentous cyanobacteria, herbivorous zooplankton, and edible algae is rather intricate, but an obvious implication of the inedibility is that grazing mortality will in general be lower for filamentous blue-greens than for edible algae. It can be inferred from the model results that this difference will tend to make the hysteresis more pronounced, as it enhances the already existing difference in (nongrazing related) loss rates ([d.sub.b] [less than] [d.sub.g]) that is one of the four basic inequalities (6) causing the hysteresis.

Although photoinhibition and inedibility should thus promote the expected hysteresis further, an absolute monoculture of filamentous blue-greens as predicted by the minimal model is never observed in real lakes [ILLUSTRATION FOR FIGURE 1 OMITTED]. Obviously, the monoculture prediction is an artefact of simplification. Many studies have shown that spatial heterogeneity and temporal variation of the environment help to prevent competitive exclusion, and it seems reasonable to assume that both factors play a role in algal communities as well.

In large lakes, depth as well as concentrations of suspended solids, nutrients, and algae can show a considerable horizontal variation. In such cases, it may well be that the competitive balance is in favor of blue-greens in only part of the lake. A simple thought experiment suffices to show that this may promote coexistence. Imagine a lake with distinct shallow and deep regions. Suppose that in case of complete isolation of the regions, cyanobacteria can dominate in the deeper parts while losing the competition in the shallow regions. Now consider a continuous slight mixing causing a very small input of the competitive inferior group in each part. Because of the stability of both equilibria such minor changes are not sufficient to destroy the dominance of the other group. However, the continuous mixing will prevent competitive exclusion and cause coexistence in all regions. Very strong mixing between the parts will cause the system to be homogeneous again, and cause cyanobacteria to be either dominant or absent from the whole lake. It can thus be inferred that coexistence should be favored in spatially heterogeneous lakes or interconnected sets of lakes where horizontal mixing is not too strong.

It has been demonstrated that temporal variation of the environment is another important process preventing competitive exclusion in algal communities (e.g., Padisak et al. 1993). This surely applies to Oscillatoria dynamics. Although these algae can stay dominant throughout the year in eutrophic lakes (Sas 1989) the seasonal pattern depends on the temperature conditions. In Denmark, filamentous blue-greens rarely over-winter (E. Jeppesen, personal communication), while in the milder climate of The Netherlands, the dominant Planktothrix agardhii disappears from the eutrophic shallow lakes only in cold winters (Berger 1975). Winter can apparently bring the system past the breakpoint below which blue-green dominance ends. The sensitivity of Planktothrix agardhii to cold winters fits with the observation that the growth of this species, like that of most large algae, drops relatively steeply with temperature (Reynolds 1988). Obviously, seasonal alternation between blue-greens and other algae implies "coexistence" during the transitional phase, and averages over a period including a transition, especially, will suggest coexistence.

Although the field patterns as well as the model results indicate that nutrients, through their effect on shade, influence the competition between Oscillatoriaceae and other algae, it is clear that temperature and flush rate are also important for the competitive balance. Recent studies have pointed out a fourth potentially important factor that may affect cyanobacterial dominance. Various aquatic macrophytes have been shown to release substances that inhibit the growth of cyanobacteria while having a much smaller impact on the development of other algae (Gross and Sutfeld 1994, Jasser 1995), and bag experiments in the field demonstrated that plants tend to cause a switch from cyanobacterial dominance to a dominance by green algae even though total algal biomass is not significantly affected (Jasser 1995).

The current information is insufficient to see exactly the interaction of the effects of nutrients (shade), flush rate, temperature and allelopathic substances on the competition. In general, however, a catastrophic system will show hysteresis in its response to all control variables. Also the "threshold value" for one variable will normally depend on the value of the other variables. The latter is illustrated for the combination of flushing and nutrients by the model analysis [ILLUSTRATION FOR FIGURES 8 AND 9 OMITTED]. At low nutrient levels, the sensitivity to flushing increases. An example of the combined effects of nutrients and temperature is provided by the history of eutrophication of Lake Albufera in Spain (Romo and Miracle 1994). In the 1970s eutrophication had caused the phytoplankton community to be dominated by Oscillatoriaceae in summer and autumn, but in the spring chlorophytes and diatoms were still dominant. Ongoing enrichment in the 1980s, however, led the chlorophyll levels to increase further, and Oscillatoria became dominant throughout the season, suggesting that the cyanobacterial dominance is less sensitive to the low temperatures when nutrient levels are higher.

In conclusion, field patterns as well as our physiology-based model indicate that dominance by Oscillatoriaceae can be an alternative stable state of the algal community of shallow lakes because these shade-tolerant cyanobacteria are able to cause an increase in turbidity that favors their competitive advantage. The relative inedibility of filaments to zooplankton may further enhance the stability of blue-green dominance. The model and field observations indicate that high flush rates reduce the probability of blue-green dominance because of their relatively slow growth rates. In addition, there is evidence that low winter temperatures and allelopathic substances from aquatic macrophytes can affect the competitive balance in favor of other algae.


We thank Erik Jeppesen, Jens-Peder Jensen, Paul Boers, Diederik van der Molen, Jef Huisman, and the editor, Donald DeAngelis, and two anonymous reviewers for useful comments. We also acknowledge the STOWA for permission to use unpublished data included in Figs. 1, 2, 3, and 6.

This work was carried out at the International Institute of Applied Systems Analysis, Laxenburg, Austria, and has been partially supported by the Italian Ministry of Scientific Research and Technology, contract MURST 40% Teoria dei sistemi e del controllo.


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Author:Scheffer, Marten; Rinaldi, Sergio; Gragnani, Alessandra; Mur, Luuc R.; Nes, Egbert H. van
Date:Jan 1, 1997
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