What we expect is often what we get …

In a recent post I posed the question of whether healthy ecology in rivers could be considered to be a “steady state” (see “Making what is important measurable …”). I asked this question because, following pioneering work by Brian Moss and others on the Norfolk Broads, the idea of “alternative steady states” in shallow lakes is well established. However, there is a deep-seated assumption that changes in rivers, and many other ecosystems, are gradual shifts along a continuous gradient: increase the “dose” of a pollutant or other pressure, and there is a concomitant “response” in the biology.   My earlier post referred to “good ecological status” as the goal of water management in Europe – implying that we should be trying to achieve a “state”.   Most of the approaches to ecological assessment define this state simply in terms of a threshold on a gradient but could there be other ways of interpreting such data?

Suppose that, for the sake of argument, algae in rivers exist in three “states” with respect to nutrients:

  • Low nutrients, high oxygen concentration – the natural “state” in most cases, where the river is naturally nutrient-poor and algae adapted to living with low concentrations of nutrients are selected.
  • High nutrients, high oxygen concentration – concentrations of inorganic nutrients are elevated due to agricultural or other enrichment, and conditions now favour competitive algae such as Cladophora over algae adapted to living in nutrient-stressed conditions.
  • High nutrients, low oxygen concentration – conditions associated with organic pollution, where there is substantial heterotrophic activity using up dissolved oxygen; conditions favour species of algae (such as some Nitzschia species) that can tolerate reducing conditions and which are facultative heterotrophs.   As this state is often associated with highly polluted conditions, nutrient concentrations will be higher than in the “high nutrient, high oxygen concentration” state.

If this model is true and we sampled diatoms across a number of similar rivers along a phosphorus gradient, then we might expect similar results from locations that shared the same state, as illustrated in the Fig. 1.   Note how the ranges for the different states overlap along our nutrient gradient.   Changes from one state to another are not driven solely by nutrient concentrations but may be induced by changes in other factors (e.g. grazing intensity).


Fig. 1.   Hyptothetical data assuming that algae in rivers exist in three alternative but overlapping “states”, which are expressed as three values of the Trophic Diatom Index (TDI): low nutrient, high oxygen (closed circles); high nutrient, high oxygen (open circles) and high nutrient, low oxygen (closed squares). Arrows indicate changes between the overlapping states.

Now let us assume that there is a second factor that can influence the composition of the diatom assemblage and, therefore, indices such as the TDI.   Local geology is known to have such effects, and can be summarised in terms of variables such as alkalinity or calcium concentration.   Let’s apply this variable at random by up to six TDI units to each level and plot the results:


Fig. 2. The same data as for Fig. 1 but this time with TDI values varying by ± 6 units due to a random variable.   Regression statistics: F: 48.8; P < 0.001; adjusted r2: 0.77.

This now looks less like three distinct stable states and more like the gradients that most stream ecologists like to see (especially if you ignore the three different symbols that I used to define the stable states). Gradients are, after all, amenable to all sorts of statistical methods including regression analysis and it is even possible to start contemplating predicting how the diatom assemblage might change if the phosphorus concentration was reduced by a known amount.   Of course, good ecologists should be aware of such factors, and control for them in any models that they construct but this does not always happen …

Finally, let’s assume that our second variable does not vary randomly but is, itself, weakly correlated with nutrients.   This time, the scatterplot looks even more impressive (see below). Yet it is the same scenario as in Fig. 1, only with some additional “noise” stirred in.   And I have only included a single additional factor when, in reality, there will be a number of different physical, chemical and biological factors working to influence the composition of the algal assemblage at any point in time and disguise the existence of three states.


Fig. 3. The same data as Figs 1 and 2 but this time with TDI values varying by ± 6 units due to a variable that is correlated with the x axis. Regression statistics: F: 152; P < 0.001; adjusted r2: 0.92.

As I said earlier, a good ecologist should understand these factors and control for them when building a model. However, this only ever works up to a point. Firstly, we can only control for what can be measured, and these additional measurements are limited by the resources available to a researcher as well as by the assumptions that s/he brings to the study design.   But this leads into my second point: we too often bring the assumption that we are observing changes along a gradient which, in turn, can make us blind to the possibility that the situation is more complex, and that we may be dealing with alternative stable states. The final point is that most of the studies from which inferences about algal ecology are made are based on spatial surveys with limited temporal coverage.   Any community that we observe in a river is the product both of the environment that we can try to capture with our measurements, but also of its history, and of events that may have taken place upstream. As Louis Pasteur once said, “fortune favours the prepared mind”. If we approach our data expecting to see a gradient then we are not surprised when, after some gentle cosseting with statistical package, a gradient usually appears.


I should point out, for the sake of completeness, that there is also a significant relationship between TDI and P for the data plotted in Fig. 1 (F: 46; P < 0.001; adjusted r2: 0.77).   My point is that it does not look like a gradient and a viewer is more likely to contemplate the possibility of alternative stable states.

I also suspect that these states can co-exist at the same site but more about this in a future post.

A good introduction to the application of alternative stable states to shallow lakes can be found in: Moss, B. (2010). Ecology of Freshwaters: A View for the Twenty-first Century. 4th Edition. Wiley-Blackwell, Chichester.


One thought on “What we expect is often what we get …

  1. Pingback: What does it all mean? – microscopesandmonsters

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