Dealing with ecosystems III: Causal thickets and changing correlations

Graham Harris v3By Graham Harris

This blog is continued from Thinking Systems #9

This is a good place to stop for a while and read William Wimsatt’s (2007) book Re-engineering philosophy for limited beings: piecewise approximations to reality. Wimsatt’s goal in writing that book was to provide a guide to bounded rationalism and heuristics for a messy world.  The book draws on a wide range of sources including Andreas Wagner and one of my favourite books, Daniel Dennett’s (1995) “Darwin’s dangerous idea: evolution and the meanings of life. Dennett pointed out anyone that takes a consequentialist view whilst living in the middle of a system can only ever have partial knowledge.

Everything I have written so far centers around the concepts of bounded rationality, of satisficing rather than seeking optimal solutions, of the partiality of concepts and models and of the limitations on prediction. In his book Wimsatt developed the idea of “causal thickets” – messy situations that arise when the boundaries between differing perspectives (each with only partial explanatory power) begin to break down with further increases in complexity. New insights can arise from conceptual and methodological disputes and, as Wimsatt argues, progress is often made from error rather than from success. When progress is not made it is because those who hold fast to dominant paradigms fail to accept new data as evidence of the need for change. Extinction may result.

One pertinent example for this blog lies in the use of rationalist simulation and decision support models in ecology. It was evident from early days (e.g. the early 1970s computer models of the Laurentian Great Lakes) that these models only captured some of the central tendencies in the data, and did not capture the small-scale dynamics that we actually saw in the lakes. Richard Vollenweider made this point about the models at the time.

Over the years it has proved to be not too difficult to get the general pattern of the response of lakes to altered nutrient loads correct, because it is possible to model physiological constraints, but most modelers have avoided rigorous statistical validation of their models. Instead there has been much visual comparison of time series plots and a lot of hand waving. As Keith Beven has shown, rigorous statistical analysis of model performance usually reveals that the vast majority of environmental simulation models are non-performing due to epistemic, structural and other uncertainties.

Taking the black box, ecological approach as the dominant perspective has led to fine scale ecological variability being dismissed as being unimportant – and therefore able to be averaged out. Wimsatt discusses the strengths and the limitations of many such partial approaches at length: they have their place but can lead us astray.

There is much spatial and temporal heterogeneity in ecosystems, indeed this is fundamental to their functioning and robustness. Ecosystems possess distributed robustness, so chance and necessity – choice under uncertainty and error – allow the system to explore the adjacent possible configurations in terms of species composition and physiological and behavioural strategies. Errors are winnowed out through evolution so uncertainty and error are part and parcel of ecological functioning.

In ecological pattern and process much information and meaning is coded in stoichiometric relationships. (Stoichiometry is the relative abundances of major nutrient elements; see the classic Ecological stoichiometry: the biology of elements from molecules to the biosphere (2002) by Robert Sterner and James Elser). Life only evolved once so that molecular elemental ratios determine life’s requirements. There is a vital interaction between molecular biology, physiology and nutrient cycling within and between organisms. Different species have subtly different physiologies, metabolic pathways and elemental requirements so that things like Carbon:Nitrogen:Phosphorus ratios and the ways in which these elements are cycled and stored within organisms and ecosystems at small scales control the large scale ecological responses.

Even rivers and lakes show considerable small-scale biological patchiness – when we might expect them to be well mixed – and this patchiness usually frustrates attempts to seek statistical correlations and evidence of cause and effect in watershed management. Many years ago Richard Vollenweider resorted to the use of moving correlations in time series analysis of C:N:P data to try to understand why there was no overall correlation between these ecological variables measured in Adriatic coastal waters; even when he had good reason the believe that there should have been a relationship (because of stoichiometric constraints).

Work on the ecology of plankton in lakes as long ago as the 1980s (by Harris & Trimbee in the Journal of Plankton Research) showed epochs in the data series when correlations switched sign in the middle of the observations. So stoichiometry is not fixed over short time periods and at small scales. Just as we can save to and borrow from our bank accounts and investments, organisms can do likewise with their own nutrient stores and with stocks elsewhere in the system. Differing physiological strategies determine success or failure in uncertain environments. Evolved anticipatory models guide the choices made.

We know from the work of William Davison and co-workers in UK that elemental cycling in ecosystems can be controlled by patchiness in the populations of bacterial consortia at scales as small as 10s-100s of microns. So distributed robustness occurs across a wide range of scales in time and space. There is much apparent local noise but the stoichiometry of life on Earth is preserved as a central limit phenomenon.

Louise Heathwaite and I further extended Vollenweider’s work into rivers in papers in the Journal of Hydrology and in Freshwater Biology. Spatial/temporal heterogeneity in pattern and process gave highly “noisy” nutrient data but what was once again revealed was a pattern of sign switching in the stoichiometric correlations in different patches of water and at different times. There was no apparent overall correlation in the data but at small scales the correlation coefficients switched rapidly from almost +1 to -1. Much saving and borrowing was going on by the interaction of biological and chemical processes both in the watershed draining into the rivers and in the river itself.

Organisms possess their own perspectives in the form of evolved anticipatory models, which guide their actions and choices. Each sees their environment in different ways. Because organisms are working with partial, local information they are boundedly rational and are not performing optimally – they are satisficers (Dennett, 1995) – so what we have, effectively, is a causal thicket which extends all the way down from human concepts and practices to species responses – even to scales of fractions of a millimeter. Every living being is operating as best it can under uncertainty.

The probability density functions of the moving correlations were decidedly non-normal but closer inspection revealed that there were subtle patterns in these data, which revealed process information that was covered over by the extreme patch-to-patch variability. So this variability, combined with 1/f scaling in the overall time series data, meant that it was very difficult to discern cause and effect. Evidence of ecological pattern and process and of the effects of management works and measures was buried in a huge amount of (ecologically important) small-scale dynamics. The context was being constantly changed by the interaction of simultaneous top down management action and bottom up biological dynamics.

The usual practice of analysing river water quality data is to average all the time series data from rivers so as to produce summary statistics. Most of the ecological data on small sale dynamics is not normally distributed; indeed it is customary to transform these data in various ways to make them tractable for routine (frequentist) statistical analysis. Customary practice destroys information.

Distributed robustness, 2nd order cybernetic interactions and the local working out of system dynamics – not optimisation by the organisms but satisficing under the circumstances – leads to these kinds of complex and unpredictable patterns. Chance and necessity at small scales play into and interact with larger scale, emergent, patterns so that we can, on occasion, see emergent order and The collapse of chaos (Cohen & Stewart, 1994).

By controlling the movement of elements to and from sources and sinks, organisms actively construct their environments and the planet we inhabit. Organism-environment interactions are real, fundamental and 2nd order, and they lead to development and Darwinian evolution so, like Rosen, we need a relational explanation for what we see.

What we see in Nature is not optimal, but it is not random either. Dispersal and advection, reaction and diffusion, take place across multi-fractal landscapes – information and meaning are created and detected at all scales. Ignacio Rodriguez-Iturbe and colleagues have looked at dispersal of humans and organisms across fractal landscapes and waterscapes, and have shown that the bulk properties of watersheds, for example, lie, as we might expect, somewhere between the random and the optimal.

Dealing with these kinds of ecological data requires a new approach and our expectations need to be more modest. Ecological data are most often not normally distributed and are not stationary; generating functions and variances are not consistent throughout data sets. Physics envy does not work here. As Michael Hauhs, Holger Lange and others have shown, ecological time series are characteristic of 2nd order complex systems so they require meta-statistics – statistics about statistics – information measures and variances of variances. Even so we end up with summary meta-statistics of non-stationary data series that show differences between systems but we are unable (at least at present) to understand why this might be.

We only see Wagner’s neutral zones – the persistent states – and they do seem to only occupy a subset of all possible state spaces. There is high level order (see Cohen & Stewart, 1994) and there is also convergent evolution or homoplasy: analogous features reoccur in Nature but they arise in different ways.

So to reiterate: these systems operate at many scales and levels and they are not trivial systems. Uncertainty is rife, “noise” is everywhere, error is important and our rationality is bounded at best. Organisms acting reflexively within these systems (and that includes us) cannot have complete knowledge of pattern and process at all levels. Our rationality and our morality is bounded by the distributed robustness: anticipatory models determine what ought to be done, the actual environment determines what can be done. Following Wimsatt we seek heuristics that will allow us to re-engineer philosophy and practice for us as limited beings. We seek piecewise approximations to ecological and ethical reality.

In the next two blogs I turn to context and meaning to seek a way forward.

This discussion will be continued in Thinking Systems #11.

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