“Despairing empiricism” is a phrase I invented some years ago to describe a disease that has infected modellers trying to describe ecosystems numerically since they first started to do so, circa 1980. The underlying idea is that since biological phenomena are (supposedly) not subject to universal laws, the only way they can be modelled is as physical systems with large numbers of parameters that have to be measured, and prescribed – as they can’t be predicted.
This view is fundamentally wrong because it neglects the most universal law of biology. Natural selection ensures that inefficient combinations of traits are eliminated – and thus, it enforces strong optimality criteria that vastly reduce the dimensionality of variation in the morphology and physiology of organisms. Unfortunately, the principle of optimization by natural selection has been largely neglected in the development of ecosystem models. As a result, models are far more complex than they need to be and contain far more uncertain parameters than they should.
A key theme of my current programme is the intrinsic predictability of leaf photosynthetic traits. Graham Farquhar’s model of photosynthesis lies at the core of plant ecophysiology, and most terrestrial models use it in some form or other. But it describes a leaf-level, instantaneous, physiological process. To make predictions with the Farquhar model for larger spatial and temporal scales requires certain highly variable quantities to be known: the maximum rate of carboxylation (Vcmax), the maximum rate of electron transport (Jmax), and the ratio of leaf-internal to ambient CO2 concentration (χ). Certain regularities in the relationships between these quantities have been noted repeatedly. In particular, the ratio Jmax/Vcmax seems to be quite conservative, although lower at higher temperatures; χ is very conservative, although lower in dry environments; Jmax and Vcmax tend to be higher under high illumination and lower in the shade, as seen for example in the vertical gradient of maximum assimilation rates in dense canopies. From time to time, optimality considerations have been invoked to explain such observations, and as empirical generalizations they have been used to simplify models in various ways. But there has not previously been any systematic attempt to develop and test theory about just what is optimized, or to test previously unappreciated predictions of the theory.
A previous post by Wang Han verified some of the consequences of the ‘least cost hypothesis’ as first propounded by Ian Wright (Macquarie). Wang Han showed how this hypothesis – that plants tend to minimize the sum of the unit costs of carboxylation and transpiration, which are intimately coupled through stomatal behaviour – leads to quantitatively correct predictions not only of the accepted response of χ to vapour pressure deficit, but also of the relationship of χ to temperature (discovered in field data by Dong Ning), and a relationship to elevation that has actually been known, but previously eluded explanation, for over thirty years. Moreover, this trait appears to be highly plastic, showing a ‘universal’ response to environment that is identical within and between species.
Another plank of our theory in development is the ‘co-ordination hypothesis’ – that under typical daytime field conditions the rates of Rubisco- and electron transport-limited photosynthesis tend to be equal. This is a long-standing idea, obviously corresponding to an optimality hypothesis (plants gain nothing from over-investment in either carboxylation or electron transport) although alternative interpretations have been put forward. The idea had its origin in A–ci curves, as it is found that the typical operating point (typical values of A and ci) is usually near the co-limitation point. (The idea can easily be forgotten, however, when photosynthesis measurements are routinely made at saturating, as opposed to ambient, illumination – thus ensuring that Rubisco limitation holds, and in doing so, setting up temperature and CO2 responses that are quite different from those that apply in the real world.)
We have refined the co-ordination hypothesis by taking into account the costs of maintaining electron transport capacity, which lead to a specified degree of curvature in the light response curve of assimilation below the co-limitation point. The presumed mechanism behind the co-ordination hypothesis is the acclimation of the photosynthetic traits Vcmax and Jmax to environmental variations, on time scales that are not quite clear, but are evidently longer than the diurnal cycle and shorter than the seasonal cycle.
The co-ordination hypothesis is extraordinarily powerful. The following are some of its predictions.
- Vcmax when measured at ambient growth temperature should increase with temperature, but less steeply than the kinetic response of Rubisco. The increase is due to the declining affinity of Rubisco for CO2 with increasing temperature. On the other hand, Vcmax when corrected to a standard temperature, e.g. 25˚C, should decline with temperature. That is, the quantity of active Rubisco should be reduced, compensating for the enzyme’s greater efficiency at higher temperatures. Henrique Togashi’s fieldwork has quantitatively confirmed both of these predictions for multiple woody species in the Great Western Woodlands, Australia.
- Jmax/Vcmax has a predictable value that varies with growth temperature in the same way as has been shown in experiments (demonstrated by Wang Han). This variation, again, is not due to the kinetics of the enzymes involved in the processes, but arises because of the different intrinsic temperature responses of the two limiting reaction rates in the Farquhar model. On the other hand, the ratio after both quantities have been corrected to 25˚C shows little variation with growth temperature – as has been observed.
- The metabolic component of leaf N, generally assumed to be proportional to Vcmax at a standard temperature, should be proportional to illumination; decline with increasing growth temperature; decrease with increasing χ; and be independent of N supply (e.g., whether the species is N-fixing or not). Analyses by Dong Ning have recently confirmed all four predictions, for community mean values derived from Ausplots field collections on a geographic gradient across the centre of Australia.
There are many more predictions, and many ways to test them. Yan-Shih Lin is assembling a large set of A–ci curves to test the global predictability of Vcmax and Jmax. We have access to a large recent global compilation of leaf respiration (Rdark) data. According to the Farquhar model, leaf respiration should be proportional to Vcmax. A recent multi-author paper by Owen Atkin (ANU) and others indicates that Rdark acclimates to temperature, so that the ratio of Rdark in cold and warm climates is much less than would be predicted by short-term enzyme kinetics.
The hypothesis also predicts how photosynthetic traits should respond to increased CO2 concentration. Vcmax and leaf N should decline – just as they are observed to do. This is usually explained in the literature as an effect of dilution or limiting N uptake. These explanations are redundant, and anyway they fail to explain why the actual assimilation rate always increases.
The co-ordination hypothesis has an important practical consequence for modelling gross primary production, GPP. On monthly timescales GPP should be co-limited by Rubisco activity and electron transport, so either equation could be used to predict GPP. But where we have flux measurements, we don’t know the effective canopy value of Vcmax. We do know the illumination (from meteorological data) and we know the green vegetation cover (from satellite measurements), so we know how much light is absorbed (the product of these two quantities) and we can apply the equation for electron transport-limited photosynthesis at the predicted co-limitation point – which turns out to be proportional to absorbed light.
Hardly a month seems to go by without the publication of yet another ‘Light Use Efficiency’ (LUE) model – models in which GPP is, indeed, assumed to be proportional to absorbed light. It is a good empirical generalization, as shown in work with flux data over the last couple of years by Brad Evans (using the Ozflux data) and Tyler Davis (using the ‘free and fair use’ publicly available subset of the global FLUXNET data set). What the co-ordination hypothesis does, however, and the authors of LUE models do not, is to explain why it works so well. Moreover, the co-ordination hypothesis allows us to predict how GPP as predicted by LUE models should be expected to respond to environmental variables, including ambient CO2.
Finally, all of this has a bearing on the response of GPP to temperature. We profess to be interested in the effects of global warming on primary production. An outsider to the field might expect that this response would be well established. It is not. Current models don’t even agree on whether the net effect of warming, at a global scale, is an increase or a decrease in GPP. The co-ordination hypothesis appears to make a bold (and counter-intuitive) prediction that so long as temperatures stay above the threshold for cold inhibition (10˚ or 15˚C?) the effect of increasing temperature on GPP should be a gradual decline. It remains to be seen whether this is true. Watch this space.