CORRESPONDENCE Flux control in ecosystems Setting sail to explore an unknown coast is essential to science, so Schulze’s recent suggestion1 to study ecosystems by means of metabolic control analysis can only be applauded. On the other hand, I am not sure whether Schulze really appreciates the nature and peculiarities of his vessel. Metabolic control analysis (MCA) (see Ref. 2 for a review) is essentially a sensitivity analysis of metabolic systems in the steady state. It allows one to calculate by analytical means the sensitivity of, say, the flux through a metabolic pathway towards a change in enzyme concentration. In this respect, MCA can be described as a classical analysis of parameter sensitivities applied to metabolic systems. Part of the beauty and popularity of this concept is due to two properties of metabolic pathways: (1) they obey the law of conservation of mass, and (2) the pathway flux and metabolite concentrations are frequently homogeneous functions of the enzyme concentrations. The concept of metabolic control analysis is different from that of (optimal) control3 of dynamic systems, which deals with the steering of systems -for instance, to adjust them to a specific state. Application of sensitivity analysis or MCA to ecosystems usually requires the formulation of a mathematical model of the system one wants to study. Thus, applying control analysis to ecology means in the first place constructing quantitative models. From the literature, it is evident that numerical sensitivity analysis has been applied repeatedly to such ecosystem models4-7. Also, the analytically oriented concept of MCA has been transferred to ecosystem models*. Here, some of the appeal that this approach has for metabolic systems is lost, since ecosystem models are not - and frequently cannot be-formulated in such a way that they consider conservation of mass, nor is there normally a set of model parameters in which the ecosystem flux is homogeneous. Nevertheless, for small models, or for models with a high degree of symmetryg, an analytical sensitivity analysis produces surprising insights into the sensitivity structure of models, which may prompt the search for such sensitivity patterns in nature. But we cannot expect to ‘approach understanding of control in complex and multi- species systems’1 from application of MCA to ecosystem models. However, perhaps Schulze does not have MCA in mind but rather, by collecting and combining approaches from different disciplines, he is aiming to create a novel tool in ecosystem analysis. If this is his intention, this tool should be described more clearly and the specific aspects of ecosystem functioning that he wants to explore should be made more explicit. C. Giersch Botanisches Institut der T.H. Darmstadt, Schnittspahnstr. 3-5, D-64287 Darmstadt, Germany References 1 Schulze, E-D. (1995) Trends Ecol. Evol. 10, 40-43 2 Fell. D.A. (1992) Blochem. J. 286, 313-330 TREE uol. IO. no. 6 June 1995 3 Cohen, Y., ed. (1987) Application ofcontrol Theory m Ecology Springer-Verlag 4 Astor, P.H., Patten, B.C. and Estberg, G.N. (1976) in Systems Analysis and Simulation in Ecology (Vol. 4) (Patten, B.C., ed.), pp. 390-429. Academic Press 5 Gardner, R.H., O’Neill, V.R.V., Mankin, J.B. and Carney. J.H. (1981) Ecol. Mode//ingl2,173-190 6 Overton, W.S. (1977) in Ecosystem Modelling in Theoryand Practice (Hall, C.A.S. and Day, J.W., eds), pp. 76-114, Wiley 7 Brylinski, M. (1972) in Systems Analysis and Simulation in Ecology(Vol. 2) (Patten, B.C., ed.), pp. 81-101, Academic Press 8 Giersch, C. (1991) Ecol. Modelling53,131-146 9 Wennekers, Th. and Giersch, C. (1991) Ecol. Modelling 54, 265-276 While pleased to see Schulze’s recent TREE article1 describing application of the principles of metabolic control analysis (MCA) to the control of ecosystem fluxes, we feel that the article fell short of doing justice to MCA and to its potential for application to ecological problems. Therefore, we outline how we, as biochemists, feel that the principles of MCA could be applied in ecology. First is the critical question of the correspondence between elements of biochemical and ecological systems as used in MCA. Schulze regards species as being equivalent to the action of enzymes. However, if we are interested in fluxes of matter or energy, it is logical to view species (pools of matter/energy) as corresponding to pools of metabolites, while the processes inter- converting the pools (photosynthesis, grazing, etc.) correspond to enzyme-catalysed metabolic processes. Thus, the rate of such a process, not the concentration of the organism causing it, would be equivalent to the concentration/rate of an enzyme. Schulze correctly points out that application of MCA is limited to certain situations, the asymptotically stable steady state being the most well known, but it can also be applied to time- dependent systems2. Schulze also states that it is necessary for enzyme concentrations to be constant, while pointing out that organism concentrations in an ecosystem do change. However, as organisms are analogous to pools, not processes, and pool sizes do not change in the steady state, it is the constancy of the functions relating pool sizes and process rates that is critical. Indeed, MCA can deal with altering process rates, either by allowing for a specific expansion flux3 or by considering a time frame that is short with respect to the rate of change of the process rate: there is no necessity to use hierarchical control analysis4. Space does not permit description of the full range of mathematical tools central to MCA that can be applied to ecosystems: the use of scaled control coefficients, the flux control coefficient summation theorems, the definition of a control coefficient and corresponding summation theorem for a concentration (pool size)6, the quantification of local effects (e.g. predator/prey interactions) in terms of elasticity coefficients, and their use to calculate control coefficients (already applied to ecological systems?). Finally, there is the question of relevance to ecologists’ needs. For biochemists, the concept of change of rate of a particular step is a meaningful one: quantities of enzymes in an organism can be experimentally altered, and the effect on fluxes and/or pool sizes can be measured. Such a concept is perhaps more artificial for an ecologist. An analogy could be the replacement of a carbon- fixing organism with one that has a different rate of fixation/unit mass. One area where MCA could be applied is in quantifying the response of an ecosystem to changes in its external parameters. Schulze stated that organism-imposed changes in the habitat invalidate the use of MCA. However, MCA defines response coefficients quantifying the effect of changes in external parameters (such as the example given: the pH of rain) on fluxes and pool sizes within the systems. To summarize, we feel that MCA can be applied to ecological processes, as long as one is clear about what questions can actually be answered. Simon Thomas Joao-Pedro Moniz-Barreto David A. Fell John H. Woods Mark G. Poolman School of Biological & Molecular Sciences, Oxford Brookes University, Headington, Oxford, UK OX3 OBP References Schulze, E-D. (1995) Trends Ecol. Evol. IO. 40-43 Acerenza, L., Sauro, H.M. and Kacser, H. (1989) J. Theor. Biol. 137,423-444 Flint, H.J. et al. (1981) Biochem. J. 200, 231-246 Kahn, D. and Westerhoff, H.V. (1991) J. Theor. Biol. 153, 255-285 Kacser, H. and Burns, J.A. (1973) Symp. Sot. Expl. Biol. 27, 65-104 Heinrich, R. and Rapoport, T.A. (1974) Eur. J. Biochem. 42,89-95 Giersch, C. (1991) Ecol. Modelling53, 131-146 Reply from E-D. Schulze Does it make any difference to the functioning of an ecological system if there are many species or a few? This is one of the key questions asked by the ‘Diversitas’ programme of IUBS and SCOPE, and there are very few quantitative data in order to clarify this issuel. I think both comments agree that metabolic control analysis (MCA) may be one approach to understanding complex systems, which might be better than simply calculating nutrient-, water- and other use-efficiencies of highly non-linear processes. It is quite clear that the biochemical view of using processes as driving variables and of considering the changes in pools as response would be the approach that has been tested at the cellular level. Pools would be equivalent to matter accumulated in species, and processes converting the pools would be enzyme reactions (Thomas et a/.). This approach would be more ‘clear’ in a physiological-biochemical sense, but it would not address the problem stated above. There are many ecosystem functions where the pool size accumulated in species is small and the flux is high, for example, the flux of water (a sunflower leaf may lose 10 times its weight on a summer 245