skip to primary navigationskip to content
 

General theories of macro-ecology

Introduction: It is just over a decade since West, Brown and Enquist (WBE) developed one of the most intriguing ecological theories ever published. Based on the idea that the dimensions of pipes within vascular transport systems had evolved to minimize hydraulic resistivity, they derived a function which showed that resistivity could be completely invariant of the path length travelled by water on its way to the leaves. This idea may sound arcane, but it's physiological implications are anything but, suggesting that a plant's ability to supply water to photosynthetic tissues is completely unconstrained by its size, sharply contrasting with long-held beliefs that age-related declines in photosynthesis and productivity arise from hydraulic limitation1. In a series of high profile publications, WBE and collaborators took their ideas further, developing a metabolic scaling theory (MST) which made predictions about a wide range of ecological processes, including changes in productivity, forest size structure, and biodiversity along environmental gradients.

Testing the WBE theory of vascular design: WBE makes specific predictions about how the dimensions of pipes should vary along the vascular transport pathway in order to achieve size-invariant resistivity. We performed one of the first tests of WBE theory by exploring whether scaling relationships within tree vascular systems were similar to those predicted by the theory. Conduits were observed to narrow towards the periphery of vascular system of all 45 trees of three species we investigated, and scaling relationships were hardly affected by the environment, despite us sampling along strong gradients of nutrient supply and temperature)2. Our paper supported the concept that plants have evolved vascular systems which have resistance-reducing properties, whilst highlighting departures of empirical data from the theory's predictions2. WBE theory does not include any consideration of leaves, which is unfortunate given that leaf vascular systems may account for as much as 1/3 of all hydraulic resistance. We showed that conduit widths within leaf veins narrow along the pathway from petioles to fine veins, but that scaling relationships depart substantially from WBE predictions, because planar leaves have a different systems for delivering water than the fractal-like branching systems in stems3,4.

Testing Metabolic Scaling Theory: MST has proven immensely stimulating to plant ecologists because it provides a quantitative, predictive framework for understanding the structure and dynamics of an average idealized forest’ (Enquist, West & Brown 2009). Proponents of theory maintain that it enables useful generalizations to be made by focusing attention on two key processes – the optimization of water transport through the xylem and the biomechanics of stem wood. The counterargument is that other processes which are well known to contribute to resource capture, transportation and metabolism have a significant influence on forest processes, and that their omission, or superficial treatment, gives rise to mismatches between MST predictions and empirical realities1,5. We have tested several MST predictions using forest inventory data from New Zealand, Spain and the USA (see below). These tests have highlighted shortcomings in MST, but we have shown that the inclusion of three fundamental ecological processes - asymmetric competition for light, disturbance, and plastic resource allocation- leads to improvements in the model's predictive ability 6 .

We tested the following predictions:

  • Trees in natural forests have invariant tree size distributions, with density scaling as a -2 power of stem diameter. We found that trees < 18 cm diameter followed an appropriately power-law size distributions in New Zealand and global datasets, but we observed significant departures of the scaling exponents from -2. For larger trees, MST greatly over-predicted densities because the theory did not include the effects of exogenous disturbance on forest processes7. We later showed that size distributions in stands of New Zealand mountain beech were influenced strongly by competitive processes during stand development, and were Weibull distributed. The overall structure of 9000 hectare of forest (i.e. the composite structure of multiple stands) was heavily influenced by disturbance events which occurred over 19 years of monitoring, and simulations demonstrated that size structure could vary substantially over a 50 year time period8.
  • Tree diameter growth scales as a 1/3 power function of stem diameter. Analyses of the New Zealand forest inventory indicates that growth curves often departing from the 1/3 scaling law9,10,11, a finding corroborated by several other studies. We re-analysed the dataset originally used to support in support of the theory, but found it to be so small and noisy that it was impossible to draw strong inferences from it. Our re-analyses showed that MST predictions were contained within very broad 95% confidence intervals, creating an illusion of close adherence to theoretical predictions11,12. We have shown that the size-dependency of growth is greatly influenced by competition11, particularly in high-productivity forests where competition for light is intense12.
  • Tree mortality scales as a -2/3 power function of stem diameter. It takes very big datasets to test this prediction, because mortality occurs only infrequently. We used Bayesian analysis of over 430,000 tree records from a large eastern US forest database to characterise tree mortality as a function of climate, soils, species and stem diameter13. We found that mortality was U-shaped vs. stem diameter for all 21 species examined, consistent with the idea that large trees are particularly likely to die during disturbance events (or suffer senescence). Similar results were found in New Zealand forests14. Thus, the MST prediction is not supported by empirical evidence.
  • Tree height scales invariantly as the 2/3 power of stem diameter. this was tested using data from 700,000 trees of 26 species extracted from the Spain forest inventory. The local competitive environment had a strong influence on aboveground allometry, but all trees were far shorter than predicted by MST, suggesting that factors other than biomechanics are important. Species that dominate in arid and cold habitats were much shorter (for a given diameter) than those from benign conditions, perhaps to reduce embolism risk, but within-species heights did not vary strongly across climatic gradients15.
  • Leaf Area Index (LAI) remains constant over the course of stand development. We measured LAIs, leaf angles, and nutrient concentrations in naturally monospecific Nothofagus stands, and found that LAI varied greatly with stand age16. We show that subtle changes in leaf angle and nutrient deployment in older stands may serve to increase their productivity16,6

Building upon the foundations of MST: We have developed an improved theoretical framework that includes the effects of competition, disturbance and plasticity6,7,8, and have used it to model forest carbon dynamics6. By very nature, disturbance is rather unpredictable, but we have used a MST-inspired forest simulator to explore the extent to which sporadic tree loss influences landscape-scale carbon fluxes6. Finally, we are working on the idea that vegetation self-organises in such a way as to increase entropy production, by increasing latent heat loss and reducing sensible heat loss17. We have found some evidence for increased entropy production during vegetation development, from analyses of flux data collected from towers over grassland and forest in the Amazon18.

  1. Coomes, D.A. (2006) Challenges to the generality of WBE scaling theory. Trends In Ecology & Evolution, 21, 593-596. DOI link
  2. Coomes, D.A., Jenkins, K.L., & Cole, L.E.S. (2007) Scaling of tree vascular transport systems along gradients of nutrient supply and altitude. Biology Letters, 3, 86-89. DOI link
  3. Coomes, D.A., Heathcote, S., Godfrey, E.R., Shepherd, J.J., and Sack, L. (2008) Scaling of xylem vessels and veins within the leaves of oak species. Biology Letters 4, 302-306. DOI link pdf (password needed)
  4. Coomes, D.A. & Sack, L. (2009) Response to comment on Coomes et al. ‘Scaling of xylem vessels and veins within the leaves of oak species’. Biology Letters, 5, 381-382.
  5. Price, C. A., Weitz, J. S., Savage, V. M., Stegen, J., Clarke, A., Coomes, D.A., … Swenson, N. G. (2012) Testing the metabolic theory of ecology. Ecology Letters. DOI link
  6. Coomes, D.A., Holdaway, R. J., Kobe, R. K., Lines, E. R., & Allen, R. B. (2012) A general integrative framework for modelling woody biomass production and carbon sequestration rates in forests. Journal of Ecology, 100, 42-64.
  7. Coomes, D.A., Duncan, R.P., Allen, R.B., & Truscott, J. (2003) Disturbances prevent stem size-density distributions in natural forests from following scaling relationships. Ecology Letters, 6, 980-989. click
  8. Coomes, D.A & Allen, R.B. (2007) Mortality and tree-size distributions in natural mixed-age forests. Journal of Ecology, 95, 27-40. DOI link
  9. Coomes, D.A. & Allen, R.B. (2009) Testing the metabolic scaling theory of tree growth. Journal of Ecology, 97, 1369–1373. DOI link
  10. Russo, S., Wiser, S.W., & Coomes, D.A. (2007) Growth-size scaling relationships of woody plant species differ from predictions of the Metabolic Theory of Ecology. Ecology Letters, 10, 889–901. DOI link
  11. Coomes, D.A. & Allen, R.B. (2007) Effects of size, competition and altitude on tree growth. Journal of Ecology 95, 1084–1097. DOI link pdf (password needed)
  12. Coomes, D.A., Lines, E. R., & Allen, R. B. (2011). Moving on from Metabolic Scaling Theory: hierarchical models of tree growth and asymmetric competition for light. Journal of Ecology, 99(3), 748-756. DOI link
  13. Lines E.R., Coomes D.A., Purves D.W. (2010) Influences of Forest Structure, Climate and Species Composition on Tree Mortality across the Eastern US. PLoS ONE 5(10): e13212. DOI link
  14. Hurst, J. M., Allen, R. B., Coomes, D.A., & Duncan, R. P. (2011). Size-specific tree mortality varies with neighbourhood crowding and disturbance in a Montane Nothofagus forest. PLoS One, 6(10), e26670. doi:10.1371/journal.pone.0026670
  15. Lines, E. R., Zavala, M. A., Purves, D. W., & Coomes, D.A. (2012) Predictable changes in aboveground allometry of trees along gradients of temperature, aridity and competition. Global Ecology and Biogeography, 21, 1017–1028. DOI link
  16. Holdaway, R.J., Allen, R.B., Clinton, P.W., Davis, M.R. & Coomes,D.A.(2008) Intraspecific changes in forest canopy allometries during self-thinning. Functional Ecology DOI link
  17. Holdaway,R.J., Sparrow, A.D., Coomes, D.A. (invited resubmission) A thermodynamic framework for understanding the development of terrestrial ecosystems. Biological Reviews.
  18. Holdaway,R.J., Sparrow, A.D., Coomes, D.A. (2010) Trends in entropy production during ecosystem development in the Amazon Basin. Philosophical Transactions of the Royal Society, B. 365, 1437-1447. DOI link