Optimality as a concept to understand and model vegetation at different scales

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Abstract:

Observations made at different scales are often incomparable, because they reveal different patterns within the same entity. The change in observed pattern with the change in scale of observation is often abrupt, a phenomenon referred to as ‘break in scale’. Linking patterns with different scales of observation has become a major challenge in all sciences; however, it appears that the better our ability to observe patterns becomes, the more ‘breaks in scales’ we find. This article links breaks in scales to hierarchical levels of organisation. It is argued that organisation is linked with optimality and that optimality is predictable to a certain degree. It is further argued that in some cases heterogeneity within a level of organisation can be neglected if this heterogeneity is assumed to be a result of optimisation; hence, the implementation of vegetation optimality in models can lead to a new degree of predictability in ecohydrology.

Reference:

Geography Compass, 2/5, 1580-1598.
Weblink to publisher's web page.
Postprint of this manuscript (accepted version of the paper formatted by author).
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Figure 1: Different levels of organisation and their ranges of dimensions in space and time. Coloured lines delimit the estimated range of dimensions for each level. Dots represent the values in the inserted table.

Figure 2: Cross-section through a pine needle. Copyright: Michael W. Davidson, National High Magnetic Field Laboratory, Florida State University. Reprinted with permission.

Figure 3: Organisation levels within the same entity at different scales: (A) thylakoid membranes within a chloroplast, (B) chloroplast, (C) cross-section through a mesophyll cell, (D) cross-section through a pine needle, (E) pine branch and (F) canopy. Images are taken from different plant species. Images (A) and (C) from ‘Plant Cell Biology on DVD – Information for Students and a Resource for Teachers’, by B. E. S. Gunning, www.plantcellbiologyonDVD.com; image (B) copyright: Dennis Kunkel Microscopy Inc., 2004; image (D) copyright: Michael W. Davidson, National High Magnetic Field Laboratory, Florida State University; and images (E) and (F) photographed in the Bohemian Forest in the Czech Republic. Reprinted with kind permission from the copyright owners.

Figure 4: Rate of CO₂ assimilation (A) as limited by either electron flux (A_j) or RUBISCO (A_v). C_i denotes the internal partial CO₂ pressure, which increases with stomatal conductance, tending towards the external partial CO₂ pressure (C_a) for infinite conductance. Modelled after von Caemmerer (2000), with model parameters as in Figure 2.6 in von Caemmerer (2000).

Figure 5: Flow diagram of gas exchange in a leaf. A photosynthesising cell (bottom) is a CO₂ sink and H₂O source at the same time. As CO₂ enters the inside of the leaf through the stomata, water vapour exits the leaf. Both fluxes follow the concentration gradient.

Figure 6: Relationship between transpiration (E_t) and CO₂ assimilation (A_g) for a given electron transport rate (J_e) and atmospheric water deficit (D_v). Increasing stomatal conductance (G_s) leads to a linear increase in E_t, while A_g approaches a limit. The limit is determined by the light-induced electron transport rate (J_e) and corresponds to A_j at C_i = C_a in Figure 4. The slope of the curve (λ) is initially determined by D_v and increases towards infinity as A_g approaches its limit. For any point along the curve, A_g/E_t gives the corresponding water use efficiency, while the light use efficiency is directly proportional to A_g.

Figure 7: Net Carbon Profit as the difference between carbon acquired by photosynthesis and the carbon used for the construction and maintenance of organs necessary for its uptake. As CO₂ uptake from the atmosphere is inevitably linked to the loss of water from the leaves, the root system as well as water transport and storage tissues are essential to support photosynthesis. Soil water supply, atmospheric water demand and daily radiation constitute the environmental forcing. Within those constraints, vegetation is assumed to optimise foliage, transport and storage tissues, roots and stomata dynamically to maximise its net carbon profit.

Figure 8: Modelled (black) and observed (grey) daily evapotranspiration rates (E_T, top) and CO₂ uptake rates (A_g,tot, bottom). Observed and modelled total CO₂ uptake during the plotted period was 629 mol/m² and 725 mol/m², respectively. The dashed line shows scaled daily averages of the validity flag values, ranging between −0.2 for a whole day of valid measurements and −0.4 for a whole day of missing data where a neural network approach was used to fill the gaps (data taken from Schymanski 2007; Schymanski et al. 2008b).