A brief review of progress and some remaining challenges in modelling plant development

Vince Gutschick (October 1, 2010)

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As part of a selective review of progress in modelling of plant development, I wish to offer a larger context, extending to the evolutionary scale, and mostly to pose a set of questions or challenges to modellers.

First, I would like to affirm some premises that I believe are widely shared by modellers. Why do we make models?: 1) to predict plant (or stand or ecosystem) performance, though this is relatively rare, because vast knowledge is required unless the universe of possible environments is much restricted; 2) to simplify the design of multi-factorial experiments, reducing their dimension by eliminating those factors or combinations of factors that are least likely to be informative; 3) to develop testable hypotheses of plant responses based on combining our firm knowledge with our shakier estimates; witness the successful erect-leaf hypothesis of the '60's or my own model prediction that reduced leaf chlorophyll allows gains in crop yield, and 4) to synthesize our knowledge, so that we may understand emergent properties, or be inspired to develop new hypotheses.

We do aim, I hope, for ultimate utility of our models, both in applications and for use by other modellers who may develop a synergy with us. The essence of utility is often simplification. A maxim to keep in mind is that of Einstein, reported by chemist John Ross: "Simplify as much as possible, but no further." We may recall the chaos in modelling the biochemistry of photosyntheses through the '60's and '70's until Farquhar, von Caemmer, and Berry offered their elegant, simple, yet accurate model of C3 photosynthesis in 1980, followed by one for C4 photosynthesis. Necessarily elaborate and computationally-intensive models of radiative transport in plant stands became simplified (initially, over-simplified) as turbid-medium models or two-flux models, with a (final?), accurate simplification of the truly high-order processes via the concept of nested radiosity - alas, more applied by moviemakers than by us modellers. On larger spatial scales, modelling of biogeochemical fluxes must retain some empirical simplifications that need our attention. For estimating evapotranspiration (ET), is fractional cover or fractional PAR interception better than leaf area index when ET is mostly energy-limited... but is it much inferior to using LAI for estimating photosynthetic CO2 flux? Related to simplification but not identical to it is user-friendliness of our algorithms. A major practical use of models is in irrigation management, arising from the simple fact that 36% of all crop biomass is produced on the 16% of the land that is irrigated and thus 3-fold more productive than the rest. Farmers and water managers demand simple interfaces partly because of their lesser sophistication in process understanding but even more so because of the insupportability of data-hungry models and the diversity of other demands on their time. Even considering the community of other modellers, we must examine our models carefully for the tradeoffs between complexity (process-inclusiveness) and ability to parametrize models; the brief comparison by Vogel et al. (1995) is worth reading. We may ask, How do evaluate our models, for both accuracy and usability. We can do sensitivity analyses to see that parameters are most important for accuracy. To assess sensitivity to forcing variables, is it worth the effort to develop adjoint equations numerically? Are ensembles of models useful, as in climate research? Do we have the right statistics to express our sensitivity studies? It is harder yet to analyze what processes are most important - that is, What is a good model structure? Replacement of submodels with empirical (often algebraic) relations is a test, though not an easy one nor one with clear endpoints.

One key use of models is optimization. I risk an over-emphasis on the topic here, even without expanding the discussion to mathematical methods. Optimization of plant performance is a tool for crop management, for ideotype development, and for exploring the evolutionary physiology and ecology of plants. The first two uses are perhaps obvious and familiar. The third use, in evolutionary studies, presents interesting opportunities. Of course, to assume that plants evolved to optimal function is to risk the Panglossian fallacy of adaptationism, if only because all species necessarily lag in adapting to neighbors' evolution (the Red Queen phenomenon). Moreover, we are not privy to the full range of selection pressures and (phylogenetic) constraints faced by organisms. Nevertheless, evidence of near-optimization is abundant, as in the Ci/Ca setpoint for leaf gas exchange or the distribution of leaf N within a canopy. Assuming optimization is a starting point, first, to fill out our process understanding, and, second, to discover the constraints and competing selection pressures. - e.g., the compromise of a higher specific leaf area than that which optimizes canopy photosynthesis, in order to shade competitors (Gutschick and Wiegel, 1988; Schieving and Poorter, 1999). I now offer several questions about optimization or adaptiveness of key plant traits: 1) Why do plants not have higher N content, particularly the ruderals? It is generally not that costs of metabolizing N exceed photosynthetic benefit. Is it risk of herbivory, lack of metabolic "room," or other constraints?; 2) What is the tradeoff between high photosynthetic rate per mass and strong depletion of seasonal water supplies?; 3) How far have we progressed in understanding trait selection, especially developmental times (anthesis... ) in environments with stochasticity (risks), that are abiotic, such as frosts, or biotic, such as herbivory and disease?; 4) What would a comprehensive look like for explaining the set-points of major plant traits - physiological, such as Ci/Ca, developmental, such as allocation (leaf/shoot, hydraulic conductivity attributes, phenology etc.), and ecological, such as disease susceptibility?; 5) What combination of trait complexes and environmental variation (space and time) explain coexistence of species, given that most models of extinction (under competition or other pressures) generate a winner-take-all result. Multiple resource competition and spatial patchiness only expand the number of species modestly, and alternating selection only delays the winnowing of species.

The mechanistic description of development demands that we understand the proximate signals that trigger developmental events - direct environmental cues (here, much is known) and integrated cues such as C and N reserves (here, less is known). The signals for root development - elongation rates, branching, gravitropic patterns - that arise from water and nutrient status (plant and soil) are probably the most poorly known, if only because of the difficulties of studying roots in soil. We need process models for these signals from experiment and, conversely, we need to help interpret experimental studies. Among the pressing questions economically and intellectually are, What causes alternate bearing in tree crops?, and, How does elevated CO2 cause shifts in N status of diverse tissues in a species-specific manner?

For plant breeders, evolutionary biologists, and evolutionary ecologists, the Holy Grail is understanding the links from genes and genomes to phenotype and performance. Advances have occurred in quantitative genetics and the study of regulatory networks. Challenges remain in understanding epigenetic effects and, at the population level, the constraints to genetic adaptation posed by population genetic structure, sensu Lande. Expanding upon the genetic constraints, we may profitably pay attention to the degree to which populations have lost adaptive genetic variation for growth at elevated CO2 over the past 20 My.

Selected references:

* V. P.Gutschick. 1984. Photosynthesis model for C3 leaves incorporating CO2 transport, radiation propagation, and biochemistry.. 2. Ecological and agricultural utility. Photosynthetica 18: 569-595.
* W. T. Pettigrew, J. D. Hesketh, D. B. Peters, et al. 1989. Characterization Of canopy photosynthesis of chlorophyll-deficient soybean isolines. Crop Sci. 29: 1025-1029.