Assessment of uncertainty in functional-structural plant models.

BACKGROUND AND AIMS Constructing functional-structural plant models (FSPMs) is a valuable method for examining how physiology and morphology interact in determining plant processes. However, such models always have uncertainty concerned with whether model components have been selected and represented effectively, with the number of model outputs simulated and with the quality of data used in assessment. We provide a procedure for defining uncertainty of an FSPM and how this uncertainty can be reduced. METHODS An important characteristic of FSPMs is that typically they calculate many variables. These can be variables that the model is designed to predict and also variables that give indications of how the model functions. Together these variables are used as criteria in a method of multi-criteria assessment. Expected ranges are defined and an evolutionary computation algorithm searches for model parameters that achieve criteria within these ranges. Typically, different combinations of model parameter values provide solutions achieving different combinations of variables within their specified ranges. We show how these solutions define a Pareto Frontier that can inform about the functioning of the model. KEY RESULTS The method of multi-criteria assessment is applied to development of BRANCHPRO, an FSPM for foliage reiteration on old-growth branches of Pseudotsuga menziesii. A geometric model utilizing probabilities for bud growth is developed into a causal explanation for the pattern of reiteration found on these branches and how this pattern may contribute to the longevity of this species. CONCLUSIONS FSPMs should be assessed by their ability to simulate multiple criteria simultaneously. When different combinations of parameter values achieve different groups of assessment criteria effectively a Pareto Frontier can be calculated and used to define the sources of model uncertainty.

[1]  Demetris Koutsoyiannis,et al.  One decade of multi-objective calibration approaches in hydrological modelling: a review , 2010 .

[2]  M. Zimmermann.  Hydraulic architecture of some diffuse-porous trees , 1978 .

[3]  M. G. Ryan,et al.  Effects of branch height on leaf gas exchange, branch hydraulic conductance and branch sap flux in open-grown ponderosa pine. , 2002, Tree physiology.

[4]  B. Bond,et al.  Does turgor limit growth in tall trees , 2004 .

[5]  E. David Ford,et al.  Definition and calculation of uncertainty in ecological process models , 2009 .

[6]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.

[7]  B. Bond.  Age-related changes in photosynthesis of woody plants. , 2000, Trends in plant science.

[8]  Keith Beven,et al.  A manifesto for the equifinality thesis , 2006 .

[9]  R. Fisher,et al.  On the Mathematical Foundations of Theoretical Statistics , 1922 .

[10]  E. David Ford,et al.  The use of multi-criteria assessment in developing a process model , 2006 .

[11]  M. G. Ryan,et al.  Evidence that hydraulic conductance limits photosynthesis in old Pinus ponderosa trees. , 1999, Tree physiology.

[12]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[13]  J. Brooks,et al.  Branch junctions and the flow of water through xylem in Douglas-fir and ponderosa pine stems. , 2003, Journal of experimental botany.

[14]  Ignacio Lira.  Evaluating the Measurement Uncertainty: Fundamentals and Practical Guidance , 2002 .

[15]  Xiaopeng Zhang,et al.  Plant growth modelling and applications: the increasing importance of plant architecture in growth models. , 2007, Annals of botany.

[16]  M. C. Kennedy,et al.  Model analysis of the importance of reiteration for branch longevity in Pseudotsuga menziesii compared with Abies grandis , 2004 .

[17]  M. Zimmermann,et al.  The hydraulic architecture of eastern hemlock (Tsuga canadensis) , 1984 .

[18]  M. G. Ryan,et al.  Hydraulic Limits to Tree Height and Tree Growth , 1997 .

[19]  M. C. Kennedy,et al.  Physiological and ecological implications of adaptive reiteration as a mechanism for crown maintenance and longevity. , 2007, Tree physiology.

[20]  M. C. Kennedy,et al.  Two-criteria model assessment shows that foliage maintenance in old-growth Pseudotsuga menziesii requires both delayed and sequential reiteration , 2009, Trees.

[21]  E. David Ford,et al.  The role of epicormic shoot production in maintaining foliage in old Pseudotsuga menziesii (Douglas-fir) trees , 2001 .

[22]  M. Cannell.  Physiological basis of wood production: A review , 1989 .

[23]  Maureen C. Kennedy,et al.  Functional–structural models optimize the placement of foliage units for multiple whole-canopy functions , 2010, Ecological Research.

[24]  Hiroyuki Muraoka,et al.  Crown architecture in sun and shade environments: assessing function and trade-offs with a three-dimensional simulation model. , 2005, The New phytologist.

[25]  M. C. Kennedy,et al.  Defining how aging Pseudotsuga and Abies compensate for multiple stresses through multi-criteria assessment of a functional-structural model. , 2010, Tree physiology.

[26]  Martin H. Zimmermann,et al.  The hydraulic architecture of balsam fir (Abies balsamea) , 1984 .

[27]  E. David Ford,et al.  MULTI-CRITERIA ASSESSMENT OF ECOLOGICAL PROCESS MODELS , 1999 .

[28]  C. Raghavendra Rao,et al.  On model selection , 2001 .

[29]  Jerry F. Franklin,et al.  Thirty-six years of tree population change in an old-growth Pseudotsuga–Tsuga forest , 1988 .

[30]  C. C. Grier,et al.  Old‐Growth Pseudotsuga menziesii Communities of a Western Oregon Watershed: Biomass Distribution and Production Budgets , 1977 .

[31]  Maureen C. Kennedy,et al.  Multi-objective optimization for ecological model assessment and theory development , 2008 .

[32]  Christophe Godin,et al.  Functional-structural plant modelling. , 2005, The New phytologist.

[33]  E. Hunt,et al.  Factors controlling the decline of net primary production with stand age for balsam fir in Newfoundland assessed using an ecosystem simulation model , 1999 .