Using optimisation theory to understand emergent properties in
plants
Science is about making the diversity and complexity of natural phenomena more
tractable by finding common threads -- rules, laws of nature, constraints
-- that enable prediction and are comprehensible to the human mind. Biology is
unique among the natural sciences, both in the diversity of complex emergent
phenomena it seeks to predict and in the diversity of constraints available to
understand those phenomena. We have Newton, Gibbs and Helmholtz -- the laws of
classical physics and their corollaries in physical and organic chemistry. But
we also have Darwin, Mendel and Waston & Crick -- evolution of species by
natural selection and a mechanism for inheritance of phenotypic characters.
Theoretical progress in biology often occurs along two distinct lines: the
mechanistic and the teleological, representing physico-chemical and
biomolecular constraints, and the force of natural selection, respectively.
I believe great opportunities for progress reside in the tension between these
two axes of thought. After all, life must obey both sets of constraints. The
idea is that evolved genotypes tend to maximise the procurement of resources
that limit reproductive success, subject to the constraints of biophysics,
environment and phenotypic plasticity. If we can characterise those constraints
and identify "optimal" patterns of behaviour or resource allocation
within the realistic space they define, we can do a pretty good job of building
generic models of organism function that are robust to environmental change on
sub-evolutionary time scales. Optimisation-based models are also very useful
for "scaling up" process based models. For most higher plant species,
this includes the time scale of anthropogenic climate change.
For much of my career I have been building the components of that constraint
structure: process models of plant function, and mathematical and computational
structures to identify optimal values of undetermined, resource-dependent
parameters in those process models. I have also been trying to merge these
models as I go. To be less abstract, the process models include models of
stomatal conductance in relation to water transport and photosynthesis; a paradermally
explicit but analytical model of photosynthesis that applies to both
isobilateral and bifacial leaves; and a model of leaf respiration in the light
and dark based on stiochiometric flux balance of metabolic co-factors that link
catabolism, anabolism and photosynthesis in leaves. I've been modeling
optimisation of nitrogen and water use over time and among leaves in plant
crowns, and of carbon allocation among functional pools in growing trees.
My continuing research in optimisation theory focuses on (i) incorporating
greater mechanistic rigour in the analysis of optimal crown distributions of
photosynthetic nitrogen and transpirable water, and (ii) extending my previous
work on optimal carbon allocation in trees to include more general and time-integrated
goal functions than simply maximising carbon growth continuously.