Using optimisation theory to understand emergent properties in
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.