Hi John, thanks for the links! I should read Brendan Fong's thesis. I wish I could find a good summary of Howard Odum's work (that doesn't skimp on the math). Combining traditional community and population ecology ideas (like the rate equations in the Stochastic Mechanics book) with physics-based ideas (tracking energy, matter flows, thermodynamics) has been a longterm goal in ecology (well theoretical ecology at least).
You might interested in this [paper: Allen et al. (2005) Using L-systems for modeling source–sink interactions, architecture and physiology of growing trees: the L-PEACH model ](https://cloudfront.escholarship.org/dist/prd/content/qt9rn2x7t8/qt9rn2x7t8.pdf). This is a model of plant physiology rather than ecology like Odum's stuff. But here again there's a heavy use of circuits and dynamics on graphs.
You might heard of L-systems before, but roughly the idea is that the plant is modeled structurally as a graph (with some spatial embedding). Resource transport is simulated by treating the graph as a circuit, and then the graph changes over time to capture growth (through graph rewriting).
There are more recent versions (See [L-Almond](https://www.actahort.org/books/1160/1160_7.htm) or [IMapple](https://ieeexplore.ieee.org/document/7818293/)). These models come from people with a more computer science background, so there's heavy emphasis on computer simulation and not necessarily on theorem-proofs (which biologists don't really have much appetite for either).
One of my hopes in taking the Applied Category theory course was to be able to develop ideas/theorems/heuristics to analyze these types of models. Ideally, then produce experimental predictions that can be tested and/or provide insight beyond a few particular models.