Theory

the model, from the ground up

These pages explain what plant solves, why the model is built that way, and how the pieces fit together. They bring material from papers and vignettes into one route through the theory. The sections below, and the contents pane on the left, follow the recommended reading order.

1. Foundations

Start here for the demographic framework shared by the biological models. If you are new to plant, begin with the big picture. The next two pages introduce the mathematics in stages before the full population equation.

The big picture — the mental model in plain language, no equations. Start here.
The maths, gently — the core equations built up one step at a time.
The maths, worked through — the same equations pushed through one small numerical example, bridging the primer and the full PDE.
The size-structured PDE — demography of individuals, patches, and metacommunities.

2. Models and physiology

Next, see how different biological strategies supply growth, fecundity, and mortality rates to the shared demographic framework. Begin with the models overview, then follow the models and physiological processes in dependency order.

FF16 — the trait-based functional-balance model and the starting point for the more detailed physiology.
Assimilation & hydraulics — the leaf-level carbon and water economy.
TF24 — the hydraulically coupled leaf model, plus its TF24f acclimation-lag variant.
Soil water & root uptake — where transpired water comes from: the multi-layer soil balance and the root-collar solve that feeds it to the leaf model.
K93 — Kohyama’s basal-area competition model.

3. Adaptive dynamics

After learning how resident plants grow and compete, move on to invasion fitness and evolutionary change.

Adaptive dynamics — the main ideas and evolutionary endpoints.
Models in regnans — four small models for learning and checking the workflow.
DD99 — competition and evolutionary branching.
GK98 — adaptation across different habitats.
GM99 — the evolution of seed size.
JJ12 — the evolution of migratory arrival time.
Finding evolutionary attractors — selection gradients in the full plant model.
Community assembly with simple models — how repeated invasion builds a community.
Maximum-fitness community assembly — assembly in plant using the best available mutant.
Stochastic assembly — assembly using random mutational steps.

4. Implementation

These pages explain how the equations are solved on a computer. See the implementation overview for an introduction.

5. Prediction and reproducibility

Finish with a cross-cutting topic that matters when interpreting, comparing, or forecasting with model results.

Scientific versioning of models — how to distinguish changes in the scientific model from changes in the software.