The P Model module

The pmodel module implements the P Model and extensions. The P Model implements an eco-evolutionary optimality (EEO) theory of plant productivity: that plants optimise their behaviour to balance the costs and gains of photosynthesis.

The module provides implementations of the standard and subdaily forms of the P Model. Much of the code and theory is shared between these implementations and is described in the documentation for the shared components.

The two specific model implementations are then:

Note that the predictions of these models differ from instantaneous models of leaf level ecophysiology, where the overall assimilation rate is found as the minimum of the assimilation rate limited by carboxylation (\(A_c\)) and the assimilation rate limited by electron transport \(A_j\), given the internal \(\ce{CO2}\) concentration (\(c_i\)). For more details on fitting instantaneous responses see, for example, the R package plantecophys.

Instead, the P Model follows the coordination hypothesis (Haxeltine and Prentice, 1996, Maire et al., 2012), which asserts that plants coordinate investment in those two assimilation rates, such that \(A_c = A_j\). Note that this coordination requires time and so the standard P Model is typically used to make predictions from average conditions on the scale of weeks to months. The subdaily P Model also follows the coordination hypothesis, but coordinates on the specific conditions encountered during a daytime acclimation window and includes lags in how quickly the coordinated investment adjusts to changing conditions.

Both the standard and subdaily P Model implementations use the “big leaf” approximation to approximate assimilation rates at a canopy scale. The two_leaf module provides an alternative model of canopy assimilation, using the “two leaf, two stream” model of :cite:p:depury:1997a. This explicitly models a canopy layer with depth and partitions incoming radiation into direct and scattered light streams that can be absorbed by sunlit and shaded leaves. This assimilation model can be fitted using an existing instance of either the standard or subdaily P Model: a worked example is shown in the user documentation for the two leaf model.

In addition to the two P Model forms, this module also provides two extensions that build on the P Model:

  • The process of photosynthesis discriminates between the carbon isotopes occurring in air, leaving characteristic isotopic signatures. The Isotopic discrimination module estimates the isotopic signatures from different P Models.

  • The relative advantages of the C3 and C4 photosynthetic pathways differ with environmental conditions. The C3 / C4 plant competition model uses the relative advantage to estimate the expected fraction of C4 plants in a community.