Modelling nonlinear dynamics of Crassulacean acid metabolism productivity and water use for global predictions.

Crassulacean acid metabolism (CAM) crops are important agricultural commodities in water-limited environments across the globe, yet modelling of CAM productivity lacks the sophistication of widely used C3 and C4 crop models, in part due to the complex responses of the CAM cycle to environmental conditions. This work builds on recent advances in CAM modelling to provide a framework for estimating CAM biomass yield and water use efficiency from basic principles. These advances, which integrate the CAM circadian rhythm with established models of carbon fixation, stomatal conductance and the soil-plant-atmosphere continuum, are coupled to models of light attenuation, plant respiration and biomass partitioning.

Jump processes with deterministic and stochastic controls.

We consider the dynamics of a one-dimensional system evolving according to a deterministic drift and randomly forced by two types of jump processes, one representing an external, uncontrolled forcing and the other one a control that instantaneously resets the system according to specified protocols (either deterministic or stochastic). We develop a general theory, which includes a different formulation of the master equation using antecedent and posterior jump states, and obtain an analytical solution for steady state. The relevance of the theory is illustrated with reference to stochastic irrigation to assess crop-failure risk, a problem of interest for environmental geophysics.

Nonlinear dynamics of the CAM circadian rhythm in response to environmental forcing.

Crassulacean acid metabolism (CAM) photosynthesis functions as an endogenous circadian rhythm coupled to external environmental forcings of energy and water availability. This paper explores the nonlinear dynamics of a new CAM photosynthesis model (Bartlett et al., 2014) and investigates the responses of CAM plant carbon assimilation to different combinations of environmental conditions.