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. Resulting biomass yield and transpiration for Opuntia ficus-indica and Agave tequilana are validated against field data and compared with predictions of CAM productivity obtained using the empirically based environmental productivity index. By representing regulation of the circadian state as a nonlinear oscillator, the modelling approach captures the diurnal dynamics of CAM stomatal conductance, allowing the prediction of CAM transpiration and water use efficiency for the first time at the plot scale. This approach may improve estimates of CAM productivity under light-limiting conditions when compared with previous methods.

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. The CAM model (Bartlett et al., 2014) consists of a Calvin cycle typical of C3 plants coupled to an oscillator of the type employed in the Van der Pol and FitzHugh-Nagumo systems. This coupled system is a function of environmental variables including leaf temperature, leaf moisture potential, and irradiance. Here, we explore the qualitative response of the system and the expected carbon assimilation under constant and periodically forced environmental conditions. The model results show how the diurnal evolution of these variables entrains the CAM cycle with prevailing environmental conditions. While constant environmental conditions generate either steady-state or periodically oscillating responses in malic acid uptake and release, forcing the CAM system with periodic daily fluctuations in light exposure and leaf temperature results in quasi-periodicity and possible chaos for certain ranges of these variables. This analysis is a first step in quantifying changes in CAM plant productivity with variables such as the mean temperature, daily temperature range, irradiance, and leaf moisture potential. Results may also be used to inform model parametrization based on the observed fluctuating regime.