An application of stochastic compartmental theory to modeling plant growth and crop yield

Abstract

The cumulant generating functions are derived for the n-compartment irreversible catenary systems for constant transfer rates and for time-dependent transfer rates. Furthermore higher order residence time moments or survival time moments E[T^j] , for j = 1 ,2 ,3 ,..., are derived for time-dependent staging processes and for semi-Markov age-dependent irreversible catenary systems. Also the cumulant generating functions for five-compartment parallel irreversible systems for constant transfer rates and for time-dependent or generalized staging processes are derived. In addition, solutions of the probability transfer matrix P(t) using a semi-Markov approach for this system are derived. Finally, the result of transfer probabilities p11,ℓk(t), i.e. the transfer probabilities that a unit starting at compartment 1 of stage 1 at time t=0 is in compartment k of stage A are applied, using constant transfer rates and time-dependent transfer rates, to model corn plant growth and crop yield forecast. A model with shifted power-of-time rate functions seems adequate to describe the data.