First-order differential equation models with estimable parameters as functions of environmental variables and their application to a study of vascular development in young hybrid aspen stems

A novel method is described for solving systems of differential equations pertaining to organism development, where this development is assumed to be directly influenced by fluctuation in measurable environmental variables. The system parameters are written as functions of these variables and, because these functions involve the accumulation of “environment time” (e.g., “day-degrees”), the system is therefore regulated by the prevailing environmental conditions. This method contrasts with the more usual descriptions of development along a time-line. The parameters of the differential equations involved are estimated by modelling data, which show evidence of changes in the dependent variable(s), i.e. the components of the system. They are expressed in terms of their response to continuous fluctuations in one or more independent, environmental variables. Accumulated thermal time (including day-degrees) or more complex units may be derived by using either linear or nonlinear functions. Critical environmental parameters such as the basal thresholds of a given developmental process or parameters describing a nonlinear relationship with the environment may then be estimated. This paper develops the methodology of this environmentally driven approach to describing organism development in general terms, and gives a specific example of its application with reference to the cellular development within the secondary vascular tissues in the stems of young hybrid aspen trees.