Computer modeling of dynamically changing distributions of random variables

Physiological characteristics of populations are often described with two types of data and with analyses that coexist in mutual independence. One type targets global measures like mean and standard deviation, prevalence, incidence, or distributions of weights, sizes, or some physiological markers, while the other type describes physiological or metabolic processes in individuals, such as growth or the accumulation of a metabolite. The paper describes a methodological framework for bridging the gap between the two aspects. It shows how a dynamic model that characterizes the accumulation process in individuals and is represented by a set of ordinary differential equations can be reformulated as a transformation function that changes the statistical distribution of the physiological marker over time. The method and its limitations are illustrated with data describing growth and size distributions of loblolly pine (Pinus taeda).