A two-dimensional mathematical model was developed to describe the time course of root growth and its spatial distribution for container-grown plants, using chrysanthemum [Dendranthema ×grandiflorum (Ramat.) Kitamura] as the model system. Potential root growth was considered as consisting of several concurrent processes, including branching, extension, and death. Branching rate was assumed to be related sigmoidally to existing root weight density. Root growth extension rate was assumed to be proportional to the existing root weight density above some threshold root weight density in adjacent cells. The senescence rate of root weight density was assumed to be proportional to existing root mass. The effects of soil matric potential and temperature on root growth were quantified with an exponential function and the modified Arrhenius equation, respectively. The actual root growth rate was limited by the amount of carbohydrate supplied by the canopy to roots. Parameters in the model were estimated by fitting the model to experimental data using nonlinear regression. Required inputs into the model included initial root dry weight density distribution, soil temperature, and soil water potential data. Being a submodel of the whole-plant growth model, the supply of carbohydrates from canopy to roots was required; the total root weight incremental rate was used to represent this factor. Rather than linking to a complex whole-plant C balance model, the total root weight growth over time was described by a logistic equation. The model was validated by comparing the predicted results with independently measured data. The model described root growth dynamics and its spatial distribution well. A sensitivity analysis of modeled root weight density to the estimated parameters indicated that the model was more sensitive to carbohydrate supply parameters than to root growth distribution parameters.
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Associate Professor and Extension Specialist, corresponding author.