A MATHEMATICAL THEOREM TO RELATE SEASONAL DRY MATTER TO HARVEST INTERVAL FOR THE EXPANDED GROWTH MODEL1*

Abstract

The expanded growth model has proven very useful for describing accumulation of dry matter by forage grasses with time. This includes both annuals such as corn (Zea mays) and perennials such as bermudagrass (Cynodon dactylon), bahiagrass (Paspalum notatum), and tall fescue (F. arundinacea Schreb.). Analysis of field data for perennials has shown that normalized dry matter distribution follows the probability function and that seasonal dry matter yield follows a linear-exponential function of harvest interval. The mathematical basis for these facts has not been clear. This article presents a mathematical theorem which gives a more rigorous foundation for both of these observations, and clearly demonstrates the dependence of the model on both calendar time and harvest interval. * Florida Agricultural Experiment Station Journal Series No. R-07341.