Accumulation of dry matter by warm-season annuals depends upon time of season, including planting time. A mathematical model has been developed to simulate the growth process. The model contains a Gaussian environmental function and a linear-exponential intrinsic growth function. Previous work has shown the applicability of the model to data for the perennials bahiagrass (Paspalum notatum) and bermudagrass (Cynodon dactylon). This article applies the model to field data for the annual corn (Zea mays) from four locations. Only two of the five parameters are varied for the different studies to match dry matter simulation with data. A hyperbolic relationship between plant nutrient accumulation [nitrogen (N), phosphorus (P), or potassium (K)] and dry matter accumulation has been included. Parameters for the hyperbolic equation for plant N agree closely for the three locations where plant N was measured. Results for P and K varied. Since the total plant dry matter accumulates at a faster rate than plant nutrients, plant nutrient concentrations for N, P, and K all decrease rapidly with age.

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The extended logistic model has been used extensively to relate seasonal crop production to applied nutrients (such as nitrogen). Model estimates include dry matter yield, plant nutrient uptake, and plant nutrient concentration. It has been applied to perennials such as bermudagrass (Cynodon dactylon L.), bahiagrass (Paspalum notatum Flügge), dallisgrass (Paspalum dilatatum Poir), ryegrass (Lolium perenne L.), tall fescue (F. arundinacea Schreb.), and annuals such as corn (Zea mays L.). Dependence of response to such factors as water availability and harvest frequency (for perennials) can be incorporated into the model. On occasion readers still question the utility of the logistic model over other models (such as polynomials). This article attempts to clarify this point and offers a defense of the logistic model for analysis, design, and management of crop production systems.

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Biomass yield of agronomic crops is influenced by a number of factors, including crop species, soil type, applied nutrients, water availability, and plant population. This article is focused on dependence of biomass yield (Mg ha−1 and g plant−1) on plant population (plants m−2). Analysis includes data from the literature for three independent studies with the warm-season annual corn (Zea mays L.) grown in the United States. Data are analyzed with a simple exponential mathematical model which contains two parameters, viz. Ym (Mg ha−1) for maximum yield at high plant population and c (m2 plant−1) for the population response coefficient. This analysis leads to a new parameter called characteristic plant population, xc = 1/c (plants m−2). The model is shown to describe the data rather well for the three field studies. In one study measurements were made of solar radiation at different positions in the plant canopy. The coefficient of absorption of solar energy was assumed to be the same as c and provided a physical basis for the exponential model. The three studies showed no definitive peak in yield with plant population, but generally exhibited asymptotic approach to maximum yield with increased plant population. Values of xc were very similar for the three field studies with the same crop species.