A. R. Overman

Mathematical Models of Crop Growth and Yield

INTRODUCTION Historic Background Yield Response Models Growth Models Environmental Input Summary Exercises References SEASONAL RESPONSE MODELS Background Extended Logistic Model Extended Multiple Logistic Model Water Availability Legume/Grass Interaction Summary Exercises References GROWTH RESPONSE MODELS Background Empirical Growth Model Extended Empirical Growth Model Phenomenological Growth Model Expanded Growth Model Exercises References MATHEMATICAL CHARACTERISTICS OF MODELS Background Phenomenological Growth Model Expanded Growth Model Rational Basis for Logistic Model Coupling Among Applied Soil and Plant Components Accumulation of Dry Matter and Plant Nutrients Exercises References PASTURE SYSTEMS Background Quadratic Model Linear Exponential Model Summary Exercises References NONLINEAR REGRESSION FOR MATHEMATICAL MODELS Background Logistic Model Probability Model Confidence Contours Sensitivity Analysis Dimensionless Plots Correlation Coefficient Exercises References Index

A logistic equation for yield response of forage grass to nitrogen.

Abstract A logistic equation was used to relate dry matter yield to applied nitrogen for Pensacola bahiagrass. Data from Georgia with 5 N rates and for 5 years were used. Procedures were outlined for evaluation of the 3 parameters. The 2nd order Newton‐Raphson method was used to optimize parameters. The error matrix provided estimates of the standard error for each parameter, which were used for sensitivity analysis. Probability contours were constructed for the nonlinear parameters at 75% and 95% confidence levels. Finally, it was shown by analysis of variance that each parameter had a common value for all 5 years of data. Additional work is underway to relate model parameters to water availability and harvest interval.

Rational basis for the logistic model for forage grasses

Abstract The logistic model has proven very useful in relating dry matter yields and plant N uptake of forage grasses to applied N. In the past the model has been treated simply as a regression model. This article provides a more rational mathematical foundation for the model. Differential response of dry matter to applied N was related to the product of filled and unfilled dry matter capacity of the system. Characteristics of the logistic and gaussian distributions were compared and refection symmetry of both noted. Symmetry in the logistic model was related to conservation of potential dry matter yield. At lower yields the logistic model approximates exponential behavior, while at higher yields it approximates the Mitscherlich model. Dry matter was coupled to plant N uptake through a hyperbolic equation. As a consequence, plant N uptake was also shown to follow logistic response to applied N with the same N response coefficient as for dry matter. In addition, plant N concentration exhibited linear depen...

Municipal Water Reuse at Tallahassee, Florida

Characteristics of municipal reclaimed water (treated wastewater) and of the soil affect design and operation of a land application system for crop production. In this study field measurements showed an exponential decrease with soil depth in organic matter, cation exchange capacity, exchangeable acidity, and available phosphorus. A linear increase in dry matter yield, plant N uptake, and plant K uptake with harvest interval was observed for warm-season bermudagrass. For a harvest interval of six weeks and a seasonal loading rate of 194 kg N/ha, 33 kg P/ha, and 97 kg K/ha, bermudagrass production was estimated as 7.43 Mg/ha dry matter yield and plant uptake of 108 kg N/ha, 22 kg P/ha, and 53 kg K/ha. Corresponding values for winter rye were 4.25 Mg/ha, 145 kg N/ha, 23 kg P/ha, and 66 kg K/ha. The cation exchange capacity of the soil was dominated by calcium, due to calcium in the city water supply from a limestone aquifer, with only about 2% occupied by potassium. Soil pH stabilized at 7.0 in response to reclaimed water pH of 7.5. At the soil surface soil phosphorus was 90 mg P/kg soil, cation exchange capacity 3.0 meq/100 g soil, and organic matter 1%. Flexibility in management proved essential for success of the farming operation. A Farm Information Committee meets quarterly to discuss matters of mutual interest for the farm, public utility, and research.

An expanded growth model for grasses

Abstract A growth model is needed which will account for time of planting and stage of growth for annual grasses and for time of season and harvest interval for perennial grasses. A linear intrinsic growth function was assumed previously which described response of dry matter accumulation to harvest interval for a warm‐season perennial. Field data indicated that this model was appropriate for intervals up to about six weeks. Beyond this range yields peaked and then declined with increased interval. This article assumes a linear‐exponential intrinsic growth function which more accurately describes the data and removes the restriction on harvest interval. The model describes dependence of dry matter accumulation on time of season and harvest interval for a warm‐season perennial Coastal bermudagrass (Cynodon dactylon). Mean time and standard deviation of the distribution are independent of harvest interval. The model also accounts for time of planting and time in the season for the warm‐season annual corn (Z...

Bahiagrass response to applied nitrogen and harvest interval

Abstract A growth model has been developed for warm‐season perennial grasses which relates seasonal distribution of dry matter to calendar time through the probability equation, and which relates total seasonal dry matter to harvest interval through a linear‐exponential equation. The model is used to describe response of ‘Tifton‐9’ bahiagrass (Paspalum notatum Flogge) to time and harvest interval at Quincy, FL. It is also shown that yield response to applied nitrogen (N) is described by the logistic equation, in agreement with earlier results for bahiagrass and other forage grasses. This model removes the restriction of harvest interval to 6 or 7 wk of the previous linear growth model. Maximum dry matter yield exceeded 20 Mg ha‐1. Maximum incremental dry matter response to applied N occurred at approximately 140 kg N ha‐1. A harvest interval of 8 wk provided peak dry matter production. The mean and standard deviation of dry matter distribution were 28.5 wk and 6.0 wk, respectively. Correlation coefficient...

Estimation of corn response to water and applied nitrogen 1

Abstract The objective of this work was to use the logistic equation to relate grain and total plant yield of corn [Zea mays (L.)] to water and applied N. Data from field Studies in Florida and Georgia were used in the analysis. Nonlinear correlation coefficients R > 0.98 were obtained. Variation among hybrids, between plant components (grain and total plant), and among years (rainfall) was accounted for in the linear model parameter A, with constant exponential parameters b and c. The linear model parameter A exhibited linear dependence on seasonal rainfall for corn in Georgia. Data from a third study in Florida showed linear dependence of A upon seasonal rainfall plus irrigation for total amounts up to 70 cm. This model provides a convenient tool for relating corn yields to applied N and available water, with the response function separating into the product of a term depending upon water and another depending upon applied N. The equation is mathematically well‐behaved and is easy to use on a pocket cal...

CORN RESPONSE TO IRRIGATION AND APPLIED NITROGEN

Yield of corn (Zea mays L.) is very dependent on water availability and applied nitrogen (N). In this article data from the literature are used to establish dependence of yield upon each of these factors and the two in combination. The three separate studies involved surface irrigation of corn. From the first study an exponential relationship is established between dry matter yields (grain and total) and evapotranspiration (ET). Yield at the highest ET rate was shown to be about 80% of the maximum potential yield for three soils studied. Grain was shown to constitute about 50% of total dry matter at all ET rates. Analysis of data from the second study confirmed the utility of the logistic equation for yield response to applied N. The third study included three irrigation rates and six rates of applied N. Analysis showed that the model could be written as the product of a logistic term for applied N and an exponential term for ET. This represents an improvement over the previous linear model for dependence of yield on water availability. *Florida Agricultural Experiment Station Journal Series No. R-08371.

Model for accumulation of dry matter and plant nutrients by corn

Abstract 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 pla...

Coupling among applied, soil, root, and top components for forage crop production

Abstract This analysis establishes linkage among (a) applied nutrients nitrogen (N), phosphorus (P), and potassium (K), (b) available soil nutrients, (c) root dry matter and nutrient content, (d) top dry matter and nutrient content, and (e) leaf area and carbon dioxide (CO2) concentration. It was previously shown that (a) and (d) are coupled by logistic equations with a common response coefficient c between dry matter and plant nutrient uptake with each applied nutrient. As a consequence of the common c, it has been shown that dry matter and plant nutrient removal are coupled by a hyperbolic equation. Furthermore, a model has been developed which includes N, P, and K as inputs. In the present work, (a) and (b) were coupled by a logistic equation as were (a) and (c). It was then shown that plant nutrient removal was coupled to available soil nutrients through a hyperbolic equation. The hyperbolic relationship was also shown to link dry matter between roots and tops, as well as plant N removal between roots...