Model Development for a Deferred-Grazing System

Abstract

A model of the early growth of an annual pasture and liveweight response of grazing sheep was built using first order differential equations to study the practice of deferred grazing. The dynamic behavior of the system over time was simulated by solving the equations on a computer. The model is an interpretative representation of a subterranean clover pasture in Western Australia and relates to a specific site and set of seasonal conditions. Use was made of the literature and a recent grazing experiment to develop the model. Herbage growth is estimated from known relationships with radiation received, leaf area exposed, soil moisture, and herbage removed by grazing. Change in soil moisture is estimated from rainfall and pan evaporation data. Defoliation is based on stocking rate, pasture weight, and pasture height to account for the effects of animal numbers and availability of pasture. Liveweight change of the consuming animal is calculated as a function of intake, digestibility, and the partitioning of metabolizable energy between maintenance and weight change. Validation of the model by results observed in the grazing experiment is presented. The early productivity of mediterranean annual pastures and the resulting weight gain of Merino sheep depend on interactions among pasture plants, climate, soil, and animals (Smith et al., 1972, 1973). It is beyond the scope of any single grazing experiment to control and vary individually all these factors. However, knowledge concerning processes that determine the liveweight response of sheep grazing a mediterranean annual type pasture is sufficient to attempt an integrating model. The objective of this study was to synthesize these relationships into a dynamic model to aid our understanding of the system. The model relates to a single species sward (subterranean clover 'Woogenellup,' Trifolium subterraneum) and a specific site and set of climatic conditions in Western Australia. Its construction was motivated by a desire to generalize from a specific field experiment (Smith et al.,

Simple Simulation Models for Yield Prediction Applied to Alfalfa in the Northeast1

“…In this model, a soil water budget and water-stress growth effect was added to model a. The Fitzpatrick and Nix (9) water budget model as modified by Smith and Williams (21) was used. It calculates the water supply of the rooting zone as the difference between input for precipitation and losses to evapotranspiration and runoff and deep percolation.…”

Crossbred Lamb Production from Columbia and Suffolk Ewes II. Simulation of the Sheep Flock; Net Return Per Ewe

“…Additional equations were developed to simulate the pasture intake of the lactating ewe. Energy requirements of the ewes were calculated using formulas modified from Smith and Williams (1973) and Young and Corbett (1968). Maintenance ME requirements were calculated from the Young and Corbett formula:…”

“…In the present instance, the model developed by Smith and Williams (1973) was chosen because of its versatility and the philosophy implicit in its construction. Equa-tions were developed which had biological meaning and validity, and any changes in those equations had to be justified by known biological changes in the real system that was being simulated.…”

“…Defoliation by grazing sheep was calculated as a function of stocking rate, pasture weight, and height of pasture.The liveweight change of ewes and lambs was determined by the amount of pasture intake, the digestibility of the pasture and the partitioning of metabolizable energy (ME) of ingested pasture among maintenance, lactation and growth requirements. Full details of the model are reported elsewhere(Smith and Williams, 1973).…”

A quantitative model of energy intake and partition in grazing sheep in various physiological states

“…Several attempts have therefore been made at dynamic representation of the performance of grazing livestock by means of computer-simulated models (e.g. Freer, Davidson, Armstrong and Donnelly, 1970;Arnold and Campbell, 1972;Smith and Williams, 1973;Rice, Morris, Maeda and Baldwin, 1974). All of these models either have been restricted to a particular physiological condition or have ignored important environmental variables.…”