A dynamical systems model for optimizing rotational grazing : a thesis presented in partial fulfilment of the requirements for the degree of Ph. D. in Mathematics at Massey University

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Massey University
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This thesis considers modelling agricultural grazing using dynamical systems. It is in five chapters, some of which have been or will be published in international refereed journals. The first chapter considers grazing a two-paddock system at low pasture mass in order to maximise herbage conservation and/or herbage intake. For the latter objective, there is an optimal swap-over time which depends on the initial herbage masses and the stocking densities. In general, optimal swap-over gives only small improvements in herbage intake compared to continuous grazing or rotational grazing in which animals spend equal time in each paddock. The second chapter applies this to comparing continuous, rotational, and optimal grazing strategies over a range of stocking rates. As stocking rate increases optimal rotational grazing can increase herbage intake. The third chapter deals with grazing a multi-paddock system in order to maximise intake. Animals are shifted at regular time intervals. Stocking rate and average initial herbage have the greatest effect on herbage growth, conservation, and intake. Grazing strategy effects are less significant. However, traditional strategies of rotational grazing perform poorly in some cases, and in these cases a "greedy" grazing strategy can give imporoved production. The difficulties of finding optimal strategies are discussed. The fourth chapter examines modelling senescence in grazed grass pasture using a differential-delay equation where senescence rates are explicitly dependent on leaf age. A simple differential-delay model is formulated and appraised by comparison to data from a published grazing experiment. This simple model describes subtle features of pasture dynamics. The fifth chapter uses this delay model to make a simple comparison between rotational and continuous grazing. The average rate of senescence is higher under rotational grazing and this is exacerbated by delay effects. For this reason, production is likely to be lower under rotational grazing.
Grazing, Mathematical models