Grazing and Production in Seasonal Pastures: Analysis of a Simple Model

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Abstract
A model is postulated to describe biomass dynamics in pastures that are grazed continuously throughout a limited growing season. It assumes that rates of growth and intake both depend only on total green biomass (V); that each dependence can be expressed by 2 linear segments; and that the growing season starts with a low initial biomass (V0) and ends after a fixed time (te). Within each of 3 phases of the season, dV/dt is then a function which is linear in V, and can be integrated analytically. Explicit expressions were obtained for biomass, cumulated primary production and cumulated animal intake at any time in the season and particularly at its end. The sensitivity of the final values of these variables to animal density (H) and to pasture and animal parameters was examined by numerical examples.