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A Stochastic Model of Grass Growth Under Grazing

In: Biomathematics and Related Computational Problems

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  • Louis J. Gross

    (University of Tennessee, Department of Mathematics and Graduate Program in Ecology)

Abstract

I present a mathematical model of the dynamics of grass leaf length in a grass sward which is grazed according to a stochastic process. The model is phenomenological, rather than mechanistic, taking into account the logical consequences of the observations which have been made on grazed swards. It is assumed that the number of times a given leaf is grazed through its lifespan follows a renewal process in which the distribution of interarrival times is a function of the density of grazers, and this also affects the amount of leaf material removed in each grazing event. The model assumes that a leaf will regrow following a grazing event, if the leaf is in the growth phase which occurs during the early part of leaf lifespan. I calculate the distribution of leaf length through time in a uniform initial sward, give an explicit formula for the mean in a simplified case, discuss some extensions of the basic model, and examine some implications regarding the effects of herbivory.

Suggested Citation

  • Louis J. Gross, 1988. "A Stochastic Model of Grass Growth Under Grazing," Springer Books, in: Luigi M. Ricciardi (ed.), Biomathematics and Related Computational Problems, pages 177-185, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-2975-3_16
    DOI: 10.1007/978-94-009-2975-3_16
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