Ecological Archives E089-087-A1

Martyn G. Murray and David R. Baird. 2008. Resource-ratio theory applied to large herbivores. Ecology 89:1445–1456.

Appendix A. The mouth size competition model.

Topi and wildebeest are assumed to spend 10 hours of the day foraging and to require a metabolizable energy intake of 19 to break even (Murray 1991). The ME intake that they actually obtain is determined by a digestibility constraint that varies according to the content of green leaf in the diet. The heights of stem (hstem) and green leaf (hGL) are used as substitutes for biomass per m2, allowing the proportion of green leaf in the sward (GLsward) to be calculated as GLsward = hGL / hstem. The content of green leaf in the diet depends upon this proportion and on how selective the animal is, and is calculated from Eqs. 1 and 2 in Murray and Illius (2000):

logit(GLT) = -5.78 + 45.1GLsward[proportion]
logit(GLW) = -6.83 + 45.1GLsward[proportion]

where GLT, GLW are proportions of green leaf in the diets of topi and wildebeest, respectively.

On lower quality swards, digestion takes longer and metabolizable energy intake (ME) falls. The reduction is modelled using Eq. 4 in Murray (1991):

ME[] = 14.023(qL + GL(qHqL)) + 61.968( qL + GL(qHqL))2

This equation requires the metabolizability of the low and high quality components of the diet (stem and green leaf), and the proportion of green leaf in the diet (GL). The metabolizabilities are qL = 0.345, qH = 0.489 (Murray 1991).

On short swards, dry matter intakes of topi (Iveg,T) and wildebeest (Iveg,W) are determined by the height of the vegetative sward (hveg) according to expressions in Murray and Illius (2000):

Iveg,T[g.min-1] = -77.2 + 69.6hveg[cm]
Iveg,W[g.min-1] = 37.3 + 69.6hveg[cm]

and converted to ME intake using MEGL = 8.91 DM and MEstem = 6.14 DM (Murray 1991).


Murray, M. G. 1991. Maximizing energy retention in grazing ruminants. Journal of Animal Ecology 60:1029–1045.

Murray, M. G., and A. W. Illius. 2000. Vegetation monitoring and resource competition in ungulates. Oikos 89:501–508.

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