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Andrew Illius, School of Biological Sciences

Andrew Illius Research

Definition of nonequilibrium and the role of key resource

The important role played by temporal and spatial heterogeneity in the dynamics of semi-arid grazing systems is well recognised. Highly variable rainfall causes episodic drought-induced mortality in herbivore populations. Livestock populations exploit spatial variation in resource abundance and are dependent on 'key resource' areas during the dry season. In contrast to the earlier view that plants and animals exist in some sort of equilibrium, it is now argued that, due to environmental variability, their populations are governed by fundamentally different, 'nonequilbrial' processes in which plant and animal dynamics are largely independent of one-another. We need to clarify these concepts, in ecological terms.

We can define 'key resource' in relation to the key factor: given that the key factor determining animal population size is survival over the season of plant dormancy, key resources are those eaten then. In other words, we can posit that key resources limit population size via the key factor, and that a reduction in these resources would cause the population to decline. Modelling results show that this is indeed the case: long-term mean animal abundance was very largely determined by the quantity of resources available during the dry season, when the key factor of mortality operates, and scarcely at all by resources available in the wet season.

Environmental variability disturbs the equilibrium that could be reached between consumers and resources under stable conditions. This condition of disequilibrium, arising from climatic variation, is different from nonequilibrium, which could usefully be defined as the absence of coupling between the animal population’s dynamics and the subset of resources not associated with key factors. Wet season rangeland can therefore be classed as a nonequilibrium resource, because the animal population’s dynamics are not coupled to it. Superabundance of non-key resources is likely to be observed during the growing season, because the animal population is typically limited by scarcer, high quality resources during the dormant season. Diet selection from heterogeneous resources will naturally cause the animal population’s dynamics to depend differentially on different resources. But this is not primarily the consequence of climatic variability, and nor can we characterise entire grazing systems in highly variable climates as ‘nonequilibrial’.

The extent to which the nonequilibrium part of consumer-resource systems is prone to impact depends on the relative abundance of the two resource types, because animal numbers are regulated by key resources and are not coupled to nonequilibrium resources. Thus, high ratios of key:nonequilibrium resources could support animal populations which are sufficient to result in quite high defoliation intensities of the nonequilibrium resources. An extreme case of this effect would occur if animals were maintained on supplementary food over the dry season. Then, their numbers would tend to become completely uncoupled from range resources, and defoliation intensity of the wet season range would be a function of the numbers maintained.


Illius, A.W., Derry, J.F. & Gordon, I.J. (1998) Evaluation of strategies for tracking climatic variation in semi-arid grazing systems. Special Issue on Drought, Agricultural Systems 57, 381-398

Illius, A.W. & O'Connor, T.G. (1999) On the relevance of nonequilibrium concepts to semi-arid grazing systems. Ecol. Applic. 9, 798-813

Illius, A.W. & O'Connor, T.G. (1999) When is grazing a major determinant of rangeland condition and productivity? Proc VI Intl Rangelands Cong. 1, 419-423

Illius, A.W. & O'Connor, T.G. (2000) Resource heterogeneity and ungulate population dynamics. Oikos 89, 283-294

Illius, A.W., Derry, J.F. and Gordon, I.J. (2000) Corrigendum - Evaluation of strategies for tracking climatic variation in semi-arid grazing systems. Agricultural Systems 63, 73-74.

Some other (non-nonequilibrium) references:

Shipley, L.A., Illius, A.W., Danell, K., Hobbs, N.T. & Spalinger, D.E. (1999) Predicting bite size selection of mammalian herbivores: A test of a general model of diet optimization. Oikos 84, 55-68.

Illius, A.W. (1999) Advances and retreats in specifying the constraints on intake in grazing ruminants. In J.G. Buchanan-Smith, L.D. Bailey and P. McCaughey (Eds.) Proc. XVIII International Grassland Congress. 3, 39-44. Association Management Centre, Calgary.

Illius, A.W., Gordon, I.J., Elston, D.A. & Milne, J.D. (1999) Diet selection in grazing ruminants: A test of intake rate maximization. Ecology 80, 1008-1018

Illius, A.W. & Gordon, I.J. (1999) Physiological ecology of mammalian herbivory. In: H.-J. G. Jung and G. C. Fahey, Jr. (Ed.) Vth International Symposium on the Nutrition of Herbivores. American Society of Animal Science, Savoy, IL, pp 71-96

Milner, J.M., Albon ,S.D., Illius, A.W., Pemberton, J.M. & Clutton-Brock, T.H. (1999) Repeated selection on morphometric traits in the Soay sheep on St. Kilda. J. Anim. Ecol. 68, 472-488.

Fryxell, J.M., Crease, T. & Illius, A.W. (1999) Population cycles can maintain foraging polymorphism. Proc Roy Soc Lond. B. 266, 1277-1281

Illius, A.W. Jessop, N.S. & Gill, M. (2000) Mathematical models of food intake and metabolism in ruminants. In Ruminant Physiology: digestion, metabolism, growth and reproduction. (ed Cronjé, P.B.) CABI, Wallingford. pp21-40

Murray, M.G. & Illius, A.W. (2000) Vegetation modification and resource competition in grazing ungulate communities. Oikos 89, 501-508

Pérez-Barberia, F, Gordon, IJ & Illius, AW (2001) Phylogenetic analysis of stomach adaptation in digestive strategies in African ruminants. Oecologia (Berlin) 129, 498-508.

Yearsley, J., Tolkamp, B. J. and Illius, A. W. (2001) Theoretical developments in the study and prediction of food intake. Proceedings of the Nutrition Society 60 145—156

Yearsley JM, Hastings IM, Gordon IJ, Kyriazakis I & Illius AW (2002) A lifetime perspective on foraging and mortality. Journal of Theoretical Biology 215, 385-397.

Fritz H, Duncan P, Gordon IJ, Illius AW (2002) Megaherbivores influence trophic guilds structure in African ungulate communities. Oecologia (Berlin) 131, 620-625

Illius, AW and Fryxell, JM (2002) Methodological problems with estimating patch depression during resource depletion. Oikos 98, 558-559

Illius, AW, Duncan, P, Richard, C and Mesochina, P (2002) Mechanisms of functional response and resource exploitation in browsing roe deer. J. Anim. Ecol. 71, 723-734

Illius, A. W., Tolkamp, B. J.. and Yearsley, J. (2002) The evolution of the control of food intake Proceedings of the Nutrition Society 61, 465-472

Pettorelli N, Dray S, Gaillard JM, Chessel D, Duncan P, Illius A, Guillon N, Klein F, Van Laere G. (2003) Spatial variation in springtime food resources influences the winter body mass of roe deer fawns. Oecologia 137, 363-369.

Perez-Barberia FJ, Elston DA, Gordon IJ, Illius AW (2004) The evolution of phylogenetic differences in the efficiency of digestion in ruminants. Proc Roy Soc Lond. B. 271 1081-1090.

de Garine-Wichatitsky, M., Fritz, H., Gordon, I.J., Illius, A.W. (2004) Bush selection along foraging pathways by sympatric impala and greater kudu. Oecologia 141, 66-75

This site is no longer maintained and has been left for archival purposes

Text and links may be out of date