Modelling the complex dynamics of vegetation, livestock and rainfall in asemiarid rangeland in South Africa

References

• Acocks , JPH. 1988 . Veld types of South Africa (3rd edn). Memoirs of the Botanical Survey of South Africa No. 57 , Pretoria : Botanical Research Institute .
   Google Scholar
• Anon . 1923 . Final report of the Drought Investigation Commission , Cape Town : Government Printer .
   Google Scholar
• Allen , T FH and Starr , T B . 1982 . Hierarchy, perspectives for ecological complexity , Chicago : University of Chicago Press .
   Google Scholar
• Archer , S and Bowman , A . 2002 . “ Understanding and managing rangeland plant communities ” . In Global rangelands: progress and prospects , Edited by: Grice , A C and Hodgkinson , K C . Wallingford : CAB International .
   Google Scholar
• Behnke , R H and Scoones , I . 1993 . “ Rethinking range ecology: implications for rangeland management in Africa ” . In Range ecology at disequilibrium , Edited by: Behnke , R H , Scoones , I and Kerven , C . 1 – 30 . London : Overseas Development Institute .
   Google Scholar
• Bransby , DJ. 1984 . A model for predicting livemass gain from stocking rate and annual rainfall . Journal of the Grassland Society of South Africa , 1 : 22 – 26 .
   Google Scholar
• Burrin , D G , Ferrell , C L , Brittton , R A and Bauer , M . 1990 . Level of nutrition and visceral organ size and metabolic activity in sheep . British Journal of Nutrition , 64 : 439 – 448 .
   PubMed Web of Science ®Google Scholar
• Dean , W RJ and MacDonald , I AW . 1994 . Historical changes in stocking rates of domestic livestock as a measure of semi-arid and arid rangeland degradation in the Cape Province, South Africa . Journal of Arid Environments , 26 : 281 – 298 .
   Web of Science ®Google Scholar
• DeAngelis , D L and Waterhouse , J C . 1987 . Equilibrium and non-equilibrium concepts in ecological models . Ecological Monographs , 57 : 1 – 21 .
   Web of Science ®Google Scholar
• Ellis , GFR. 2005 . Physics and the real world . Physics Today , 58 : 49 – 54 .
   Google Scholar
• Ellis , J E and Swift , D M . 1988 . Stability of African pastoral ecosystems: alternate paradigms and implications for development . Journal of Range Management , 41 : 450 – 459 .
   Google Scholar
• Esler , K J , Milton , S J and Dean , W RJ , eds. 2006 . Karoo veld: ecology and management , Pretoria : Briza Publications .
   Google Scholar
• Gillard , R and Monypenny , R . 1990 . A decision support model to evaluate the effects of drought and stocking rate on beef cattle properties in northern Australia . Agricultural Systems , 34 : 37 – 52 .
   Google Scholar
• Gillson , L and Hoffman , M T . 2007 . Rangeland ecology in a changing world . Science , 315 : 53 – 54 .
   PubMed Web of Science ®Google Scholar
• Hahn , B D , Richardson , F D and Starfield , A M . 1999 . Frame-based modelling as a method of simulating rangeland production systems in the long term . Agricultural Systems , 62 : 29 – 99 .
   Web of Science ®Google Scholar
• Hahn , B D , Richardson , F D , Hoffman , M T , Roberts , R , Todd , S W and Carrick , P . 2005 . A simulation model of long-term climate, livestock and vegetation interactions on communal rangelands in the semi-arid Succulent Karoo, Namaqualand, South Africa . Ecological Modelling , 183 : 211 – 230 .
   Web of Science ®Google Scholar
• Higgins , S J , Kantelhardt , J , Scheiter , S and Boerner , J . 2007 . Sustainable management of extensively managed rangelands . Ecological Economics , 62 : 102 – 114 .
   Google Scholar
• Hoffman , M T , Barr , G D and Cowling , R M . 1990 . Vegetation dynamics in the semi-arid eastern Karoo, South Africa: the effect of seasonal rainfall and competition on grass and shrub basal cover . South African Journal of Science. , 86 : 462 – 463 .
   Web of Science ®Google Scholar
• Hoffman , M T and Cowling , R M . 1990 . Vegetation change in the semi-arid eastern Karoo over the last 200 years: an expanding Karoo—fact or fiction . South African Journal of Science , 86 : 286 – 294 .
   Web of Science ®Google Scholar
• Hoffman , M T , Cousins , B , Meyer , T , Petersen , A and Hendricks , H . 1999a . “ Historical and contemporary land use and the desertification of the Karoo ” . In The Karoo: ecological patterns and processes. , Edited by: Dean , W JR and Milton , S J . 257 – 273 . Cambridge : Cambridge University Press .
   Google Scholar
• Hoffman , M T , Todd , S , Ntshona , Z and Turner , S . 1999b . Land degradation in South Africa , Claremont : National Botanical Institute .
   Google Scholar
• Illius , A W and O’Connor , T G . 1999 . The relevance of non-equilibrium concepts to arid and semi-arid grazing systems . Ecological Applications , 9 : 798 – 813 .
   Web of Science ®Google Scholar
• Illius , A W and O’Connor , T G . 2004 . “ The definition of non-equilibrium and the role of key resource—an ecological perspective ” . In Rangelands at equilibrium and non-equilibrium , Edited by: Vetter , S . 16 Cape Town : Programme for Land and Agrarian Studies, University of the Western Cape .
   Google Scholar
• Johnson , I R and Parsons , A J . 1985 . A theoretical analysis of grass growth under grazing . Journal of Theoretical Biology , 112 : 345 – 367 .
   Web of Science ®Google Scholar
• Jones , R J and Sandland , R J . 1974 . The relation between animal gain and stocking rate: derivation of the relation from the results of grazing trials . Journal of Agricultural Science, Cambridge , 83 : 335 – 341 .
   Web of Science ®Google Scholar
• Ledger , H P and Sayers , A R . 1977 . The utilization of dietary energy by steers during periods of restricted food intake and subsequent realimentation. 1. The effect of time on the maintenance requirement of steers held at constant liveweights . Journal of Agricultural Science, Cambridge , 88 : 11 – 26 .
   Google Scholar
• Lockwood , J A and Lockwood , D R . 1993 . Catastrophe theory: a unified paradigm for rangeland ecosystem dynamics . Journal of Range Management , 46 : 282 – 288 .
   Google Scholar
• Milton , S J and Dean , W RJ . 1996 . Karoo veld: ecology and management , Pretoria : ARC–Range and Forage Institute .
   Google Scholar
• Milton , S J , Dean , W RJ , du Plessis , M A and Siegfried , W R . 1994 . A conceptual model of arid rangeland degradation: the escalating cost of declining productivity . Bioscience , 44 : 70 – 76 .
   Web of Science ®Google Scholar
• Milton , S J and Hoffman , M T . 1994 . The application of state-andtransition models to rangeland research and management in arid succulent and semi-arid grassy Karoo, South Africa . African Journal of Range and Forage Science , 11 : 18 – 26 .
   Google Scholar
• Nicolis , G and Prigogine , I . 1989 . Exploring complexity , New York : WH Freeman and Co .
   Google Scholar
• O’Neill , R V , De Angelis , D , Waide , J and Allen , T . 1986 . A hierarchical concept of ecosystems , Princeton : Princeton University Press .
   Google Scholar
• Renshaw , E. 1991 . Modelling biological populations in space and time , Cambridge : Cambridge University Press .
   Google Scholar
• Richardson , F D , Hahn , B D and Hoffman , M T . 2004 . “ Understanding arid and semi-arid grazing systems: why both equilibrium and non-equilibrium concepts are inadequate ” . In Rangelands at equilibrium and non-equilibrium , Edited by: Vetter , S . 17 – 29 . Cape Town : Programme for Land and Agrarian Studies, University of the Western Cape .
   Google Scholar
• Richardson , F D , Hahn , B D and Schoeman , S J . 2000 . “ Modelling nutrient utilization by livestock grazing semi-arid rangeland ” . In Modelling nutrient utilization in farm animals , Edited by: McNamara , J P , France , J and Beever , D . 263 – 280 . Wallingford : CAB International .
   Google Scholar
• Richardson , F D , Hahn , B D and Hoffman , M T . 2005 . On the dynamics of grazing systems in the semi-arid Succulent Karoo: the relevance of equilibrium and non-equilibrium concepts to the sustainability of semi-arid pastoral systems . Ecological Modelling , 187 : 491 – 512 .
   Web of Science ®Google Scholar
• Richardson , F D and Hahn , B D . 2007a . A short-term mechanistic model of forage and livestock in the semi-arid Succulent Karoo: 1. Description of the model and sensitivity analyses . Agricultural Systems , 95 : 49 – 61 .
   Google Scholar
• Richardson , F D and Hahn , B D . 2007b . A short-term mechanistic model of forage and livestock in the semi-arid Succulent Karoo: 2. Evaluation and application . Agricultural Systems , 95 : 62 – 75 .
   Google Scholar
• Richardson , F D , Hahn , B D and Hoffman , M T . 2007 . Modelling the productivity and sustainability of pastoral systems in the communal areas of Namaqualand . Journal of Arid Environments , 70 : 701 – 717 .
   Web of Science ®Google Scholar
• Sandford , S. 1995 . “ Improving the efficiency of opportunism: new directions for pastoral development ” . In Living with uncertainty , Edited by: Scoones , I . 174 – 182 . London : Intermediate Technology Publications .
   Google Scholar
• Scoones , I. 1993 . “ Why are there so many animals? Cattle population dynamics in the communal areas of Zimbabwe ” . In Range ecology at equilibrium , Edited by: Behnke , R H , Scoones , I and Kerven , C . 62 – 76 . London : Overseas Development Institute .
   Google Scholar
• Scoones , I. 1995 . “ New directions in pastoral development in Africa ” . In Living with uncertainty , Edited by: Scoones , I . 1 – 36 . London : Intermediate Technology Publications .
   Google Scholar
• Stoddart , L A , Smith , A D and Box , T W . 1975 . Range management. , New York : McGraw-Hill .
   Google Scholar
• Tainton , N M . 1981 . Veld and pasture management in South Africa , Pietermaritzburg : University of Natal Press .
   Google Scholar
• Thornley , JHM. 1998 . Grassland dynamics: an ecosystem simulation model , Wallingford : CAB International .
   Google Scholar
• Thornley , J HM and France , J . 2007 . Mathematical models in agriculture , Wallingford : CAB International .
   Google Scholar
• Todd , S W and Hoffman , M T . 1999 . A fence line contrast reveals effects of heavy grazing on plant species diversity and community composition in Namaqualand, South Africa . Plant Ecology , 142 : 169 – 178 .
   Web of Science ®Google Scholar
• Vetter , S , Bond , W J and Trollope , W SW . 1998 . “ How does one assess the costs of degradation in South African communal rangelands ” . In Communal rangelands in southern Africa: a synthesis of knowledge , Edited by: de Bruyn , T D and Scogings , P F . 59 – 76 . Alice : Department of Livestock and Pasture Science, University of Fort Hare .
   Google Scholar
• Ward , D , Ngairorue , B T , Kathena , J , Samuels , R and Ofran , Y . 1998 . Land degradation is not a necessary outcome of communal pastoralism in arid Namibia . Journal of Arid Environments , 40 : 357 – 371 .
   Web of Science ®Google Scholar
• Westoby , M , Walker , B H and Noy-Meir , I . 1989 . Opportunistic management for rangelands not at equilibrium . Journal of Range Management. , 42 : 266 – 274 .
   Google Scholar
• Wu , J and Loucks , O . 1995 . From balance of nature to hierarchical patch dynamics: a paradigm shift in ecology . Quarterly Review of Biology , 70 : 439 – 466 .
   Web of Science ®Google Scholar