Rangeland Modelling Group

Department of Mathematics & Applied Mathematics
University of Cape Town
Rondebosch 7701
South Africa

Staff



email: fd.rich@mweb.co.za
telephone: +27-21-852-4833
fax:           +27-21-650-2334
 


email: gareth@maths.uct.ac.za
telephone: +27-21-650-3201

Objectives

















We have developed a suite of mechanistic production system models based on differential equations which predict animal dry matter intake, weight gains and milk yields on a daily basis, given rainfall (actual or simulated), soil type, vegetation and stocking rate. Output from these production system models are incorporated into simulations of entire rangelands over many decades using the frame-based modelling paradigm.

Future projects

Models developed for the following projects could form the basis of an MSc or PhD thesis. These are multi-disciplinary projects and honours graduates in any branch of science or agriculture will be considered. Some knowledge of computer programming would be helpful. NRF funding is available.

Namaqualand livestock-ecosystem model

In collaboration with the National Botanical Institute and the Department of Animal Science at the University of Fort Hare we are developing a series of computer simulation models of livestock production and the ecosystem for communal rangelands in Namaqualand. You will develop a computer simulation model of diet selection and nutrient utilization by sheep and goats grazing succulent Karoo. This is a multidisciplinary project that will involve both some experimental work in the field and computer modelling.

Goat model

Recent results from the rangeland modelling project have indicated the important influence of goats on the stability and sustainability of rangeland systems. Consequently rangeland models depend on accurate representation of the performance of goats and their impact on the vegetation and on the productivity of the whole system. The sub-models that simulate diet selection, nutrient utilisation, production (meat, milk, fibre), reproduction and mortality of free ranging goats need to be further developed.

Frame-based models of the rumen

The end products of microbial fermentation in the rumen provide the major proportion of nutrients available to the host animal. Many microbial species are present in the rumen and most are selective fermenters. The pattern of end products produced and rate of fermentation varies with the relative proportions of species present and the food eaten. The rumen microbial population varies with the diet, amount eaten and time since a specific food was eaten. The different organisms interact with one another and with the rumen contents. Rumen models that simulate changes in the proportions of different microbial species are very complex even if only three types of organism are represented. To date no model incorporates rumen anaerobic fungi which may play important roles in the digestion of lignified rangeland plants. There is an opportunity to develop a simple model of rumen fermentation using frame-based modelling techniques.

Recent work
 

  1. Richardson F D, B D Hahn and P I Wilke (1991). A model for the evaluation of different production strategies for animal production from rangeland in developing areas: an overview. Journal of the Grasslands Society of Southern Africa 8, 153-159.
  2. Hahn B D, F D Richardson and A M Starfield (1998). A frame-based model for rangeland production systems. BSAS/KARI Proceedings of an International Conference on Food, Lands and Livelihoods: Setting Research Agendas for Animal Science (Nairobi, January 27-30). Edinburgh. 99-100.
  3. Richardson F D, B D Hahn and S J Schoeman (1998). Simulation models of rangeland production systems for developing areas. BSAS/KARI Proceedings of an International Conference on Food, Lands and Livelihoods: Setting Research Agendas for Animal Science (Nairobi, January 27-30). Edinburgh. 16-17.
  4. Richardson, F D and G Q Witten (1998). A simulation model of the short- and long-term effects of undernutrition on body weight and composition of growing cattle. BSAS/KARI Proceedings of an International Conference on Food, Lands and Livelihoods: Setting Research Agendas for Animal Science (Nairobi, January 27-30). Edinburgh. 101-102.
  5. Hahn B D, F D Richardson and A M Starfield (1998). A simple frame-based model of a complex rangeland system. Proceedings of the 36th National Congress of SASAS: Animal Production in Harmony with the Environment (Stellenbosch, April 5-8). 225-226.
  6. Richardson F D, B D Hahn and S J Schoeman (1998). Simulation models for managing rangeland systems. Proceedings of the 36th National Congress of SASAS: Animal Production in Harmony with the Environment (Stellenbosch, April 5-8). 223-224.
  7. Richardson, F D and G Q Witten (1998). A simulation model of the short- and long-term effects of undernutrition on body weight and composition of growing cattle: model development and sensitivity analysis. Proceedings of the 36th National Congress of SASAS: Animal Production in Harmony with the Environment (Stellenbosch, April 5-8). 227-228.
  8. Hahn B D, F D Richardson and A M Starfield (1998). Frame-based models as tools for evaluating rangeland management strategies. Communal Rangelands in Southern Africa: A synthesis of knowledge (Grasslands Society of SA, Fort Hare, July 6-9). 269-273.
  9. Richardson F D, B D Hahn and S J Schoeman (1998). The role of simulation models in understanding communal rangeland systems in Southern Africa. Communal Rangelands in Southern Africa: A synthesis of knowledge (Grasslands Society of SA, Fort Hare, July 6-9).119-123.
  10. Hahn B D,  F D Richardson and A M Starfield (1999). Frame-based modelling as a method of simulating rangeland production systems in the long term. Agricultural Systems 62, 29-49.
  11. Hahn B D, S Todd, P Carrick, T Hoffmann, F D Richardson and R Roberts (1999). A frame-based model of plant, climate and animal interactions in a communal area of Namaqualand. Arid Zone Ecology Forum (Vanrhynsdorp, September 6-8).
  12. Richardson F D, B D Hahn and M T Hoffman (1999). Simulation models of Namaqualand pastoral systems: simple and complex. Arid Zone Ecology Forum (Vanrhynsdorp, September 6-8).
  13. Richardson F D, B D Hahn and S J Schoeman (2000). Modelling nutrient utilization by livestock grazing semi-arid rangeland. In Modelling Nutrient Utilization in Farm Animals, ed. J P McNamara, J France and D Beever, CABI Publishing, Wallingford UK and New York, 263-280.
  14. Witten G Q and F D Richardson (2000). Modelling nutrient utilization in growing cattle subjected to short or long periods of moderate to severe undernutrition. In Modelling Nutrient Utilization in Farm Animals, ed. J P McNamara, J France and D Beever, CABI Publishing, Wallingford UK and New York, 241-252.
  15. Witten G Q and F D Richardson (2000). Dynamic control of ammonia and urea diffusion across the rumen wall. Mathematical Modeling in Nutrition and the Health Sciences (Penn State University, USA, July 29 - August 1).
  16. Witten G Q (2000). Modelling the control of energy partitioning between protein and fat during undernutrition. International Conference on Mathematical Biology (University of Utah, USA, August 3-5).
  17. Richardson F D, B D Hahn, M T Hoffman and R Roberts (2001). Simulation models of a Namaqualand pastoral production system. Grasslands Society of Southern Africa (Aventura Aldam, Free State, January).
  18. Witten G Q and F D Richardson (2001). Competition of three aggregated microbial species for complementary substrates in the rumen. South African Society for Numerical and Applied Mathematics (Stellenbosch, April 9-11).
  19. Hahn B D, F D Richardson, M T Hoffman, R Roberts, S W Todd and P Carrick (2001). An overview of a simulation model of long-term climate, livestock and vegetation interactions and sustainability on communal rangelands in the semi-arid Succulent Karoo, Namaqualand. Arid Zone Ecology Forum (Calitzdorp, September 5-7).
  20. Richardson F D, B D Hahn and M T Hoffman (2001). Modelling the influences of rangeland degradation, rainfall and management on livestock productivity in Namaqualand. Arid Zone Ecology Forum (Calitzdorp, September 5-7).
  21. Witten G Q and F D Richardson (2001). Managing arid and semi-arid rangelands accounting for the variability of key factors over space and time. Arid Zone Ecology Forum (Calitzdorp, September 5-7).
  22. Richardson F D, B D Hahn and M T Hoffman (2001). Modelling sheep and goat production in a communal area of Namaqualand. Developing Areas Interest Group of the South African Society of Animal Science (Nooitgedacht, Ermelo, 30 October 30-November 1)
  23. Witten G Q and F D Richardson (2002). Competition of three aggregated microbial species for four substrates in the rumen. Ecological Modelling (in press)
  24. Witten G Q and F D Richardson (2002). Modelling rumen function: the effects of different N supplements on low quality roughages. Journal of Agricultural Science (submitted)
  25. Richardson F D, B D Hahn and M T Hoffman(2002). Instability leads to sustainability in a Namaqualand pastoral system. Third Biomathematics Symposium (University of Cape Town, February 8).
  26. Richardson F D, B D Hahn and S J Schoeman (2002). Modelling milk production in suckling ruminants: driven by potential and demand, but limited by nutrient supply. South African Society for Numerical and Applied Mathematics (Stellenbosch, April 3-5).
  27. Chawatama S, L R Ndlovu, F D Richardson, F Mhlanga and K Dzama (2003). A simulation model of draught animal power in smallholder farming systems. Part I: Context and structural overview. Agricultural Systems 76, 415-440.
  28. Chawatama S, L R Ndlovu, F D Richardson, F Mhlanga and K Dzama (2003). A simulation model of draught animal power in smallholder farming systems. Part II: Model evaluation and application. Agricultural Systems 76, 441-455.
  29. Richardson F D, B D Hahn and M T Hoffman(2003). Understanding arid and semi-arid grazing systems: why both equilibrium and non-equilibrium concepts are inadequate. Fourth Biomathematics Symposium (University of Cape Town, February 6-7).
  30. Hahn B D, F D Richardson and M T Hoffman (2003). A simulation model of long-term climate, livestock and vegetation interactions on communal rangelands in the semi-arid Succulent Karoo, Namaqualand, South Africa. Fourth Biomathematics Symposium (University of Cape Town, February 6-7).
  31. Hahn B D, F D Richardson and M T Hoffman (2003). On the dynamic behaviour of grazing systems. South African Society for Numerical and Applied Mathematics (Stellenbosch, March 31–April 2).
  32. Richardson F D, B D Hahn and M T Hoffman (2003). Modelling the dynamics of a Namaqualand pastoral system. Proceedings of the VIIth International Rangeland Congress (Durban, July 26–August 1), African Journal of Range & Forage Science 20(2):142.
  33. Richardson F D, B D Hahn and M T Hoffman (2003). The dynamics of  arid and semi-arid grazing systems. Professional workshop 01: Rangelands in equilibrium and disequilibrium, pp.38–54. VII International Rangeland Congress, Durban, 25–26 July.
  34. Richardson F D, B D Hahn and M T Hoffman (2004). Understanding arid and semi-arid grazing systems: why both equilibrium and non-equilibrium concepts are inadequate. In: S. Vetter (Editor), Rangelands at equilibrium and non-equilibrium, Programme for Land and Agrarian Studies, School of Government, University of the Western Cape, Cape Town, pp. 17–29.
  35. Hahn B D, F D Richardson and M T Hoffman (2004). Modelling the impact of management interventions and climatic change on rangeland condition and livestock production on communal rangelands in the semi-arid Succulent Karoo. Arid Zone Ecology Forum (Victoria West, 30 August – 2 September).
  36. Richardson F D (2004). Simulation models of rangeland production systems: simple and complex. PhD thesis, University of Cape Town (unpublished).
  37. Hahn B D, F D Richardson, M T Hoffman, R Roberts, S W Todd and P Carrick (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 (in press).
  38. Richardson F D, B D Hahn and M T Hoffman (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 (accepted).
  39. Richardson F D and B D Hahn (2005). A mechanistic model of semi-arid rangeland to simulate within years the effects of rainfall, stocking rate and range condition on the productivity of forage and livestock: 1. Overview of the model and description of the sub-models of soil moisture, plant growth, diet selection and food intake by goats and cattle on arid shrubland and savanna. Agricultural Systems (submitted).
  40. Richardson F D and B D Hahn (2005). A mechanistic model of semi-arid rangeland to simulate within years the effects of rainfall, stocking rate and range condition on the productivity of forage and livestock: 2. Description of the sub-models of utilisation of dietary energy by, and reproduction and survival of, goats and cattle on arid shrubland and savanna. Agricultural Systems (submitted).
  41. Richardson F D and B D Hahn (2005). A mechanistic model of semi-arid rangeland to simulate within years the effects of rainfall, stocking rate and range condition on the productivity of forage and livestock: 3. Implementation, evaluation and application. Agricultural Systems (submitted).


Last updated: 10 January 2005 by Brian Hahn