1. General Model Information
Name: Grass/Clover Grazing Model
Main medium: terrestrial
Main subject: populationdynamics
Organization level: population
Type of model: ordinary differential equations
Keywords: grazing systems, diet selection, grass, legume, nitrogen cycle, pasture composition,plant population dynamics
Department of Biology
Texas State University
601 University Drive
312 Supple Science Bldg
Texas State University
San Marcos, TX 78666, USA
Phone: (512) 245-3753
Fax: (512) 245-8713
Susan Schwinning and A.J. Parsons (email: ParsonsT@agresearch.cri.nz )
Susan Schwinning (personal homepage)
The GCGM model is a synthesis of understanding gained from previous physiological models by Thornley and colleagues (Johnson & Thornley 1983, 1985, 1987; Thornley & Johnson 1990; Thornley & Verberne 1991), models of herbivore foraging in ryegrass and clover (Parsons et al.1994; Newman et al. 1995) and experimental work on nitrogen fixation in white clover (Davidson & Robson 1985, 1986a,b).
GCGM is based on Thornley's original model (Thornley et al. 1995), but is simpler in structure despite of having a grazing algorithm added to it. The model is aimed at improving the understanding of grass-legume dynamics in pasture systems, and examines the effects of diet selection on both pasture state and herbivore intake. It is described schematically in Fig. 1.
Parameter values were derived from the references mentioned above. In a simplified model, it is often necessary to include parameters that summarize several component processes, and the values of such parameters represent composites of several more detailed parameters. There is some uncertainty about such simplifications, thus, where composite parameters were used, we ensured that the model behaved appropriately. For example, we checked that the growth curves for both plant species at a range of fixed soil N levels were quantitatively realistic. The parameter values describing soil processes were less certain, since many soil processes are simply not known well enough. To address this uncertainty, we explored model solutions across a wide range of soil parameter space. We solved the model using small discrete time steps (0.2 days). This step size proved to be adequate for approximating continuous dynamics and minimized computation time.
Figure 1: Flow chart of GCGM (= Grass/Clover Grazing Model). The 8 state variables are boxed.
II. Technical Information
III. Mathematical Information
Initial conditions of state variables:
- structural carbon (XC) density of grass and clover (g XC per sqm ground area)
- substrate carbon (SC) and nitrogen (SN) density for grass and clover (g SC or SN per sqmground area)
- mineral (MN) and organic (ON) nitrogen content of the soil (g MN or ON per sqm ground area)
- ratio of structural N (XN) to structural C in biomass for both plant species (g XN per g XC)
- maximal intrinsic growth rate for both plant species (per day)
- Michaelis-Menten constants for the dependence of growth rate on tissue concentrations of substrate carbon and nitrogen concentrations (g SC or SN per g XC)
- relative rate of senescence (per day)
- maximal rates of net carbon assimilation for both plant species (g SC per sqm leaf area per day)
- leaf area per structural carbon for both plant species (sqm leaf area per g XC)
- leaf area index at which the rate of net carbon assimilation is half-maximal (sqm leaf area persqm ground area)
- maximal specific rates of mineral N uptake for both species (g MN per g XC per day)
- soil mineral N density at which the specific rates of mineral N uptake are half-maximal for both plant species (g MN per sqm ground area)
- maximal fraction of clover's uptake of mineral N (no unit)
- relative efficiency of N fixation vs. mineral N uptake (no unit)
- maximal rate of herbivory, depending on stocking rate (g XC per sqm ground area per day)
- relative preference for grass by grazers (no unit)
- structural carbon density at which herbivory is half-maximal (g XC per sqm ground area)
- relative rate of mineralization of organic N (per day)
- relative rate of mineral N loss through leaching or volatization (per day)
- absolute rate of fertilization (g MN per day)
- mineral N dosage in single urine application (g MN per sqm ground)
- dynamics of the 8 state variables and derived variables (e.g. tissue N concentrations)
- dynamics of herbivore intake of grass and clover, frequency of disturbance by urine application
Davidson, I.A. and Robson, M.J.,1985. Effects of nitrogen supply on the grass and clover components of simulated mixed swards grown under favourable environmental conditions. 2.Nitrogen fixation and nitrate uptake. Annals of Botany, 55, 697-703.
Davidson, I.A. and Robson, M.J.,1985a. Effects of temperature and nitrogen supply on the growth of perennial ryegrass and white clover. 1. Carbon and nitrogen economies of mixed swards at low temperature. Annals of Botany, 57, 697-708.
Davidson, I.A. and Robson, M.J.,1985b. Effects of temperature and nitrogen supply on the growth of perennial ryegrass and white clover. 2.Comparison of monocultures and mixed swards. Annals of Botany, 57, 709-719.
Johnson, I.R. and Thornley, J.H.M., 1983. Vegetative crop growth model incorporating leaf expansion and senescence and applied to grass. Plant, Cell and Environment, 6, 721-729.
Johnson, I.R. and Thornley, J.H.M., 1985. Dynamic model of the response of a vegetative grass crop to light, temperature and nitrogen. Plant, Cell and Environment, 8, 485-499.
Johnson, I.R. and Thornley, J.H.M., 1987. A model of shoot: root partition with optimal growth. Annals of Botany, 60, 133-142.
Newman, J.A., Parsons, A. J., Thornley, J.H.M. and Penning, P.D., 1995. Optimal diet selection by a generalist grazing herbivore. Functional Ecology 9, 255-268.
Parsons, A.J., Thornley, J.H.M., Newman, J.A. and Penning, P.D., 1994. A mechanistic model of some physical determinants of intake rate and diet selection in a two-species temperate grassland sward. Functional Ecology, 8, 187-204.
Thornley, J.H.M. and Johnson, I.R., 1990. Plant and Crop Modelling. Clarendon Press, Oxford.
Thornley, J.H.M., Bergelson, J. and Parsons, A.J., 1995. Complex dynamics in a carbon-nitrogen model of a grass-legume pasture. Annals of Botany 75, 79-94.
Schwinning, S. and Parsons, A.J., 1996a. Analysis of the coexistence mechanisms for grasses and legumes in grazing systems. Journal of Ecology, 84, 799-813. (pdf)
Schwinning, S. and Parsons, A.J., 1996b. A spatially explicity model of stoloniferous N-fixing legumes in mixed pasture with grass. Journal of Ecology, 84, 815-826.  (pdf)
Schwinning, S. and Parsons, A.J., 1996b. Interactions between grasses and legumes: Understanding variability in species composition. In: Legumes in Sustainable Farming Systems. Younie, D. (ed). Occasional Symposium No. 30 British Grassland Society, Aberdeen.
Thornley, J.H.M. and Verberne, E.L.J., 1991. A model of nitrogen flows in grassland. Plant,Cell and Environment, 12, 863-886.
V. Further information in the World-Wide-Web
VI. Additional remarks
Last review of this document by: 16. November 1997
Status of the document: updated by S.Schwinning
last modified by
Joachim Benz Wed May 20 01:55:36 CEST 2015