Abstract:
Proc. Aust. Soc. Anim. Prod. (1972) 9: 10 MODELLING SOIL-PLANT-ANIMAL SYSTEMS K. J. HUTCHINSON* Summary Models are essential parts of systems research, and the structure of soil-plantanimal models is described. Three productivity models that are based on the movement of water and energy are used as examples. The role of computer modelling in the overall strategy of grazing research is discussed. I. INTRODUCTION Systems research has two major aims, namely, the prediction of output, and the assessment of the relative importance of the internal processes which may lead to a better control of the existing system, or to the design of new ones (Wright 1970). Model building is the essence of systems research whether the approach is through experiments that use real systems as the units, from microcosms to grazed plots, or through the use of computer experiments. Research workers have always used models, but often these have been mental images of a problem. However a model can provide an explicit statement that is based on the known processes that operate within a system. Soil-plant-animal systems are complex and highly interactive. The purpose of this paper is to introduce the main features of soil-plant-animal models using a number of examples. The four papers that follow will give details of structure, programming and output from working computer models in this field. II. BASIC STRUCTURES Most soil-plant-animal models are dynamic, that is, they are concerned with changes in the properties of the system with time. They also deal mainly with productivity, with the relevant attributes including energy, carbon, water, minerals, biomass, individuals and populations (Dale 1970). Models may be restricted to a single attribute of the system or they may include a mixture of attributes. Homogeneous models have the advantage that the internal transactions may be structured more easily to yield an accountable total, for example, an energy summation that accords with the First Law of Thermodynamics. The boundary of any system should be defined together with those exogenous factors that `drive' the system but which are not influenced by the system. The endogenous elements can generally be grouped into two categories, namely, pools (levels) that represent the distribution of materials in a system at any point of time, and processes that involve the rates of input and output of materials to and *CSIRO, Division of Animal Physiology, Pastoral Research Laboratory, Armidale, New South Wales, 2350. from the pools. Pools are frequently termed state variables and the processes are represented by rate parameters that are functions of the state variables or other factors. Changes with time in the state variables are termed transients; familiar transients in grazing systems are seasonal changes in herbage availability, and the bodyweights of grazing animals. III. EXAMPLES a 0 A soil moisture model A model for calculating a transient for soil moisture in grazed pasture is shown in Figure 1. Change in soil moisture status (AM) is obtained from the difference between the rates of input and output of four processes, namely, precipitation (p'), underground drainage (u'), net surface runoff (s') and actual evapotranspiration (e'>. The dimensions of the soil water pool may be defined by the effective root profile; s' can be assumed to be a function of rainfall intensity, canopy and surface cover and e' may be represented as a function of season stocking intensity, tank evaporation (e'T) and the current level of iM. Input of p' 11 in excess of the field capacity for A4 is assumed to be lost as s'. Given an initial value for IM then AM can be calculated from the difference equation, A M = p' - U' - s' - e' over a selected time (step) interval. The value of 1M can then be updated and the operation repeated to produce the transient required. This type of water budgeting model is versatile and has been used for a range of crops and pastures (Baier and Robertson 1965; McAlpine 1970; Willatt 1971). The parameter values will vary between environments, but if the aim is to predict M for a particular site, then the relationships in the model can be `tuned' to give , a 1: 1 correspondence between actual observations and values calculated by the model. 0 A pasture productivity model A simple model for calculating the above-ground productivity of a grazed pasture is shown in Figure 2. It consists of pools of living (A) and dead (0) / herbage biomass, the levels of which are controlled by four processes, namely, growth (g'), ingestion from the two pools (&,?n), mortality (m') and decomposition (d') . Production may be measured as dry matter, organic matter or energy and the 12 transactions may be represented by two difference equations:Rearrangement of the equations gives:Over the annual cycle the terms for A A and AD are small and plant chemical energy (g') flows either through domestic grazing animals (i'a + i'o) or through other consumers : and decomposers (d'). This model can be extended in a number of ways. An intermediate pool of standing dead material can be included to account for the process of leaf fall. A whole plant model would require an additional pool for roots with its own growth, death, abscission and consumption processes, and provision for the transfer of assimilates to and from the tops. However complexity per se in a model is not always desirable, and it may be better to use a simpler model provided that it includes the processes that are quantitatively important and that give sufficient biological insight into the problem under study. The pasture productivity model can be developed to include the processes of (c) A grazing/ fodder conservation model energy utilization by grazing animals. Fodder conservation management aims at increasing the flow of primary (plant) production through domestic livestock (Hutchinson 1971). The example given in Figure 3 is for wool production, but models can be constructed for any form of animal production. Fodder is conserved in the spring as hay (H) and fed back to the flock in winter. The structure of the model (Fig. 3) shows the sources of energy loss that may reduce the effectiveness of this management practice:i 0 The withdrawal*of a part of the grazing area for the hay crop may restrict the amount of herbage available for grazing and cause reductions in grazing intake, wool production, and the amounts of body energy stored. (ii) Variable losses are involved in haymaking. (iii) Feed refusals (R) may occur; the efficiency of feeding is represented as (iv> Reduction in grazing intake may be associated with hay consumption; this 0V Cw~)/m* effect may be represented by a `substitution' coefficient (c). The difference between the energy value of the hay eaten (MEhas) and the pasture eaten (MEDasture) during the feeding period is reflected by the difference in annual excretal return. These losses can be combined into a single expression:Annual nutritional gain as metabolizable energy (ME) from hay made and fed This `static' relationship can be used in sensitivity tests to calculate the relative importance of the different pathways of energy loss. Dynamic production changes can be predicted if the model is extended to include functional relationships between climate and shoot growth and dietary factors involved in the grazing process. An example of a population model is given in the paper to be presented by Barger, Benyon and Southcott. The processes that determine changes in the numbers of animals are rates of birth, development, and death from aging, predation and disease. The exogenous variables that may affect these processes include climate, habitat and food resources. The transfer of 3% in pasture grazed by sheep provides an example of a nutrient cycling model (Till and May 1970). These workers used a five pool system and, with an analogue computer, derived solutions for the transfer rates of sulphur from an analysis of the transient for 35s in wool. IV. PROGRAMMING, VALIDATION AND THE USE OF MODELS In simulation studies of soil-plant-animal systems digital computers have mainly been used; increments have been calculated by numerical methods using short step intervals. Most computer models have been programmed in Fortran, although a number of dynamic languages are available. More recently analogue simulation languages have been used in combination with visual display systems. 14 Cd) Other productivity models Validationg is involved at all stages of the develonment of a model. It may comprise the inclusion of new processes, or improvements in the functional forms of the processes already accounted for. However the main test is to compare the outputs from the model with independent sets of data output from real systems. Standard statistical tests, for example, `t' tests and regression analysis, can be used to measure the correspondence between observed and predicted values. Experimentation with computer models can follow several lines. The sensitivity of the outputs to changes in the model's parameters can indicate the relative importance of the various processes as they affect productivity, and these tests may indicate research or management priorities. Computer models and conventional experiments can properly be regarded as complementary, and in these cases the basis for inference can be broadened substantially by simulating production outputs over a long run of either historical or randomly generated climatic years. Computer models may also be used for management `games' which utilize the intrinsic flexibility of the approach. Results from these exercises can be of considerable use in optimizing operations involved in management practices. Forrester (197 1) has pointed out that the human mind is not well adapted for making intuitive predictions about the operations of complex systems where feedback features strongly; exact calculations can be made with computerized models. Finally there are important intangible gains that come from using the modelling approach. Modelling can provide additional biological insight into the operation of systems, because it is based on synthesis as well as analysis, and it requires the inter-disciplinary communication that has been so lacking in our agricultural research in the past. V. REFERENCES Baier, W., and Robertson, G. W. (1965). Canadian Journal of Plant Science, 46: 299. Dale, M. B. (1970). Ecology, 51: 2. Forrester, J. W. (1971). Technology Review, 73: 53. Hutchinson, K. J. (1971). Herbage Abstracts, 41: 1. McAlpine, J. R. (1970). Proceedings of 1 Ith International Grassland Congress, Surfers ParaTill, A. R., and May, P. F. (1970). Australian Journal of Agricultural Research, 21: 253. Willatt, S. T. (1971). Agricultura.1 Meteorology, 8: 341. Wright, A. (1970). Farm Management Bulletin No. 4., University of New England, Armidale. dise, 484. * Validate: `To make sound, defensible, well grounded' [O.E.D.]. 15