F.D. Richardson

Frame-based modelling as a method of simulating rangeland production systems in the long term

Abstract Rangelands are complex systems with many interacting components. Modelling such systems presents two particular and interrelated problems. Firstly, the processes involved operate on greatly differing time scales: long-term changes in rangelands typically depend on much shorter-term processes such as rainfall, vegetation growth and livestock growth. Secondly, while complex mechanistic models of single animals or small herds have been developed (also involving differing time scales, from minutes to months), extending such models to an entire multi-species rangeland is generally an intractable problem. Recently, a new modelling paradigm has been introduced which facilitates the building of ‘economical’ systems models by using the concept of a frame. Frames are chosen to represent distinct states of the system (e.g. grassland with scattered mature trees, as opposed to dense bush cover). Independent models are constructed for each frame; these models simulate the key processes identified within that frame (and may themselves be simplifications of more complex models). Rules are established for switching frames. In this paper we describe a frame-based model of a typical Southern African rangeland supporting cattle and goats. Simple quantitative models for each frame are developed from the output of a complex mechanistic model, depending on rainfall, stocking density and animal condition. Results from the overall frames model show how long-term responses of the system (in terms of production and vegetation state) to various management strategies (such as livestock sales) may be predicted, and in this way allows comparison of different management strategies.

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

Predicting the effect of different management strategies on range condition is a challenge for farmers in highly variable environments. A model that explains how the relations between rainfall, livestock and vegetation composition vary over time and interact is needed. Rangeland ecosystems have a hierarchical structure that can be described in terms of vegetation composition, stocking rate and rainfall at the ecosystem level, and the performance of individual animals and plants at the lower level. In this paper, we present mathematical models that incorporate ideas from complex systems theory to integrate several strands of rangeland theory in a hierarchical framework. Compared with observed data from South Africa, the model successfully predicted the relationship between rainfall, vegetation composition and animal numbers over 30 years. Extending model runs over 100 years suggested that initial starting conditions can have a major effect on rangeland dynamics (divergence), and that hysteresis is more likely during a series of low rainfall years. Our model suggests that applying an upper threshold to animal numbers may help to conserve the biodiversity and resilience of grazing systems, whilst maintaining farmers’ ability to respond to changing environmental conditions, a management option here termed controlled disequilibrium.

A model for the evaluation of different production strategies for animal production from rangeland in developing areas: an overview.

An interactive user‐friendly computer package is being developed to assist planners and managers with the evaluation of different livestock production strategies in semi‐arid regions. It comprises a hierarchy of simulation models that predict over time the effects of past and present rainfall, stocking rates, milking and sales policies on herbage availability, body mass of cows and their progeny, output of milk for sale and herd composition. Herbage on offer is modelled daily in relation to soil moisture and defoliation. Herbage and energy consumption by each animal are functions of its size, physiological status and previous nutrition, supplementary feeding and the availability and composition of herbage. In calves the effect of milk consumption on solid food intake is also considered. Dietary energy is partitioned within the animal according to potential between body tissues, milk production and the conceptus. The inputs for the model are rainfall for every day of the period, initial body mass for each ...

Competition of three aggregated microbial species for four substrates in the rumen

Rumen microorganisms play a vital role in the digestion of food and the supply of energy and amino acids to the host in the form of volatile fatty acids (VFA) and microbial protein. Because the products of rumen digestion are affected by microbial numbers and species composition, it is necessary to understand the population dynamics of different types of microorganisms. Mathematical models have been developed to represent the behaviour of rumen microbes, and these models have been included in whole-rumen models, however, several challenges still remain which include representing changes in microbe numbers and the interactions between microbial species or groups of species. We have developed a mathematical model based on a chemostat-type model of competition between functional representatives of microbes in the rumen and have studied the system numerically. Our objective was to develop and evaluate a mathematical model to examine the effect of changing the proportions of substrate and the effect of ammonia supplementation on the abundance of each species.

A simulation model of draught animal power in smallholder farming systems. Part I: Context and structural overview

Abstract This paper presents the context, approach, and overview of a computer based draught animal power simulation model named Draught Animal Power Simulator (DAP-Simulator). The model was developed using data from literature and modified components and modules of existing models. The overall objective of this study was to provide a decision support system for agricultural planners and development agencies in the evaluation of different strategies of improving the efficiency of DAP use in crop production. The model was coded in Turbo PASCAL 7.0 and implemented in the interactive modelling package, DRIVER. The traction module of the PCHERD model was modified and interfaced with dynamic, empirical and deterministic sub-routines that simulate energy requirements for work (ploughing or carting loads), maintenance, pregnancy, lactation, feed intake, digestion and absorption, and daily weight changes. It can be used as a tool for the strategic use of draught animals, estimating effects of work stress on animal performance and calculation of work requirements. The development of this model indicated that more research work needs to be carried out in quantifying rolling resistance; estimating specific soil resistance, energy requirements for maintenance in Bos indicus cattle; effects of disease; animal behaviour (temperament); and partition of endogenous and exogenous energy. A subsequent paper will present detailed descriptions of model validation, sensitivity analysis, and application.

A simulation model of draught animal power in smallholder farming systems. Part II: Model evaluation and application

Draught Animal Power Simulator (DAP-Simulator) is a computer simulation model developed for smallholder farming systems in which animals are the main source of draught power and nutrition is the main constraint. The description of the model was presented in an earlier serial paper. The objectives of this study were to evaluate the adequacy of the DAP-Simulator model and to demonstrate its application as a decision support system. The predictive performance of the model was evaluated using independent data sets from literature. Linear regression analysis showed (P<0.05) that force requirements when carting (r2=0.72; constant=−0.07 and slope=1.2) and when ploughing (r2=0.57; constant=0.01 and slope=0.78), area ploughed per day (r2=0.97; constant=0.01 and slope=1.03), daily energy requirements for maintenance (r2=0.99; constant=−3.1 and slope=1.09) can be described by this model. The model over-estimated daily weight changes (16%) and also over-estimated feed intake, energy intake and dry matter (DM) digestibility, ranging from 0.4 to 7.8%, for working animals. While the fits obtained were satisfactory, the results emphasised the importance of estimating parameters by more detailed experimentation. Sensitivity analysis was used to examine the response of the model variables to specific changes in the values of the parameters. This is particularly useful as it can be indicative of parameters that management can manipulate so as to increase productivity and reduce costs. The sensitivity analysis indicated that ploughing width (sensitivity index=0.49), ploughing depth (0.58), fraction of soil moved by implement (0.59) and specific soil resistance (0.60) were of limited importance in the estimation of force requirements for ploughing. The force requirements for pulling carts were most sensitive to the weight of the cart (1.76) and the frictional resistance force (1.24). The weight of the load (0.32) and the horizontal component of the pull angle (0.04) had very small effects on the forces for carting loads. It is, therefore, not important to estimate the angle of pull accurately as it has little effect on the output. Area ploughed per day was mainly affected by speed (5), number of passes (4.76), and ploughing width. The most important parameters in simulation of feed intake were fractional rate of passage (3.31), and fractions of degradable (2.5) and indegradable (2.3) fibres. Rate of digestion was most sensitive to fraction of degradable fibre (4.1), with relatively small effects of fractional rates of passage (1.4) and degradation (1.16). A situational analysis of draught power management options and strategies showed that the computer-based simulation model can aid decision-making in complex and dynamic smallholder agricultural production systems.