Modelling main stem barley spike development : Computer simulation and sensitivity analysis : A thesis submitted in partial fulfilment of the requirements for the Degree of Master of Applied Science in the Lincoln University

Abstract

The development of mathematical formulations are considered as they relate to the barley main stem spike growth model system and growth models in general. Source and sink models are reviewed and applied to simulation of a barley grain filling model. The network model suggested here may still have a modifying role. Their use requires both agronomic experimental data and biochemical data describing dry matter production and translocation. Since this thesis was based only on non replicated agronomic data (5 sowing date and 4 thinning treatments) testing of these models for mechanistic viability will depend on the collection of biochemical data for independent validation. To model individual kernel growth on the main stem of barley, ordinary logistic, Gompertz logistic and segmented models have been fitted to the agronomic data. The relationships between the parameters of logistic models and segmented models are considered. The analysis of non replicated ex eriments using two way interaction plots, shows that there were interactions between sowing and thinning treatments for growth rate and less so for yield, but there was no interaction for duration. The partial correlations showed that the effect of growth rate on yield due to difference in thinning treatments was higher than the effect of duration on yield for all five sowing dates. The correlations between environmental measurements (from weather station data) during the phases of linear kernel growth were found to have higher correlations with final caryopsis weight than with the other growth parameters. The sensitivity of the network model was perfonned to evaluate effects on resistances to photosynthate flow and source 1 photosynthate levels (plant supplied photosynthate). This was useful especially to validate model parameters. The simulation model and sensitivity analysis showed that in order to establish a realistic physiological model of barley spike development, information on resistances to and structure of, carbohydrate transport in barley spike needs to be collected. The extension of sensitivity analysis has been applied to evaluate the fit (sensitivity neighbourhood) of ordinary and Gompertz logistic models to growth data. The sensitivity neighbourhood method derived here (also called the "confidence interval" or "inference of parameters estimates") was considered in evaluating the fit of a model regression with the given data. The algorithm to generate sensitivity neighbourhoods is given. Also given is the formulation and notation used for describing the sensitivity neighbourhood by utilising the Cauchy-Schwarz equation and its extension. Discretization is described which introduces the upper bound for the underestimate region (e.g. the maximum rectangle that can be fitted in the sensitivity neighbourhood ellipse) and lower bound of the overestimate region (e.g. the minimum rectangle that can include the sensitivity neighbourhood ellipse).