Análisis del impacto

4.1 I ntroduction

Thornley and 10hnson ( 1 990) reviewed extensively the usefulness of modelling in plant physiology, the types of models available at the time, and a number of

physiological topics with relevance to modelling approaches. They advocated a focus on dynamic deterministic models that would address the mechanism of a biological process at different levels, as opposed to empirical models that would purely evaluate

experimental data without seeking the underlying mechanism. The need for dynamic recording and analysis at different plant levels is especially useful in developmental research due to the dynamic nature of the phenomenon itself (Borchert, 1 976). Experimental, mathematical and some statistical requirements and methods of growth modelling have been examined in detail by Hunt ( 1 982), Causton ( 1 986), Ratkowsky ( 1 990) and Zeide ( 1 993b). These studies identified two main obstacles that have to be addressed in order to proceed with dynamic tree growth modelling, and which often prevent wider use of this otherwise effective research tool . These are firstly, the development of a method for recording representative parameter/s of tree growth and development.. Such a method needs to be non-destructive so that repeated measurements over time can be obtained. Secondly, a suitable growth model and statistical analyses have to be selected or developed in order to analyse these

repeated measurements of plant growth with respect to the biological assumptions of the model .

In the current study, the issue o f biometrics was addressed in the previous chapter, i n which the topological M etrosideros Model, dynamic data recording and architecture parameter calculations were described. This chapter is concerned with the second part of dynamic growth modelling. It describes how a suitable growth function model

was selected that would fit the experimental data. From the modelled growth function, growth parameters were estimated and these were statistically analysed with respect to the effects of experimental factors.

The growth modelling exercise presented an opportunity to test the Metrosideros Model. Because the topological, two-dimensional method of measuring growth was new, as opposed to the more typical single-dimension metric measure (Thomley and Johnson, 1 990), its suitability to represent plant growth and architecture of the whole canopy was also examined.

The Metrosideros Model and its parameters combined two factors of biological growth. It recorded the growth in terms of topological segments (units, equivalent to meristems in botanical terms) as well as the synchronisation (or its absence) of appearance of these units within the population of individual shoots within the crown. Both of these factors affect the character of the biological growth multiplicity (Ratkowsky, 1 990) and thus the shape and growth rate (Causton, 1 99 1 ; 1 994) of the resulting growth function. Moreover, the parameters of complexity and size­

complexity factor also accommodated a structural dimension of crown growth. In their 'two-dimensional ' character, the examined topological growth parameters were different from the growth parameters used elsewhere. For example, they differed from those used by Karlsson and Heins ( 1 994) in modelling shoot elongation, or by Garcia and Antor ( 1 995) in modelling dry weight as a plant size parameter.

Therefore, the dynamic behaviour of the topological parameters may not necessarily be identical to one-dimensional size parameters, such as weight or length (Thomley and 10hnson, 1 990). Thus, the effect of dimensionality and in fact the ability of the model to quantify the architectural information was tested in this chapter through the biological growth modelling and analysis of experimental data.

Lately, examples of dynamic modelling of shoot growth have become more common in the literature ( Leakey and Logman, 1 986; Karlsson and Heins, 1 994;

Prusinkiewicz et aI., 1 994; Deleuze and RoBier, 1 995; Baltunis and Greenwood, 1 999; Godin et aI., 1 999). Some of these studies used modelling as a tool for enhancing the effectiveness of 'conventional' non-linear data analyses (Borchert

1 976; Thornley, 1 977; Causton, 1 985; Thornley and Johnson, 1 990) by seeking the

mechanism underlying biological processes of growth. There were also attempts to model the growth of crown development through recording a branching mechanism (Michalewicz, 1 997). H owever, no report was found that would enable the

examination of the growth of a complete population of shoots in the crown recorded at the level of individual axillary and apical meristems. In this respect, the growth analysis of the Metrosideros Model parameters is unique and important in both model evaluation and the architectural effects of developmental state and temperature treatments.

Dynamic growth modelling was employed in this chapter to achieve three main objectives. These were:

To test the suitability of the architectural Metrosideros Model to represent biological growth in general.

To test the Metrosideros Model and its parameters for the ability to capture quantitatively information about two-dimensional tree structure and its dynamic change during plant growth.

To model the experimental data with a growth function, estimate growth parameters for each plant, and analyse these growth parameters with respect to the effect of developmental state and temperature treatments. By analysing the effect of experimental factors on three fundamentally important topological parameters, the hypothesis that tree architecture and/or its rate of change are affected by developmental state was tested. In this respect, it was also of interest to examine how the architecture growth parameters were affected by different temperature treatments. From any identified interactions of temperature with

developmental state, an optimal treatment to accelerate the progress of phase change in juvenile plants and plantlets could possibly be deduced.

In order to facilitate the dynamic growth analysis, available mathematical models for plant growth, and statistical methods for their application to the experimental data were examined. To take full advantages of the means of non-linear analysis, the selected parameters of Chapman-Richards function were examined for content of biologically meaningful information. In this respect, estimated values of the intrinsic

growth rate coefficient were compared with the information gained from the conventionally calculated time-dependent calculated relative growth rate for its ability to identify ontogenetic characteristics. The growth rate-related shape

parameter b of the Chapman-Richards function was also examined for its biological properties, and possible future use in long-term modelling of developmental

processes.

4.2 Methods