These results showed that rootstocks/interstocks affect the type of growth units produced during the annual growth cycle, reducing the number of extension growth units, thus affecting the composition and vigour of annual shoots. This effect is particularly amplified by the transition to flowering induced by dwarfing rootstocks. The division of annual shoot into growth units will also be useful for measuring and modelling effects of age on apple tree architecture.

Architectural analysis was applied to study branch development of 'Royal Gala' apple trees grafted with dwarfing and non-dwarfing rootstock/interstock combinations, which had been chosen to produce trees with a wide range of vigour. Using AMAPmod methodology, the structure of 3-year-old branches was described at four levels of representation: branch; annual shoot; growth unit; and node. Three types of growth units were distinguished: extension growth unit (vegetative unit with internode extension); vegetative spur with minimal internode extension; and fruiting spur or bourse. The aim of the analysis was to describe exactly how the rootstock/interstock combinations affected the structure building process. The number of extension growth units, vegetative spurs and fruiting spurs per annual shoot changed over the years, but this was not affected by rootstock/interstock combination. Compared with MM.106 rootstock, M.9 rootstock reduced the number of nodes per extension growth unit. In most cases, rootstock/interstock combination had no effect on the linear relationship between extension growth unit length and node number (R(2) = 0.88). Average internode length depended on unit node number, with internodes being shorter for units with fewer nodes. Thus the difference in apple branch size induced by the rootstock/interstock combinations was mainly due to a reduction in the length and number of neoformed nodes produced on extension growth units. As percentage budbreak of axillary buds on extension growth units was not affected by rootstock/interstock combination, differences in numbers of axillary annual shoots per branch were entirely due to differences in the total numbers of nodes extended during the previous year.

The model is able to reproduce differences in vine and fruit growth arising from various experimental treatments. This implies it will be a valuable tool for refining our understanding of kiwifruit growth and for identifying strategies to improve production.

An approach to study the time-dependent quantum oscillator with the Schrodinger operator S(Q(t)) = - '[p2+02(t)x ] i(-d/dt) is presented. A family of unitary operators [W&, ltl} is found such that S(Q(t)) = W&, (t)S(co)W&, (t), where z =z(t) is a certain function and co is a positive number. Wave vectors, the boson creation and destruction operators, the evolution operator, and invariants for the time-dependent oscillator are obtained by means of [W"(t)}.The approach is applied to calculate transition probabilities, Berry phases, and to study coherent states of the time-dependent oscillator.

We developed a framework for the quantitative description of Actinidia vine architecture, classifying shoots into three types (short, medium and long) corresponding to the modes of node number distribution and the presence/ absence of neoformed nodes. Short and medium shoots were self-terminated and had only preformed nodes. Based on the cut-off point between their two modes of node number distribution, short shoots were defined as having nine or less nodes, and medium shoots as having more than nine nodes. Long shoots were non-terminated and had a number of neoformed nodes; the total number of nodes per shoot was up to 90. Branching patterns for each parent shoot type were represented by a succession of branching zones. Probabilities of different types of axillary production (latent bud, short, medium or long shoot) and the distributions of length for each branching zone were estimated from experimental data using hidden semi-Markov chain stochastic models. Branching was acrotonic on short and medium parent shoots, with most axillary shoots being located near the shoot tip. For long parent shoots, branching was mesotonic, with most long axillary shoots being located in the transition zone between the preformed and neoformed part of the parent shoot. Although the shoot classification is based on node number distribution there was a marked difference in average (per shoot) internode length between the shoot types, with mean values of 9, 27 and 47 mm for short, medium and long shoots, respectively. Bud and shoot development is discussed in terms of environmental controls.