Modelling the spatiotemporal dynamics of a tropical rainforest canopy

In this work the spatiotemporal dynamics of tropical rainforest canopy gaps are modelled using the computer intensive technique of cellular automata. A canopy gap is defined to be an area where the canopy height is below a threshold. The focus of this work is on developing and testing two new models, called the Recursive Transition Expansion Model and the Local Transition Expansion Model, of which the former model is capable of reproducing the annual canopy gap dynamics that are observed on the Barro Colorado Island in Panama and reported in the literature. These new models are extensions of a previously used model of canopy dynamics called the Kubo Iwasa Furumoto model. It is also shown, by calculating the phase diagram, that a different previously used model, called the Forest Game model, is not capable of reproducing the observed gap pattern on the Barro Colorado Island. Some limitations on an analytical approximation technique used for the Kubo Iwasa Furumoto model, called the pair approximation, are given. It is also discovered that the size distributions of gap formation and closure events in the Barro Colorado Island forest are power laws.; This thesis is structured as follows: An introduction to the general modelling process is given. The importance of canopy gaps to forest ecology, as described in the literature, is reviewed. The phenomena of power laws, scale-invariance and phase transitions are reviewed, especially within the context of percolation theory, which provides important tools used for the analysis of the data used in this thesis. The percolation model is studied in some detail by the author. The percolation model is modified to include time evolution, and the occupation (gap) density is calculated analytically as a function of time. The phase diagram is calculated in order to verify the critical density at which a phase transition occurs. Models that were previously used in the literature to fit the gap pattern on the Barro Colorado Island are reviewed. The gap dynamics observed on the Barro Colorado Island are analyzed by the author and the global and local densities of gaps; the gap-size distribution, the neighbourhood-dependend gap formation and closure rates, the correlation functions and the Fourier transforms are calculated. The limitations of some of tire previously used models are given in order to justify to creation of new models of gap dynamics. The gap dynamics obtained from the models are analyzed in the same way as the Barro Colorado Island data and the goodness of fit of the models to the observed data is assessed. Finally, the models are used to make some long-term predictions about the dynamics of the Barro Colorado Island forest canopy. The time it takes for the gap pattern to reach equilibrium from an arbitrary initial condition is predicted by calculating the gap densities as functions of time. By defining a spatiotemporal correlation function, a measure of the 'memory' of the gap pattern is also predicted.