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Mathematical Modelling of Rain Forest Regeneration Dynamics: a Case Study in Sabah, Malaysia (D.Phil. 2004, Oxford)

Rain forests exhibit enormous tree species diversity, but the mechanisms for establishing and maintaining such diversity have proven to be intractable to observational studies. The aim of this project is to try and identify the key mechanisms that permit long-term species coexistence. Our continuation of a 16 year study of the Dipterocarpaceae of Sabah, Borneo, provide extensive field knowledge which we use to derive our models.

Firstly, we explore the competition-colonisation trade-off (Tilman, 1994), modifying the original model to include realistic mechanisms for tropical tree species. We consider both exploitative and pre-emptive interspecific competition. Analysis shows that neither can exhibit species diversity. The addition of temporal variability, via the phenomenon of random mast fruiting events, can result in long-term coexistence of many species. However, the parameter values required to simulate such behaviour are more realistic for pre-emptive than exploitative competition.

Removing the assumption that seedlings instantaneously become adults, we develop a model that describes a stage-structured population. The model describes the population dynamics of different species, partitioned into four stage classes: seedlings; saplings; adult trees; and senescent trees. An investigation of the timescales involved reveals that the model can be decoupled indicating that the processes affecting the seedling and sapling populations occur on much shorter timescales compared to those for the adult populations. Ecologically, this suggests that understorey dynamics have little effect on the overall structure of the canopy. The stage-structured model does not allow species coexistence: a dominant species emerges, dictated by initial conditions rather than a particular parameter regime.

Finally, we develop a cellular automaton model that describes a spatially explicit stage-structured population (stratified into seedlings; saplings; and adult trees). Simulations are used to investigate the dynamical behaviour of the model and investigate the life history strategy parameter space that allows for tree species coexistence. Statistical model reduction collapses the number of species into functional groups. Neighbourhood competition indices are also investigated in relation to an individual's growth.


University of Alberta

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Centre for Mathematical Biology