The role of size inequality in self-thinning: A pattern-oriented simulation model for arid savannas

The self-thinning line is a very robust pattern, which can be obtained in modeling studies by a variety of different mechanistic assumptions. Our opinion is that we can only advance in our understanding of mechanisms leading to the self-thinning relationship if we demand that the model also reproduces several other characteristic features (patterns) of the self-thinning process such as the degree of size inequality and the average size. We use a pattern-oriented modeling approach to develop a model of self-thinning under size inequality in overcrowded, even-aged stands, which reproduces these three patterns simultaneously. Our approach is to first develop an initial model based on our current ecological knowledge and then to refine the model by modifying the initial model to derive the model that reproduces all patterns of interest. The initial model is as simple as possible while avoiding incidental, ecologically unjustified, assumptions. It is a further development of zone of influence-simulation models: each plant is described by two circles, one describing a minimum-domain-area and one describing the zone of influence. In the initial model, mortality is "death-by-contact" of minimum-domain-areas and growth is a function of inter-tree competition, i.e. overlapping zones of influence. Model parameterization is based on field data on Acacia reficiens in southern Africa. Simulations follow patches of initially small trees through time for up to 1000 years with five parameters, three describing growth and two describing inter-tree competition. A sensitivity analysis shows that all parameters of the initial model contribute significantly to the number and size of plants through time. The two competition parameters, which describe competitive asymmetry and the size of the zone of influence relative to canopy size, are both important for generating size inequality. Thus, both competitive asymmetry and spatial pattern contribute to size inequality, and their relative importance may vary greatly. The sensitivity analysis suggests that all processes included in the initial model are essential to the evolution of size inequality. However, size inequality under the initial model is below field values, meaning that additional, as yet unconsidered processes, contribute to size inequality. Our best-fit model additionally contains details on growth stochasticity. This study establishes the often-proposed direct link between mortality driven by local competition and self-thinning and highlights the importance of stochasticity in ecological processes.