From a mechanistic point of view, all previous models are rather simple, and thus make strong assumptions that could be challenged by both empirical and theoretical evidence. However, models are logical devices that convert a series of assumptions into predictions. If predictions are incorrect, then some assumptions of the simplest model should be rejected and replaced by more realistic representations of the system, leading to more complexity and less mathematical tractability. By comparing predictions of his simple resource-reduction model to that of a detailed compartment model of competition in size-structured plant cohorts called ALLOCATE, Tilman in 1998 concluded that the incorporation of various ecophysiolo-gical processes, such as mineralization, uptake and allocation of nutrients, nutrient- and light-dependent photosynthesis, respiration rates for roots, leaves, and stems, light interception along a vertical gradient, and reproductive strategies do not invalidate the predictions of the simple model. However, because this complex model still relies on the mean-field assumption, it incorporates neither horizontal structure nor neighborhood competition. Therefore, spatially explicit models of plant competition have been developed that include morphology, life history, physiological processes, and spatiotemporal environment heterogeneity.
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