Theoretical models of plant competition are useful tools to explore various hypotheses and theories on the role of competition in explaining community structure and dynamics (patterns and dynamics of species abundances, conditions for coexistence of two or more populations, species diversity, primary or secondary plant succession, invasion of plant communities by alien populations, etc.). These hypotheses are derived from observations in natural communities, and experimental time series are used to calibrate or validate the models. In these studies, competition is measured only indirectly through its effects on the performance of competitors. Since these effects may be confounded with many other sources of changes in plant communities, models are necessary to link observations and theories.
Models of plant competition may apply to individual organisms or populations identified as species or plant functional types. In these models, the 'average abundance' of components may be represented either by population size or density (number of individuals per unit area), biomass (with sometimes distinguishing aboveground and belowground biomass), or other measurable performance attributes (cover, biovolume, leaf area index, etc.).
Because plants, contrary to most animals, show generally a great variability and adaptability in shape and growth, competition in plants might be discussed firstly as the regulation of biomass rather than of density. The 'self-thinning rule' describes the relationship between individual plant biomass and density in even-aged populations of a single species. This relationship is described by the ' — 3/2 power rule':
where B is the average plant biomass, N the plant density, and c a constant. It highlights the effect of intraspecific competition on plant growth, such that the biomass of an individual becomes smaller as population density increases. This phenomenological law has proved to apply both within any given plant species and among different plant species in a given community.
Most dynamic models of community assembly include intra- and interspecific competition, either in a phenomenological or a mechanistic way. The simplest models are nonspatial or spatially implicit, deterministic, and use ordinary differential equations, seeking equilibria and analyzing stability. Very often, they were originally designed and calibrated for the simulation of microbial or aquatic animal populations and thereafter adapted to plant communities. Spatially explicit models are more complex and diverse. They require more parameters and generally incorporate additional mechanisms including stochastic processes. Individual-based models utilize various simulation techniques and are well suited for trees or annual plants. However, the concept of 'individual' derived from animal biology is not appropriate for modeling interactions among perennial plants with clonal reproduction. Finally, the most complex models explicitly include critical aspects of morphology, physiology, and life history as well as the complexity of the plant environment. They may distinguish explicitly development stages in size-structured populations, or plant compartments, such as photosynthetic parts (leaves) and nonphotosynthetic parts (roots, stems, and seeds).
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