In natural communities around Earth, competition among species is pervasive. Competition regulates the traits and abundance of tens to hundreds of species in natural communities, thus structuring the community. Despite the high diversity found in natural communities, most theoretical work on competition focuses on pairwise competition. While insights from pairwise competition models explain how pairs of species can coexist, these models fail to explain how high levels of diversity are maintained. Further, more diverse communities display complex dynamics that cannot be predicted by simple models of competition. My dissertation aims to fill this gap in our understanding by developing mathematical models that investigate how multi-species competition maintains diversity in various ecological contexts. In my first chapter, I analyse the role of the shape and width of the resource spectra in maintaining large, diverse communities. Further, I investigate how the shape of resource spectra impacts the trait structure of diverse communities. In my second chapter, I focus on coexistence of up to three primary producers when they are competing for two resources and sharing a grazer. Further, I try to understand the coexistence mechanisms in the presence of three limiting factors (two resources and a grazer) and how changing resource supplies might change the competitive outcome. In my third chapter, I investigate three-species competition, a logical extension of pairwise competition. I develop a framework to predict three-species competition outcome, and analyse how three-species outcomes relate to pairwise outcomes. My results indicate that when the number of competing species is lower than or equal to the number of environmental factors, maintaining diversity through multi-species competition requires differentiation between the competing species and careful balancing of environmental conditions. However, when resource distributions are wide, competition allows diverse communities. The shape of resource distributions primarily impacts the abundance of the species, and is not discernible from the trait structure of the community except at low densities. Finally, intransitivity among triplets is a key determinant of three-species competitive outcome and destabilises the triplet, particularly when the species have relatively balanced intrinsic growth rates. In conclusion, I show that multi-species competition is markedly more complex than pairwise competition and outline specific ways in which our understanding from pairwise competition models is limited. Thus, I argue for moving beyond pairwise competition models and investigating the role of multi-species competition in maintaining natural communities.
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