This thesis uses theoretical models to answer questions that revolve around the ecological processes that maintain diversity. Chapter 1 studies the importance of competitive asymmetry on the likelihood of coexistence. Considering a competition-fecundity trade-off, we find conditions that allow coexistence of two species, and show the likelihood of these species coexisting increases with competitive asymmetry. Further, we demonstrate that asymmetry allows for the coexistence of an arbitrarily large number of species, although the likelihood of coexistence decreases as more species are considered. Chapters 2, 3 and 4 are all concerned with the effects of disturbance on diversity. In Chapter 2, we demonstrate that the frequency and intensity of disturbance events can affect the community dynamics in different ways. We demonstrate that the diversity-disturbance relationship can take several different forms as frequency and intensity interact to determine overall disturbance regimes. Chapter 3 examines which of three predicted trade-offs are likely to contribute most to coexistence. In particular, we derive the likelihood of two species coexisting as defence against disturbance, fecundity and juvenile growth rates vary between species. We show that a fecundity-defence trade-off is particularly sensitive to parameters, and is not expected to contribute to diversity in large communities. Further, we conclude that a fecundity-growth trade-off contributes more to the maintenance of diversity than a growth-defence trade-off, although the latter is expected to have some effect. In Chapter 4, we consider the effects of disturbance extent on the likelihood of three species coexistence. We demonstrate that in a single, well mixed community a fecundity-growth trade-off cannot support three species. We then use a metapopulation structure to show that spatial heterogeneity in disturbance regimes can increase diversity; showing that a community protected from disturbance can contribute to increase regional diversity, and increase diversity in a neighbouring patch with disturbance
