Perturbed Neutrality - beyond null models of biodiversity

Ecologists have long puzzled over the mechanisms that maintain biological diversity - that permit so many natural species to live alongside others with which they compete for resources. Many biologists would maintain that species coexist by exploiting their environment in different ways, and patterns of abundance and rarity reflect the distinct roles played by different species in the community. This view was supported by Charles Darwin, who wrote in 1859 `When we look at the plants and bushes clothing an entangled bank, we are tempted to attribute their proportional numbers and kinds to what we call chance. But how false a view is this!' However, a recent theory by Stephen P. Hubbell asserts the opposite: that individuals in ecological communities behave as if they were exactly the same, and that a species is only `rare' or `common' because of purely random, chance events. This theory has been remarkably successful at describing the patterns of rarity and abundance in many natural systems. However, not even Hubbell himself would claim that the `assumption of ecological equivalence' that underpins his theory is a faithful description of how species interact. The question is: why do natural systems behave as if their constituents are ecologically equivalent, when this is not true? This project will address this question by studying models where individuals of different species are not ecologically equivalent. While similar models have been studied before, they are so complicated that they cannot be solved mathematically, which makes it difficult to compare them to data. By contrast, Hubbell's model is relatively simple, and its properties can be studied in great detail. However, by studying models that are only slightly different from Hubbell's, we can use the exact solution to Hubbell's model to calculate how the predictions of our models differ from his. This method of piggy-backing on an exactly solvable model to study an unsolvable one is a well-established practice in applied mathematics. We shall investigate how differences in competitive ability and in species' preferences for different habitat contribute to patterns of biodiversity. This will show us how strong these processes would need to be to produce noticeably different predictions from Hubbell's model. We shall use our models to analyse data for highly diverse systems such as tropical forests and coral reefs. In this way, we shall measure and distinguish between the different processes that make these systems so diverse.