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Maximum Entropy for Resource Allocation: a quantitative theory of species coexistence and population demographics

Abstract

In the past few decades, ecology has gone through exciting breakthroughs in developing and applying quantitative methods to more accurately describe and predict patterns and dynamics. However, a theoretical framework under which models could be built and results interpreted in one language is still missing, impeding the communication and collaboration among subfields of ecology. To serve the ultimate goal of developing such a framework, in this dissertation, a theory is developed to make unified predictions of several facets of ecology that have so far been addressed mostly in independent ways: starting from a simple scenario of resource allocation, the theory simultaneously predicts species coexistence, community-level energy distribution, population demographic growth function, evolutionary tradeoffs and life history strategies. The approach of maximizing information entropy (MaxEnt) is used to make sure that the theory makes the most objective predictions from the fewest ad hoc assumptions. Previous applications of MaxEnt in ecology are reviewed in Chapter 1. In Chapter 2, the fundamental framework and a first model of the theory is introduced. Based on the same framework, several different approaches to expand model predictions are explored in Chapters 3 and 4. As is discussed in Chapters 2-4, the assumptions and parameters of the theory can be related to many important concepts in ecology (e.g. fitness equality, stabilizing effect, niche and neutrality), and the predictions reveal many previously unidentified links between patterns and processes at the population and community level to metabolism and functional traits. Combining all above, the work in this dissertation is potentially a first step towards a unified theoretical framework of ecology.

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