Since at least the time of Darwin biologists have searched for a simple set of universal governing mechanisms that dictate the dynamics of biodiversity. While much progress has been made in understanding system-specific processes and in documenting the context-dependent roles of such mechanisms as competition and facilitation, we still lack a universal governing rule set. The goal of understanding and predicting biodiversity dynamics comes at a critical moment when human systems are disrupting those very dynamics. In this thesis I approach this long-standing problem with the hypothesis that general patterns in biodiversity emerge from a combination of the statistical mechanics of large systems and the unique non-equilibrium dynamics imparted to biological systems by their evolutionary history. Statistical mechanics provides the key analytical approaches to abstracting the complex details of biodiversity into general macroscopic predictions that I show receive support from empirical data. However, key deviations from the simplest statistical mechanics of biodiversity reveal the key role of biological evolution in driving systems away from the idealized steady state predicted by statistical mechanics.
In Chapter 1 I expand a branch of non-equilibrial statistical mechanics, known as super statistics, to explain previously unaccounted for wild fluctuations in the richness of taxa through the Phanerozoic marine invertebrate fossil record and show how this non-equilibrium is driven by clades' punctuated exploration of their adaptive landscapes. This theory provides a novel explanation for deep time diversity dynamics invoking emergence of lineage-level traits as the drivers of complexity via the same mechanisms by which complexity emerges in large physical and social systems. In the context of fossil diversity I show how this complexity arises naturally from the uniquely biological mechanisms of punctuated adaptive radiation followed by long durations of niche conservatism, and thus identify these mechanisms as sufficient and necessary to produce observed patterns in the fossil record. I test this theory using two seminal fossil datasets.
In Chapter 2 I use the chronosequence afforded by the Hawaiian Islands to capture evolutionary snapshots of arthropod communities at different ages and stages of assembly to understand how the history underlying an assemblage determine its contemporary biodiversity patterns. I apply static ecological theory of trophic networks based on statistical mechanics to these rapidly evolving ecosystems to highlight what about the evolutionary process drives communities away from statistical idealizations. This study indicates that rapid assembly from immigration and speciation in young ecosystems and extinction in old ecosystems could drive observed patterns.
In Chapter 3 I highlight and explain the computational requirements to testing one statistical theory of biodiversity--the Maximum Entropy Theory of Ecology--with real data and make those test available in a stream-lined framework via the R package meteR that I authored.
