Scaling limits of a model for selection at two scales

The dynamics of a population undergoing selection is a central topic in evolutionary biology. This question is particularly intriguing in the case where selective forces act in opposing directions at two population scales. For example, a fast-replicating virus strain outcompetes slower-replicating strains at the within-host scale. However, if the fast-replicating strain causes host morbidity and is less frequently transmitted, it can be outcompeted by slower-replicating strains at the between-host scale. Here we consider a stochastic ball-and-urn process which models this type of phenomenon. We prove the weak convergence of this process under two natural scalings. The first scaling leads to a deterministic nonlinear integro-partial differential equation on the interval $[0,1]$ with dependence on a single parameter, $\lambda$. We show that the fixed points of this differential equation are Beta distributions and that their stability depends on $\lambda$ and the behavior of the initial data around $1$. The second scaling leads to a measure-valued Fleming-Viot process, an infinite dimensional stochastic process that is frequently associated with a population genetics.

A Philosophy of Operatic Storytelling

This dissertation presents the first theoretical model for understanding narration and point of view in opera, examining repertoire from Richard Wagner to Benjamin Britten. Prior music scholarship on musical narratives and narrativity has drawn primarily on continental literary theory and philosophy of the 1960s to the middle of the 1980s. This study, by contrast, engages with current debates in the analytic branch of aesthetic philosophy. One reason why the concept of point of view has not been more extensively explored in opera studies is the widespread belief that operas are not narratives. This study questions key premises on which this assumption rests. In so doing, it presents a new definition of narrative. Arguably, a narrative is an utterance intended to communicate a story, where "story" is understood to involve the representation of a particular agent or agents exercising their agency. This study explores the role of narrators in opera, introducing the first taxonomy of explicit fictional operatic narrators. Through a close analysis of Britten and Myfanwy Piper's Owen Wingrave, it offers an explanation of music's power to orient spectators to the points of view of opera characters by providing audiences with access to characters' perceptual experiences and cognitive, affective, and psychological states. My analysis also helps account for how our subjective access to fictional characters may engender sympathy for them. The second half of the dissertation focuses on opera in performance. Current thinking in music scholarship predominantly holds that fidelity is an outmoded concern. I argue that performing a work-for-performance is a matter of intentionally modelling one's performance on the work-for-performance's features and achieving a moderate degree of fidelity or matching between the two. Finally, this study investigates how the creative decisions of the performers and director impact the point of view from which an opera is told.