UC Berkeley

Ecologists commonly make strong parametric assumptions when formulating statistical models. Such assumptions have sparked repeated debates in the literature about statistical identifiability of species distribution and abundance models, among others. Part I of this dissertation draws upon the econometrics literature to introduce a broader view of the identifiability problem than has been taken in ecological debates. In particular we use a simulation approach to illustrate the concepts of non-parametric and parametric identifiability and their implications for ecologists. The fact that all models are approximations has very different implications for these two cases of identifiability. When non-parametric identifiability holds, even a mis-specified parametric model provides a useful approximation to the truth, and the fit of alternative models can be compared. When non-parametric identifiability does not hold, parametric assumptions create artificial identifiability, and alternative models cannot be distinguished empirically.

Joint species distribution models (JSDMs) have become a popular tool for helping ecologists understand properties of a community while accounting for relationships between species. Part II of this dissertation stress tests a foundational JSDM to understand how well properties of the community are estimated in the presence of model mis-specification. Community diversity metrics summarize community characteristics that ecologists have historically been interested in, so it is of interest to ask whether estimation of these more complicated metrics is robust to inevitable model mis-specification.

Being a statistician is a "hands-on" job that requires communicating with stakeholders and researchers in a variety of fields. Part III of this dissertation leverages the communication skills I have built while working at the intersection of ecology and statistics to teach statistics students how to write about statistical analyses in an accessible way that is still faithful to the data. A pedagogical approach is described that builds upon that of traditional writing and science communication. This approach adds to the solid foundation with concrete examples in the context of statistics, particular focus on the nuances of statistical language, and a focus on narrative that carries throughout the data analysis process itself.