Author ORCID Identifier

https://orcid.org/0000-0003-1926-5407

Date of Award

Spring 6-13-2026

Document Type

Thesis (Ph.D.)

Department or Program

Mathematics

First Advisor

Peter J. Mucha

Abstract

This dissertation develops mathematical and statistical methods for extracting reliable information from network data across biological applications, with an emphasis on understanding what observed network structure can and cannot resolve. The first study leverages protein–protein interaction network topology in the c-di-GMP signaling system of Pseudomonas fluorescens, showing that node centrality measures accurately classify protein domain types and that physical interaction structure contributes statistically significant predictive power for biofilm formation phenotypes across nearly 200 environments, while gene expression does not. The second study examines sampling bias in lemur-plant trophic interaction networks in Madagascar, demonstrating that differential detection of diurnal versus nocturnal species confounds trait-based predictors of dietary richness and that sampling effort mediates key functional trait effects. The third study formalizes this bias problem in a Bayesian framework, analyzing the identifiability of latent Poisson rates under unequal detection probabilities and characterizing the conditions under which informative priors on detection can and cannot disentangle true rate differences from observational artifacts. The fourth study investigates the downstream structural consequences of degree sampling bias in bipartite ecological networks, showing via simulation and spectral analysis that differential detection in one partition generates spurious modular structure in the network’s unipartite projection, and developing eigenvector alignment as a diagnostic tool for bias assessment. Taken together, these contributions form a coherent framework for network-based inference under incomplete and biased observation, with applications spanning microbiology, ecology, and statistical methodology.

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