Modeling Dependence in Ecological Data: From Mosquitoes to Human Migration 

Abstract: Ecological data are inherently dependent due to spatial and temporal autocorrelation, species interactions, seasonality, and environmental gradients. In this seminar, I will present several statistical methods that account for various forms of dependence that arise in ecological data. Technical details will be limited; emphasis is on the overall ideas. First, we'll briefly look at a dynamic population model for the analysis of abundance data, which often experience a high degree of temporal autocorrelation. The model was fit to mosquito abundance data collected across North America. An additional source of dependence came in the form of temporal preferential sampling (TPS), where data collection was informed by the observed abundance. I accounted for temporal autocorrelation and TPS in a Bayesian hierarchical model (BHM), which was specified mechanistically such that the observed abundance was related to the Gompertz growth function. Due to the mechanistic specification, inference was made for abundance and phenological quantities of interest. Next, we'll explore a BHM used to infer the relationship between population genetic data and the environment. Such data arise in the field of landscape genomics, where there is interest in the functional connectivity and migration patterns of populations. Population genetic data are highly dependent, and I accounted for spatial and temporal autocorrelation via composite likelihoods. The BHM contains a dyadic regression, which is linked to an advection-diffusion differential equation to infer how Bronze Age humans migrated throughout Europe. Finally, I'll present an analysis of spatial compositional data, which often arise in community ecology, organismal composition studies, and ecosystem forecasting. The proposed model accounts for spatial autocorrelation and the compositional nature of the data. In particular, I transformed the compositional data to directional data and modeled it using a novel hyperspheric distribution. This is the first spatial hyperspheric approach to contain fixed and latent spatial random effects, while accounting for the compositional constraints inherent to the data. I applied the model to bioacoustic signal classifications obtained from a machine learning classifier.