A collection of statistical methods for applications in tree demography

Abstract

Ecological data are often characterized by complex spatial and temporal patterns, which can be difficult to analyze and interpret. In the context of tree demography, the study of forest dynamics at both the individual and stand level is crucial for understanding forest ecosystems and their response to environmental changes. In this dissertation, we present a collection of statistical methods and practical tools for addressing ecological questions, with a particular emphasis on tree demography. We introduce two novel modeling frameworks for identifying unique trees across multiple aerial scans and estimating individual tree growth as a function of spatial and spatio-temporal covariates, and a framework for estimating and simulating from location-dependent marked spatial point processes. We first present a two-stage Bayesian spatial record linkage approach designed to identify unique trees across bi-temporal light detection and ranging (LiDAR) scans. This approach generalizes the linkage-averaging (LA) approach for record linkage to meaningfully propagate uncertainty from the linkage into a generic auxiliary data downstream modeling task. We introduce a novel approximate sampling scheme for the linkage that leverages the spatial structure of the data to achieve a degree of scalability in the model that allows it to be applied to spatial domain sizes that were previously too large to study. We apply this modeling framework with a generalized Michaelis--Menten style growth function to investigate the impact of key water and energy availability proxies on individual tree growth in a spruce-fir forest located on Snodgrass Mountain in the Gunnison National Forest of the Southern Rocky Mountains of Colorado, USA. We also provide a comprehensive set of numerical experiments on simulated data that mimics the characteristics of the empirical data from the case study. We then present the ldmppr R package, which enables the efficient estimation, evaluation, and simulation of location-dependent marked spatial point processes characterized by regularity given a reference pattern and location-specific covariate surfaces. Originally motivated by our need to simulate biologically realistic point patterns for our work in the previous chapter, this work addresses the need for a suitably flexible off-the-shelf method for working with location-dependent covariates in the mark distribution of a spatial point process. For example, we might consider the size of trees within a forest as a spatial point process where the size of a tree is a function of location-dependent covariates such as elevation, soil wetness measured by a topographic wetness index, and the aspect of the slope. We provide a detailed discussion of our modeling approach and the workflow for using the package, including a case study motivated by the empirical data from the previous chapter. Finally, we present an alternative to the two-stage modeling framework introduced in the first chapter by utilizing a joint modeling approach for temporal record linkage to simultaneously identify unique individuals across multiple aerial scans and estimate individual tree growth as a function of spatial and spatio-temporal covariates. We develop a Bayesian hierarchical model that provides exact uncertainty quantification across both the linkage and the downstream modeling task concurrently. We incorporate a mechanistic downstream growth model based on an ordinary differential equation (ODE) that approximates the underlying growth process. We consider two alternative joint model formulations, and contrast the performance of the two approaches in a series of numerical experiments considering a wide range of observable scenarios as motivated by a dataset comprised of multi-temporal aerial scans of a spruce-fir forest near the Gothic Townsite located outside of Crested Butte, Colorado. We conclude with a summary of the primary contributions of the work presented in this dissertation and the impact on the fields of tree demography, record linkage, and spatial point processes.