Environments, Social Structure, and Population Dynamics.

Understanding population dynamics is foundational to the study of ecology and evolution, and can form the basis for decision-making in management and policy arenas. Consequently, my doctoral research has sought to address some of the practical challenges in modeling populations and to develop new frameworks to explore complex dynamics and their implications. Recurring themes in my research are the influence of demographic structure and environmental variability on population dynamics. The chapters of this dissertation are more or less independent projects sampling my efforts to address different aspects of population ecology. I start by addressing a practical issue in population dynamics, namely, the decision between using stochastic and deterministic models to describe real world populations. The crux of this decision is whether the variability in the observed demographic parameters is consistent with sampling induced variability or whether there is evidence for environmentally-driven variability. I propose a non-parametric method to detect environmental variability in demographic parameters of structured populations based on data randomization using an estimated Kullback-Leibler distance as a test statistic. I show, with empirical and simulated datasets, that it can be adapted effectively to detect variability in demographic fates among populations. This metric has the potential to reveal the importance of relatively rare transitions for understanding temporal variability in demography that would not be revealed by conventional log-linear analysis. From the practical question of detecting environmentally-driven variability in the demographic parameters of structured populations, I turn to the more conceptual question of how to model hierarchically structured populations. Hierarchical population structure, where individuals are aggregated into colonies or similar groups that themselves grow, survive or perish, and potentially produce offspring groups, is an important feature of many biological systems. I present an analytical framework that provides a simple, robust, and predictive theory for the population dynamics of hierarchical organisms. The framework explicitly describes and links demographic dynamics for the different levels in the hierarchy (individuals, groups, population). I illustrate the application of the framework by developing a model for honeybees and analyzing the effects of life history traits such as worker lifespan and size at swarming on the growth rate of populations. I then turn to an exploration of population dynamics in long memory environments. Using a general random walk model I explore how long memory changes our fundamental insights and expectations compared to shorter memory processes. I describe the strength of the memory by the Hurst parameter H which governs the asymptotic rate of decay of autocorrelations. An important consequence of long memory is that the variance in the logarithmic population size increases proportional to time t2H, which is considerably faster than in short memory systems, and the logarithmic population size converges to a fractional Brownian motion. The identification of fractional Brownian motion as a limiting process for biological models provides linkages to existing theory as well as the impetus for further theoretical work. I continue the theme of stochastic population dynamics in chapter five, but return to the structured population case. An analytical approximation for the asymptotic growth rate of a structured population in a stochastic environment, as well the variance of the cumulative growth were first developed by Tuljapurkar over twenty-five years ago. I...