DYNAMICS OF THE SHORT TERM AND LONG TERM AVIAN DISTRIBUTIONS IN NORTH AMERICA - THE ROLES OF VEGETATION HEIGHT HETEROGENEITY AND CLIMATIC FACTORS

Understanding how biodiversity spatially distribute over both the short term and long term, and what factors are affecting the distribution, are critical for modeling the spatial pattern of biodiversity as well as for promoting effective conservation planning and practices. This dissertation aims to examine factors that influence short-term and long-term avian distribution from the geographical sciences perspective. The research develops landscape level habitat metrics to characterize forest height heterogeneity and examines their efficacies in modelling avian richness at the continental scale. Two types of novel vegetation-height-structured habitat metrics are created based on second order texture algorithms and the concepts of patch-based habitat metrics. I correlate the height-structured metrics with the richness of different forest guilds, and also examine their efficacies in multivariate richness models. The results suggest that height heterogeneity, beyond canopy height alone, supplements habitat characterization and richness models of two forest bird guilds. The metrics and models derived in this study demonstrate practical examples of utilizing three-dimensional vegetation data for improved characterization of spatial patterns in species richness. The second and the third projects focus on analyzing centroids of avian distributions, and testing hypotheses regarding the direction and speed of these shifts. I first showcase the usefulness of centroids analysis for characterizing the distribution changes of a few case study species. Applying the centroid method on 57 permanent resident bird species, I show that multi-directional distribution shifts occurred in large number of studied species. I also demonstrate, plain birds are not shifting their distribution faster than mountain birds, contrary to the prediction based on climate change velocity hypothesis. By modelling the abundance change rate at regional level, I show that extreme climate events and precipitation measures associate closely with some of the long-term distribution shifts. This dissertation improves our understanding on bird habitat characterization for species richness modelling, and expands our knowledge on how avian populations shifted their ranges in North America responding to changing environments in the past four decades. The results provide an important scientific foundation for more accurate predictive species distribution modeling in future.

Quantitative Derivation of Effective Evolution Equations for the Dynamics of Bose-Einstein Condensates

This thesis proves certain results concerning an important question in non-equilibrium quantum statistical mechanics which is the derivation of effective evolution equations approximating the dynamics of a system of large number of bosons initially at equilibrium (ground state at very low temperatures). The dynamics of such systems are governed by the time-dependent linear many-body Schroedinger equation from which it is typically difficult to extract useful information due to the number of particles being large. We will study quantitatively (i.e. with explicit bounds on the error) how a suitable one particle non-linear Schroedinger equation arises in the mean field limit as number of particles N → ∞ and how the appropriate corrections to the mean field will provide better approximations of the exact dynamics. In the first part of this thesis we consider the evolution of N bosons, where N is large, with two-body interactions of the form N³ᵝv(Nᵝ⋅), 0≤β≤1. The parameter β measures the strength and the range of interactions. We compare the exact evolution with an approximation which considers the evolution of a mean field coupled with an appropriate description of pair excitations, see [18,19] by Grillakis-Machedon-Margetis. We extend the results for 0 ≤ β < 1/3 in [19, 20] to the case of β < 1/2 and obtain an error bound of the form p(t)/Nᵅ, where α>0 and p(t) is a polynomial, which implies a specific rate of convergence as N → ∞. In the second part, utilizing estimates of the type discussed in the first part, we compare the exact evolution with the mean field approximation in the sense of marginals. We prove that the exact evolution is close to the approximate in trace norm for times of the order o(1)√N compared to log(o(1)N) as obtained in Chen-Lee-Schlein [6] for the Hartree evolution. Estimates of similar type are obtained for stronger interactions as well.

Essays on Uncertainty, Imperfect Information, and Investment Dynamics

Understanding how imperfect information affects firms' investment decision helps answer important questions in economics, such as how we may better measure economic uncertainty; how firms' forecasts would affect their decision-making when their beliefs are not backed by economic fundamentals; and how important are the business cycle impacts of changes in firms' productivity uncertainty in an environment of incomplete information. This dissertation provides a synthetic answer to all these questions, both empirically and theoretically. The first chapter, provides empirical evidence to demonstrate that survey-based forecast dispersion identifies a distinctive type of second moment shocks different from the canonical volatility shocks to productivity, i.e. uncertainty shocks. Such forecast disagreement disturbances can affect the distribution of firm-level beliefs regardless of whether or not belief changes are backed by changes in economic fundamentals. At the aggregate level, innovations that increase the dispersion of firms' forecasts lead to persistent declines in aggregate investment and output, which are followed by a slow recovery. On the contrary, the larger dispersion of future firm-specific productivity innovations, the standard way to measure economic uncertainty, delivers the ``wait and see" effect, such that aggregate investment experiences a sharp decline, followed by a quick rebound, and then overshoots. At the firm level, data uncovers that more productive firms increase investments given rises in productivity dispersion for the future, whereas investments drop when firms disagree more about the well-being of their future business conditions. These findings challenge the view that the dispersion of the firms' heterogeneous beliefs captures the concept of economic uncertainty, defined by a model of uncertainty shocks. The second chapter presents a general equilibrium model of heterogeneous firms subject to the real productivity uncertainty shocks and informational disagreement shocks. As firms cannot perfectly disentangle aggregate from idiosyncratic productivity because of imperfect information, information quality thus drives the wedge of difference between the unobserved productivity fundamentals, and the firms' beliefs about how productive they are. Distribution of the firms' beliefs is no longer perfectly aligned with the distribution of firm-level productivity across firms. This model not only explains why, at the macro and micro level, disagreement shocks are different from uncertainty shocks, as documented in Chapter 1, but helps reconcile a key challenge faced by the standard framework to study economic uncertainty: a trade-off between sizable business cycle effects due to changes in uncertainty, and the right amount of pro-cyclicality of firm-level investment rate dispersion, as measured by its correlation with the output cycles.