| A central goal of ecology is to understand the spatio-temporal variation of organisms. Contributing towards achievement of this goal is the statistical inference of stochastic time series models characterizing and identifying causal sources of variation.;One theoretically well-developed explanation for population fluctuations describes fluctuations in population abundance as a result of feedback between a populations density and its per capita growth rate. Chapters 1 and 2 evaluate the ability to estimate the manner in which this effect sets in from noisy time series data using either a generalized Beverton-Holt or theta-Ricker phenomenological discrete-time model. Monte Carlo simulations are first used to quantify maximum likelihood evaluators under different scenarios of sample size, endogenous dynamics, perturbations, and environmental stochasticity, and evaluate the efficacy of constructing confidence intervals based on the likelihood ratio test for each scenario. There are two main results from the simulation experiments. First, accurate inference requires information about per capita growth rates at low densities. Second, the joint profile likelihood surface is a useful diagnostic tool for assessing the reliability of point estimates determining this relationship. For the theta-Ricker model, multimodality and ridges in the likelihood surface are shown to occur frequently in both simulated and empirical data sets, with the best-fit model determined by the maximum likelihood parameter values often occurring at the biologically implausible mode. A detailed analysis of a sparrowhawk (Accipiter nisus) population reveals that the best-fit model is only slightly supported over a suite of more biologically plausible models, regardless of the phenomenological or stochastic model choice. The implications of multimodality and ridges in the likelihood surface for other methods of statistical inference are discussed.;In Chapter 3 I consider new ways of analyzing animal location time series. The primary methods are Fourier and wavelet transforms, and are evaluated with a novel stochastic diffusion model of movement. Case studies of lion (Panthera leo) and African buffalo (Syncerus caffer ) show how these methods reveal temporally complex and nonstationary movement, and in conjunction with the movement model contribute to a more accurate understanding about animal behavior beyond characterization as uncorrelated random walks. |
