Stochastic modeling of ecological time series: Animal population dynamics, complex regulation and structural changes

Modeling complex population dynamics, discovering complex population regulation processes, and assessing structural changes in the population dynamics in changing environments are of great importance in ecology. Using simple modeling approaches and testing techniques, many studies have failed to find density dependent population regulation, and decades of controversy have been caused by weak support for density dependence from field studies. Considerable debate continues regarding the theory and appropriate methodology for evaluating population regulation. In this study, I proposed a set of complex dynamics models, including new time-varying parameter models, second order and second order random coefficient models, to model the structural population dynamics, and identify complex population regulation processes due to the influences from natural enemies, resource availability, and other environmental factors in changing environments. The Kalman filter and maximum likelihood function were used to estimate the parameters in time-varying parameter models and second order models. The Akaike's information criterion (AIC), adjusted AIC (AICc), Schwarz's information criterion (SIC) were used to identify the best model. A parametric bootstrap test based on the information criterion was proposed to find the probability value of the model selection. Diagnostic techniques (CUSUM, and CUSUMSQ) were used to identify structural changes in the time series. These models were used to evaluate 20 insect and 11 vertebrate univariate time series using Kalman filter analysis.; Monte Carlo simulation results showed that time-varying parameter models perform well in approximating both systematic and stochastic parameter changes over time. The Kalman filter was found to yield efficient estimates of time-varying parameters for longer time series data, larger variations in the parameters, fewer number of the noise terms and smaller system noise. Density dependent regulation was found in 23 out of 31 cases examined, while complex population regulation was found in 18 out of these 23 density dependence cases using the SIC method. Stronger evidence of density dependent regulation in 17 out 23 cases was found to be statistically different from the density independence process at the 0.05 probability level from the parametric bootstrap test. The complex population dynamic models selected by SIC or the significant probability value were diversified in linear or nonlinear forms, which suggest various complex population regulation patterns in nature. Various topics related to ecological time series modeling are discussed in this thesis.; Population dynamics may combine density dependent, inverse density dependent and density independent processes, which may operate in different times and different density ranges in nature. Models that fail to include important density dependent factors may not be able to detect density dependent regulation and explain population dynamics. This study offers an advance for modeling complex population dynamics, discovering complex regulation patterns, improving tests for density dependence, and assessing structural changes in the population dynamics over time in changing environments using various linear and nonlinear models.