Complex population dynamics in the real world: Modeling the influence of time-varying parameters and time lags

Abstract

We propose a class of complex population dynamic models that combines new time-varying parameters and second-order time lags for describing univariate ecological time series data. The Kalman filter and likelihood function were used to estimate parameters of all models in the class for 31 data sets, and Schwarz's information criterion (SIC) was used to select the best model for each data set. Using the SIC method, models containing density-dependent processes were selected for 23 of the 31 cases examined, while models containing complex density-dependent processes were selected in 19 of these 23 density dependence cases. The density-dependent models identified by SIC had various linear or nonlinear forms, suggesting variable patterns of population regulation in nature. Population dynamics may combine density-dependent, inversely density-dependent, and density-independent processes, which may operate at different times and under different density ranges. These results suggest that our approach offers an advance for modeling complex population dynamics, discovering complex regulation processes, and estimating the distribution of extinction times in changing environments.