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.

The relative importance of intrinsic and extrinsic drivers to population growth vary among local populations of Greater Sage-Grouse: An integrated population modeling approach

“…Zeng et al (1998) demonstrated the power of the stochastic growth models we applied in detecting density dependence, complex dynamics and time lags. Lande et al (2002) demonstrated that interpreting the coefficients of delayed density dependence are quite complex involving the negative elasticity of population growth rate per generation with respect to change in population size.…”

Model selection in demographic time series using VC-bounds

“…These models are often used as alternative candidates when one has to identify the demographic mechanism underlying the available field data, and are usually compared by SIC (Zeng et al, 1998;Dennis and Otten, 2000;Taper and Gogan, 2002;Peek et al, 2002).…”

“…A milestone in this context is for instance the work of Dennis and Taper (1994), who proposed a powerful hypothesis testing framework based on parametric bootstrapping of likelihoods ratios. Despite their statistical soundness, hypothesis testing frameworks often suffered from the problem of low power, and were therefore recognized as conveying only limited information (Zeng et al, 1998). In fact, the diversity in pat-terns of natural population regulation can be hardly addressed by comparing just a couple of models and, on the other hand, managing many models through hierarchical pairwise hypothesis testing does not necessarily lead to the selection of the best model (Strong et al, 1999).…”

“…To overcome such limitations, several authors (Zeng et al, 1998;Strong et al, 1999;Dennis and Otten, 2000;Taper and Gogan, 2002) have proposed the use of information criteria (IC) to choose the best among a suite of alternative models including both density-independent and density-dependent demographies. Generally speaking, ICs address the model selection by choosing the model that minimizes the product of the squared deviation from data and a penalization factor, which is an increasing function of the ratio of free parameters d to the size q of the dataset; the rationale for such a penalization is that an optimal trade-off should be found between the quality of data fitting and model complexity.…”

“…As a consequence of these restricting hypotheses, ICs are very often applied even if their constitutive assumptions are not strictly met. In the literature, the Final Prediction Error (FPE) and in particular the Schwartz Information Criterion (SIC) appear to be the most widely used by ecologists (Strong et al, 1999;Dennis and Otten, 2000;Zeng et al, 1998;Taper and Gogan, 2002).…”