Modeling population dynamics: A quantile approach

• The paper investigates the modeling of population dynamics.
• A threshold quantile autoregression model is used to capture nonlinear dynamics.
• TQAR allows lag effects to vary with quantiles and with previous population levels.
• The model is applied to the dynamics of lynx population.
• The results show how lynx population adjusts to past population levels and shocks.

The paper investigates the modeling of population dynamics, both conceptually and empirically. It presents a reduced form representation that provides a flexible characterization of population dynamics. It leads to the specification of a threshold quantile autoregression (TQAR) model, which captures nonlinear dynamics by allowing lag effects to vary across quantiles of the distribution as well as with previous population levels. The usefulness of the model is illustrated in an application to the dynamics of lynx population. We find statistical evidence that the quantile autoregression parameters vary across quantiles (thus rejecting the AR model as well as the TAR model) as well as with past populations (thus rejecting the quantile autoregression QAR model). The results document the nature of dynamics and cycle in the lynx population over time. They show how both the period of the cycle and the speed of population adjustment vary with population level and environmental conditions.