Choice of density-dependent seedling recruitment function affects predicted transient dynamics: a case study with Platte thistle

Abstract

Modelers have to make choices about which functional forms to use for representing model components, such as the relationship between the state of individuals and their vital rates. Even though these choices significantly influence model predictions, this type of structural uncertainty has been largely ignored in theoretical ecology. In this paper, we use integral projection models (IPMs) for Platte thistle as a case study to illustrate that the choice of functional form characterizing density dependence in seedling recruitment has important implications for predicting transient dynamics (short-term population dynamics following disturbances). In one case, the seedling recruitment function is modeled as a power function, and in the other case, we derive density dependence in seedling recruitment from biological first principles. We chose parameter values for the recruitment functions such that both IPMs predicted identical equilibrium population densities and both recruitment functions fit the empirical recruitment data sufficiently well. We find that the recovery from a transient attenuation, and the magnitude of transient amplification, can vary tremendously depending on which function is used to model density-dependent seedling recruitment. When we loosen the restriction of having identical equilibrium densities, model predictions not only differ in the short term but also in the long term. We derive some mathematical properties of the IPMs to explain why the short-term differences occur.