A parametrical model to describe a stable and stationary age structure for fossil populations

Abstract

A parametric family of models based on the Weibull model was proposed to describe the age structure of a fossil population. This descriptive approach was combined with a population dynamics model based on the Leslie matrix. The stability and sustainability conditions were algebraically stated to provide an equilibrium equation for any species. The model parameters for a sustainable population were determined via numerical methods. These values represent the survival and mortality profiles for a sustainable population and are comparable between different populations. This approach tests whether an observed mortality profile might correspond to the natural mortality pattern of a stable population. Finally, the model performance was tested for three fossil Bison priscus populations (Il'Skaya, Mauran and Coudoulous) using literature data.