Dynamics of Tribolium growth: Insights into population chaos

Flour beetles (genus: Tribolium) have long been used to gain insights into the fields of biology and ecology due to their experimental amenability and adaptations to living near humans.  Tribolium have also cemented their place in mathematics in the hunt for chaos in the 1990s by the "Beetle Team" composed of Cushing, Costantino, Henson, Dennis, Desharnais, King, and Edwards. The group used the LPA (larvae-pupae-adult) model to inform experimental perturbations that would push flour beetle populations into chaotic behavior. Using new experimental data, we developed what we call the LPAA model which stratifies the adults into newly emerged and mature populations. We show local and global stability results for the extinction and positive steady-states. We explore bifurcations numerically and show that chaos is not inherent to our laboratory populations. We also discuss differences in experimental protocols which may affect the experimental, and subsequently model, dynamics.