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Abstract
The humble flour beetle (genus: Tribolium) has been living alongside humans for thousands of years and driving biological insights for hundreds. The larvae-pupae-adult (LPA) model was used on T. castaneum in the first-ever experiments inducing chaos in a laboratory population (Costantino et al. 1995). Driven by new experimental data using T. confusum, two models (one discrete and one continuous) are presented as extensions of the LPA model. The first, the larvae-pupae-adult-adult (LPAA) model, is a discrete map which stratifies adults by reproductive capability. This model outperforms the LPA model on experimental data and, while having an additional compartment, remains fully tractable to stability analysis. In addition, while the LPA model may predict chaos under certain experimental parameter regimes, the LPAA model does not. A larvae-adult (LA) continuous-time model is also presented where the pupal stage is represented using a discrete time delay. It is shown that the time delay is critical for oscillations to take place and the model performs well on experimental data. Nonlinearities introduced by cannibalism make traditional analysis of the positive equilibrium intractable, and other approaches are used to characterize its stability. These two models highlight the importance of model choice and their impact on asymptotic dynamics, particularly so given that chaos is not uncommon in discrete maps. Differences in experimental protocols and how these may affect the results are discussed, and call for further investigation on the impact of media changes as a driver of chaos.
