RESUMEN
Ageing research focuses on identifying lifespan modifiers and understanding and appropriately interpreting their effects. One of the most relevant quantities being studied is the shape of the survival curve that can reveal crucial information on the mechanism of action. Here, we introduce a bilogistic model to describe the shape of the lifespan curves of Caenorhabditis elegans populations. Using the corrected Akaike information criterion and the RMSE as goodness-of-fit tests, we show that the bilogistic model provides a better fit to the experimental data from nematode worms than other mathematical models and can identify and confirm biphasic lifespan data. Our parametric model offers a method to interpret replicate experiments data in terms of the shape parameters of the lifespan curve and enables robust statistical analysis of intra- and inter-group variance. We apply the model to novel lifespan data from C. elegans and Drosophila melanogaster and provide a rational statistical analysis of lifespan modifiers such as temperature and daf-16/FOXO mutation.
RESUMEN
Reactivity (a.k.a initial growth) is necessary for diffusion driven instability (Turing instability). Using a notion of common Lyapunov function we show that this necessary condition is a special case of a more powerful (i.e. tighter) necessary condition. Specifically, we show that if the linearised reaction matrix and the diffusion matrix share a common Lyapunov function, then Turing instability is not possible. The existence of common Lyapunov functions is readily checked using semi-definite programming. We apply this result to the Gierer-Meinhardt system modelling regenerative properties of Hydra, the Oregonator, to a host-parasite-hyperparasite system with diffusion and to a reaction-diffusion-chemotaxis model for a multi-species host-parasitoid community.