Speaker
Description
Hormesis, where low doses stimulate and high doses inhibit, is well characterised empirically, but its mechanistic basis, especially the role of exposure history, remains poorly understood. Existing statistical models describe hormetic curves effectively but impose the biphasic structure through functional form rather than biological principles. To the best of our knowledge, an explicit, interpretable memory state variable has not been integrated into a general mechanistic ODE framework for hormesis. Therefore, we propose a Minimal Mechanistic Model combining dose-dependent stimulation, saturation-type inhibition, and homeostatic recovery, with analytical conditions derived to guarantee a stable hormetic maximum. This is extended to a Memory-Augmented Model, where a leaky-integrator state variable accumulates exposure history and modulates the response through a saturating feedforward term. Both models are validated against cadmium–fecundity data~\cite{Godinho}, achieving goodness of fit comparable to empirical models. A central result is an identifiability finding: under steady-state conditions, the memory variable collapses algebraically to a rescaled dose, rendering the models observationally equivalent. We prove analytically that static endpoint data are structurally insufficient to identify memory effects. This formal result motivates an experimental prescription: time-course measurements and repeated-exposure protocols constitute the minimal data requirement for memory identification.
Bibliography
@misc{Godinho,
title = {Effect of cadmium accumulation on the performance of plants and of herbivores that cope differently with organic defenses},
author = {Godinho, D. P. et al.},
year = {2018},
doi = {10.5061/dryad.f274gs3},
}
