Hormesis and hydra effects revealed by intraspecific overcompensation models and dose–response curves

Overcompensation, defined as recovery beyond a baseline state, arises from both hormetic and hydra effects, illustrating adaptive responses to stress. The overcompensation framework of a re-evaluated fishery resource management model was examined through nonlinear growth patterns based on logistic or Ricker models, emphasizing population size over carrying capacity. This complete overcompensation model’s threshold conditions reveal an interplay between hydra and hormetic effects. Also, when dividing a population into distinct subgroups, such as susceptible and infected classes in disease transmission, the population size can be modelled as a function of the basic reproduction number ( R 0 ). A threshold condition of R 0 allows examination of how disease infectivity triggers hydra or hormetic effects and, also, development of a partial overcompensation model that elucidates the internal mechanisms of overcompensation. Analysis of data from 24 groups of U-shaped or inverted U-shaped dose–response curves validated the dose–response curves. The simplified modelling approach developed revealed the mechanisms underlying hydra and hormetic effects, highlighting the importance of strong growth or regenerative capabilities, overcompensatory responses (strong nonlinearity), mild external stimuli (weak stressors) and the baseline population size. Our new analytical techniques for overcompensation modelling can be adapted to many fields, including tumour treatment and toxicology.