The hydra and hormetic effects in a single discrete-time overcompensation model

Area of Science:

• Ecology
• Mathematical Biology
• Population Dynamics

Background:

• The hydra effect and hormesis are observed in pest management and cancer treatment.
• The interplay of intervention timing, intensity, and density-dependent compensation is not well understood.

Purpose of the Study:

• To investigate hydra and hormetic effects using a discrete-time model based on density-dependent overcompensation.
• To analyze the influence of intervention timing (early, within, late generation) and intensity on these effects.

Main Methods:

• Development of a discrete-time single-population model incorporating density-dependent overcompensation.
• Simulation of interventions at three distinct generational timings: early, within, and late.
• Analysis of how compensation strength and intervention intensity affect population dynamics.

Main Results:

• Early-generation interventions narrow the parameter range for paradoxical responses.
• Late-generation responses depend on overcompensation strength, modulating parameter regions.
• Within-generation interventions show monotonic or biphasic dose-response curves based on mortality.
• Model fits published hormesis datasets, reproducing biphasic responses.

Conclusions:

• Intervention timing and intensity critically shape nonlinear density-dependent feedback, influencing multistability, hydra effects, and hormesis.
• The discrete-time overcompensation model offers criteria for intervention thresholds in ecological management and precision medicine.