Modelling and bifurcation analysis of spatiotemporal hormetic effects on pest control.

A discrete hormetic Ricker model (HRM) of a population with instant pulse perturbation between two consecutive generations can generate hormetic effects. For example, analysis of complex three-parameter spaces with the intrinsic growth rate, intervention strength, and dose timing as parameters revealed hormetic biphasic dose and dose timing responses. These responses exhibited either a J-shaped or an inverted U-shaped pattern, yielding a homeostatic change or a catastrophic shift and hormetic effects in many parameter regions. However, whether it is pest control or the effectiveness of treatments of tumors with radiotherapy and/or chemotherapy, the phenomenon is linked to the size of the space in which the parameters are located. Thus, the occurrence of hormetic effects is associated with spatiotemporal heterogeneity. To show this, we have developed an integro-difference equation based on the HRM that can describe the complex dynamics and hormetic effects in pest populations in two-dimensional space. Our findings indicate that factors such as the spatial domain, spatial grid, the dosage, and timing of control applications, and the intrinsic growth rate of the pest can significantly affect the spatial and temporal characteristics of pest populations and diverse biological phenomena in two-dimensional space. In particular, under the same size of spatial domains (or the same number of spatial grids), the smaller the spatial grids (or the larger the spatial domain), the stronger the hormetic effects of low dose stimulation and high dose inhibition will be. These factors include larger maximum responses and higher toxic thresholds. Therefore, optimal pest control measures should not only rely on the efficiency of a pesticide and its application time but should also be based on the spatial domain and the designing of reasonable grid-based control strategies to avoid hormetic effects. • A two-dimensional spatial diffusion discrete HRM is proposed using integro-difference equation. • The dynamics of complex three-parameter spaces reveal hormetic biphasic dose and dose timing responses. • The hormetic effects are investigated in the spatial homogeneous context or heterogeneous context. • The experimental designs and analysis can be applied to pest control strategies and tumor treatment. [ABSTRACT FROM AUTHOR]