Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar, 140001, Punjab, India.
Department of Mathematics, School of Natural Sciences, Shiv Nadar Institute of Eminence, Greater Noida, Uttar Pradesh, 201314, India.
Sci Rep. 2024 Oct 24;14(1):25248. doi: 10.1038/s41598-024-66578-w.
Several experimental evidences and field data documented that zooplankton may alter its behavioral response in the presence of toxic phytoplankton, reducing its consumption to the point of starvation. This paper is devoted to the mathematical study of such interactions of toxic phytoplankton with grazer zooplankton. The non-toxic phytoplankton is assumed to adopt a density-dependent refuge strategy to avoid over-predation by zooplankton. Both groups of phytoplankton are assumed to suffer direct harm from anthropogenic toxicants, while zooplankton is affected indirectly by ingesting contaminated phytoplankton. We calibrate the proposed model with the field data from Talsari and Digha Mohana, India, and estimate some crucial model parameters consistent with the behavior of the observed data. Our results demonstrate that zooplankton grazing on toxic phytoplankton plays a key role in the emergence or mitigation of plankton blooms. We also highlight the system's potential to exhibit multiple stable configurations under the same ecological conditions. The plankton system experiences significant regime shifts, which are explored through various bifurcation scenarios, such as transcritical and saddle-node bifurcations. These shifts are influenced by changes in refuge capacity, species growth rates, and environmental carrying capacity. Furthermore, we incorporate environmental variations due to seasonal periodic or almost periodic changes, allowing the refuge parameter to be time-dependent. We observe that the forced system exhibits double periodic solutions. Moreover, stronger seasonal variations in the refuge pattern lead to irregular chaotic blooms. In conclusion, the results offer valuable insights into the sustainability of biodiversity, potentially shedding light on the origin of diverse plankton bloom phenomena.
已有一些实验证据和实地数据证明，浮游动物在遇到有毒浮游植物时可能会改变其行为反应，从而减少对其的摄食，直至达到饥饿的程度。本文致力于研究有毒浮游植物与摄食浮游动物之间的这种相互作用。假设无毒浮游植物采用密度依赖的避难策略，以避免被浮游动物过度捕食。两组浮游植物都被假设会受到人为有毒物质的直接伤害，而浮游动物则通过摄入受污染的浮游植物受到间接影响。我们使用来自印度塔尔萨里和迪加莫哈纳的实地数据对提出的模型进行了校准，并根据观测数据的行为估计了一些关键模型参数。我们的研究结果表明，浮游动物摄食有毒浮游植物在浮游植物大量繁殖的出现或缓解中起着关键作用。我们还强调了该系统在相同生态条件下表现出多种稳定配置的潜力。浮游生物系统经历了显著的状态转变，通过各种分岔情景（如跨临界和鞍结分岔）进行了探索。这些转变受到避难能力、物种增长率和环境承载能力变化的影响。此外，我们还考虑了由于季节性周期性或近乎周期性变化引起的环境变化，使避难参数成为时间相关的。我们观察到强迫系统存在双周期解。此外，避难模式的季节性变化越强，浮游植物的混沌爆发越不规则。总之，这些结果为生物多样性的可持续性提供了有价值的见解，可能为各种浮游植物大量繁殖现象的起源提供了一些线索。
