The impact of climate change on flowering plants-bees-Vespa orientalis model

Abstract

There is a dearth of mathematical models that combine climatic stress, mutualism (plant-bee), and antagonism (Vespa predation on bees) in a single ecological system, despite the fact that numerous research look at how climate change impacts particular species or paired interactions. Our capacity to forecast the cascade impacts of warming on pollination services and plant reproduction is hampered by this gap. The densities of the flowering plant depend on the behavior of the pollinators. We describe a novel pollinator model consisting of flowering plants and two pollinator species (honey bees and Vespa orientalis). It assumed that flowering plants’ densities depend on flower visitation rates by honey bees and Vespa orientalis. Also, the global warming phenomenon is assumed to harm the growth of flowering plants and honey bees. The Vespa orientalis hinders the expansion of bees, as they kill them and take the honey inside their stomachs. After presenting the model, the system’s positivity and boundedness, which are crucial for ensuring well-posedness in any dynamical model, are confirmed. The conditions under which the possible equilibrium points exist are established. Furthermore, discussed are the conditions for obtaining local stability around each equilibrium point. Uniform persistence, which ensures the simultaneous existence of all species, is executed. The required conditions for the occurrence of Hopf bifurcations are performed. Analytical confirmation is obtained by the use of numerical simulation. By manipulating the parametric values, the system displays phenomena such as stability, periodic attracts, and the eradication of some species. Therefore, the present study can assist ecologists in determining the parameters necessary to investigate and acquire significant data regarding flowering plant-pollinator systems.