[MS10] Model Bifurcations and Ecological Relevance

[MS10-06] Bottom-up effects in three-species models: is nutrient supply always beneficial?

*Debdeep Roy¹, Bapan Ghosh¹ (1. Indian Institute of Technology Indore (India))

Keywords:

Caputo fractional order model,Paradox of enrichment,Omnivore,Mean density

The Hastings-Powell (HP) model is one of the most significant in ecological systems. An intriguing extension is the omnivore model, which exhibits quite different dynamics compared to the classical one. Though the model has been explored under various scenarios, such as harvesting, time delay, intraspecific competition, and diffusion, to uncover potential ecological outcomes, studies on fractional HP models are minimal, more so for omnivorous systems. In this work, we propose a dimensionally homogeneous Caputo fractional-order HP model (and its omnivore extension) with proportional harvesting. Species enrichment in the HP model generally induces paradoxical results (destabilization). However, for the fractional HP model, nutrient supply benefits all species in the stable state, and from a mean density perspective, in non-equilibrium dynamics, it is beneficial for all species. On the other hand, in the HP omnivore model, nutrient supply favours the prey and top predator but harms the mid-predator stock in the stable state. However, the situation completely reverses after destabilization for moderate increase of carrying capacity. Sufficient nutrient supply has proved to be beneficial for all again.