Revisiting the role of top-down and bottom-up controls in stabilisation of nutrient-rich plankton communities

Understanding the conditions for successful control of phytoplankton by zooplankton in eutrophic ecosystems is a highly important research area with a wide implementation of mathematical modelling. Theoretical models generally predict destabilisation of food webs in eutrophic environments with large-amplitude oscillations of population densities which would eventually result in species extinction. On the other hand, these theoretical predic- tions are often at odds with ecological observations demonstrating stable dynamics even for a high nutrient load. This apparent discrepancy is known in the literature as Rosen- zweig’s “paradox of enrichment”. Recent theoretical works emphasize a crucial role of spa- tial heterogeneity in successful top-down control in eutrophic environment; however, the interplay between the top-down and bottom-up mechanisms as well as the role of animal movement in system stabilisation are still unclear. Here we extend previous theoretical studies on plankton interactions by considering the important scenario where main con- sumers of phytoplankton are mesozooplankton (large grazers) with a slow reproduction timescale compared to their fast movement across the column. By exploring a system of integro-differential equations, we find that stabilisation of plankton dynamics in nutrient- rich waters occurs even when the functional response of grazers shows a pronounced sat- uration, which is impossible for a well-mixed system. Unlike previous findings, we show that accumulation and feeding of zooplankton at depths with higher phytoplankton den- sity can be a destabilising factor. We find that the interplay between the two different types of light attenuation in the water –the algal self-shading and water adsorption - can result in high amplitude oscillations of plankton densities, whereas each mechanism alone acts as a stabilising factor.