Preference and switching in the Kill-the-Winner functional response: Diversity, size structure, and synergistic grazing in plankton models

Grazing by zooplankton can maintain diversity in phytoplankton communities by allowing coexistence between competitors in situations that would otherwise lead to competitive exclusion. In mathematical models, grazing is represented by a functional response that describes the consumption rate by an individual zooplankter as a function of phytoplankton concentration. Since its initial description, the Kill-the-Winner functional response has been increasingly adopted for large-scale biogeochemical modeling. Here, we analyze how two properties of the Kill-the-Winner functional response--preference and switching--interact to promote coexistence and increase diversity in two simple models: a diamond-shaped nutrient-phytoplankton-zooplankton model and a size-structured phytoplankton community model. We found that, compared to preference, switching leads to coexistence and increased diversity over a much wider range of environmental conditions (nutrient supply and mixing rate). In the absence of switching, preference only allows for coexistence within the narrow range of environmental conditions where the preference is precisely balanced against the competitive difference between phytoplankton types. We also explored a counterintuitive aspect of the Kill-the-Winner functional response that we have termed "synergistic grazing". Synergistic grazing occurs when the grazing rate on one phytoplankton type increases as the biomass of an alternative phytoplankton type increases. This unrealistic effect is most evident when switching is strong and when zooplankton have a preference for the weaker competitor.