Analytical population dynamics underlying harmful algal blooms triggered by prey avoidance
A modified version of the NPZD ecosystem model is used to analytically examine the effects of predation avoidance, a possible mechanism for triggering harmful algal blooms (HAB). To resolve HAB development caused by predation avoidance, an additional phytoplankton functional group is considered, one that has slower nutrient uptake and better predation avoidance characteristics than the non-harmful phytoplankton group used in traditional NPZD models. Because the two phytoplankton groups (one non-harmful and one HAB) compete for only one resource within the same system, steady state (equilibrium) conditions cannot occur without the presence of zooplankton; only the non-harmful phytoplankton group, which defeats the HAB group in the resource competition, can survive in the equilibrium. The presence of sufficient zooplankton effectively acts to replenish the nutrient pool by consuming the non-harmful phytoplankton. When this occurs, two equilibrium states are found: one with both phytoplankton groups coexisting, and one that only includes the HAB group. Further, the condition required for equilibrium is that the total nitrogen within the system should be larger than a threshold determined by model coefficients. The threshold and feasibility of the equilibrium are sensitive to the relative HAB predation avoidance coefficient. If the coefficient is larger than the ratio of net growth rates between the HAB and non-harmful phytoplankton group, the threshold becomes infinite, and an equilibrium is not feasible. The time scale for the system to reach an equilibrium state that includes a HAB group is determined asymptotically. The dependence of a threshold condition as a controlling factor may explain the regime shift of dominant species causing HABs. The ecosystem model is fully implemented into the Regional Ocean Modeling System and applied to an idealized coastal embayment (with depths and geometry taken from San Francisco Bay) to show numerically the dominance of prey avoidance dynamics in a natural shallow water environment that includes advection and diffusion. The analytical results improve strategies for HAB modeling and provide guidance for setting model coefficients necessary to resolve a HAB event.