Rate-induced tipping can trigger plankton blooms

Abstract

Plankton blooms are complex nonlinear phenomena whose occurrence can be described by the two-timescale (fast-slow) phytoplankton-zooplankton model introduced by Truscott and Brindley (Bulletin of Mathematical Biology 56(5):981–998, 1994). In their work, they observed that a sufficiently fast rise of the water temperature causes a critical transition from a low phytoplankton concentration to a single outburst: a so-called plankton bloom. However, the dynamical mechanism responsible for the observed transition has not been identified to the present day. Using techniques from geometric singular perturbation theory, we uncover the formerly overlooked rate-sensitive quasithreshold which is given by special trajectories called canards. The transition from low to high concentrations occurs when this rate-sensitive quasithreshold moves past the current state of the plankton system at some narrow critical range of warming rates. In this way, we identify rate-induced tipping as the underlying dynamical mechanism of largely unpredictable plankton blooms such as red tides, or more general, harmful algal blooms. Our findings explain the previously reported transitions to a single plankton bloom, and allow us to predict a new type of transition to a sequence of blooms for higher rates of warming. This could provide a possible mechanism of the observed increased frequency of harmful algal blooms.