Recent Mathematical Insights into Plankton Behavior
Plankton is a general term for a wide range of floating or drifting organisms in fresh and salt water. Plankton are of considerable scientific interest for a number of reasons. For one, they are an important food source for larger creatures. Also, they process about 60% of the marine carbon, and they consume a significant fraction of man-made CO2 and produce about half of the atmospheric oxygen. In this talk, we focus on two types of plankton, Karlodinium veneficum and Heterosigma akashiwo, that are responsible for harmful algal blooms. These are both swimming plankton, capable of inefficient photosynthesis and predation. Their behavior is a direct response of local chemical and optical cues, so a fundamental understanding of how they swim and hunt is essential to anticipating changes in marine ecology in response to climate change and ocean acidification. In this seminar, I will describe two recent investigations into plankton behavior. First, certain strains of Karlodinium give off a toxin that will slow or paralyze their prey and themselves. Under simple assumptions about collisions and predatory handling, it can be shown that toxic interactions can lead to higher rates of predation, even when both predator and prey move more slowly. To more explicitly understand the impact of localized regions of toxin in the environment, we explore a 1D Broadwell process in an inhomogeneous domain. The second investigation focuses on aggregation of Heterosigma in the presence of light and a chemical signal. I will discuss preliminary laboratory investigations of plankton pattern formation followed by modeling efforts to capture observed behavior. We propose that plankton are interacting with one another through a concentration of a chemical signal that diffuses and decays in the environment. Plankton in turn swim through the field modeled by a run and tumble process. Deposition of the signaling molecule by plankton is in response to local cues and different deposition processes will be discussed as drivers of plankton behavior.