Survey and Review

Abstract

From five thousand miles above Tahiti, the Earth appears to be all water. Almost all the land is hidden away on the back side of the globe---and even that side is half water, too. Earth is an ocean planet. Look inside any drop of that water with a microscope and you'll find it teeming with life. Thousands of species of free-floating plant and animal organisms, known as plankton, fill our oceans. They drive the aquatic food chain and generate most of the Earth's oxygen. Scientists have been studying plankton since van Leeuwenhoek (1700), and mathematicians have been modeling them since Volterra and Lotka (1925). More recently our knowledge of biology, the state of the oceans, and the relevant mathematics have all exploded. Plankton populations bloom and decay sometimes wildly in space and time, with consequences for fish and humans, and much of the irregularity can be modeled by reaction-diffusion partial differential equations. Part of the challenge of this field is to recognize when a reaction-diffusion model may capture the main phenomena, and when instead one must take into account that the spatial domain such a model depends upon will be torn apart by oceanic fluid motions. The following article by Medvinsky et al. introduces us to this beautiful subject. Like all good scientists, the authors show a recognition of the complexity of the real world they are trying to model; nearly 300 references attest that plankton and fish dynamics are not simple. Like all good mathematicians, they also show an ability to isolate, and enjoy, the simple mechanisms that play a crucial role. Take a look at Figure 10 to see how reaction-diffusion dynamics alone can lead to complex regular structures that then break down to irregular ones. To an unbiased observer of life on Earth, this turbulent teeming of the oceans is as big a story as the adventures of a few two-legged animals scuttling about on land.