Sea-urchin feeding fronts

Sea-urchin feeding fronts are a striking example of spatial pattern formation in an ecological system. If it is assumed that urchins are asocial, and that they move randomly, then the formation of these dense fronts is an apparent paradox. The key lies in observations that urchins move further in areas where their algal food is less plentiful. This naturally leads to the accumulation of urchins in areas with abundant algae. If urchin movement is represented as a random walk, with a step size that depends on algal concentration, then their movement may be described by a Fokker–Planck diffusion equation. For certain combinations of algal growth and urchin grazing, traveling wave solutions are obtained. Two-dimensional simulations of urchin algal dynamics show that an initially uniformly distributed urchin population, grazing on an alga with a smoothly varying density, may form a propagating front separating two sharply delineated regions. On one side of the front algal density is uniformly low, and on the other side of the front algal density is uniformly high. Bounds on when stable fronts will form are obtained in terms of urchin density and grazing, and algal growth.