Lichen growth

A theory of the growth of a lichen is presented, based upon the production of a carbohydrate by photosynthesis, partial consumption of it to thicken the lichen, diffusion of the remainder toward the outer edge, and its consumption there to increase the lichen radius. The mathematical formulation of the theory leads to a free boundary problem for the determination of the carbohydrate concentration, and of the lichen radius as a function of time. For the realistic case of slow growth the problem is solved approximately. The result for the growth rate is shown to fit Proctor's data fairly well.