Understanding the Shape of Ant Craters: A Continuum Model

The disposal of soil grains by ants, during excavation of their nest, results in the formation of axisymmetric craters around the nest entrance. We give a simple explanation for the shape of these biological constructs based on basic processes underlying grain transport and grain dropping. We propose that the tendency of an ant to drop a grain, in its next step, keeps increasing as it carries the grain farther away from the nest. Based on this hypothesis, a continuum mathematical model is developed to describe the soil dumping activity of ants, averaged over space and time. Consisting of a single, first-order differential equation, the model resembles that used to describe simultaneous convection and reaction of a chemical species, thus establishing a connection between ant craters and reacting flows. The model is shown to accurately describe the soil disposal data for two species of ants—M. barbarus and P. ambigua—using only two adjustable parameters- one less than previous empirical distributions. The characteristic single-hump shape of the crater is explained as follows: While the tendency to drop grains is greater at distances further away from the nest, the density of grain-bearing ants is highest close to the nest, thus most of the grains are dropped at an intermediate location and form a peak. The model predicts that steep craters with a sharp peak are always located closer to the nest entrance than craters which are more spread out; this new prediction is verified by data for M. barbarus and P. ambiguaants.