Centrifugal waste disposal and the optimization of ant nest craters

We considered how ant, Tapinoma simrothi, colonies dispose of the material generated by their nest excavations in nest entrance craters. We developed a model for optimum crater formation on both flat and sloping ground (although we have not solved it in full generality for sloping ground). We found that the ants, when working on flat ground, show a close approximation to this least costly waste disposal. Craters on slopes may not be optimal even though they will be cheaper to make than ones of a similar volume on level ground. We further tested the model with a manipulative experiment, which also suggested the simple rule of thumb that ants might use. In response to having one-quarter of their crater removed, the ants focused most of their further waste disposal in that quarter. This suggests that their rule of thumb may be to deposit material at the nearest point with an angle of elevation less than that of the optimal angle. This should generate symmetrical craters on flat ground. The model also makes certain additional and testable predictions about the fine structure of craters.