Several species of millimetric-sized termites across Africa, Asia,
Australia, and South America collectively construct large, metersized, porous mound structures that serve to regulate mound temperature, humidity, and gas concentrations. These mounds display
varied yet distinctive morphologies that range widely in size and
shape. To explain this morphological diversity, we introduce a
mathematical model that couples environmental physics to insect
behavior: The advection and diffusion of heat and pheromones
through a porous medium are modified by the mound geometry
and, in turn, modify that geometry through a minimal characterization of termite behavior. Our model captures the range of
naturally observed mound shapes in terms of a minimal set of
dimensionless parameters and makes testable hypotheses for the
response of mound morphology to external temperature oscillations and internal odors. Our approach also suggests mechanisms
by which evolutionary changes in odor production rate and construction behavior coupled to simple physical laws can alter the
characteristic mound morphology of termites.