Evolutionary analysis of pollen patterns as a curious consequence of modulated phases

Pollen grain surface morphologies are famously diverse; each species displays a unique, replicable pattern. The function of these microstructures is poorly understood, largely because it is difficult to describe these patterns in a well-defined, mathematical way. It has been shown that the templating of these patterns is created by a phase separation of a polysaccharide mixture on the cell surface. Here we present a characterization of the surface morphologies using a Landau theory of phase transitions to ordered states. We show that 10% of all morphologies can be characterized as equilibrium states with a well-defined wavelength of the pattern. The rest of the patterns have a range of wavelengths on the surface that can be recapitulated by exploring the evolution of a conserved dynamics model. We then perform an evolutionary trait reconstruction where we categorize all extant patterns into one of these two states, further binned by wavelength ranges. Surprisingly, we find that although the equilibrium states have evolved multiple times, evolution has not favored these ordered-polyhedral like shapes and perhaps their patterning is simply a natural consequence of a phase separation process without cross-linkers.