“Molecular and fossil evidence suggests that complex eukaryotic multicellularity evolved during the late Neoproterozoic era, coincident with Snowball Earth glaciations, where ice sheets covered most of the globe. During this period, environmental conditions-such as seawater temperature and the availability of photosynthetically active light in the oceans-likely changed dramatically. Such changes would have had significant effects on both resource availability and optimal phenotypes. Here, we construct and apply mechanistic models to explore (i) how environmental changes during Snowball Earth and biophysical constraints generated selective pressures, and (ii) how these pressures may have had differential effects on organisms with different forms of biological organization. By testing a series of alternative-and commonly debated-hypotheses, we demonstrate how multicellularity was likely acquired differently in eukaryotes and prokaryotes owing to selective differences on their size due to the biophysical and metabolic regimes they inhabit: decreasing temperatures and resource availability instigated by the onset of glaciations generated selective pressures towards smaller sizes in organisms in the diffusive regime and towards larger sizes in motile heterotrophs. These results suggest that changing environmental conditions during Snowball Earth glaciations gave multicellular eukaryotes an evolutionary advantage, paving the way for the complex multicellular lineages that followed.” Published in Proceedings B