  The prevalence of multicellular organisms is due in part to their ability to
form complex structures. How cells pack in these structures is a fundamental
biophysical issue, underlying their functional properties. However, much
remains unknown about how cell packing geometries arise, and how they are
affected by random noise during growth - especially absent developmental
programs. Here, we quantify the statistics of cellular neighborhoods of two
different multicellular eukaryotes: lab-evolved "snowflake" yeast and the green
alga $Volvox~carteri$. We find that despite large differences in cellular
organization, the free space associated with individual cells in both organisms
closely fits a modified gamma distribution, consistent with maximum entropy
predictions originally developed for granular materials. This 'entropic'
cellular packing ensures a degree of predictability despite noise, facilitating
parent-offspring fidelity even in the absence of developmental regulation.
Together with simulations of diverse growth morphologies, these results suggest
that gamma-distributed cell neighborhood sizes are a general feature of
multicellularity, arising from conserved statistics of cellular packing.
