A simple classification of the volvocine algae by formal languages

There are several explanations of why certain primitive multicellular organisms aggregate in particular forms and why their constituent cells cooperate with one another to a particular degree. Utilizing the framework of formal language theory, we have derived one possible simple classification of the volvocine algae-one of the primitive multicells-for some forms of aggregation and some degrees of cooperation among cells. The volvocine algae range from the unicellular Chlamydomonas to the multicellular Volvox globator, which has thousands of cells. The classification we use in this paper is based on the complexity of Parikh sets of families on Chomsky hierarchy in formal language theory. We show that an alga with almost no space closed to the environment, e.g., Gonium pectorale, can be characterized by PsFIN, one with a closed space and no cooperation, e.g., Eudorina elegans, by PsCF, and one with a closed space and cooperation, e.g., Volvox globator, by PsλuSC. This classification should provide new insights into the necessity for specific forms and degrees of cooperation in the volvocine algae.