The somatic cells commit suicide by a process known as apoptosis — programmed cell death — that I wrote about here. This process involves a minimum of several novel genes as well.
Partial alignment of representative type I and type II metacaspase predicted sequences from red algae (Porphyra yezoensis; Py), green algae (Chlamydomonas reinhardtii, Cr; Volvox carteri, Vc), vascular plants (Arabidopsis thaliana; At), excavates (Trypanosoma cruzi, Tc; Leishmania braziliensis, Lb), diatoms (Thalassiosira pseudonana, Tp; Phaeodactylum tricornutum, Pt), haptophytes (Emiliania huxleyi; Eh), pelagophytes (Auroecoccus anaphagefferens; Aa), yeasts (Schizosaccharomyces pombe, Sp; Saccharomyces cerevisiae, Sc) showing the conservation of the cysteine-histidine dyad and the insertion characteristic of plant type II metacaspases. From Nedelcu, A.M. 2009. Comparative genomics of phylogenetically diverse unicellular eukaryotes provide new insights into the genetic basis for the evolution of the programmed cell death machinery. J. Mol. Evol., 68: 256–268. doi 10.1007/s00239-009-9201-1.
…among the simplest animals to have more than one cell type
is cringe-worthy: Volvox is no more an animal than is a tomato: