  We discuss the mathematical modelling of two of the main mechanisms which
pushed forward the emergence of multicellularity: phenotype divergence in cell
differentiation, and between-cell cooperation. In line with the atavistic
theory of cancer, this disease being specific of multicellular animals, we set
special emphasis on how both mechanisms appear to be reversed, however not
totally impaired, rather hijacked, in tumour cell populations. Two settings are
considered: the completely innovating, tinkering, situation of the emergence of
multicellularity in the evolution of species, which we assume to be constrained
by external pressure on the cell populations, and the completely planned-in the
body plan-situation of the physiological construction of a developing
multicellular animal from the zygote, or of bet hedging in tumours, assumed to
be of clonal formation, although the body plan is largely-but not
completely-lost in its constituting cells. We show how cancer impacts these two
settings and we sketch mathematical models for them. We present here our
contribution to the question at stake with a background from biology, from
mathematics, and from philosophy of science.
