  A fundamental issue discussed in evolutionary biology is the transition from
unicellular to multicellular organisms. Here we develop non-robust models
provided in [1] and attempt to get robust models investigated how
differentiation of types and energy constraints influence on the optimal
behavior of colonies with different size. Constructed models show that each
large-sized colony with high initial costs of reproduction tends to full
specialization, no matter are all cells in this colony identical or are there
cells with different types in this colony. The level of type's diversity
determines the number of cells specialized in soma. In small - sized colonies
with low initial costs of reproduction, when type's diversity is week, an
unspecialized state may bring colony some benefits. However, these benefits may
be only local and in optimum in the colony some cells would be specialized,
others - unspecialized. The amount of specialized cells in small - sized colony
depends on the level of type's diversity in this colony. Adding energy
constraint, we may receive robust models even in convex case. In optimum, the
colony with different types of cells and energy restriction may be indifferent
between some optimal patterns of states. Arbitrary chosen cell may be soma or
germ in some states or may be unspecialized in other. Moreover, in each optimal
state levels of fecundity and viability of each cell lie in limited ranges.
This result reflects the fact that some cell in the colony may lose the
potential ability to achieve, for example, high level of fecundity, but does
not lose the possibility to perform a reproductive function at all. It means
that provided model can describe organisms, which represents the intermediate
between unspecialized colonies and full-specialized multicellular organisms.
