  The problem of unicellular-multicellular transition is one of the main issues
that is discussing in evolutionary biology. In [1] the fitness of a colony of
cells is considered in terms of its two basic components, viability and
fecundity. Intrinsic trade-off function of each cell defines a type of cell. We
elaborate models providing in [1]. Assuming that all intrinsic trade-off
functions are linear, we construct a model with different cell types and show
that the differentiation of these types tends to full specialization. In
addition, we attempt to consider the fact that environmental factors influence
on the fitness of the colony. Thus, we introduce an energy restriction to the
model and show that in optimum we get situations in which there exists a set of
states, each of them allowing colony to achieve the same maximum level of
fitness. In some states arbitrary chosen cell may be specialized, in some -
unspecialized, but fecundity and viability of each cell belong to limited
ranges (which are unique for each cell). It is worth pointing out that the
models from [1] are not robust. We try to overcome this disadvantage.
