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

Life history evolution and the origin of multicellularity: the case of different types of cells