MATHEMATICAL MODELING

Mathematical model of the process of specialization emergence in colonial organisms. The case of different types of cells

D. N. Tverskoi<sup>ab

a</sup> NRU HSE
^b ICS RAS

Abstract: In this paper we consider a colony of cells. We assume that each cell can contribute to two biological functions: reproductive and somatic. Each cell cannot increase its contributions to one function, without decreasing its contributions to another, i.e., cells efforts to reproductive and somatic functions are traded off. Optimal contributions of each cell to viability and fecundity are determined using the principle of fitness maximization for the whole colony. Mutations and positional effects can lead to the situations, where different cells in the colony have different inner structures. We show how this difference in inner structures influences the emergence of cells specialization in the colony, and how this influence depends on the size of the colony. Moreover, different intermediate form between unspecialized colonies and full-specialized multicellular individuals are derived from our model.

Keywords: colonies, specialization, viability, fecundity, mutations, positional effects.