Stochastic evolution of staying together

• Staying together is a crucial operation for construction of complexity in biology.
• Staying together means that cells do not separate after division.
• We study the evolution of staying together.
• We explore a stochastic process with finite population size.
• We derive exact results for the limit of weak selection.

Staying together means that replicating units do not separate after reproduction, but remain attached to each other or in close proximity. Staying together is a driving force for evolution of complexity, including the evolution of multi-cellularity and eusociality. We analyze the fixation probability of a mutant that has the ability to stay together. We assume that the size of the complex affects the reproductive rate of its units and the probability of staying together. We examine the combined effect of natural selection and random drift on the emergence of staying together in a finite sized population. The number of states in the underlying stochastic process is an exponential function of population size. We develop a framework for any intensity of selection and give closed form solutions for special cases. We derive general results for the limit of weak selection.