Exponential growth of bifurcating processes with ancestral dependence

TL;DR

This paper studies branching processes with dependent cell lifetimes, showing they still grow exponentially under certain conditions, and provides a model with explicit growth rate calculations.

Contribution

It introduces a model of bifurcating Markov chains with dependent lifetimes and proves exponential growth similar to classical models, extending understanding of cell population dynamics.

Findings

Branching processes with dependent lifetimes exhibit exponential growth.

Growth rate relates to multiplicative ergodicity exponent.

Explicit model allows calculation of growth rate and ergodicity coefficients.

Abstract

Branching processes are classical growth models in cell kinetics. In their construction, it is usually assumed that cell lifetimes are independent random variables, which has been proved false in experiments. Models of dependent lifetimes are considered here, in particular bifurcating Markov chains. Under hypotheses of stationarity and multiplicative ergodicity, the corresponding branching process is proved to have the same type of asymptotics as its classic counterpart in the i.i.d. supercritical case: the cell population grows exponentially, the growth rate being related to the exponent of multiplicative ergodicity, in a similar way as to the Laplace transform of lifetimes in the i.i.d. case. An identifiable model for which the multiplicative ergodicity coefficients and the growth rate can be explicitly computed is proposed.