Exponential growth of bifurcating processes with ancestral dependence

2013/07/01 by Sana Louhichi, Louhichi, Sana, Bernard Ycart +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #60J85 #92D25 #FOS: Biological sciences #FOS: Mathematics #Gene Regulatory Network Analysis #Mathematical Biology Tumor Growth #Populations and Evolution (q-bio.PE) #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR #msc:60J85 #msc:92D25 #q-bio.PE

paper · pdf · doi:10.48550/arxiv.1307.0343

25 pages, 1 figure

arxiv created 2013/07/01 · openalex publication_date 2013/07/01 · arxiv updated 2013/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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