Section: New Results

Statistical study od asymmetry in cell lineage data

Participants : Benoîte de Saporta, Anne Gégout-Petit.

This work proposes a rigorous methodology to study cell division data consisting in several observed genealogical trees of possibly different shapes. For instance, [93] filmed 94 colonies of Escherichia coli cells dividing between four and nine times. We propose a new rigorous approach to take into account all the available information. Indeed, we propose an inference based on a finite fixed number of replicated trees when the total number of observed cells tends to infinity. We use the missing data asymmetric BAR model introduced by [7] . In this approach, the observed genealogies are modeled with a two-type Galton Watson (GW) process. However, we propose a different least-squares estimator for the parameters of the BAR process that does not correspond to the single-tree estimators averaged on the replicated trees. We also propose an estimator of the parameters of the GW process specific to our binary tree structure and not based simply on the observation of the number of cells of each type in each generation.

Our procedure allows us to fully take into account missing observations, data from different trees as well as the dependence structure within genealogical trees. It also enables us to use all the information available without the drawbacks of low accuracy for estimators or low power for tests on small single trees. We study the consistency and asymptotic normality of our estimators and derive asymptotic confidence intervals as well as Wald's type tests to investigate the asymmetry of the data for both the BAR and GW processes. Our results are applied to the Escherichia coli data of [93] .

This work is in collaboration with Laurence Marsalle (Lille 1 University). It is submitted for publication [65] and was presented in an international conference [33] .