Extensions of the bifurcating autoregressive model for cell lineage studies

Abstract

The bifurcating autoregressive model has been used previously to model cell lineage data. A feature of this model is that each line of descendants from an initial cell follows an AR(1) model, and that the environmental effects on sisters are correlated. However, this model concentrates on modelling the correlations between mother and daughter cells and between sister cells, and does not explain the large correlations between more distant relatives observed by some authors. Here the model is extended, firstly by allowing lines of descent to follow an ARMA(p,q) model rather than an AR(1) model, and secondly by allowing correlations between the environmental effects of relatives more distant than sisters. The models are applied to several data sets consisting of independent cell lineage trees.